SIGNPOSTS TO

GOD

HOW

MODERN PHYSICS & ASTRONOMY

POINT THE WAY TO BELIEF

Peter Bussey

CONTENTS

1 Introduction

2 The World of Physics: A Quick Tour

3 Revolutions in Physics

4 Laws of Nature and of Physics

5 Dangerous Infinities?

6 Modern Astronomy: Where Has God Gone?

7 The Human-Friendly Universe

8 Implications of a Universe “Fine-Tuned” for Us

9 God as First Cause: An Argument That Seems to Hold

10 Explanations and Evidence

11 Mental Reality

12 Mystery and Ignorance

13 Beyond Physicalism

Index

Notes

Praise for Signposts to God

About the Author

More Titles from InterVarsity Press

Copyright Page

ONE

INTRODUCTION

The assumption is widespread in modern society that religious belief and science are in conflict. This is despite the fact that practicing scientists have views on religion that are as divided as those of any other section of the population, ranging from committed belief to equally firm unbelief. Although the situation is far from clear-cut, the perception of a conflict is certainly very prevalent, and there seem to be two particular reasons for it. Both are based on what can be called “social myth.”

The first of these may be thought of as a “myth of progress.” There are a number of variations on this, and the myth holds a genuine attraction because a belief in social progress can perhaps help progress to take place in practice. One perspective on progress is a confidence that human beings are steadily growing in knowledge and understanding, which is something that is spectacularly illustrated by the progress seen in science over recent centuries. It seems that, day after day, more scientific discoveries are being made. Religions by contrast appear old fashioned and static. The social progress myth, therefore, can very easily develop into an impression that the contrast between science and religion in this respect is so great as to amount to a conflict.

Religion may not be the only casualty of this kind of outlook. Another noteworthy area of human activity that seems to have been outpaced by science is philosophy. Philosophy is commonly acknowledged as valuable for scholarship and intellectual training, but the subject does not appear to be making many real advances these days, or so it might seem. There are prominent scientists who are outspokenly dismissive of philosophy.

At the level of the individual, an important version of the progress myth concerns growing up. A child may be brought up in traditional religious beliefs—Christian, let us say. Teachings about how science works do not at first appear much at school; there may be an introduction to nature studies, fossils and some astronomy. As the years progress, the young teenager is introduced to science in a stronger way, and it creates a very powerful impression. Growing up, in this version of the myth, implies taking hold of science and relinquishing religion as something childlike. This is seen as a form of “personal progress.” If the parents are believers, the young person just sees them as old fashioned. Genuine personal maturity is different, however, and means acknowledging myths and evaluating them with judgment and perception. It also means acknowledging different kinds of knowledge.

A social myth of a completely different kind is what may be called the “myth of physicalism.” Formerly more often called “materialism,” physicalism is the claim that the science of physics gives in principle a complete account of all that exists. The position has been well summarized by the University of London philosopher David Papineau, who states confidently in a book on the social sciences, “We are all physicalists now. It was not always so. A hundred years ago most educated thinkers had no doubt that non-physical processes occurred within living bodies and intelligent minds. . . . The point would have been agreed by most practising scientists of the time. Yet nowadays anybody who says that minds and bodies involve non-physical processes is regarded as a crank.” [1]

This is very strong language, but I believe that it expresses nothing more than an intellectual myth. The crucial question to be asked is, does anyone really believe in physicalism? The answer: surely almost nobody. The myth of physicalism may be given considerable publicity—it carries a message that many think they want to hear and many of its advocates speak of it as a proven fact. But in their hearts, do they actually accept it? Even though people may openly advocate physicalism with one part of their mind, in all other respects their attitudes and behaviors say something quite different. As human beings, we simply do not have any inward conviction that we are mere physical machines—we know that there is more to who we are than this. As well as the physical, which here includes the chemical and the biological, there are also mental and spiritual sides to our existence, and they need to be regarded in a very different way. It is hard to see a basic justification for assuming that one single human intellectual discipline, namely physics, should be capable of accounting for everything that exists. If the science of physics were truly at this exalted level, there would indeed be a conflict, not only with most types of religious belief, but with other areas of human culture as well.

It is easy to observe that those who claim to be physicalists are in all other respects pretty much the same as everyone else. They display emotions, opinions, values and other normal human attributes, just as the rest of us do. All this corresponds not in the least to a viewpoint on life that they are no more than functioning mechanisms—lacking therefore in free will and all the other human qualities that physics can say nothing about. The physicalists may talk physicalism, but they neither act it nor live it. It is hard to avoid the suspicion of an intellectual pose. Still, could it perhaps just be that the two sides of their brains have gotten out of balance? The rational, logical half has come to act independently of the warmer, emotional, artistic, personal human half? That is hypothetically possible, but to be frank, I believe that we are seeing a serious case of doublethink. All the indications are that physicalism is a very shallow and fashionably held concept.

A possible response to these accusations might be to say that the more “human-oriented” language and attitudes are being employed as a convenience, but they are really no more than that. This appears to be the view of many who call themselves physicalists, but it surely will not do. It is one thing to say that Joe Smith thinks in the manner of a traditional human being but is mistaken, for he is in fact really a machine. It is quite another matter to claim to know this “truth” about yourself but to continue to behave as if you did not. Hence the unavoidable charge of doublethink. Once the supposedly enlightened insight has been gained that all one’s moral convictions, personal values and so on are nothing but a product of neuron activity in the brain, then the only honest action is to demote all of these things to mere private inclinations and foibles and to be open about it all. But, of course, this is not what we actually find. The self-proclaimed physicalists are usually just as sincere as everyone else about the authenticity of human moral values, for example. Should we suspect this to be merely a play-act? A feigned position adopted in order to impress others? No—I think they do really believe in these human qualities, and it is the physicalism in which at heart they do not believe.

Much more alarming, though, are the practical implications that would follow from regarding other people as mere physical machines. Many have commented on the dangers of dehumanizing others and ourselves in this way, and there is no need for further elaboration on this here. We are saved from the evils that are a natural and logical consequence of physicalism by the fact that very few people seriously believe in it; the vast majority of its advocates remain humanly oriented despite their pretensions to the contrary. The real fear is what would ensue if people actually did believe in physicalism.

Contrary to the myths outlined above, I will argue in this book that the science of physics, together with the closely related science of astronomy, does not represent a path that should lead away from religion, but rather the opposite. Physics and astronomy offer, as it were, signposts that point toward God. It will be made clear that physics cannot provide an account of human consciousness and hence human nature in its most central aspects. Something more than just physics is required. Scientific progress is a reality, we can all happily agree, but its successes do not destroy the human aspects of our existence.

Physics is an important and fundamental branch of science, but it is not always easily understood by those outside its field. Therefore, we will first spend some time overviewing the essential aspects of the subject, avoiding technical details, so as to present the most important ideas. We will then examine the nature of laws of physics and the deep importance of the fact that the laws of physics are expressed in mathematical form.

Following this, the discussion will move on to astronomy, including cosmology, which is the study of the universe “as a whole.” Some of the questions that arise here concern the beginning of the universe, whether it needs to have an external Cause and also the remarkable fact that the universe appears to be set up in such a way as to be friendly to the development of advanced forms of life. Questions about explanations and evidence will be discussed next.

In the final chapters we will examine two basic topics, the first of which is the presence of a conscious mind in our physical brains in a physical universe. This leads to a discussion of issues concerning human nature. After this we will discuss how rationality and science have their limits, directing our attention toward aspects of existence that are in their nature non-rational. There is an element of mystery that pervades everything, and this should be sensed as something positive.

My hope is that this book will prove helpful to those who wish to connect the sciences of physics and astronomy constructively with the deeper questions of our existence. These sciences, we will see, can very reasonably provide pointers—signposts—in the direction of God. A personal faith is something that requires personal belief and commitment, and it must go further than this book can take the reader, but I hope that it may be facilitated and supported by the facts and arguments presented here.

Much of the material in these chapters first appeared in articles in the journal Science and Christian Belief, issued by the British organization Christians in Science. I should like to thank its former editor, Denis Alexander, for much support and encouragement over the years.

TWO

THE WORLD OF PHYSICS

A Quick Tour

What makes the modern age different from all earlier periods in history? There could be many answers to this question, but one that stands out prominently is the study of science. There have always been artists, farmers, soldiers and sailors, even bankers, but there have not always been scientists. Science is about a human thirst to obtain knowledge about the world and the universe that we find ourselves in, and this must be in-depth knowledge and not just practical information for navigating life. Apart from the activities of some exceptional individuals in earlier times, modern science can be said to have its beginnings in Western Europe four centuries ago. It is now a dominant feature of our lives.

Of the various branches of science, physics is usually considered the most “fundamental.” This does not of course mean it is necessarily the most humanly important, even if it were possible to rank the sciences in this way. Biology as the study of living creatures, chemistry as the study of how substances form new substances—these and other sciences also have their place at the front of the stage. But physics, as the study of the most basic aspects of matter, underlies all the other sciences in a certain sense.

It may be that among the readers of this book there are many who are already knowledgeable about physics. If this applies to you, you may skip much of the next two chapters! But I have found that most people see physics as a highly complex subject, and so it will be helpful to explain some of its most important ideas in a quick tour. Hopefully this will make it possible for readers to appreciate something of the fascination that physics holds for those of us who are fortunate to work in this area, and also to gain some insight into its central contribution to our understanding of how the universe behaves.

We will begin by discussing some of the areas of physics that are most important for everyday life: forces, gravity, electricity, magnetism, light and heat. We then discuss atoms and elementary particles, leading to a quick look at the so-called God Particle. The next chapter will introduce the more enigmatic modern topics of Einstein’s relativity theory and quantum physics. First, however, we start off with some basics.

FORCES

When you push against something that is free to move, it will start to accelerate. Imagine, for example, that you are trying to get a broken-down car to move along a road, and you are pushing it with constant force. The acceleration of the car will be small but constant, and the velocity of the car will be small at first but will gradually increase. The velocity equals the acceleration times the time over which the acceleration acts. The car will be moving twice as fast after twenty seconds as after ten—one must be patient!

Now imagine you have a helper. With a second person of similar strength to yourself, there will be twice the force. This means that there will be twice the acceleration, because the acceleration is proportional to the force that is acting. It is harder to get a heavier car moving than a light one, however. If the heavier car is twice as massive, the amount of acceleration will be halved if it is being pushed by the same number of people with the same force. Alternatively, to get the same acceleration, you could use twice as many people.

These ideas were first set out clearly by Isaac Newton in the later part of the seventeenth century. Working as a professor of mathematics at Cambridge, Newton made three crucial statements, his “laws of motion.” The first is that in order to make an object change its velocity, it is necessary to do something to it. If no force acts, a stationary object will stay stationary while a moving object will stay constantly moving. This had not always been recognized before, because usually friction is present and will make a moving object slow down. But Newton realized that friction is a force just like other forces; if it is absent, a moving object will keep moving. The purpose of putting oil in a car’s axles is to minimize friction. Once moving, a car on a flat road will continue to move for some time if it is well oiled.

Newton’s second law states that if a force acts on an object to produce an acceleration, the strength of the force is proportional to the acceleration times the mass of the object, as we have seen. His third law states that when a force is applied to an object, the object pushes back equally on the source of the force. So the people who are pushing the car feel the same force on their own hands, something we usually take for granted. To take another example, when a gun fires a bullet, the gun experiences a recoil force. In the usual words, “for every action there is an equal and opposite reaction.”

GRAVITATION

Having established his laws of motion, Newton had the means to calculate what happens in many kinds of situations, because forces are found everywhere in nature and we believe the laws of motion are universal. When an object falls, it accelerates—and so the earth must be pulling on the object with a force, an effect which we call gravity. Once friction from the air is discounted, all objects fall with equal acceleration, something that Galileo was famous for having shown a century earlier in Italy. The gravitational force is proportional to an object’s mass (the amount of matter in it). A large suitcase pulls down on your hand with more force than a small one does.

Newton realized that if the earth pulls down on every object on its surface, then presumably it pulls on other things too, such as the moon. It is because the earth exerts a gravitational force on the moon that the moon continues to move around it and does not go flying off into space. It is natural to extend this to the idea that gravitation is a universal property of everything: everything that exists pulls on everything else. The sun pulls on the planets, and so they continue to revolve in orbits around the sun. Today we are aware that all the stars in our galaxy pull on each other, and so the galaxy stays held together. Newton proposed a universal law of gravitation, stating that the gravitational force between any two objects is inversely proportional to the square of the distance between them. He was then able to prove that his laws could explain the orbits of the planets—a breakthrough in the understanding of astronomy.

Gravity always pulls things toward each other in normal circumstances—it is an “attractive” force. We do not know of any way to make “antigravity,” such as would produce a repulsive force and free us from the earth. One of Albert Einstein’s great achievements was to devise a more all-embracing theory of gravity than Newton’s, one that relates gravitational acceleration to the structure of space and time. But not even Einstein’s theory, his “general theory of relativity,” gives a practical way to make antigravity, to the frustration of hopeful space travelers.

FIRST DISCOVERIES IN ELECTRICITY AND MAGNETISM

The word electricity first appeared in the English language in the seventeenth century, [1] although electric effects had been known about since ancient times. Electricity was originally known as a kind of force generated when suitable materials were rubbed together. Today we see this most easily by rubbing a plastic rod with a cloth; this can give it an electric charge, which makes it attract small pieces of paper or material so that they stick to it.

The eighteenth century was an age of methodical scientific experiments, and gradually certain general properties of electricity became better known. The electricity associated with rubbed objects, later known as “static” electricity, could be transferred to other objects, and it behaved rather like a kind of substance that could be deposited on or removed from materials. It could flow through certain materials, especially metals, which became known as electrical conductors. In 1785, Charles-Augustin de Coulomb found that the force between two electrically charged objects decreases as the square of the distance between them, just like gravity although it was not apparent that there was any connection. Others had also discovered this fact, but Coulomb was the first to publish it, and so it was named “Coulomb’s law.”

A very important practical advance came in 1800, when Alessandro Volta in Italy invented the electric battery. This now gave researchers the ability to make electricity easily, although measuring it was still difficult—one favored method was observing the effect that it had on frogs’ legs! Electric circuits could now be constructed. Volta showed that his battery really did produce electricity by obtaining sparks when he touched the ends of a circuit together.

Magnetism was originally recognized as a property found in a small number of materials. It attracts pieces of them to each other and makes them align themselves with a north-south direction relative to the earth. Like electricity, magnetism was known about since ancient times without being understood. Iron can be magnetized by stroking it with another magnet. The main use for magnets for a long time was in compasses, which were first used in navigation by the Chinese. The eighteenth century in Europe saw experiments carried out on magnetism along with those on electricity.

FIELDS

At this point we should say something about what a “field” is in physics. Simply, a field is a property of space at any given point, such that a physical effect such as a force may be present there. When we say that a gravitational field exists somewhere, we mean that a massive object (i.e., an object with mass) placed there will experience a gravitational force, which is of course its weight. With electricity there are electric fields, such that an object carrying an electric charge will have a force on it. A gravitational or electric field points in a particular direction in space, which is the direction of the force that it causes.

Magnetic fields likewise produce forces on magnetic objects, but in a more subtle way. There are no such things as magnetic charges as far as we know, although theoretically they might exist. Magnetic objects behave like a pair of positive and negative magnetic charges—which we call for historic reasons north and south poles—placed very close together. This forms a magnet. A magnet in a magnetic field experiences forces that can make it rotate to point along the direction of the magnetic field. This is what a compass needle does, pointing along the magnetic field generated by the earth.

ELECTRICITY AND MAGNETISM TOGETHER

In 1819, Hans Christian Oersted in Denmark discovered that when an electric current flows in a wire, it produces a magnetic field that circles around the wire—a dramatic link between electricity and magnetism. Experimenters could now make magnetic fields just as they wished. This led to a natural question: if electricity can produce magnetic fields, can magnetic fields produce electricity? A breakthrough here was made in London ten years later, when Michael Faraday showed that electricity can be generated in a coil of wire by changing the amount of magnetic field that passes through the coil. One way to do this was to move a magnet into the coil, while a second way was to use an electric current flowing in another coil nearby to make a magnetic field, and then to turn this magnetic field on and off. This discovery led to the invention of electricity-generating devices, such as the electric dynamo, which works by rotating a wire coil in a magnetic field. Faraday also invented the first primitive electric motor, using the force that is obtained when an electric current flows through a conductor in a magnetic field. Both of these new developments revolutionized everyday life when they were put to use later in the nineteenth century.

Faraday simplified the subject by insisting that there was only one kind of electricity and magnetism (many people had thought that electricity is different when it is produced in different ways). The next crucial step forward came in 1873 from James Clerk Maxwell in Cambridge, who published a set of four equations that are effectively the “laws” of electricity and magnetism. Understanding Maxwell’s equations requires a fairly good knowledge of mathematics, but they describe overall how electric and magnetic fields interact with each other and how they radiate from sources such as electric charges and propagate in space.

Once Maxwell had set out his equations, it became apparent that they could be used to give an explanation for the nature of light. This was a brilliant surprise, but to understand it we first need to say something about light.

LIGHT

Human life would not be possible in a universe without light. Light enables us to see and control our lives, and the light radiated from the sun is the power source for plants, which give food for higher living creatures on our planet. It is hardly surprising that in the book of Genesis in the Bible, light is the first physical thing to be mentioned in the process of creation. The story of the scientific study of light is a long one with many contributions from many people, and here we will just look at some of the most important steps.

Light rays behave in two particularly important ways. When they hit a smooth surface, they can reflect off it, which enables mirrors to be made. They can also pass from one medium into another, and when this occurs they are usually bent through an angle, a process known as refraction. A swimming pool looks less deep than it really is, because the light from the bottom of the pool is bent when emerging from the water into the air. Glass refracts light, and this allows lenses to be made that will focus or defocus light as it passes between air and glass. In this way, microscopes and telescopes can be built, and spectacles can be used to correct eyesight. Our eyes themselves work by having a lens that focuses the light onto the retina of the eye.

But although these basic properties of light were well understood by the eighteenth century, light’s physical nature was for some time very controversial. There were two proposals: light might be a stream of particles, or it might be a kind of wave, like sound. How could these possibilities be distinguished in practice?

Newton believed that light was a stream of tiny particles, which were perhaps easier to understand than waves because they would obey his laws of motion. There could be forces acting on them, for example. To make refraction work, glass would have to pull on the particles of light as they entered the glass from the air so as to make the particles move faster and bend their path as observed. One test of this idea would be to find out whether light travels faster in glass or water than in air, but that was a very difficult measurement to do and not possible at the time.

Waves, in general, are physical disturbances that propagate through a material or through space. In the case of sound waves in air, the disturbance is in the pressure of the air. Small variations in air pressure, once started off, are sufficient to drive the wave forward because pressure differences generate forces that act on the air. Sound waves in water or in solid materials are similar and act by producing small compressions in the water or the solid. Light could be like that, but no one knew what the physical effect might be that was generating the wave. However, waves have some basic and distinctive general properties. They can combine, and when waves combine in phase, they reinforce each other and the intensity of the total wave is increased. When they combine out of phase, they can cancel each other out. These wave combination effects are called “interference.” If you view a street light through a very fine mesh curtain, you may be able to see interference effects as a pattern of bright spots that appear to be surrounding the street light.

In the early 1800s, the first experiments were carried out to find out if light can produce interference patterns. The patterns were seen, giving a convincing proof that light must consist of waves of some kind. So Newton seemed to have been mistaken on this point. Light travels at different speeds in different materials, and in a vacuum or air the speed of light was measured to be about three hundred thousand kilometers per second. Later in the nineteenth century it was found that light travels less fast in water than in air, which again confirmed its wave-like nature.

Maxwell’s equations now had something remarkable to say. Using them, it was possible to show that vibrating electric fields in space will produce vibrating magnetic fields, while vibrating magnetic fields produce vibrating electric fields. Vibrating electric and magnetic fields should propagate together through space as a wave. This was interesting in itself, but when the speed of the wave was calculated using the equations, it was found to be precisely equal to the known, measured speed of light. The conclusion was inescapable: light must surely be a wave consisting of extremely fast vibrations of electric and magnetic fields—“electromagnetic waves.”

The human eye is sensitive to light in the range of wavelengths that the sun radiates most strongly. Maxwell’s equations showed that not only these but electromagnetic waves of all kinds of wavelengths are possible. The challenge was to confirm the theory by building apparatus that would produce other kinds of electromagnetic waves, which meant that apparatus was also needed that would detect them. In this way, radio wave generators were made, along with radio sets to receive the radio waves, and of course we are now familiar with microwaves. It had long been known that there are also ultraviolet and infrared light waves that lie outside the sensitivity of our eyes to see.

The story does not stop there, however, because at the start of the twentieth century another revolution in physics came with the development of quantum theory. This will be a subject of our next chapter, and it shows that there is a sense in which Newton was right about light after all.

HEAT

Heat is a very familiar part of our existence and it is another area of physics that was for a long time very poorly understood. During the eighteenth century, heat was commonly believed to be a kind of fluid-like substance that penetrated materials and could be stored in them, and whose presence makes them hot. This made it rather like electric charge, which could be put into or removed from objects in the same kind of way. Hotness and coldness were measured as an object’s temperature, using a thermometer.

During the nineteenth century, Robert Mayer and James Joule showed that heat is actually a form of energy; in fact, it is the energy of random motion of the atoms and molecules in a substance. The atoms and molecules in a gas move around in the space occupied by the gas, while in a solid material the atoms vibrate. The hotter the material, the faster its atoms are moving. To us all this is now quite clear, but during most of the nineteenth century the existence of atoms was somewhat controversial. Many things in physics and chemistry could be explained if matter were made of atoms, but there were skeptics who claimed that atoms were too small to be ever observed and were a purely philosophical concept, not to be taken literally. Eventually the protests died out and today we have no problems with observing and measuring atoms using suitable physical apparatus.

Heat and its properties are the subject of the branch of physics called thermodynamics, and here again several physical laws have been laid out. The first of these says that energy must always be conserved in a process that involves heat. When heat is put into or taken out of a system, and mechanical work is also done, then the energy changes must balance. Overall, no energy must be lost and no energy gained, and heat is one kind of energy.

It was the so-called second law of thermodynamics that generated most notoriety when it was first stated in the nineteenth century by William Thomson, later Lord Kelvin, in Glasgow and by Rudolf Clausius in Berlin.

If a cup of hot water is placed in a room, it will cool to the temperature of the room. In fact, the room will warm up very slightly because heat energy is conserved. This kind of effect is always found when two objects at different temperatures are placed together in contact; their temperatures will eventually become the same, something that is often stated as another law of thermodynamics. Now, it is possible to build devices whose effect is to pump heat into or out of a physical system. One example is refrigerators, which contain a mechanism that pumps heat out of the cool volume of the refrigerator and into the surrounding room, since the heat energy has to go somewhere. The second law of thermodynamics can be expressed in several ways, but it states that however ingenious you are, you cannot make a refrigerator that uses no power at all but just makes its contents colder and the room a little warmer. This remains true even though the total energy could still be conserved. In general, whatever the circumstances, two objects at the same temperature can never end up at different temperatures with nothing else happening. Temperatures of things in contact always tend to equalize; they never become unequal on their own.

In fact, all the interesting things that happen in the universe seem to rely on stored energy being used up and temperature differences decreasing. This means that over the ages, the universe can be expected gradually to “run down.” Eventually, if it still exists, it will become a very boring place with nothing of interest happening at all and everything at the same cool temperature. That at least was how the nineteenth century saw the matter; there are more complex theories of the universe now, but if the universe lasts for long enough, the consequences of the second law of thermodynamics in some way have to apply. This unappealing scenario became known a little confusingly as the “heat death of the universe” and made people feel depressed.

The reason for the second law of thermodynamics is that randomness and disorder will always increase if they can. A hot object contains atoms moving with high random speeds, while a cool object has its atoms at lower speeds. Together, they form a system that has a certain amount of large-scale order, shown in the large-scale difference between the two sets of atomic speeds. When they reach the same temperature, this order disappears and the average speeds of the atoms will be everywhere the same. Large-scale differences always tend to disappear: mechanical effects turn into heat, and heat tends to average out. It is a familiar thing—a tidy room will tend to become untidy, but an untidy room will never become tidy unless some extra effort is put in. In physics, this extra effort means energy. The universe does not have an external source of physical energy and tidiness unless we believe that an outside agent can act, such as God. This is a theological point that merits discussion, but otherwise the physical universe does not have natural recuperative powers. If the effects of gravity can be ignored, the universe will tend toward a state of uniformly general randomness even if it started out in a very well-ordered state, which we believe to have been the actual case. This will be discussed further later.

Physicists have a name for the kind of disorder that is found in randomly moving atoms: entropy. In any closed physical system—one that does not interact with its surroundings—entropy will always tend to increase.

We should mention also the third law of thermodynamics, which states that it is never possible to remove from a given object absolutely all of its heat energy. This would make its absolute temperature zero, which is something that can never be achieved. For any object, a small amount of random motion in the form of heat will always remain present in its atoms. This law in practice is of interest mainly to low-temperature physicists, but it is a way of saying that “you can never achieve perfection.”

ATOMS

In the Greek world, the existence of atoms was proposed by the philosophers Leucippus and Democritus in the fifth century BC. The idea was at first just a speculation, but four hundred years later the writer Lucretius gave some plausible reasons for believing in atoms. [2] He argued that the characteristic qualities and properties of material things and living creatures must derive from internal constituents that possess well-defined qualities and properties. These internal constituents would surely have to be atoms.

The word atom means “indivisible.” Another motivation for believing in atoms was that divisibility without limit would be an “infinite” property of nature, and there was a traditional suspicion against infinities of any kind. Lucretius’s idea was that atoms must have properties and these can be associated with the properties of the materials that they make up, so as to help explain them. All this is still true today, although the properties that the ancient thinkers associated with atoms were very different from those we now know about. During the nineteenth century, the science of chemistry made great progress by supposing that chemical substances consist of different combinations of atoms associated with different chemical elements.

Belief in atoms became more or less unavoidable at the end of the nineteenth century, when it was shown that atoms are not after all indivisible. It was possible to apply voltages to metal surfaces in a high vacuum and extract radiations, known as cathode rays. In 1897, the Cambridge physicist J. J. Thomson showed that these rays had all the properties of beams of very light particles, which must have originated from atoms in the apparatus. The particles had mass and electric charge and behaved just as particles would behave. They were eventually given the name electrons and could be understood only if they were constituents of atoms. Atoms therefore had to exist and were made of smaller things.

We now know that electric current normally consists of the flow of electrons in metals and other conductors, in which some of the electrons are not tightly bound to the atoms but are free to move through the material. Electrons have negative electric charge—the sign of the electron’s charge is a matter of convention, and scientists on another planet might well decide to call it positive. But material substances are normally not electrically charged, overall. This means that some other constituent of atoms must have a positive charge that balances the charge of the electrons.

A New Zealand–born physicist working at Manchester in the north of England, Ernest Rutherford, set up a crucial experiment in 1911 to learn more about the structure of atoms. Rutherford and his colleagues bombarded the atoms in a thin metal foil with a beam of alpha particles, which are energetic particles given off by certain radioactive elements. Rutherford’s team found that some of the alpha particles bounced off the target atoms at very large angles. This was extremely surprising—they had expected that the particles would all make their way through the metal foil without being deflected very much.

There was only one conclusion: something had to exist inside the target atoms that was very small and dense, so that the alpha particles could bounce off it. This object came to be called the atomic nucleus, and it contains nearly all the mass of the atom. The electrons are thousands of times lighter, and with their negative charge they are held in the atom by the positively charged atomic nucleus, because opposite electric charges attract each other. Different chemical elements have nuclei with different amounts of positive charge and correspondingly different numbers of electrons. In an atom of a given element, the patterns of its electron configuration give rise to that element’s chemical properties.

ATOMIC PARTICLES

If atoms contain electrons and a heavy nucleus, what makes up the atomic nucleus? The lightest and simplest element is hydrogen, and the nucleus of its atoms was given the name proton, meaning “first particle.” It was supposed that atoms of heavier elements contained a number of protons bound together somehow, together with the same number of electrons so as to make the total electric charge of the atom zero. But the picture seemed incomplete, and during the early 1930s another constituent of the nucleus was identified. This was a new kind of atomic particle, or “elementary particle,” and was given the name neutron. Neutrons are similar to protons but have no electric charge. They exist in atomic nuclei alongside the protons, usually in greater numbers.

The electric force that holds electrons into atoms is not capable of holding the nucleus together. Protons and neutrons stick to each other in the nucleus by means of a new kind of force—one that is enormously stronger than anything known before and referred to as the strong nuclear force. The energy associated with this force is around a million times larger than the energy that binds electrons into an atom and that is associated with the atom’s chemistry. This factor of the order of a million is the reason why atomic bombs are so much more powerful than ordinary explosives that rely on stored chemical energy. The strong nuclear force is found in nature only in connection with atomic particles; otherwise we have no everyday experience of it.

NEW ELEMENTARY PARTICLES

After World War II and the secret research connected with the atomic bomb, there was a great deal of interest in exploring the properties of elementary particles. The new research was entirely peaceful, and it was supported by a widespread desire by world leaders that scientists should continue to do their work in the traditional way. In the United States a laboratory was set up at Brookhaven near New York, while in Europe an international laboratory called CERN was established at Geneva, in Switzerland. Both these laboratories are still flourishing. We have no space here to give more than an overview of elementary particle physics, but a general picture of this area is important in order to understand where physics stands today.

The reason that only a few elementary particles were known about at first is that most of them are very unstable and do not survive in nature. It is necessary to create them in collisions of particles accelerated to very high energies, and then they can be studied during the small fraction of a second that they exist before decaying into something else. Even neutrons are stable only when they are combined with protons in the nuclei of atoms. On its own, a neutron will decay after fifteen minutes on average, producing a proton, an electron and a particle called a neutrino (strictly, an antineutrino).

Over the years, a vast collection of new elementary particles has been discovered at the world’s accelerator laboratories, and nearly all of them are highly unstable. They have different masses and different electric charges, together with other properties, and for most of them there is also an “antiparticle.” This has the same mass as the original particle but, when possible, opposite electric charge. For example, there is an antielectron (called a positron) and an antiproton, and these are able to combine to form antihydrogen. A small number of positrons are found in cosmic rays, but the antiproton is not found in nature at all as far as we know, even though it is stable and will not decay. Our universe is made almost entirely of “normal” matter. When matter and antimatter particles come together, they usually react violently. It is often claimed that they will annihilate into “pure energy,” but that is not quite true. The energy is carried off by the products of the reaction—for example, by high-energy photons when an electron and a positron interact. In the end, with processes such as this, we do not find much antimatter in nature.

THE “MOST ELEMENTARY” PARTICLES

The bottom line of the story is that today we believe there exists a set of genuinely fundamental entities that make up all the matter we know about (apart from the “dark matter” in outer space, whose nature is at present deeply unclear). There must be more to discover, but for now here is the picture of what is called the “standard model” of elementary particles.

The electron is considered to be truly elementary—it is not known to have any further subconstituents. However, the proton is made of three smaller entities called quarks, two of one kind and one of another. Specifically, there are two “u” quarks and one “d” quark in the proton, according to the conventional nomenclature. The neutron has two “d” quarks and one “u” quark. The quarks are bound together by the nuclear force, and this force is a manifestation of another particle called a gluon. The names are perhaps not very elegant, but they serve their purpose.

Quarks exist only in combination with each other or with antiquarks, and in this way they form physical particles. There are many combinations, and therefore many different particles, because six different types of quarks exist. They are named u, d, s, c, b and t, otherwise known as up, down, strange, charm, bottom and top, but these names do not have much real meaning. Only the u and d quarks are stable. The theory of the quarks and gluons, and how they interact with each other, is called quantum chromodynamics, or QCD for short. (There is also a “particle of light” called a photon, about which we will say more later, and two more particles that are like the electron but are much more massive and also unstable.)

The quarks and gluons have the frustrating property that we cannot extract them in isolation in order to study them. In this respect they are rather like the north and south poles of a magnet; if you hit a magnet very hard with a hammer, you will not extract the north and south poles, but instead you will get a shower of tiny magnets. In a similar way, if particles with quarks and gluons are struck hard by another high-energy particle, we do not obtain quarks and gluons but a collection of lower energy particles.

In addition to the electromagnetic and nuclear forces, there are the effects of gravity, which are too small to study in particle collisions. Also, there is one more kind of force in physics, known as the weak nuclear force, or weak force, and it is responsible for the decay of many different radioactive atoms and also the decay of the neutron. When the weak force operates in a decay, a rather mysterious type of particle called a neutrino is usually given off. Neutrinos are extremely light, they have no electric charge and they are difficult to study because they react only very weakly with other matter. The universe is full of neutrinos that have been formed over the ages, and they just float around space doing very little. Neutrinos can pass through the earth and through ourselves, and we are normally completely unaware of them.

The picture of elementary particles can be summarized in a simple way by saying that there are “force” particles such as photons and gluons, and also “matter” particles, which are the quarks, electrons and neutrinos. The matter particles can be classified into three families, each of which comprises two types of quarks, an electron-like particle and a neutrino. Ordinary matter in nature is built from only one of these families, which includes the stable u and d quarks and the electron.

THE “GOD PARTICLE”

We shall now dip our feet into one of the deepest aspects of modern physics. For every force in nature there exists a physical field. Gravity has the gravitational field, and we have talked about electric and magnetic fields. Quantum theory, which we will discuss in the next chapter, says that physical fields do not exist in arbitrary states but are “quantized,” which means that they interact with each other not in a continuous way but in distinct amounts. This means that all interactions have a particle-like nature and every field provides a particle to interact with other particles. The particles are excited states—that is to say, more energized states—of the fields. The particle of the electromagnetic field is the photon, and the particle of the nuclear force field is the gluon.

The weak nuclear force has two types of “force particles” associated with it; they are very massive and unstable and are called the W and Z. Their massiveness means that they are formed with difficulty and do not take much part in most particle processes; hence the force field that is associated with them has a rather weak effect in most circumstances.

Theorists in the 1960s came to recognize a problem in this area: the best theory available at the time was unable to assign any mass to these particles at all! The solution was to propose yet another kind of physical field, whose properties were designed to produce mass in the W and Z particles. It was then realized that the new field could make the quarks massive as well. This is the so-called Higgs field, proposed by Peter Higgs in Edinburgh and by Robert Brout and François Englert in Belgium. The Higgs field is a quantum field, which means that it too should have a particle associated with it.

Quantum fields exist everywhere in space. The special property of the Higgs field is that other particles moving through it (which means moving anywhere in space) are affected by it, and the effect gives them mass. Pictorially speaking, it is a little like an object moving through an ice cloud and picking up a layer of ice. A lump of ice would also pick up a layer of ice. Other analogies have also been proposed, but to understand the situation properly, the advanced mathematics of the theory is needed.

Peter Higgs was the only one of the first proposers to mention specifically that a particle should be associated with the new field, and so this hypothetical object acquired the name “Higgs particle.” It was discovered at CERN in 2012 using a powerful new accelerator called the Large Hadron Collider. The successful identification of the Higgs particle among the many other products of the high-energy proton collisions was the culmination of years of effort by thousands of people. It vindicated the approach taken by Higgs and the other theorists to the theory of the electromagnetic and weak forces, and it meant that these forces can indeed be combined together in one unified theory, along with quarks and gluons. This was a great triumph for the notion that theoretical speculation can be a meaningful activity for the human mind.

Books have been written about the Higgs as the so-called God Particle. This nickname was first coined by an eminent US physicist, Leon Lederman, in his own book on the subject of elementary particle physics. [3] He has claimed that the title was forced upon him by his publisher! For various reasons, most physicists dislike the term. Those without belief in God do not like it for that reason, but in any case the name is not obviously appropriate, because the Higgs particle and field do not actually create anything, which perhaps a God Particle ought to do. However, the Higgs field does have some crucially important properties that affect other particles, and without this field it is hardly possible that the universe as we know it could exist.

The present theory is not the final word, and research continues. Perhaps our existing state of knowledge should be expressed in the following way. The Higgs particle that we know about now is the final link in a well-defined and complex pattern of elementary particles, which are connected by an elaborate and, one might say, highly ingenious mathematical structure such that everything holds consistently together. Only expert theorists can appreciate this structure properly, unfortunately. We expect more particles to be discovered to extend this pattern, perhaps further Higgs-like particles. Lederman, although sitting somewhat on the fence about the meaning of the title of his book, depicts God as saying, “Let us . . . give them the God Particle so that they may see how beautiful is the universe that I have made.” [4] This surely points in the right direction. If we are looking for God in the world of elementary particles, then it is in the entire structure and pattern that a divine intelligence should be perceived and held in admiration.

THREE

REVOLUTIONS IN PHYSICS

By the end of the nineteenth century, many physicists believed that the laws of physics were essentially fully understood, except for a small number of loose ends that had to be tidied up, such as the question of the structure of the atom. But more perspicacious minds realized that there were still some problems, “clouds” over the theory of physics, to quote a lecture given in London by Lord Kelvin in the spring of 1900. At that time, no one fully realized how serious these problems would turn out to be. Along with so much of the culture and outlook of this period of history, physics was to change dramatically over the next twenty-five years.

THE RELATIVITY REVOLUTION

The first area of radical change in physics consisted of Einstein’s theories of relativity. The speed of light was known to be well-defined theoretically by Maxwell’s equations, and when measured experimentally it was always found to be the same. This sounds very reasonable, but if a light ray traveling at 300 kilometers per second were to overtake an observer traveling at one kilometer per second, then surely the observer should measure the speed of this light ray to be only 299 meters per second. Strangely, this is not the case; careful measurements led to the conclusion that light in a vacuum travels at 300 kilometers per second relative to all observers, even if they are moving relative to each other. How can this be?

Einstein showed that this paradox has extremely strong implications for our understanding of space and time. If the speed of light is fixed as an absolutely universal constant, then space and time become interconnected, and this has further effects on other areas of physics. It means, for example, that to accelerate any massive object to the speed of light is impossible, because when moving close to the speed of light it becomes effectively much more massive than when it was at rest. Distances and time intervals viewed by different observers become distorted when speeds approaching that of light are involved. Short-lived particles traveling at these speeds acquire a much longer lifetime. Many of the effects have been confirmed by experiment, and nothing has been found to cast any doubt on Einstein’s theory.

Relativity theory has many physical consequences, but its central principle is philosophical. There is, said Einstein, no such thing as “absolute space” or “absolute time” but only relative distances, relative time intervals and relative velocities. The laws of physics must be the same for every constantly moving observer. Suppose two physicists are moving at a constant velocity relative to each other. If each of them carries out some experimental measurements, the numerical results will no doubt be different, but the two sets of measurements will both follow exactly the same laws of physics. This is the so-called principle of relativity. Neither of the experimenters can claim to be in a more advantageous or more special condition than the other. The importance of relative rather than absolute physical measurements gave rise to Einstein’s title for his work as the “theory of relativity.”

If the principle of relativity is true, it will follow automatically that the speed of light must be the same for anyone who measures it, [1] because the speed of light comes out of Maxwell’s equations, and these are laws of physics. This quite innocuous-sounding principle, therefore, has far-reaching implications for physics. Einstein’s genius was that he was the first to set out the arguments in a clear, logical and incontrovertible way.

Einstein continued to develop his theory—up to this point now known as the “special” theory of relativity—into a theory of gravity known as the “general” theory of relativity. This states that the presence of matter and energy in space gives rise to curvature of space and time. Curved surfaces in two dimensions, such as the surface of a sphere, are an idea that is familiar to us, but Einstein had to work this out in four dimensions, three of space plus time! Objects moving through curved space follow curved paths, and we interpret this as gravitational acceleration. General relativity also predicts the existence of black holes, which result when the immense gravity of a sufficiently small and massive object prevents anything at all from escaping, even light. Gravity affects time measurements, and this must be accounted for and corrected when accurate clocks are used in satellites orbiting the earth.

A further prediction of the theory is that curvature can propagate through space as a wave, known as a gravitational wave, which travels at the same speed as light. Extremely sensitive apparatus on the earth is now able to detect these waves.

It is important to appreciate that Einstein himself expressly denied that the ideas employed in his theories of relativity could be transferred from physics to other areas of human life, such as moral values. The catch phrase “everything is relative” is extremely misleading. In fact, relativity theory is founded on the assumption that physical laws themselves are always the same, relative to different observers. The theory might well be called “physical democracy”—“all observers are equal”—but again, human political theory has no connection with this.

THE BIG BANG

Before the modern scientific era, the age of the universe was not something that could be measured, and Europeans accepted the story given in the first chapters of the book of Genesis in the Bible. This implied that the universe is some six thousand years old. Doubts were cast on this figure when geologists began to discover strata of rocks in the earth’s crust that were surely laid down over periods of many thousands if not millions of years. By the end of the nineteenth century, the belief was widely held among scientists that our world had a finite age that was certainly much longer than a few thousand years and that the universe itself was likely to be infinitely old. The actual age of the earth was a matter of scientific debate.

Two developments took place in the first decades of the twentieth century that radically changed this point of view. The first was theoretical: Einstein’s general theory of relativity showed that it is mathematically possible to have a universe that is finite or infinite in spatial extent and likewise finite or infinite in its age. All these possibilities were present in the theory and were therefore valid topics for scientific discussion. As we shall see, this was not welcome to everyone. The second development was experimental: through the work of astronomers such as Georges Lemaȋtre and Edwin Hubble, it was discovered that our universe appears to be expanding.

The expansion of the universe was shown by the fact that distant galaxies are moving away from us. We see a galaxy by observing the light given out by the hot gas in the galaxy or by its stars, and this light has a spectrum that covers a range of wavelengths. It is absent at wavelengths where it is absorbed by chemical elements that may be present, such as hydrogen; here there are dark lines in the spectrum. If the galaxy is moving toward us or away from us, then the light waves become compressed or stretched, and so we see different wavelengths from those that were originally emitted or absorbed. Light from a galaxy moving away from us becomes redder in color. This effect is seen in physical waves of all kinds; it is known as the Doppler effect, and we are made aware of it when an emergency vehicle passes us in the street. As the vehicle speeds by, we hear the pitch of its siren go down: because of the movement of the vehicle away from us, the sound that reaches us is now being stretched to longer wavelengths and lower frequencies.

There are ways of estimating the distances of galaxies by measuring the brightness of certain types of stars that they contain. We can also measure the Doppler-shifted wavelengths of their light and so work out their apparent speed relative to us. In this way it is found that the more distant galaxies are moving away from us faster than those that are closer, at a rate that is roughly proportional to their distance. Two possible causes for this were proposed.

One suggestion was that the entire universe might have been subject to a massive explosion in its early history and that the galaxies that were flung off fastest are now at larger distances from us. However, it is believed that the true explanation is that the galaxies themselves are not moving at any very high speeds by cosmic standards, but that the space that constitutes the universe is expanding. Einstein’s general relativity provides a theoretical basis for this to happen. An expansion of space will have exactly the same observable effect as a physical movement of the galaxies. Two pictures are commonly proposed to illustrate this idea.

The first is that the universe is like a balloon that is being blown up. [2] We can easily visualize how ink marks on the surface of the balloon, representing galaxies, will become more and more widely separated as the balloon expands. It is not that the ink marks are moving on the balloon; the balloon itself is expanding. Of course, the surface of a balloon is only two-dimensional; a three-dimensional analog for the universe could be a currant cake in an oven, expanding as the cake cooks. Again, the currants, representing galaxies, are not themselves moving through the cake; the substance of the cake is expanding so that the distance between the currants becomes bigger. The difference between these pictures and the real universe is that the universe is not expanding into a larger space, as the balloon and the cake are doing. The universe is spatially self-contained, and in its own intrinsic nature it can become larger (or smaller). However, we do not know whether the universe is finite or infinite in its spatial extent.

If the universe is expanding as observed, then at some point in the past it must have had a small or zero size. The rate of expansion is given by a number called the Hubble parameter, and recent measurements indicate that the universe is approximately fourteen billion years old. At the very beginning, it was as if everything came into existence through a violent event, referred to as the Big Bang, that set everything into activity. The expansion of the universe is governed by the equations of general relativity, which state how space and time will behave if there are given starting conditions and densities of matter and energy in the universe. We will make use of these ideas in later chapters.

LIGHT AS PARTICLES AFTER ALL

Even more revolutionary than relativity theory was a transformation in our physical understanding that is alternatively known as quantum physics, quantum theory or quantum mechanics. This again started with some experimental results that could not be reconciled with the existing ideas.

What physicists call black-body radiation is the heat or light radiated at a given temperature by a hot object that is in a certain sense perfect at absorbing and radiating. So, heated to a temperature of some hundreds of degrees Celsius, an object will become red hot and radiate heat, together with some light so that it glows red. At a few thousand degrees, it will radiate more strongly and will appear white hot, as with a tungsten light bulb or the surface of the sun. The radiation spectrum can be measured—for example, whether the radiation is strongest in the infrared region as heat waves, or at shorter wavelengths as light waves. In Germany, the theorist Max Planck was among those who were trying to use the principles of thermodynamics to calculate the black-body radiation spectrum, and he failed. The only way to make the shape of the spectrum come right, he found, was to invent an entirely new principle of physics in which heat and light are not radiated or absorbed continuously as had been believed. Instead, the heat and light come in “lumps,” which Planck called quanta. This was a desperate measure, but it gave the right results, and Planck announced it at a meeting in Berlin in December 1900, a year which therefore marks the birth of quantum theory.

A few years later, Einstein showed that another observed physical effect, the photoelectric effect, also seemed to suggest that light behaves as quanta. The photoelectric effect is the property of certain metal surfaces that when they are irradiated with light, they give off electrons, whose energy can be measured. One quantum of light releases one electron, Einstein suggested. Detailed measurements of this effect were in complete confirmation of Planck’s idea and were hard to account for otherwise.

During the nineteenth century, the world of physics had been left in no doubt that light propagates through space as waves. However, it was now becoming apparent that whenever light is radiated or absorbed, this happens only in terms of “quanta” that resemble particles of some kind. These “particles of light” were given the name photons, and they play an important part in our lives. For example, when a photograph is taken using film, one molecule at a time of a light-sensitive chemical, such as a silver salt, is converted into another chemical, such as a silver atom, by absorbing one photon of incoming light.

The particle-like aspects of light are related to its wave properties by well-defined mathematical formulas. That is, the energy of one photon always equals the frequency of the associated light wave multiplied by a fixed quantity; this is known as Planck’s constant and was first evaluated by Planck when he made his original successful calculations. In physics, the term constant refers to any numerical physical quantity that takes a fixed value.

THE QUANTUM REVOLUTION

The next stage in the quantum revolution was even more revolutionary than the first and was the work of a number of theoretical physicists. In 1913, Niels Bohr in Denmark had made the remarkable discovery that the wavelengths of the light given off by hydrogen atoms can be precisely calculated if the electrons in the atoms are assumed to have a “quantum” property. This was that the electrons should go around the atomic nucleus only in certain definite orbits, given by a particular formula. Bohr had no real explanation why this should be so, but it worked, and it implied that quantum ideas must apply in some way to electrons as well as to light. All of this was brought together in 1925 by a French physicist, Louis de Broglie, who made the radical but logical proposal that all physical objects should have both wave properties and also particle properties.

This meant that a completely new theory of physics was needed now, one that would treat light, electrons and other atomic particles all in the same fundamental way—not just as particles but also as waves. Also, there was a need for some good experimental evidence to confirm the new hypothesis. This evidence was soon found when it was shown that if a beam of energetic electrons scatters off a crystalline material, it can give angular patterns that are like those given by scattered x-rays. X-rays are electromagnetic waves—they resemble high-energy light rays—and the patterns are interference patterns, characteristic of waves. The electrons, then, were displaying wave-like properties just as de Broglie had proposed. Since then, many different kinds of experiments involving neutrons and various other elementary particles have confirmed that particles of matter propagate through space in a wave-like way, and there is no serious doubt about this. Techniques have now improved to the extent that even compound objects such as atoms and quite large molecules can be put into apparatus and show interference effects that indicate wave properties. There are hopes to do similar experiments with viruses.

In principle, we know of no theoretical limits to the size of an object that can behave as a wave; the present limits are entirely practical and due to the great delicacy that is needed to set up experiments that can study wave-like properties of large molecules. No apparatus is technically possible that would show the quantum wave properties of a football, but they ought to be there! On the other hand, the reason why everyday rays of light do not show particle-like properties in an obvious way is that the photon energies are very small. It is like the fact that a stream of water from a hose is made of water molecules, but they are too small and numerous to be noticeable individually.

A suitable new theory of physics was soon put forward. Newton’s second law of motion had to be replaced by an equivalent law that would deal with the wave properties of particles. This new law was expressed by an equation called the Schrödinger equation, after its Austrian inventor. Again, proficiency in mathematics is needed to appreciate this equation, but it enables us to predict how a “particle wave” propagates through space and how it is affected by forces, expressed in terms of energies, when the particle interacts with something. The energies of electrons in atoms can now be calculated with greater precision, replacing Bohr’s earlier simple model. The whole of chemistry depends on energies of electrons in atoms and molecules, which in principle can be calculated using the Schrödinger equation, together with a later extension known as the Dirac equation. It was perhaps the most major step forward in physics since Newton.

QUANTUM COMPLEMENTARITY

So far we have described the particle properties of photons, say, in terms of how they interact in a “quantized” way with other things, one photon at a time. This is one aspect of the particle-like nature of quantum objects, but there is another, different aspect, and the two are often confused. Traditional waves have properties that are not at all particle-like. A wave must occupy a range of locations if it is to have a well-defined wavelength, while a particle can be in only one place at one time. Can these features be reconciled?

The solution is to realize that waves of different wavelengths can combine to form pulses that can have any shape at all. For example, when an aircraft breaks the sound barrier it emits a “sonic boom,” which is an abrupt, narrow pulse of sound. All possible sound wavelengths are present within this pulse, which can be particularly damaging to buildings. This approach can be carried over into quantum physics, where it means that pulse-like waves of photons, electrons or any other particle can in principle be formed.

The energy or momentum of a quantum wave is well-defined only when the wave has a wave-like form, with vibrations extending over a distance of many wavelengths. But then the “position” of the wave has no well-defined value, because the wave exists over a wide range of positions. On the other hand, if the wave exists in the form of a narrow pulse, this contains a wide range of wavelengths so that “wavelength” is now not a well-defined quantity. Energy and momentum, along with the wavelength, are now badly defined.

This means that a quantum object can possess a well-defined position, or a well-defined wavelength—usually interpretable as energy or momentum—but not both together. The more precisely defined one of these quantities is, the more ill-defined is the other. This idea is known as complementarity, and it carries over into experimental measurements, where it is called the Heisenberg uncertainty principle, after its inventor. With a quantum object, one cannot accurately measure position and momentum both at once. An apparatus that measures position well measures momentum badly, and vice versa. There are other pairs of complementary physical quantities that cannot be possessed or measured accurately together; in each case the experimenter must make a choice between them.

Philosophical issues arise here. Up to the early twentieth century, scientists habitually used a way of thinking inherited from Greek and Roman times, and which to most of us would still seem simple common sense. It says that any physical object has properties—for example, position or momentum—and these properties have definite values, which exist whether they are measured or not. The idea that the value of a property can be indeterminate, diffuse or “fuzzy” does not fit well with this way of thinking—still less, that its degree of indeterminacy may depend on how the state of the object is prepared. A quantum object is able to have a broader set of properties than a traditional particle could have—both position and wavelength are there, for example—but this is compensated by the fact that the value of a given property may not be well-defined. It is important to appreciate that the value of an indeterminate quantum quantity is intrinsically ill-defined. It is not the case that the value is precisely there but we do not know what it is.

RANDOMNESS IN QUANTUM PHYSICS

This leads to a practical question. A physicist can expose a quantum particle—a photon, say—to a piece of apparatus to make a measurement of a property of the particle. What happens if the particle does not have a well-defined value of this property? For example, the photon may have been generated so that its wave spreads over a wide area of space. What happens if the measurement is made only at definite points? This will oblige the measured photon to be in one position at one of these points. For example, a photon might enter a camera, and if the focusing is bad, its wave can spread over a wide area of the film. There are many light-sensitive molecules within this area, any one of which could absorb the photon, thereby effectively measuring the photon to be at the position of that molecule. What will happen?

The answer is that just one of the many molecules absorbs the photon, and which one does this will be to a large extent random. The probability for a given molecule at a given point to absorb the photon is proportional to the intensity of the light at that point. As the light shines on the film, and more and more photons are received, a picture becomes built up on the film. In an electronic camera it would be similar and, in principle, we could identify which photon is absorbed where by means of electronic signals.

There are many examples of randomness in atomic physics, because it is a general feature of quantum processes. When a radioactive substance decays, there is a well-defined half-life that represents the average time needed for half of a large sample of atoms to decay. The time when a particular atom decays is random, but of the order of the half-life.

What I have just outlined is the conventional view of quantum processes, known as the Copenhagen interpretation, which Bohr always strove to defend. There are other interpretations, which we will discuss shortly. In “classical” physics (that is to say, pre-quantum physics) it was always assumed that a principle of determinism holds. This means that a physical system has no choice how to behave: it will behave according to the strict application of the relevant laws of physics. The abandonment of this principle represented a serious blow to the earlier philosophies of nature. It could have been imagined that laws of physics are in some sense “perfect” and that a perfect universe should exhibit perfectly determined behavior. This was Einstein’s belief. In earlier physics, when everything took place continuously, precise laws governed the entire process: Newton’s laws, Maxwell’s equations and so on. This viewpoint now needs serious modification. A random quantum process must in some sense happen discontinuously, and these discontinuous processes are often referred to as quantum events. An event-like process may not have to be random, but if it is random, it probably has to be event-like.

The author C. S. Lewis, who certainly believed that human beings possess qualities that go beyond the laws of physics, wrote in the 1940s,

The older scientists believed that the smallest particles of matter moved according to strict laws. . . . Some modern scientists seem to think, if I understand them, that this is not so. They seem to think that the individual unit of matter . . . moves in an indeterminate or random fashion. . . . Those who like myself have had a philosophical rather than a scientific education find it almost impossible to believe that the scientists really mean what they seem to be saying. [3]

Einstein too could not accept this development, and he regarded the appearance of randomness in the quantum phenomena as something misleading and provisional. He frequently made the statement that “God does not play dice with the world.” [4] Both then and now, the consensus among physical scientists has been that Einstein was mistaken here, but the introduction of randomness into physics was clearly a controversial step.

SPLITTINGS OF WAYS AND OF WORLDS

By the end of 1926 the basic ideas of quantum physics had been set out, and within a short time there was agreement about how to calculate a wide range of physical quantities at the level of molecules, atoms or smaller particles, at least in principle. This included the energies of particles in atoms and the probability to get results of interest in experiments with particles and atoms. So far, so good, and most users of quantum theory remain in practice quite content with this. However, although the theory works excellently, we do not fully know how to interpret it.

The theory is commonly written in terms of a mathematical expression called the wave function, which represents how a particle exists in space as a wave. The Schrödinger equation states how the wave function behaves with time, and there is no randomness associated with this behavior. Something random happens when the particle enters any kind of measuring apparatus, and why and how this random quantum event occurs is something that we still do not exactly understand. The intensity of the wave, as given by the wave function, tells us the probability to find the particle at any given point in space, but only in the form of a probability. The actual point where any one particle will be found is not predictable. But although the probabilities of all the possible results of an experiment can be calculated, one might still ask why the particle wave does not just continue to propagate through the apparatus in a continuous way. When it interacts with the apparatus, why should nature make a choice between different possibilities?

Bohr and his colleagues at Copenhagen started with the perception that random quantum events do occur, and they accepted that. The quantum mathematics tells us about the various probabilities for the events, and the experimental results agree successfully with the theory. However, Schrödinger and other physicists remained unhappy, because to them the wave-like behavior of the particle came first, and the random events did not have a proper explanation. We have seen that Einstein was also one of these objectors.

The dilemma was summed up by Schrödinger in his famous “cat paradox.” He pointed out that if the theory does not say how nature makes a choice between different possibilities, then how do we know that it makes a choice at all? On the other hand, if all the possibilities remain in existence, then the world consists of possibilities but never any actualities. One could set up a quantum experiment in which one possibility is that a cat could be killed and another possibility is that it remains alive. Can we seriously imagine a cat in a parallel condition of being alive and dead at the same time? This seems ridiculous, Schrödinger thought. Something needs to be added or amended in the theory.

So there are two aspects to the problem. One is the fact that we do not really know how quantum events occur. The other is in their randomness.

Several schools of opinion have developed regarding these issues. One, following the Copenhagen example, believes that this is not a fruitful area of discussion and that we should just work out the answers and be happy. “Shut up and calculate!” Most of the other schools of opinion object to the importation of randomness into physics. One suggested possibility—the “hidden variables” proposal—is that there is an unobserved, and probably unobservable, underlying mechanism that determines the outcome of everything precisely. Nothing is really random after all. Another idea is that the quantum events happen because of a natural tendency for large physical systems, such as pieces of apparatus, to “sort themselves out”—but there is no natural explanation as to why this should be so. Here, randomness can be retained.

A third possibility is much more radical. The “many worlds” interpretation, originated by Hugh Everett in 1957, alleges that the so-called quantum events do not really occur at all. They are perceived by ourselves as random choices made by nature, one outcome of a measurement or another, but actually all the possible outcomes of a situation always take place, in parallel. This means that the world is in a sense splitting into branches, in each of which one possible outcome is present. In one branch the cat is alive; in another it is dead. Both branches are still there. Human observers are also splitting all the time, and one version of you or me is present in every branch of the universe that forms when a quantum measurement takes place. Each version of you or me is aware of just one particular outcome of the process. There are many, many versions of everything in the universe by now, and that includes many versions of ourselves too. Quantum theory was already rather strange, we are told, and so how can one object to a bit more strangeness? However, it might be considered a little odd to object to the presence of random quantum events but choose a multiple splitting of the universe instead. [5]

A further proposed way out of the impasse is to point out that the only means by which we actually know that quantum events happen is by having a conscious awareness that they happen. Therefore, some have said, it is the interaction with a conscious mind that obliges the quantum system to make a choice. We discuss this radical option further in a later chapter.

These various viewpoints bear witness to a fundamental philosophical uncertainty in the area of quantum physics, and there is plentiful literature on the subject that discusses the problem in depth. [6] One point to emphasize is that experimental observations have so far been unable to distinguish between any of the interpretations that have been mentioned. This is mainly because when the interpretations are set up, enough mathematical flexibility is built in so as to make sure that the calculated results will be in agreement with standard observations. So it could be argued that these are not really scientific hypotheses. However, there is always a possibility that an ingenious experiment could be devised that confirms or rejects a given interpretation, something that has not convincingly happened yet.

Why trouble ourselves with ideas such as these? They seem to range from the subtle to the arcane. The most basic answer is that as scientists and as human beings, we would like to have a good understanding of how the universe operates. But more than this, such an understanding can have possible repercussions on how we interpret the further meaning of a number of things. There is also the question of whether randomness—in other words, a lack of precise physical determinism—may affect our understanding of ourselves as more than just physical machines. Especially it would be very significant if a conscious mind could interact with the world in this proposed way.

The most important conclusion to draw is that “old-fashioned materialism” is a philosophy that is now dead. It is hard for us now to say definitely what constitutes materiality—even though the observable behavior of elementary particles and atoms is given very accurately by the mathematics of quantum theory. This is why the term materialism has nowadays tended to give place to physicalism as the philosophy of those who claim that everything is physics and nothing more. But it is clear that we still do not have a well-agreed philosophical and metaphysical understanding of what is going on, so that beneath the surface there is a serious lack of precision even about what “physicalism” really means and entails. It is to a large extent a faith position like others.

FOUR

LAWS OF NATURE AND OF PHYSICS

The idea of laws of nature was apparently first used in the Roman period. It was an important feature of Roman society that human affairs were regulated by a legal code, set up by an authorized body such as the Roman Senate and applying universally to everybody in Rome’s territories. This could be contrasted with other ancient societies in which laws were the edicts of an autocratic ruler, or else were local customs. One of the Romans’ major boasts, as they ruled over their subject peoples, was that they brought with them a rule of law that was fair and just for all. The prominent politician Marcus Tullius Cicero stated that in an organized society, well-formulated laws should reflect the way that is “natural” for well-disposed human beings to behave. It was perhaps easy, then, for Roman writers to carry this idea over to an understanding of how all nature appeared to have well-regulated behavior.

The relevance of laws of nature took a back seat in later centuries, as Western European scholarship became dominated by the teachings of Aristotle, whose accounts of most areas of human experience acquired an authority that was not easy to contest. His presentation of physics was based on the view that things in the world have their own natures (forms, properties and tendencies) and that their behavior is governed by these and by their interactions with other things. This approach to natural philosophy has certain points in its favor, but it tends to understate what we now see as the unity of physical nature. It also tends to be rather qualitative.

As modern science took root in Europe many centuries later, the concept of laws of nature was reaffirmed, and Newton explicitly called his three laws of motion “laws.” We will now try to understand more deeply what is implied by a “law of nature.” Are laws of nature the same as laws of physics? Are laws of nature merely descriptions of what happens, or do they actually determine what happens?

LAWS AT DIFFERENT LEVELS

The modern view is that every area of science, particularly the physical and chemical sciences, is governed by laws—laws of nature—but some laws are more basic than others. It is commonly believed that all the laws of the various sciences reduce in the end to laws of physics, as the most basic of all. However, laws can relate to each other in a number of ways. A law can be a special instance of an underlying law which is of more general application. The laws that apply in a given physical or biological system can depend on the structure and arrangement of the system, as well as on the laws that apply to its component parts. A law can sometimes be derived from other laws.

In the early seventeenth century, astronomer Johannes Kepler showed that the orbits of planets around the sun are formed by ellipses, not circles as had been supposed before. These ellipses have the sun at one focus, and the line joining the sun to the planet moves over equal areas in equal times. Also, the orbital period of the planet—that is, its “year”—has a precise relationship to its distance from the sun. These statements became known as Kepler’s laws of planetary motion; they were derived from astronomical observations and seemed to be always true. Newton later proved that all of this followed mathematically from his laws of motion and of gravity. This means that Kepler’s laws represent a special instance of Newton’s laws, as applied to planets. Newton’s laws are therefore more general and basic.

Newton’s laws themselves apply very widely, but only when certain conditions are fulfilled. When the masses of gravitating objects are very large, or when very high precision is needed, then Einstein’s general theory of relativity must be used. General relativity is believed to be true and accurate, but its mathematical expression is extremely complex. However, in the case of small enough masses and speeds, the mathematics can be expressed more simply and becomes just the same as Newton’s mathematics. In other words, Newton’s laws are true to a certain approximation, and this is very accurate indeed in most circumstances. Einstein’s theory is therefore more general than Newton’s.

There is finally the question of “higher-level” laws that operate in systems, which may be biological or technological, such as plants and animals and electronic devices. Higher-level laws depend on how the system is formed or constructed (for example, logic circuitry in calculators and computers has its own operational “laws” built in), but every such system still relies on the behavior of its basic components, namely atoms and electrons. These are physical, and so their laws are the laws of physics.

THE MEDIEVAL SCHOLARS

Before considering the laws of nature further, it will be helpful to look at the views held in the medieval period, during which the study of philosophy held a high esteem among European scholars as they sought to obtain a unified understanding of nature. [1] Seen from a modern perspective, this quest was seriously hampered by a lack of experimental input and by an over-reliance on Aristotle, and concepts were used that we would not normally employ today. Despite this, and perhaps surprisingly, we shall see that the medieval ideas still have a relevance to modern questions.

The basic Aristotelian standpoint on physics was that any object exists as a union between a “forming idea” and matter. At the end of the Roman period, Saint Augustine had taught that every existing thing receives its form from God, and that without its form it would cease to be. In the thirteenth century, the leading theologian Thomas Aquinas took over this position, which integrates the Christian concept of God into Aristotle’s philosophy. Within the mind of God, Aquinas said, there exist as many forms, or ideas, as there are existing creatures in the world, for which the divine ideas are “exemplars.” [2] In the created order, these forming ideas are incorporated in material things, and they have no other mode of existence. By contrast, Plato had taught that ideas have an absolute existence of their own, independent of both creation and Creator. The later medieval scholar John Duns Scotus took an intermediate view that ideas can exist on their own as created entities. [3] But in any case it is always the matter-form union that gives a physical thing its existence and its identity, referred to as its “essence.” This is not an esoteric inner quality of something, we should note, but simply designates “what it is.” [4]

Like others at the time, Aquinas was aware only of what we would call large-scale objects. Thus he regarded every plant, rock and human being individually, having its own God-given form. Although atomic theories of matter had existed since Greek times, Aquinas took little notice of them, making use instead of the commonly employed concept of “primary matter,” out of which all physical things are formed. He taught that primary matter cannot exist on its own, without being given form, except “in potential.” [5] The medieval scholars, however, were not in full consensus about this.

Saint Augustine had considered the human body and soul to be two separate things. The medieval scholars sought to unite them, while also allowing the soul to be immortal. This meant that the soul (or intellect or mind) is not just a static form or idea implanted in matter, but is something active. Aquinas ended up with complex souls that differ according to their possessors: the soul is merely a simple bodily form in inanimate things and plants, but in a human being it is a substantial and dynamical intellectual entity, while at the same time retaining the function of providing bodily form. Duns Scotus argued for the presence of more than one soul in human beings: one to give form to the body (“embodied form”) and also one to give life to it (“animate form”). [6]

All this was connected with a longstanding philosophical dispute concerning the question of “nominalism” as opposed to “universalism.” Nominalists believed that ideas as such have no existence, and that even the mind of God is obscure to human beings. Only particular instances of things exist, although it is often correct to make general statements about them, and the ideas corresponding to these can exist in the human mind. In the medieval period, a school of nominalist philosophy was based on the teaching of William of Ockham, who worked at Oxford among other places. Universalists asserted that ideas have a reality. Plato believed that ideas have a substantive existence, and therefore was a universalist. Aristotle took a less strong form of universalism but was not a nominalist, saying that an attribute of something represented more than just an individual particularity. [7]

Can these seemingly obscure teachings be relevant to a modern scientific worldview? Their virtue at the time was that they offered a unified account of natural existence, including both physics and the human mind. Applying them in their original way to modern science is of course very difficult. Even so, the medieval philosophies are still able to cast light on issues that are important today.

LAWS OF NATURE IN MODERN SCIENCE

It is interesting to find that the two main medieval views regarding forms and ideas in nature, namely nominalism and universalism, have approximate counterparts in modern ways of thinking about laws of nature. Here there are again two major viewpoints.

The first of these is that laws of nature are no more than human descriptions of observed regularities in nature’s behavior. The facts of nature are the fundamental reality, and nothing underlies them. This viewpoint has been referred to as “regularism” or “Humeanism,” since the philosopher David Hume was for a long time believed to have upheld it. I shall use the term nominalism, since it has similarities to the medieval school of thought. In other words, a law of nature is simply a name that we give to a pattern observed in nature.

The second viewpoint holds that the laws have a reality about them that makes the course of physical events necessary. The laws of nature are principles that are built objectively into nature, and they generate the regular features that we observe. They are not just manmade notions that we find convenient or appealing. I shall call this “realism” and will argue here in favor of this position. It has a similarity to the medieval universalist point of view.

Arguments for these two viewpoints have frequently been given by modern philosophers. [8] For nominalism, the main argument is officially based on economy. Its adherents feel that we can do without any unobservable “underlying principles” in nature, and they appeal to the medieval nominalist William of Ockham, who declared that entities should not be multiplied unnecessarily. It is pointed out that a number of tricky problems, such as how to treat mental processes or the behavior of people in society, simply vanish if everything is regarded phenomenologically and all the so-called deeper questions are simply denied. That is, we just accept what is observed and try to describe it.

The justification for the realist position is that our experience and understanding of nature require it. Many arguments can be made in favor of realism for laws of nature:

- Laws as real things can help to provide explanation for why things in nature behave as they do. It is part of the scientific enterprise to seek and find explanations for natural phenomena, and these explanations often involve laws of nature. It is the same if we ask for “sufficient reason” for something. The important point to appreciate is that a description is not an explanation. So if laws of nature are merely descriptive of nature’s behaviors, they cannot give an explanation for them.

- Laws understood as something real can take part in determining and causing physical phenomena. Governing is another word that could be used. In the Aristotelian view, individual things have natural properties, and these properties will cause and determine the behavior. But without either of these concepts, familiar and well-used terms such as causation or determination can be hard to understand and apply if all we are doing is describing phenomena.

- Following from this, given a knowledge of the relevant conditions now, realist laws of nature give reliable and accurate knowledge of events in the future. If a law is no more than a summary of observations that have been made hitherto, then it cannot have predictive power. The nominalist must just resort to “coincidence” if the future turns out to resemble the past.

- Laws of nature are normally believed to be universal, meaning that they apply everywhere and always, or at least in a wide range of circumstances. A realist and universal viewpoint has the potential to explain why all objects of a given type have the same properties. For example, the universe contains vast numbers of identical protons, identical electrons and so on. The choice seems to be of believing in the determining action of universal principles, or in massive coincidences, or in divine miracles. The modern nominalist will probably have to resort to massive coincidences, while the medieval nominalist would attribute all of it to the will of God.

- Relatively simple laws of nature—often in conjunction with each other (for example, Maxwell’s four equations)—frequently can account for many and diverse sets of observations. The nominalist just has to appeal to coincidence again.

- Small numbers of universal laws are conceptually more economical than large numbers of diverse sets of observed regularities. They simplify our picture of nature and push our level of understanding back one step.

- If we are able to make rational statements about nature that are true, which is surely the case, this implies a reference to something rational within nature. Nominalism sacrifices our understanding of nature by saying that there is nothing there to be understood, but only to be known about.

- We are able to rely on the behavior of things that we may or may not choose to make happen—such as computers we could build or spaceships we could launch. Our plans work, and realist laws of nature provide both a reason for this and a viable means of planning. In other words, the laws truthfully account for as yet unrealized possibilities.

- Realist laws also explain why some things may be impossible, which is not a category that can be derived from observation. All that the nominalist can do is state that the phenomenon in question has not been observed yet.

- Probability seems to be a valid aspect of physical nature, and probabilities are abstract things that seem to have a real application to physics, although they cannot be derived rigorously from a set of observations. Quantum physics calculates probabilities precisely from theory using the Schrödinger equation, which was derived abstractly and not as a description of a set of observations.

- Modern theoretical physics is based on ideas and is believed to be a valid pursuit. Theoretical ideas are proposals for laws of nature or their consequences, and useful theoretical ideas have often preceded observation, have gone far beyond existing observations or have been based very loosely on observation. Since these ideas often work, there must be something fundamentally real about them. The Higgs particle, like others before it, was found in response to a theoretical prediction, vindicating the validity of theoretical ideas. The nominalist has a problem in taking theoretical ideas seriously.

- Laws and theories can be related to each other and can be derived from other laws and other theories. It is true that a description might be implied by a more general description, but deeper kinds of interrelationships can be quite dubious if they are mere descriptions. [9]

The many considerations listed above would seem to make it inescapable that laws of nature exist in an objectively real way. To deny this results in a viewpoint that is too impoverished to be useful or acceptable.

MORE COMMENTS ON NOMINALISM AND REALISM

A description, we have said, is merely a statement about observations. For example, the stars of the constellation Leo form the shape of a lion; this is an accurate description, but it tells us nothing further. How then can nominalism be argued? A standard answer is that nature displays regularities, that these are describable and that this is all one needs to know. But there is an element of cheating here. In the first place, only limited sets of observations of nature are ever available at a given time. To infer that the whole of nature is “regular” implies an assumption of universality; the nominalist has no rigorous way to justify this, and so the assumption just sneaks into the argument.

Further, the regularities are assumed to apply in the indefinite future, about which of course we have no experimental information. When people say that a law of nature is a description of “how nature behaves,” they usually mean to assert that nature has behaved thus in the past and will do so at all times in the future. The present tense is being used in a universal mode, and the word always is implied (“how nature behaves and will always behave”). This is justifiable only if something akin to a deterministic law of nature is acting, contrary to nominalist principles, for otherwise why should the universal regularity be believed in? We are all well aware of the investors’ warning that the past performance of a financial scheme “is not necessarily a guide to the future.” The nominalist silently assumes that this does not apply in physics, where past performance is invariably a guide to the future! [10] But why should this be? The statement goes far beyond simple description of observations.

Now, scientists in my experience can be a little inconsistent in their attitudes. In professional practice, they nearly always adopt a realist view of laws of nature. There is a difference between a “model,” which may be largely just descriptive, and a “theory,” which implies something basic and explanatory. Laws are regarded substantively, and related issues of causation and underlying explanation are fully built into scientific discourse and procedure. Put on the spot, however, scientists will often insist that laws of nature are purely descriptive, and that they themselves are nominalists. When the occasion passes, they revert to being realists again. It is like being married to someone but denying the relationship in public!

Interestingly, deterministic materialism or physicalism seems obliged to affirm a hard, realist notion of natural law, because otherwise nothing can be actually determined but merely “is.” With nominalism there is no basis to discriminate between “physical” and “mental” phenomena or even miraculous phenomena; all are merely phenomena, to be accepted as observed. The physicalist must either reject mental phenomena arbitrarily, or else reject them as not determined by laws of physics, which must therefore be “real” if they are to determine anything.

Some revealing comments have been made by the philosopher Norman Swartz. [11] As he states the matter, “regularists” (that is, nominalists, of which he is one) consider that “necessitarians” (that is, realists) “have merely replaced God with Physical Necessity” in making laws of nature into “inviolable edicts imposed on the universe.” He continues: “Such a view, Regularists claim, is simply a holdover from a theistic view. It is time, they insist, to adopt a thoroughly naturalistic philosophy of science, one which is not only purged of the hand of God, but is also purged of its unempirical latter-day surrogate, viz. nomological necessity”—that is, necessity deriving from a law. If this is the motivation behind modern nominalism, then an extra-philosophical agenda is very clearly at work. However, from a theological point of view, it is ill-founded. The hand of God could still impose by direct fiat all the features of the universe that are observed. That is indeed what the medieval nominalists believed. But it is interesting that realist laws of nature remind Swartz of the hand of God.

Up to a point, it does not matter greatly whether we talk about “natural laws,” “intrinsic properties” of things or “inbuilt principles.” These have similar deterministic and explanatory implications, from a realist point of view. However, “properties” do not necessarily have to be universal, whereas laws by implication must be. What may bother some people about the terminology of “laws” is that in human society a law is something distinct from the society and may be either imposed or not. As far as physical laws are concerned, this is not the case. They must be taken as an integral part of nature, but perhaps nature is deeper than we think.

NATURE AND MATHEMATICS

Laws of physics have a universal quality that governs the behavior of particular things, and an important aspect of the nature of these laws is that it is mathematical. In the ancient world, it was probably Pythagoras who first realized that the harmonies made by musical instruments depended on mathematical relationships—for example, on the lengths of vibrating strings or musical pipes. For many centuries, however, mathematics was largely equated with geometry, which was seen as the main branch of mathematics and could be studied by means of Euclid’s theorems.

But Euclidean geometry is based only on limited forms of mathematics. Aristotle had to a large extent ignored mathematics in nature, apart from using circles to describe orbits of planets. He preferred to make qualitative statements about most aspects of nature, and in fact he wrote that mathematics, with its intrinsic precision, did not apply to the understanding of physical matter. [12] Improved mathematics turned out to be an important key to further progress in the physical sciences, and the development of modern algebra starting in the Middle Ages was a critical step forward. A second important step occurred in the seventeenth century, when Descartes introduced a new kind of geometry in which spatial relationships were based on algebraic quantities; so, for example, a point on a sheet of paper has coordinates that can be called x and y. Algebraic calculations in terms of the x and y values of points can then replace geometric theorems and are often much more powerful and convenient.

Galileo had already written that the book of nature “is written in the language of mathematics.” [13] Newton transformed physics by developing new algebra-based techniques, known today as calculus, and showing that these techniques could be employed as a basis for physical and astronomical calculations. His most important publication was very significantly titled “Mathematical Principles of Natural Philosophy.” Mathematical principles allow statements about nature to be made with quantitative precision, something Aristotle had dismissed.

The primacy of mathematical principles over qualitative statements should not at all be taken for granted. The quantum physicist Eugene Wigner, who was particularly impressed by the ability of extremely complex mathematics to apply precisely in nature, made the famous comment, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” [14] The pioneering quantum theorist Paul Dirac, in his later years, wrote, “[The] fundamental physical laws are described in terms of a mathematical theory of great beauty and power. . . . One could perhaps describe the situation by saying that God is a mathematician of a very high order and He used very advanced mathematics in constructing the universe.” [15]

At all levels, physical nature is impregnated with mathematics. For example, one can write down an equation that states how the acceleration of the bob of a simple pendulum depends on three quantities: its displacement from the rest position, the acceleration due to gravity and the length of the pendulum. The equation can be solved, and it tells us that the time for one complete swing of the pendulum is two times pi, times the square root of the division of the length by the acceleration due to gravity. Here pi is the familiar mathematical constant equal to the ratio of the circumference of a circle to its diameter. This raises some interesting questions. First, how can one divide two very different things by each other, such as a length by an acceleration? Second, can nature really take square roots?

Human mathematics is written and expressed in a way that resembles a language. At the same time, physical quantities are measured numerically in terms of units, such as meters for lengths, which means that their magnitudes can be represented as numbers. The ideas expressed in the mathematical language can therefore be applied to nature. The numbers can be subject to mathematical operations, and by doing this a human scientist can, for example, in effect divide or multiply a length by an acceleration. Nature does this in its own way in the manner of an analog computer whose physical operations can form the relevant quantities directly; this has the effect of performing mathematical calculations, such as taking square roots. The human mathematical calculation may be different in style from the way nature does it, but the result is the same. Ideas are present in nature and also in our own mathematical language; they correspond to each other but are expressed in alternative ways.

To say it again, the laws of physics express relationships between magnitudes of physical quantities. These relationships can be represented in terms of mathematical equations. In numerical terms, one physical quantity can equal a combination of other physical quantities, and a law of physics provides the “equals sign” in the mathematical equation.

It might be argued against Wigner’s position that we originally obtained our mathematics from nature, and this is why we say nature is mathematical. [16] This is a historical argument, though, and it does not say why the two should even be connected. At most, some of our mathematics may have derived from geometry, which is not the same as physics. But both the physics and the mathematics have long since diverged from this, and yet the correspondence between the two remains. No modern mathematician would say that mathematics is really physics in disguise. Mathematics seems to have a life of its own, and it does things that were not at all obvious at first, as does physics. Today we have mathematics that would have been utterly unforeseeable when geometry or calculus was first developed, and it is associated with physical phenomena that were not even a dream when Pythagoras made his first discoveries or when Newton worked on his laws of motion.

Statements, principles and conclusions in mathematics can be logically true or false without referring to anything physical. They seem to possess a universal quality. Even though there exist many mathematical notations and methods, scholars all over the world will agree on the truth of the same theorems, and we would expect the same from mathematicians from a distant planet. The universality of mathematics supports and underlies the universality evident in the laws of physics, while being of a different and more abstract kind. The mathematician Srinavasa Ramanujan said, “An equation for me has no meaning unless it expresses a thought of God.” [17]

Mathematics would surely be included in most people’s list of “mental” things, and this suggests an identification of the laws of nature with principles that are in some corresponding sense “mental,” present in nature. We can think about nature, mathematically and accurately, and there is an affinity between the operations of nature and our corresponding thoughts. The laws of nature resemble ideas that direct and govern the course of the physical universe. The astronomer Arthur Eddington wrote, “The stuff of the world is mind-stuff.” [18] The designation “stuff” here merely denotes a function “as a basis of world-building.” He added, “I certainly do not intend to materialise or substantialise mind.” In fact, he went so far as to consider the notion of material substance to be an “illusion.” [19]

Although perhaps going a little too far, Eddington’s proposal seems very interesting. His universal category of the mental is not to be identified with the human conscious mind, nor even with its possible extension to the subconscious. Rather, “beyond that we must postulate something indefinite but yet continuous with our mental nature.” [20] We might decide to refer to this continuum as a mental dimension to existence, taking the word dimension in a very general sense.

LAWS OF NATURE AS IDEAS BUILT INTO NATURE

To repeat, with a realist view of the laws of nature, together with their mathematical structure, we can see them as “formative ideas” built into the fabric of the universe, quantitatively determining the characteristics of physical things. This has a resemblance to the medieval picture, but there are also ways in which the pictures differ.

Medieval thinking dealt exclusively with what we see now as large-scale physical systems, while the modern view requires the relevant principles to act on the atomic scale. The microscopic action of laws then adds up to large-scale formational principles; for example, the physical form of a crystal comes from its structure, and both this and the crystal’s overall behavior are consequences of the laws of physics acting at the atomic level. The observed form of a chicken has certainly not been imposed template-like upon a selection of chemicals, as the medieval scholars might have imagined. Instead, through a long-term process of evolutionary development involving physical laws at all levels, the present species has come to be. In the end, then, laws and “forms” are compatible notions, since large-scale forms can arise from laws.

A second point is that the medieval teaching called many secondary attributes of objects accidents: not part of the object’s basic identity. In modern physics, however, all physical attributes of a natural object are law-determined or law-guided or else just a given part of its physical nature. The laws of nature in their turn act within bounding and constraining conditions such as the initial state of a system. All this adds complexity, but it means that the difference between primary attributes and accidentals is not relevant now unless we are talking about designed systems, such as calculators or cars. In these cases, the human designer has indeed imposed a basic form that defines the object’s identity, but variations in color and style might be considered as “accidentals.”

Importantly, modern physicists are accustomed to thinking about space and time together. If forming principles are present to produce structures and patterns, then they should also act in time, since space-time is a four-dimensional structure now. The persistence of spatial form over time, or its change, should be regarded as “temporal form.” It comes from the laws of nature, and physical conservation principles can be important. The spatial and temporal aspects of laws of nature are not easily separated; Schrödinger’s equation, for example, expresses the mathematics that determines the structural form of an atom and also its behavior in time. Other equations apply to the elementary particles that make up atoms, and without such determining principles, particles and atoms of all kinds would not exist. The laws governing a rare kind of unstable particle seem to have a real and factual existence, even if no such particle happens to exist in the universe at this moment.

Physics at the atomic level is quantum physics, and not completely law determined. Even so, laws do govern the behavior of the wave functions and give the mathematical probabilities for the various possibilities in a situation. They may be said to provide a guiding form for an atomic particle’s behavior. The behavior of large-scale objects is not sensitive to the random effects because they average out, resulting in an overall pattern that is mathematically well-defined and predictable.

If the laws that shape and direct the physical universe are considered as ideas existing as part of the natural order, then such a viewpoint is universalist in the medieval sense and closer to Duns Scotus than to Aquinas. This mode of existence gives the laws an objective status, and scientific questions can be distinguished from theological questions. At the same time, it can invite us to see them further as created expressions of the mind of a God who is an accomplished mathematician. An alternative position is that the laws of nature could themselves be identified as the “mind of God,” or as some aspect of it. This viewpoint would be consistent with certain statements made by the cosmologist Stephen Hawking. Einstein held this kind of view, which implies that the created order and the Deity do not have distinct existences, effectively some kind of pantheism. He wrote, “We followers of Spinoza see our God in the wonderful order and lawfulness of all that exists.” [21]

Duns Scotus believed that ideas and primary matter can both exist on their own, and this must remain an open question. But what, in the modern picture, is primary matter? This elusive concept has no place in the original Copenhagen interpretation of quantum mechanics, but it may perhaps be applied to quantum fields, as we shall see.

THE MATTER PROBLEM

There is a common agreement among philosophers of nature that we do not have direct perceptual knowledge of physical matter. Light, sound and other effects originating from a physical object are received by our sense organs, and the resulting data are mediated through the brain into a conscious experience, which we then interpret. However, the information that we obtain, even by means of scientific instruments, always refers to the object’s form, attributes and behavior and not to its material substance as such—whatever that may be.

If this is our situation at the everyday level, then a difficulty in thinking about physical matter at the quantum level comes as no surprise. Various physical and mathematical concepts are available here, such as observables, measurements and wave functions; but the quantum particle “as such” is elusive. The ways of thinking that serve well at the everyday level are less helpful now. At both levels, though, the notion of matter must be considered as an abstraction from our experiences. In ordinary life we habitually and confidently make this abstraction; at the quantum level our imagination runs into difficulties.

From Aristotle to the medieval scholars such as Aquinas, it was considered that so-called primary matter has no describable characteristics. In the eighteenth century, Immanuel Kant distinguished between the phenomenal aspects of an object, which are known through experience—ultimately sense-experience—and the so-called thing-in-itself, which is beyond the experiences while being the origin of them. For Kant, the thing-in-itself was “transcendent” and outside the scope of physical language. [22] What the medievals thought of as primary matter is to some extent compatible with Kant’s thing-in-itself.

Kant’s view that the thing-in-itself is the origin of the appearances points in the opposite direction to Aquinas, however, for whom form has causal primacy over matter. [23] Certain other thinkers, such as Eddington as we have seen, have gone to the extreme of disowning matter altogether. For the medieval philosophers, central identity (“essence”) is always to be found in the union of form and matter, [24] and overall it would seem that modern physics, using the language of physical laws, is somewhat closer to the medieval scholars than to Kant. There may be further parallels. According to Aquinas, matter exists “in potential” until a form actualizes it; particle physics uses the concept of “virtual particles” that materialize as real particles only if law-given physical processes actualize them.

QUANTUM FIELDS—A CANDIDATE FOR PRIMARY MATTER?

The most basic elements of modern physics at present are quantum fields. These are physical quantities that are believed to exist everywhere in space. As quantum objects, their numerical values are not in general precisely given, but over different points in space and time they can show strong correlations in the form of mathematical patterns. The attributes of an elementary particle, such as its energy and momentum, are associated with field patterns of certain types—in these cases given by the mathematics of sine waves. But the elementary particle itself is not material in a familiar way. It is an excitation of the field, which is represented as a new mathematical pattern in space. When it moves, no “thing” seems to move; it is rather that its mathematical pattern moves so as to be present in the quantum fields in a different region of space. We may well ask, then, is matter now vanished, with only patterns remaining, like the lingering smile of a vanished Cheshire Cat? Or is it everywhere? The answer is unclear.

The prominent theorist Frank Wilczek refers to quantum fields as “ur-stuff” [25]—in other words, primary matter. No doubt they are currently our best candidate for this. Their apparent ability to exist on their own, without being excited into particles, is in a certain accord with Duns Scotus’s ideas. However, they do possess attributes such as energy, and physical laws apply to them; thus they do not constitute the featureless primary matter envisaged by the medieval scholars or perhaps by Kant.

This is as far as we can attempt to go at present. Matter is that in which physical ideas are instantiated. The “idea” of an electron or photon—that is, those physical laws and forms that determine how it can exist—is present in each and every actual electron or photon, perhaps in its quantum field patterns.

MORE ON “MIRACLES”

The “miracle” of the appropriateness of mathematics in formulating the laws of physics invites a final comment. Einstein wrote, “The eternally incomprehensible thing about the world is its comprehensibility,” and called our ability to make sense of it a “miracle.” [26] There are in fact several associated miracles. One is that factors of a purely rational kind have an actual existence, and a second is that the universe incorporates such factors in a sophisticated and structured way. This enables the universe to exist. A third miracle is the fact that we humans have intellectual ability at a high enough level to understand such things, to which we can claim no natural entitlement since this gift was in no clear way necessary for our evolutionary development and survival. Remarkably, these miracles are connected together: the universe is in a deep way rationally structured, and we can comprehend it. At the center is the idea of mathematics. All this makes for a clear pointer to something Mental that undergirds the universe in a very profound way, providing both for the physics and for our own mental nature. Einstein remarked on another occasion that there are not laws without a lawgiver, [27] and we will read more about his views in this area later. The proposal that a creative super-intelligence is at work—let us call it a divine intelligence—is both suggested and supported by perceptions such as these.

FIVE

DANGEROUS INFINITIES?

Many years after the event, the astrophysicist C. F. von Weizsäcker described an experience that occurred in the year 1938 in Berlin and left a lasting impression on him. [1] He had been giving a university colloquium on nuclear processes in the sun and proudly remarked that his ideas fitted in well with current thinking regarding the age of the universe. But this aroused excited opposition from Walther Nernst, a distinguished elderly physical chemist who was present. The age of the universe, Nernst expostulated, was not science; science demanded the “infinite duration of time.” The age of the universe should not even be put forward as a hypothesis—this “contradicted the very foundations of science.” The older scientist held these views in an evidently very emotional way.

Reflecting on the incident, von Weizsäcker concluded that the problems Nernst had with a universe of finite duration were not of a scientific nature. Why was he so angry? The answer seemed to be that in Nernst’s outlook “the everlasting universe had taken the place both of the eternal God and the immortal soul.” A deeply irrational trait was revealed in what purported to be a scientific opinion. For him, the world had taken the place of God, and it was blasphemy to deny it God’s attributes.

In later chapters we will consider whether the universe may be infinitely old or perhaps infinitely large. Here we first discuss more generally the place of ideas of the infinite in the physical universe and their impact, or otherwise, on Christian belief in God. If God is considered as infinite or at least beyond our human conception, it will appear that if one chooses not to believe in God, then an alternative belief in something physically infinite may be tempting. Scientists whose opinions derive from theological skepticism may not openly admit this. Still, there are those who are quite explicit about such matters. In his book The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, [2] the theorist Leonard Susskind makes his viewpoint proudly clear that in a quasi-infinite number of infinite physical universes, of which ours is just one, advanced life is expected to occur and God need not be brought into the discussion. Here the intentions are in no way hidden, although Susskind believes that these ideas are good science anyway. [3] Questions surrounding the multiverse hypothesis will be discussed in chapter eight.

We first will consider a historical perspective on thoughts of infinity and the infinite, starting in the context of medieval Europe. Then we will survey some specific ways in which the infinite has been introduced into human attempts to understand the physical universe. These include whether the universe is infinitely old or infinite in spatial extent or whether there is an infinite number of universes. Finally, we will draw some conclusions about the implications, if any, that all this may have for religious belief.

A BRIEF HISTORICAL OVERVIEW

The world of the medieval philosophers may again seem a surprising starting point for a discussion of modern physics. However, the thinkers of this period exposed and discussed many basic questions in the area of natural philosophy, [4] and these included the idea of infinity in mathematics and in physical nature, including both space and time. The academic debate of the medieval period may be regarded in many ways as reactions to the teachings of Aristotle. Scientific knowledge was limited, but some of the philosophical arguments were relatively sophisticated. A number of the debated questions in mathematics were dealt with properly only after the development of differential calculus by Newton and Leibniz in the seventeenth century, and of infinite set theory by Cantor in the nineteenth century.

In discussing the validity of infinite quantities, the most basic distinction to be made is between what are known as potential and actual infinities. A potential infinity is a quantity that can be as large as we choose, without limit, but in any given circumstance is always finite in size. An actual infinity is a quantity or a set of quantities that really is infinite in reality. A further important distinction is between infinities as purely mathematical concepts and the possibility that a physical object or system may be actually infinite in reality. Much debate has taken place over whether the latter possibility makes any sense. Can an actual infinity exist in nature?

Aristotle rejected the existence of any kind of physically infinite quantity. His universe was finite in extent, comprising a set of concentric spheres centered on the earth, and time was also finite. In fact, he believed in a series of cyclic recurrences of the history of the universe. His medieval followers had to adjust his views on the latter topic, since the church’s teaching was clear that time began just once at the world’s creation and it will have an end.

The central new task for the medieval philosophers was to incorporate Christian teaching on the nature of God into their critique of Aristotle’s ideas. God’s assumed infiniteness is especially relevant in the present context, because it may allow him to create infinite things, provided they are of a lesser kind of infinity than his own. Thomas Aquinas therefore taught that God could create any kind of infinite thing that did not imply an inner or logical contradiction. However, he also believed that an infinite object always entailed some kind of philosophical contradiction, and so was not creatable. Medieval thinkers generally accepted that talking about potentially infinite things is allowable. Thus a geometric line is potentially infinite if it can be extended as far as one wishes, and numbers are potentially infinite likewise. However, an actually infinite number presented problems, as did the idea of an actually infinite line. The philosophers fell into two camps according to whether or not they felt that these difficulties were surmountable.

The French scholar Jean Buridan put forward what turned into a classic problem. It was accepted that a finite number could be the sum of an infinite number of subdivisions: thus one equals one-half, plus one-quarter, plus one-eighth and so on. So, proposed Buridan, let us imagine a cylinder of height one unit that is subdivided in this way into sections with height one-half, one-quarter, one-eighth of a unit and so on, starting at the bottom of the cylinder. Further, let us imagine that within each of these sections, a line is drawn obliquely once around the circumference of the cylinder, starting at the lower edge of the section and ending at the upper. These lines can be joined at their ends so as to make one overall spiral line. Since the number of sections is infinite, the spiral line will be infinitely long. Buridan himself did not believe that such a line could exist, because he did not believe in actual infinities. Others disagreed, and so opinions were divided, a difference of opinion that is not completely resolved.

Concerning infinite space, views also differed. There were two issues here, one of which was whether more than one universe (or “world”) could exist. In 1277 Bishop Tempier of Paris issued a list of prohibitions of opinions that he considered erroneous, among which he declared that to deny the possibility of multiple worlds was to deny God’s creative power. After this the philosophers of the University of Paris were obliged to consider other worlds as possible, at least in principle; however, they spent much effort expounding the difficulties presented by the idea. Nobody in the medieval period, it seemed, positively believed in other worlds, but merely—following Bishop Tempier—in their possibility. A notable later exception was the Scottish-born Parisian scholar John Major, who taught around the year 1500. His view was that an infinite number of worlds exist, simply because “one cannot give a convincing reason for the opposite of this opinion.” [5]

Even with only one universe, the question needed to be asked as to what lay outside it. Possibly this might be an infinite void, if a void could exist, which was another hotly debated topic. Thomas Bradwardine of Oxford, in the fourteenth century, held that since God was infinite and was intimately related to the universe, an infinite outer space should exist simply as a manifestation of God’s own immensity. But a universe that is infinite in too many ways is problematic. It risks contravening an objection raised by the fourteenth-century John of Bassols that while God can create a universe that is infinite in a few ways, one that is infinite in every way would trespass on God’s own infinitude and look like something resembling another God. If the universe is “acceptably” infinite, we might be tempted to associate God with it in a strongly immanent sense. This can easily develop into a form of pantheism, something that Bradwardine strove to avoid by using language that was sufficiently vague.

Belief in a finite universe generally prevailed until after Copernicus and Galileo placed the sun, rather than the earth, at the center of the cosmic stage. Galileo was at heart a practical astronomer, however. He interpreted his findings along Copernican lines but was not primarily interested in speculating about the nature of the cosmos as a whole—maybe feeling that he had enough controversy to deal with already. His approach was above all to seek to justify his views by means of experimental observations. It was Newton who presented a broader picture, since his theory of gravity provided a set of ideas that were sufficiently powerful to give a framework for cosmology.

In Newton’s view the universe was infinite, and his reasons for believing this were very much connected with his view of God as filling all space and time. [6] “By existing always and everywhere, he constitutes duration and space. . . . Each and every particle of space is always, and each and every indivisible moment of duration is everywhere.” Bradwardine had not identified God quite so closely with the physical universe, but these were similar ideas, reflecting a deity whose immanence in the universe meant that the universe has to share physically in the divine infinite nature. In attempting to model the universe, Newton had his own law of gravity very much in mind. He believed that if the universe consisted of matter that occupied a finite volume of space, the matter would eventually all fall in on itself through its all-pervasive gravitational attraction. However, if the matter were “evenly disposed throughout an infinite space,” it could condense in local clumps to form the sun and the stars, scattered over great distances as is observed.

Later physicists were not convinced by Newton’s arguments, and in the nineteenth century the most commonly held view was of a universe that comprised infinite space except for one major congregation of matter, our own galaxy. This had to rotate so that it did not fall in upon itself. A highly important change of view was from seeing the world as a few thousand years old, following the traditional interpretation of the biblical book of Genesis, to many millions of years old as argued by geologists, but the details were the subject of intense debate. Many people posited an infinitely old universe. Faint objects called “nebulae” are visible through telescopes, and twentieth-century astronomers realized that just as the stars are bodies like our own sun, so the nebulae are in many cases galaxies like our own. What had formerly been an infinite outer void was now occupied by these galaxies—in this way producing a vision of the universe that was perhaps not too unlike that of Newton.

INFINITIES IN MATHEMATICS

In the thirteenth century, Duns Scotus may have been the first scholar to warn that magnitudes of infinite quantities cannot easily be compared so as to say that one is more or less than another; usually, infinite is infinite and one must leave it at that. His statements did not amount to a clear mathematical treatment, but they did at least help his followers to avoid simplistic errors.

It was Georg Cantor, six hundred years later, who put the mathematical understanding of the infinite on a better footing. [7] Mathematically speaking, the set of whole numbers is infinite, but the set of possible lengths of a line is “more infinite.” The set of whole numbers is infinite in a countable sense: we can count them as 1, 2, 3 and so on indefinitely, and any specified member of the set will be reached eventually in this way. There is no upper limit to the counting process, and suitable ways can be used to deal satisfactorily with the “entire infinite set” of whole numbers. On the other hand, the set of possible lengths of a line, or equivalently the set of all decimal numbers between zero and one, is continuously infinite. No counting procedure can be devised such that any particular decimal number will be counted sooner or later, and it was the achievement of Cantor and his followers to make these ideas mathematically rigorous. Further classes of “more infinite infinities” can be defined, but these examples will do for us here.

Infinities could now be dealt with mathematically, an essential step to their credibility as potential descriptors of physical quantities, although it should be mentioned that there is a school of mathematical philosophy called intuitionism that denies actual infinities in mathematics. It is important to appreciate that despite common use of the term, infinity is not a “number.” Its mathematical properties are very different from those of a normal numerical quantity, and it is better to call it a “magnitude.” If we add any quantity, finite or infinite, to an infinite quantity, the result is again infinity. Thus with infinities, addition is possible but ineffectual, as is multiplication. On the other hand, if we subtract one infinite quantity from another, we may obtain zero, a finite result, or an infinite result, depending on the situation. Subtraction of infinities from each other is thus not a universally well-defined mathematical operation, and neither is division.

What Cantor’s work made clear is that infinity is in no way a simple concept, and the further development of his ideas has been a major area of mathematical research since then. Cantor himself became firmly convinced that God, as Absolute, was the “true infinity” beyond the series of infinities uncovered in the mathematical realm. At least by analogy, God can therefore be “more infinite” than an infinite universe if the latter exists—a theme that had its place in the medieval discussion of infinities.

IS PHYSICAL INFINITY REAL?

When discussing the possibility of physical infinities, the situation is somewhat different from the case of mathematical infinities. In mathematics, we can define a potential infinity and then conceptually extrapolate it into an actual infinity, using appropriate logical methods. In physics, there is no such process as “extrapolating a finite physical object into an infinite object.” An object is simply there as it is, and we ask if it is finite or infinite. The first task is to discard any infinite quantity that is introduced artificially by our description of a system. The Greek philosopher Zeno produced his famous paradox of Achilles apparently never overtaking a tortoise by choosing to subdivide the time needed into an infinite number of intervals. This is not a genuine physical infinity, because a better mode of description will make it go away. We just calculate by the use of algebra or relative velocity when Achilles will overtake the tortoise.

A second category consists of physical situations that are potentially infinite, in that they would become infinite if time goes on for ever. A finite but expanding universe could be like this, although at any finite time it is still finite. In general, a given physical system is either finite or actually infinite, if the latter is possible. Although a consistent mathematical account of actual infinities can be set out, bizarre situations can arise if physical entities are actually infinite. The question is whether we should just learn to live with this, or whether the situations are unacceptably paradoxical. We will now examine a selection of paradoxes in this area. The central issue is whether the physical implementation of an actual infinity can introduce factors that are present neither in the mathematics as such, nor in finite physics.

1. Hilbert’s hotel. The best-known physical-infinity paradox was devised by the mathematician David Hilbert, who was enthusiastic about mathematical infinities but a skeptic regarding their physical realization. [8] He proposed a hotel with an infinite set of rooms, which are all fully occupied one evening when a new guest appears. “No worry,” says the hotel owner, and he proceeds to move the guest from room one into room two, the guest from room two into room three and so on ad infinitum. Now room one is empty for the new guest, despite the fact that the hotel had been full before, and indeed one can fit any number of new guests into the hotel in this way! This is paradoxical since the physical idea of a hotel being “full” seems intuitively well-defined.

2. Craig’s library. William Lane Craig has proposed a number of paradoxical tricks that could be played with a library that contains an infinite number of books. [9] These are numbered on the spine with odd and even numbers. For example, we could remove the odd-numbered books one by one, and each time move the remaining books up to close the gap. Amazingly, after an infinity of odd-numbered books have been removed, the bookshelves are still completely full!

3. Benardete’s book. It is proposed that we have a book with an infinite number of pages. [10] The first page is half a centimeter thick, the second is a quarter-centimeter thick, the third one-eighth and so on. The total thickness can be shown to add up to one centimeter. We read page one and then page two, and then turn the book over and open the back cover to read the final page. But it seems that there cannot be a final page! What is its page number? Can one count backwards through the pages of this book? If not, why not? In other words, Benardete’s book is mathematically describable but physically unrealizable.

4. The infinite sphere. [11] In three-dimensional space, four non-coplanar points define a sphere. We place three non-colinear points at finite distances from the zero of coordinates and a fourth point in a well-defined direction but at an infinite radial distance. It then follows (as can be seen by first imagining the fourth point at a very large finite distance) that the sphere through the four points must include the infinite flat plane on which the first three points lie. The same conclusion holds for any fourth point at infinity, placed in any direction, either side of this plane. Do all points at infinity therefore lie on the same infinite sphere? Alternatively, this same flat plane lies on an infinite number of different infinite spheres, or maybe the infinite sphere does not really exist. Geometry in infinite space seems to break down from our normal point of view.

5. Tristram Shandy. [12] The literary character Tristram Shandy is writing his autobiography but takes a year to write up one day of his life! In this version he is imagined to live from minus infinity to plus infinity in time, an infinite set of days. Mathematically, it is possible to put the single days in this set into one-to-one correspondence with sequences of 365 days, to allow the book to be written. But physically it is not possible to do this so that each single day precedes in time its corresponding set of 365 days. And if he has been writing ever since a time of minus infinity, what is the date he is currently writing about? The entire task becomes physically unspecifiable when an infinitely negative physical starting date is proposed—a paradox.

6. Hilbert’s hotel with change of bed linen. We now suppose that the hotel owner refuses to move a guest without first changing the bed linen in the new room. So guest three must move out of room three, whose bed linen can then be changed so that guest two can move in. The same now happens in room two, and finally the bed linen in the vacated room one can be changed and the new guest can enter. This sounds like a very reasonable scheme from a physical (and hygienic) point of view. But it cannot be done for an infinite hotel! The hotelkeeper must start at room number infinity, but how? It is, in short, impossible to “count back from infinity,” and yet from a physical point of view the operation sounds very plausible.

7. Craig’s library with shelf-clearance. In this operation on Craig’s library, the odd-numbered books are once again all removed. But this time, we move the remaining books along to clear the shelf space, starting from the original position of book number one. After a million books have been removed, there is a very long stretch of cleared space. When all the odd-numbered books are gone, the length of clear shelving is infinite: there is not a book anywhere in sight. Yet we know that an infinite number of even-numbered books must still be in the library somewhere! On top of this, the situation is observationally indistinguishable from the case where there really are no books in the library at all.

8. The bouncing ball. A hard ball is dropped onto a hard surface. It bounces such that each bounce is less high than the previous one. In the ideal mathematical case, the ball will then bounce an infinite number of times before coming to rest, after a finite time interval. But although Newtonian physics is in principle time-reversible, there is no way to make this process happen in reverse, even if energy is supplied! This seems paradoxical. (In practice, the motion will be damped, removing the infinity, and one may speculate that this applies to other singular physical processes.)

A number of problems have been illustrated here, quite apart from the anomalous algebraic properties of infinities. Some paradoxical physical tasks, it might be objected, just take an infinite time to complete. But this does not cover all the problems, and the possibility of infinite time is one of the questions at issue. Hilbert’s hotelier could perhaps succeed in moving all his guests in a finite time in a Newtonian universe, where instantaneous messages are permitted, but not in an Einsteinian universe, where messages can travel no faster than the speed of light. Overall, physical infinities present a variety of difficulties:

1. It is impossible to initiate a count through an infinite sequence starting at the infinite end, although physically we might reasonably expect to do such an operation.

2. Infinite magnitudes can have mathematical properties of a different kind from finite numerical quantities. Physical systems are characterized by their mathematical properties. So an infinite physical entity could differ in kind from a corresponding finite physical entity. An infinite hotel, book or library is qualitatively different from a finite hotel, book or library. The infinite physical object may not be realizable.

3. In mathematics, something infinite often requires to be an extrapolation or a transformation from something finite. In a physical situation, this is most likely impossible: the thing that is alleged to be physically infinite just has to be “there.”

4. It may be that physical “action at infinity,” involving structures or processes occurring at infinity, could have paradoxical effects on the observable finite region of the physics.

5. All our measurements, techniques and experiences are finite. It follows that no experimental evidence is available, or indeed possible, to demonstrate that a given physical thing is actually infinite. Physical infinities therefore have a certain mythical quality about them.

Reasons such as these make it quite reasonable to reject physical infinities outright as incompatible with our practical understanding of nature. However, it could perhaps be that in a given situation the unacceptable features might be avoided with sufficient care, and so a more cautious approach may be better. What is certainly not admissible is to talk about infinity in a glib way, simple-mindedly asserting that some given physical system “could be infinite.” It must be strictly insisted that the onus lies on the proposer to justify the infinite proposal. That is, its properties must be demonstrably well-defined and workable. Otherwise, the default position is not to accept it.

AN INFINITELY OLD OR LARGE UNIVERSE?

Bishop Tempier’s prohibitions included the advocacy of an infinitely old universe. The earlier medieval scholars had occasionally mentioned the subject but only as a philosophical possibility with many qualifications. [13] Thomas Aquinas had avoided taking strong sides on the matter, saying that nothing could be demonstrated. After Bishop Tempier, most opinions settled on the orthodox teaching that the history of the universe is finite. The issue was a matter of debate during the following centuries, although it was later realized that having a universe of finite size or finite age could avoid the Olbers paradox, which we discuss in chapter six.

The most important cosmological development during the twentieth century was the observationally based discovery that our universe is expanding. This seems to put a finite age to the universe. There was much interest, therefore, when in the late 1940s three physicists in Britain proposed a new theory in which the expanding universe was both infinite in extent and also infinitely old—the so-called steady-state theory of the universe by Hermann Bondi, Thomas Gold and Fred Hoyle. [14]

At the center of the steady-state theory was the idea that the universe should possess the property of having the same appearance at all places and at all times, the so-called Perfect Cosmological Principle. All three physicists concurred in stating that their motivations were “philosophical.” There were initially two variations on the theory: Bondi and Gold’s theory was more explicitly based on the Perfect Cosmological Principle, while Hoyle sought more to avoid the Big Bang. In either case, the theorists postulated a universal expansion of space in which matter continually appeared spontaneously throughout the universe, its mean density always staying the same. (The matter creation was an ad hoc assumption made in order to get the theory to work.)

The steady-state theory had some more concrete motivations. One was that the measured rate of expansion at that time gave a finite age of the universe that seemed too young, a discrepancy that was eventually rectified by better experimental data. Another motivation, stated openly by Hoyle, was to avoid having a finite starting point to time. He wrote, “It seemed absurd to have all the matter created as if by magic. . . . I therefore began to see if the creation of matter could be put into a rational mathematical scheme.” [15] Whether such a motivation is “philosophical” or based on antipathy to religion is clearly a delicate question. None of the originators of the steady-state theory wished to admit to the latter as a scientific reason, but all three had attitudes to religion ranging from skeptical to hostile. In a series of BBC radio broadcasts written up in a widely selling book, [16] Hoyle took the opportunity to make a naive attack on Christian beliefs, although his attitudes toward religion softened in his later years. [17] Bondi, while in principle courteously agnostic, remained very antagonistic toward revealed religion. [18]

Bondi was later to accept the standard Big Bang theory when the experimental evidence became stronger, but Hoyle, still staunchly opposed, went on with colleague Jayant Narlikar to develop a revised theory that allowed a quasi-steady-state viewpoint to be formulated on a broader temporal scale. He referred to God impersonally as “the system of laws that govern the Universe, what are often called the laws of physics.” [19] Later, reflecting on the enormous and subtle implications of the Dirac equation in quantum mechanics, he became willing to think of God more explicitly as a great theoretical physicist. He wrote in 1994, “It is because of this incredible chain of subtlety that I doubt the nineteenth century denial of a purposive universe.” [20] He still rejected “fundamentalism” but was now dismissive of atheism. [21]

It is hard to know whether antireligious sentiment really formed a part of the motivation for the steady-state theory, but it fitted in with its authors’ predispositions. An infinite age of the universe appears to make it possible to avoid the question of whether the universe requires a First Cause and therefore what this First Cause might be. This will be the subject of chapter nine. An infinite past timescale for the universe can perhaps play the role of a God substitute. It is always there present in the past, its contents providing the ultimate efficient cause of any given situation. In this kind of area there is a fine line between philosophy and religious avoidance.

In practice, Christian believers were able to accommodate themselves to the steady-state theory. God could still be attributed as the cause of the infinitude of creative processes that generated the matter that was always appearing in space. This was not such a powerful argument as the traditional First Cause argument, however, because the spontaneous appearance of atoms might be asserted as a “property of space”—although completely unexplained [22]—while a truly causeless spontaneous appearance of a universe challenges one’s credulity.

As we have noted, the medieval universe was believed to be spatially finite. The system of concentric celestial spheres allowed the intuitively satisfying picture of having God’s heavenly realm located physically in the region surrounding the universe. In contrast, Newton’s universe was of infinite size. However, the basic existence of God, as an item of primary faith, did not seem much affected by whichever choice was made. Neither did it seem to matter whether the universe was infinite and full of stars, as with Newton, or whether an infinite void lay outside our galaxy, as in later opinion.

Setting aside the problematic notion of physical infinities, does either a finite or an infinite universe, as such, make it easier or harder for a person to believe in God? A finite universe is conceptually simpler, perhaps more aesthetic according to taste and possibly easier to place in relation to God since we can consider it as a whole. An infinite universe can still be accommodated, however, as with Thomas Bradwardine and the prevailing opinion of most seventeenth- to nineteenth-century physicists who were believers. Indeed for pantheists who want an infinite God, it may be essential to make the universe infinite.

Recent measurements of the energy density of the universe—which seems to contain matter of different kinds and a mysterious unidentified component known as “dark energy”—appear to be very close to a critical value at which and below which the universe may be infinite. These results involve experimental uncertainties, however, and it is very possible that our measurements will never be able to distinguish between a finite and an infinite universe. If the universe actually has the critical energy density, then no measurement with a finite uncertainty could ever establish this precisely.

Another point is that our direct experimental knowledge is confined to the portion of the universe that is observable to us. The limited observations may be able to disprove certain models of the universe, but to prove that the universe is truly infinite seems a virtual impossibility. Even if we could show that the mean density of the observed universe is lower than the critical density, it might still be possible to embed it into a larger but still finite structure. Conversely, an apparently finite observable universe might be part of a larger infinite structure.

All this ignores the possible problems with physical infinities, however.

COMMENTS AND CONCLUSIONS

The relationship between a finite or infinite universe and belief or unbelief in God might be regarded as a purely subjective matter. Even though not all unbelievers require an infinite universe as a substitute for a deity, it probably helps. On the other hand, an infinite universe, whether in space or in time, can be accommodated by placing stress on God’s own infinitude. One should be aware that not all cosmologists are necessarily trying to eliminate God, even those without religious belief. There are those such as Martin Rees who are willing to express “humility in the face of the persistent great unknowns.” [23] Andre Linde is on record as saying, “It doesn’t mean that there is no place for God, just that there are some new possibilities. I am not a religious person or an antireligious person; I am just trying to figure out what I can say without emotion.” [24] Like Stephen Hawking, [25] he acknowledges that there is a deep mystery about why the universe (or universes) should exist at all, and this is something beyond the scope of science to answer. These are metaphysical questions.

An infinite universe might seem to make it harder for God to have personal interests in human beings on a small planet, but perhaps this is not a judgment we can make, especially in view of the bizarrenesses of an infinite universe. A Christian response might be to quote the statement of Jesus that not a sparrow falls to the ground without the heavenly Father knowing about it. We have pointed out that every electron in the universe is identical, as is every proton and so on. God is a God of details, of the small as well as the large. While it seems common for cosmologists to express unbelief in a “personal” deity, they are maybe looking for that in the wrong place. The personal is to be found in connection with the personal, and so it is in our own personhood and relationship to God that God’s personal nature is to be found. This is not even primarily something intellectual.

In the background to any cosmological discussion is the question as to whether a physical infinity, which is never demonstrable by experiment, lies too far beyond our normal experience to be accessible to our rational or even intuitive intellects, and what this might imply. Is a mathematical concept on its own good enough? There are mathematically infinite conceptual structures that do not appear to be physically realizable.

Some types of hypothetical physical infinities clearly look like substitutes for God, and we shall shortly explore this area in more detail. But scientific theories should not depend on theological or anti-theological motivations, and any attempt to design theories with this kind of goal should be recognized as having an extra-scientific motivation. The basic choices must depend on sense and reasonableness, something that may be very difficult to quantify. There will be in any case mystery at the bottom level, and then the final choice will be for each of us to decide what kind of mystery we prefer.

A final point should be made. If physical infinities are to be considered, why stop there? Why should we not indeed allow infinities to exist also of a mental and of a spiritual nature? These of course are associated with the mode of existence of God. It makes no particular sense to confine infinity to the physical.

SIX

MODERN ASTRONOMY

Where Has God Gone?

In this book’s first chapters we examined some of the ways in which the world of nature is governed by physical laws and principles acting at the smallest level. Now we move on to think about the universe on a much larger scale by looking at the subject of astronomy. Atoms, molecules and elementary particles are not observable to us without specialized apparatus, but the stars and planets in the night sky are a familiar sight for everyone. The regular and mostly predictable movements of the heavenly bodies have held a fascination for people of all cultures from the earliest days of the human race.

Most societies in the past have regarded the heavens as having a special interest from a religious point of view, but this might now seem to have changed. Both the small and the large appear to be well understood in terms of the laws of physics, and the heavens are no longer special. From the modern, scientific perspective, even for believers, it is not completely obvious whether the realm of astronomy has a relevance to religious belief, but there still remains an instinctive tendency to feel that there is a connection. This can give rise to intellectual and emotional tensions, which we will explore in this chapter.

THE MEDIEVAL PICTURE OF THE UNIVERSE

A widely held error in the popular view of history is a belief that people in the Middle Ages thought that the earth is flat. This is untrue! The ordinary people in those days did not leave written records, but we do know what the more educated sections of medieval society believed. Especially, we know what the church and the universities in Europe normally taught about the shape of our planet and, then as now, it was that the earth is round.

European understanding of astronomy in the Middle Ages came from the ideas held in late Roman times, which were based on the earlier teachings of Aristotle and other Greek philosophers. [1] The most important developments were made in the second century of our era by the scholar Claudius Ptolemy, who lived in Alexandria. For him as for others at the time, everything in astronomy was related to how the stars and planets appear from the human perspective, which is that of an observer on the earth. Given this, it seemed natural to take the earth as a stationary sphere at the center of the universe, while the moon, the sun, the other planets and the stars moved around it. All of these were believed to be mounted on invisible, transparent structures that were referred to as “celestial spheres” and were located at various distances from the earth, revolving around it at various speeds and carrying the planets with them. Closest to us are spheres holding the moon and the sun, after which there are the other planets. Then there is a sphere that holds the stars, and outside this is a final sphere holding the true heavenly regions which are the dwelling place of God. God therefore surrounds everything.

The Islamic scriptures, it may be added, also seem to present a system in which the earth and planets are surrounded by stars in a “lower heaven,” beyond which is the heaven where God resides. In this depiction, stars, comets and meteors are portrayed as protecting the highest heavenly regions from interloping evil spirits. [2]

The heavenly bodies were originally assumed to travel around the earth with uniform circular motion on the grounds that the circle is the most perfect of geometric figures and the heavens are the realm of perfection. However, from very early on it was realized that simple circular motion will not do. Such a motion would be in disagreement with what is actually seen, because as the planets move night by night across the sky, relative to the stars, their speed varies; it is not constant as simple circular motion would imply. In fact, in what is known as retrograde motion, planets can even change their apparent direction in the sky and move backwards for a while as viewed by ourselves. So in order to preserve the idea that everything in the heavens is based on circles, Ptolemy and his followers employed secondary geometric constructions known as equants and epicycles. This meant that the heavenly spheres could be mounted off-center and there could also be spheres on spheres—wheels within wheels, as it were. This made the system inelegantly complicated, but it gave a fairly good agreement with the observations.

Throughout the centuries the earth was taken to be spherical, during the medieval period just as earlier in the Roman period and in the days of the Greek philosophers. In the church, only a small handful of voices are ever recorded as advocating a flat earth; how then did the “medieval flat earth” belief come about? The historian Jeffrey Burton Russell has shown that the idea of a medieval belief in a flat earth is in fact a case of later “misinformation.” [3] The erroneous notion was set up in the nineteenth century by some writers whose feelings of enlightened superiority led them to regard the medieval age as irretrievably steeped in superstition and ignorance, and so obviously it must have been a time when people would believe in a flat earth. Particularly in America, this version of history found a receptive audience and was extensively circulated in school textbooks. The anti-medieval message was clearly one that many people wanted to hear. It is an irony of intellectual history that the actual credulity on this subject was found in the very writers who were alleging it in others.

Since ancient times, people have had good reasons to believe in a spherical earth. Ships pass below the horizon when they are viewed sailing away from a port. Conversely, as a ship sails toward land with mountains, these appear to its crew to rise up from the sea. The constellations are seen differently if we voyage north or south. The shadow of the earth on the moon during lunar eclipses is circular. All this was recognized since Greek and Roman times. What medieval people were unsure about was whether the southerly antipodean regions of the earth were inhabitable, since the climate seemed to become hotter and hotter as one traveled south.

The medieval universe was of course still very different from our own. Heaven was spatially located in the region outside the planets and stars, while hell lay somewhere beneath the surface of the earth. The image of heaven as “high” and “up above” and of the earth as “low”—and hell lower still—was thus taken literally. Popular artistic depictions—for example, in church wall paintings—made the universe appear relatively small and intimate. However, Ptolemy and later scholars realized that by earthly measures the universe was actually very large. [4] The sphere of the fixed stars, located somewhere outside that of the planet Saturn, had an estimated radius of over one hundred million of our miles. This is now known to be a great underestimate, of course, but to the imaginations of the time it was enormous. [5] The educated medieval picture in Europe, then, was of a universe that was large but finite and centered on a spherical earth.

Columbus and his crews were under no illusion that they might sail off the edge of the earth. The spherical earth turned out to be larger than they had thought, but they firmly expected to reach India by sailing around it.

THE RENAISSANCE REVOLUTION IN ASTRONOMY

The beginnings of modern astronomy can be dated from the telescope observations made by Galileo, starting in 1610, whose consequences the human mind has probably even now not fully digested. Galileo’s many achievements with quite small telescopes were remarkable. He succeeded among other things in discovering the craters on the moon, sunspots, the largest moons of Jupiter and the phases of Venus—a series of major discoveries that transformed the face of astronomy. The one step he did not take was to realize that circle-based planetary orbits were unsatisfactory, but we should bear in mind that his observations were mainly of the heavenly objects themselves, viewed for the first time under telescopic magnification, rather than of their large-scale movement in the skies. He used his new instruments for what they were best at.

As regards the structure of the universe as a whole, Galileo strongly followed the ideas of the astronomer and mathematician Nicolaus Copernicus, who had proposed that it is the earth that moves around the stationary sun, not the sun around the earth. Gradually this was to become universally accepted, but at the time the only geometrical concepts that Copernicus had available to express it with were the traditional circles and epicycles. So his system was still very complicated. It agreed well enough with the existing observations of the planets, but then so did Ptolemy’s system. For a long time Copernicus was very cautious about making his proposals public, even though a number of highly placed ecclesiastics expressed great interest. He died in 1543, just as the publication of his work was in its final stages. What Copernicus started was effectively completed by Johannes Kepler, who was a contemporary of Galileo and had available the very latest and best set of planetary observation data. Kepler rejected the circle-based system, showing that the observations could be much better described by employing elliptical orbits to describe the motion of the planets around the sun. [6]

The next crucial step was made in 1687 by Isaac Newton. In his book Mathematical Principles of Natural Philosophy, commonly referred to by the short Latin title Principia, Newton used his new law of gravitation and some new mathematics to prove that elliptical planetary orbits were to be expected. This, it seems, finally convinced the remaining skeptics. With the sun at the center, it was from now on a “solar” system. Together with the many other new observations, this amounted to a revolution in astronomical science, which set in motion a drastic change in people’s concepts of the heavens. Heavenly bodies became seen as ordinary physical objects, just as the earth is. Human beings no longer had a special location in the universe. The concept of heavenly perfection was radically transformed away from being imagined in terms of circular forms and into more general mathematical terms. Kepler, like Galileo and Copernicus, was a devout Christian, and he believed that his new mathematical and geometrical description of the heavens still reflected the glory of God. In Copernicus’s published book, however, the outermost divine heavenly sphere was absent from his pictorial depiction of the heavens, and it seems to have vanished with the appearance of the new system. In this way the heavens became in an important sense demystified.

From the ordinary person’s point of view, the most important issues were probably not intellectual. In its unified vision of the world and the universe, the medieval picture assisted Christian believers in connecting with certain truths of their faith and in feeling a sense of the presence of spiritual realities. If you believe that the earth is related in a simple, spatial way to heaven—where God dwells—so that the heavenly realm really does surround the earth at a great height, then several helpful consequences follow. The divine presence is conceived relatively clearly: the human being can visualize how, dwelling in heaven, God is able to look down on all that happens on earth. We say, “There’s One above who sees!” Moreover we are quite literally living inside God’s domain. Since heaven encloses the universe, there is absolutely no metaphor or figure of speech in saying that we humans dwell within the realm of God. The problems and difficulties of life on earth come about because the earth’s surface is the boundary, and hence the battleground, between the heavenly forces above and the subterranean forces of hell. Again the physical picture reinforces the spiritual teachings.

With the abandonment of literal pictures such as this, an inversion of viewpoint takes place. Instead of human beings dwelling inside deepest Reality, this dimension now seems to dwell only within a human being. That is, faith now has its basis and life in our own minds and hearts alone; spirituality has become an internalized thing that relies on the individual. But is this sufficient? In the next sections we will look at these matters more closely.

POETIC REACTIONS

Among educated circles in the seventeenth century, the new astronomical discoveries and ideas generated an interest that was reflected in the literature of the time. [7] The new knowledge also contributed to an increased awareness of the heavens’ magnificence, at least among protestants, and was often viewed positively from a religious point of view. The poet John Milton wrote that the Milky Way was a “broad and ample road whose dust is gold and pavement stars.” [8] Dryden had no theological problem with a more elaborate universe: [9]

Perhaps a thousand other worlds that lie

Remote from us, and latent in the sky,

Are lightened by [God’s] beams, and kindly nurs’d.

At the same time, other currents of thought were also beginning to emerge, as demonstrated in John Donne as early as 1611:

And new Philosophy calls all in doubt,

The Element of fire is quite put out;

The Sun is lost, and th’earth and no man’s wit

Can well direct him where to look for it. . . .

’Tis all in peeces, all cohaerence gone. [10]

By “Philosophy,” Donne means what we would call science. Perhaps these are slightly incoherent reactions in themselves, but the poet clearly feels more than a little lost with the new discoveries. William Drummond commented, following Donne’s poem, that the sciences were leaving the imagination “in a thousand labyrinths.” [11]

Milton wrote his Paradise Lost in 1667 as a cosmic epic on the grandest scale and borrowed from the new astronomical vision of the heavens, even though he was uncertain whether the earth revolved around the sun, or vice versa, and found the old viewpoint easier. Astronomical thinking may even have influenced Milton’s description of primeval Chaos as

the hoary Deep—a dark

Illimitable ocean, without bound,

Without dimension; where length, breadth, and height,

And time, and place, are lost. [12]

The primeval Deep in the Bible is indeed like a sea, but now outer space is also unfathomable like the ocean (we talk about the “depths” of space), and cosmic and marine imagery seem to overlap. Space and the ocean depths are both dark. The sea, however, possesses a creative potential that may be absent from space. Milton’s Hell is guarded by a “void profound of unessential Night,” [13] and Satan traverses a “vast, unbounded deep.” [14] Paradise Lost makes enthusiastic use of astronomical imagery, and Milton’s faith found no difficulty with the new developments, whatever the arrangement of the earth, sun and planets might be. God’s works are vast:

Boundless the Deep, because I am who fill

Infinitude; nor vacuous the space. [15]

Extended passages in Paradise Lost give glory to God in the whole of creation, even if its nature is beyond our understanding. A bit of humility is good for the human race. God built, in order

That Man may know he dwells not in his own;

An edifice too large for him to fill. [16]

LOST IN SPACE

A poetic mindset was helpful to Milton, whose darker imagery, inspired apparently by the new astronomy, was relegated to the Abyss and similar regions. But it would not easily stay there. At about the same time in France, Blaise Pascal was describing a very different kind of mood in the collection of writings that were later put together as his Pensées (or “Thoughts”):

I see these horrifying spaces of the universe which shut me in, and I find myself attached to one corner of this vast expanse, without knowing why I am placed in this spot rather than another; nor why this little time which is given me to live is assigned to me at this point rather than at another. . . . I see nothing but infinities on every side, and they shut me in like an atom and like a [passing] shadow. . . .

Engulfed in the infinite immensities of space, which I do not know and which do not know me, I am frightened. . . .

The eternal silence of these infinite spaces frightens me. [17]

These, however, are not Pascal’s personal sentiments! The first passage quoted above comes from a longer essay in which he makes it clear that he sees the “lost in space” attitude as unreasonable and characteristically held by unbelievers, and that those who profess it are in serious spiritual and personal trouble. This kind of feeling, he says, is the accompaniment to a deliberate and fashionable rejection of God on the part of some of his contemporaries. Pascal is appalled by all this unnecessary and unwise negativity.

At the very least, these are expressions of an enormous loss of cosmic confidence. The infinite spaces and timescales terrify by making the human being feel insignificant and without status, but this is not a very logical kind of fear. Our earthly environment remains unchanged, governed by the sun and the moon and perhaps to some extent the planets. We can still live our lives without regard to the rest of the universe. It is strange that such things are seen as personally important, and curiously paradoxical to feel “shut in” by infinity.

CHANGES OF DIRECTION

As we have seen, the old, familiar imagery had now become seriously perturbed. Previously, the earth’s position in the universe was humble through being low: the fact of being at the center of it all by no means implied that our planet possessed any particular merit. It was much like the arenas in the Roman Empire, in which the most prestigious people were the onlookers, and certainly not those at the actual center of the show! The medieval earth was similarly an arena within which good and evil were often in battle, and the outermost heavenly sphere was where God and the angelic beings witnessed it all. With the new cosmology, however, the earth’s place is humble through being physically insignificant and inconsequential: ours is an ordinary planet revolving in no special position about an average star.

At the center of the planetary system is now the sun, symbolizing not “lowness” but light, power and glory. It is often suggested that in this period of history, rising generations of European rulers may have been inspired to new heights of despotic magnificence by the new astronomical imagery. Louis XIV, the so-called Sun King of France, would be a prominent example: as the sun rules the planets absolutely, so such a king rules his country. The sun no longer moves as a servant of the earth; it directs and controls it instead. Attempts were sometimes made to identify the sun symbolically with God, but such a concrete and crude portrayal of the Deity is unsatisfactory. More recent astronomy has in fact demoted even the sun from this kind of symbolic position, positioning it in an average location in an average galaxy at a random place in the universe.

The new cosmic order also deprives everyday human language and thought of some of its power. If heaven is literally high, then the metaphorical usage of the word coincides with the literal. We have a sizable vocabulary of words expressing value of this kind: high, elevated, superior, as opposed to low, inferior, base and so on. No longer echoed in the cosmos, however, our sense of absolute values can easily seem undermined. Indeed, what now is “height”? Today we look “up” into the “depths” of space—an odd state of affairs!

ROCK POOLS?

If the universe is literally and actually surrounded by heaven, then the earth in space resembles an island in a vast cosmic sea filled with the divine influence. We all live in this milieu, and it helps bind us together. With the abolition of this worldview, it is all too easy to lose along with it the concept of the environmental nature of God’s presence, and human beings tend to become individualized. Vestiges of faith remain within a number of us, like rock pools when the tide has gone out. The individual can easily have a sense of spiritual isolation; no longer does the rock dwell within the sea, but traces of sea merely remain enclosed within certain fortunate rocks. This is probably the central spiritual problem introduced by modern astronomy. For many, alas, the pools seem to be empty.

By the later nineteenth century, the consequences of these and other developments were beginning to be felt increasingly widely. On the surface, this was a period of flourishing churches and widespread religious belief and observance. But undercurrents of unease and unbelief had begun to grow and to be expressed in graphic terms. Writing in 1882, Friedrich Nietzsche in Germany took the kind of emotion and imagery depicted by Pascal a critical step further and asked, “Where is God gone . . . ? We have killed him. . . . But how have we done it? How were we able to drink up the sea? Who gave us the sponge to wipe away the whole horizon?” The new situation was not at present apparent, however; it needed time to make itself felt by the human race: “As yet the deed is even further from them than the furthest stars.” [18] The turn of phrase is interesting, for this is precisely where the medieval scheme had located God.

Nietzsche finished with a notorious statement that “God is dead,” though without fully explaining why this should be so. In a more pensive style, Matthew Arnold had written in his much-quoted 1867 poem Dover Beach:

The Sea of Faith

Was once, too, at the full and round earth’s shore

Lay like the folds of a bright girdle furled.

But now I only hear

Its melancholy, long withdrawing roar,

Retreating, to the breath

Of the night wind, down the vast edges drear

And naked shingles of the world.

No more sea now, just global dryness and darkness. The world was beginning to seem an inhospitable place.

NIGHT WINDS

Our argument has been that modern astronomy has accompanied and encouraged a view of the universe as “despiritualized.” Only within ourselves does faith now lie, and often with difficulty. Is this all a little over-melodramatic? Many believers would reply that they have never worried much about astronomical matters, that the Scriptures have little concern with the subject and that their faith is not affected by these things. It is difficult to argue with this viewpoint, but one suspects that there are many others who are indeed affected by modern astronomy, consciously or unconsciously, for the kinds of reasons suggested above. Astronomy has always tended to have a connection with religion.

So let us take a closer first look at the astronomical picture that has now emerged. The first point to note, as already mentioned, is the sheer size of the universe. The earth is large indeed compared with the scales of ordinary human life, but our planet’s diameter is less than a hundredth of that of the sun, and the distance between the sun and the earth is a hundred times larger still. For light to travel from the sun to us takes eight minutes. Some two hundred thousand times this distance, several light years away, is the nearest star, and we have still scarcely begun to penetrate our galaxy, the Milky Way. This is found to be a disc approximately 100,000 light years in diameter, and it contains of the order of a hundred thousand million stars, one of which number is our sun.

From our own galaxy to the Andromeda Galaxy, the nearest large neighbor to ours, is over two million light years, and even here we are still within just one group of neighboring galaxies. Whether the universe is finite or infinite remains unknown, but there are estimated to be some hundred billion galaxies in the portion that is observable by ourselves, whose radius is some fifty billion light years. Long before this point, the normal human sense of scale has evaporated. The sheer mind-bending size of it all is one reason that human beings do not easily feel “at home” in the modern universe. And yet the immensity of the universe is not the main problem really; as we have seen, Ptolemy and his medieval followers were already to some extent aware of it, and Milton reveled in it. More serious is the feeling of insignificance and an inability to relate to the structure as a whole. We no longer really look “up” into the heavens—but in some random direction into an indeterminate distance. All this may tend to confuse a sense of relationship with its Creator.

Also apparent through the telescope, quietly dominating the view, is a background of blackness! However we may seek to penetrate it, blackness still seems to lie beyond. In ordinary life, the darkness of night is accepted because we know that it is temporary and will be followed by the light of the day. But the telescope deprives us of such consolations, for it seems to be suggesting a saddening truth about the universe: darkness always lies in the background. No heavenly realms beyond. Where is God now to be found?

In his essay quoted above, Nietzsche wondered what had become of the earth. “Is there still an above and below?” he wrote. “Are we not straying as if through an endless nothingness? Is the empty space not breathing upon us? Has it not become colder? Does there not constantly come night and more night?” These echoes of Pascal’s unbelievers were now being proclaimed by a self-acclaimed militant atheist. Pascal could reject such sentiments from a standpoint of personal faith in God, but Nietzsche had nothing left but a faith in humanity.

It seems, then, that modern astronomy may have generated a dramatic effect on the human outlook. The celestial spheres have been taken away, the nettle offered by the new system firmly grasped and the entire former edifice now turned inside out! It is no longer heaven that surrounds us, but an outer darkness. Earth is apparently the best heaven we have. Human beings dwell and rule in this substitute heaven as a substitute for God. “Man has become the measure of all things”—but something important seems to have been lost.

INFINITE SPACES

Pascal’s unbelievers’ reaction to the new and vast universe merits further examination. The problem is about more than just intellectual knowledge but concerns an “encounter.” Through the use of telescopes, something like a physical relationship between human beings and the universe is unveiled. The universe “confronts” us. Now, there is a natural animal tendency to be alarmed by anything really large: it gives a feeling of impotence, helplessness, insecurity, as if one is under a threat. It seems that the universe itself may sometimes have this effect on us. In the words of one of London’s inimitable taxi drivers, philosophizing during a trip I once made in his cab: “It’s a way to go potty, looking up at the stars. I mean, if you look at all that lot and think, ‘This goes on for ever,’ you’d go round the bend!”

But there is a contrasting point of view. Feelings of awe regarding nature and its wonders can have powerful overtones that positively kindle a sense of religious awareness. To stand beneath the starlit sky at night can be a celebrated way to experience this kind of effect. In the psalmist’s words:

When I consider your heavens,

the work of your fingers,

the moon and the stars,

which you have set in place,

what is mankind that you are mindful of them,

human beings that you care for them? (Ps 8:3-4)

We may well ask, then, what generates the difference between awe and wonder of this kind, shared it seems by Milton, Dryden and others, and the unease and fear reported by Pascal, while Nietzsche whistled in the dark.

One part of the answer, no doubt, is that the universe simply feels a more comfortable place if one has faith in God. A relationship with the Creator assists the relationship with creation. Otherwise, one is much more prone to the bleak, “modern” impression. But also, when we stand and look up at the night sky, our feet remain comfortably on the earth. Viewing through a telescope—even by means of a photograph—is a more isolating kind of experience that conceptually detaches us from our home planet. Although the telescopic view of the stars and planets and galaxies can be deeply impressive, there is also something strange and impersonal about it. Unfortunately the modern universe tends to resist any attempt of the imagination, as opposed to the intellect, to come to grips with it so as to give a sense of familiarity. It is also very hard for most people to comprehend the modern universe as a whole.

A further problem area concerns the question of life. In earlier ages, in a rudimentary way, the planets moving in the night sky seemed to possess something akin to having life, and they became associated with deities or with human fortune through astrological lore. In any case, one had become accustomed to the planets and stars as rather like nocturnal companions. But with few exceptions, they are now found to possess environments that are inhospitable or hostile to life. There can be no more companionship with heavenly bodies that are known to be dead, with a total indifference to ourselves.

We do not know, of course, that there really is no life on other planets. But if no such life exists—would it matter? A part of our problem may then consist of a deep-rooted unease that, with regard to the rest of the universe, we may be in a kind of inescapable physical relationship with something totally vast and dead. These regions “do not know me.” Such feelings are irrational, it may be replied: if all the rest of the universe were lifeless, what practical difference does it make to us? But we are certainly extremely keen to discover other living planets if they are there. This is more to us than just an interesting scientific question, as was shown by the great excitement caused by the orbiting Kepler telescope’s discovery that many other planets exist around stars in our galaxy. [19] Could some of them harbor life? That would help us to feel less alone and in a more comfortable-feeling universe.

But perhaps after all it is really God that we are looking for. Even if there are other life-bearing planets, most of the spatial domain of the universe is undoubtedly dead. In lifelessness there lurks a deeper suspicion of godlessness. If God is no longer beyond the outermost heavenly sphere, as a kind of ever-present backdrop to the universe, where then is he? It is of course a naive question: for the modern believer God dwells “outside” the universe in a non-spatial sense for which we have no adequate language. Milton tried to express it in poetry: “God in heaven Is centre, yet extends to all.” [20] But it is extremely easy even today to hanker after a spatially located God. If not outside the circumference of the universe, then perhaps inside it? In particular, being associated with life, God might be discovered in the living world of nature. Perhaps, in the poet’s words, “One is nearer God’s heart in a garden than anywhere else on earth.” [21] Many today regard nature in ways that have strong religious associations.

Even so, none of this removes the fact that the universe is to a large extent almost-empty space, with immense distances punctuated only occasionally by stars, dust and interstellar debris. Quantum fields are no doubt present as well, as modern theory requires, but these do not seem to be much help here. Can we avoid the sense that these are divinely and humanly useless regions and that there is a kind of godforsakenness about outer space? In these dark and desolate reaches, no sparrow falls to the ground. Dust and rocks might seem to be no subject of divine concern. No life, no presence of God?

AT HOME IN A LARGE UNIVERSE

It is evident that the modern view of the universe presents some profound challenges to us as human beings. One of them is whether we can hope to explain why the universe is so vast. A second concerns what kind of psychological attitude toward it would be most helpful. More deeply, there is the question of what kind of spiritual attitude should be implied.

The physical question. Perhaps surprisingly, there are strong indications that the first question may be answerable. Modern cosmology offers compelling suggestions, to which we return more fully later, that the size of the universe is connected with its development in time since the initial Big Bang. A “small” universe with a mere few galaxies in it (though even this would still seem huge to us) would have a very much shorter lifetime than the present age of our own universe. As a consequence, it could not actually give rise to stars stable over the many millions of years needed for advanced life to develop on a planet such as ours. [22] It is over this long, necessary timespan that the universe has expanded to the huge size that we now observe, the original dense matter having become so dispersed that most of the universe is now almost-empty space. Part of the answer, then, may be that God has set up a universe that is actually big enough to work, big enough to provide a home for creatures such as ourselves. It looks as if such a universe must be very big indeed.

If large numbers seem disturbing, it may be helpful to bear in mind that they are an inescapable part of our physical existence. Our bodies contain over 10^27 atoms! That means that the atoms in our body far outnumber the stars in the observable universe. There is no avoiding the fact that we are in a universe of mind-stretchingly large numerical quantities. In the next chapter we shall consider in more detail a set of reasons for believing that the universe seems to be just right for ourselves and is, perhaps surprisingly, “human friendly.”

The psychological question. At the psychological level, there may be difficulties in connection with a sense of human cosmic loneliness and desolation. It might be tempting to imagine the earth as a kind of oasis in a vast cosmic waste. From the point of view of any kind of religious belief, though, God must surely be in contact with all parts of the universe and not just our own world. One way out of these perceptual problems may perhaps be found in connection to how we relate to myth. To entertain and educate their children, parents teach them various myths and tales. These may contain certain important truths, but the imagery is not literally true, and part of the process of growing up is to discern the difference between mythology and objective truth. Nonetheless, it is wrong to throw away the truth in the myths. I would suggest that the theological and human truth behind the medieval cosmos myth is something we need to retain, while acknowledging that the picture itself is not to be taken literally.

In fact, it will be clear by now that far beyond merely abolishing the medieval picture of the cosmos, which could be called a myth with pro-God and pro-human elements, modern astronomy has had a certain tendency to present a picture with anti-God and dehumanizing elements. The picture is literally and scientifically true, but its effects on human imaginations and emotions can be essentially just as mythological as the medieval picture, while working in the opposite direction. We need to distance ourselves psychologically from the negative modern mythology.

Accurately speaking, the background night sky is not really black, but our eyes lack the ability to see its true “color.” At the early stages of our universe, space was filled with extremely hot radiation that included a great deal of light in our visible range of wavelengths. As the universe expanded, the radiation became stretched in wavelength, so that it now softly irradiates us in the form of microwaves, which are undetectable to our eyes but can be observed by means of radio telescopes. So the night sky is actually “microwave colored.”

The fact that the night sky is dark is something we take for granted but which is actually paradoxical. It might have been expected to be very bright indeed. If the universe were infinite, static and full of stars, then in every direction we would see the surface of a star, and the sky would be so bright that our planet would be in a kind of furnace in which no life could exist. This puzzle is known as “Olbers’s paradox” (after the German astronomer Heinrich Olbers), and there are two main explanations. One is the finite age of the stars, which means that beyond a certain distance the light would take longer to reach us than the age of the stars. The other is the expansion of the universe, which has the effect that stars and galaxies beyond a certain distance from us are receding at an apparent speed greater than that of light, so that light and heat from them cannot reach us. In this way we receive light from a limited number of stars, and so the restful darkness of the night sky is the only alternative to a universe in which our existence would be impossible.

All this means that in evaluating our attitude toward the universe, negative subjective impressions must be treated with great caution. Is it really implausible to say that God created such an immensely vast universe? As we shall explore further later, it may well have been essential. Neither is the dark night sky an issue of importance. There is no need to be nervous about the universe! Indeed, the psalmist was right, and we are compelled to marvel at the wonders of physical creation.

The spiritual question. Regarding the Western conception of God and the universe, several factors are of importance. One is the doctrine of creation. Christians, Jews and Muslims believe that God has created the universe; this means that it possesses an existence of its own, distinct from God, which in turn implies a certain degree of separation between God and the universe. The modern reaction to the universe is liable to exaggerate this separation, but at some level it is there, and we must find a way to live with it as part of our human situation.

A second factor is that pictorial images of God have always been in principle forbidden in these faiths. [23] We might like to form an understanding of God’s relation to the universe capable of replacing that of the Middle Ages, but it is an understanding that is needed, and not a “picture.” The troubles have come about largely because of visual thinking and its limitations. The ban on images must now be extended to pictorial thinking about “where God is,” or we will find ourselves in trouble.

A third factor is that, nevertheless, God has always been considered as close to creation. The nature of this closeness is a subject far beyond the scope of this present discussion, but it must be closeness in a spiritual rather than physical sense. Although a spatially located God is sought in vain, there is a need to find a God who is always and everywhere present in relation to the human seeker, no matter how far into outer space we might go. Space, to recall Milton, is not then “vacuous.” It means that if we are indeed “rock pools,” then there is always a source of water that is able to seep up and fill each pool. So the image has to change: if God is really an omnipresent source of spiritual provision for us, then we must sense ourselves more as springs than as rock pools!

At the same time, the believer should remember the psalmist’s own answer to the question “What is humankind?” It is, “You have made them a little lower than the angels and crowned them with glory and honor.” This is an affirmation of human significance that modern astronomy appears to deny—but it is at the spiritual level, not the physical. Belief in God and belief in ourselves go together.

A writer whose outlook remains very relevant is Saint Augustine, who lived around the year 400. In contemplating God’s relationship with the universe, it became clear to him that the “heavens” that surround the earth could not possibly be the dwelling place of God. God, he wrote, dwells in the “Heaven of Heavens,” something with a confusingly similar name to the ordinary “heavens” above the earth but actually quite different. It is timeless, he says, and an “intellectual” creation. [24] This opens many questions, but it points the way to an understanding involving more than just the physical dimensions of space. Like Saint Augustine, we can recognize today that the spiritual dimension is not to be visualized as any kind of quasi-spatial extension to the physical universe. The size of the universe is in the end irrelevant. It is in other ways that the spiritual is to be sought. We shall have more to say about this later after discussing human nature as being more than just physical.

SEVEN

THE HUMAN-FRIENDLY UNIVERSE

The previous chapter contrasted the prescientific picture of the universe with the modern perspective, which is one that can easily give a somewhat bleak impression. But appearances can be misleading. In this chapter we will find that modern physics and astronomy reveal a collection of remarkable facts about the universe that suggest that it is set up in a rather friendly way toward human life after all.

THE ANTHROPIC PRINCIPLE

Our survey of the science of physics has shown that the structure of the universe is based on unifying principles. Various laws govern the way that elementary particles and forces exist and behave. Along with these laws, there are constants of nature that appear to be given facts about the universe, not necessarily generated by the laws—for example, the strength of gravity, the electric charge on the electron and so on. If these physical constants were different, the universe would function differently. Future theoretical discoveries in the subject might constrain the values of some or all of them, but at present many of them are not known to be theoretically determined.

It was realized by Brandon Carter in 1973 that if a universe operates according to laws and constants of physics of the general type that we know about, then it can in no automatic way be taken for granted that stars and planets will be formed that can provide homes for life, especially for advanced life forms such as our own human species. The physical requirements for this to take place are somewhat rigorous, and it is remarkable that our universe satisfies them. Several forms of this idea, which Carter termed the anthropic principle, have been formulated. At the very least, our own planet must be of a suitable kind, located in a suitable region of the universe, such that human life is possible on it. This is obviously true, and there are many planets for which it is not true, drawing our attention to the fact that not all planets can generate advanced life.

Much more significant is the fact that for us to be here, the universe itself must have suitable properties. These we shall discuss in the following sections. This statement is normally called the “weak anthropic principle.” Many of the necessary conditions were spelled out in a classic work by Barrow and Tipler in 1986. [1] Although since then there have been refinements of the various arguments, which Barrow and Tipler presented in considerable detail, the basic position remains unchanged.

Much more debatable is the so-called strong anthropic principle, which asserts that a universe is actually obliged to be capable of bearing life. Barrow and Tipler also defined a “final anthropic principle,” more speculative still, which is concerned with life and its information-generating capacities coming to a permanent existence in the universe.

Of the various statements of the anthropic principle, it is clear that the weak version is logically undeniable. What is interesting are its implications, and whether these imply some form of the “strong” principle. We will not deal here with the “final” anthropic principle. Of importance is the interpretation to be given to the observed physical facts. The weak anthropic principle is more than just an alert to the non-inevitability of life. It points out that the universe is such as to support our presence, and asks how this can be translated into a set of physical statements, and whether something beyond normal physics is required to make sense of the situation.

An “anthropic coincidence” is the name given to an apparently uncaused agreement between the actual value of a physical quantity and the magnitude that it must have if the universe is to produce advanced life. There are many of these coincidences. To examine them we will start by outlining the cosmic history of our universe. Then we will assemble a list of the most important physical requirements that seem to be necessary for our existence, and after that we will look at the ways in which these requirements are fulfilled in practice.

A BRIEF HISTORY OF THE UNIVERSE

Earlier we outlined how our universe is believed to have had a beginning in an explosive event some 14 billion years ago known as the Big Bang. Its subsequent history is rather complicated, and the picture that we possess is the result of extensive astronomical observations of stars and galaxies, together with our understanding of many nuclear physics processes.

Immediately after the Big Bang, the very earliest instants of the universe are not well understood, but things happened very quickly. After 10-32 of a second, elementary particles were being formed out of quarks and gluons that had just been made. A great deal of energy was present and available. After about three seconds, essentially all the protons were formed that now exist. These are the protons that we ourselves are made out of today. A large number of neutrons were also formed.

At this point the universe was still very small and dense, and its temperatures were extremely high, as they now are inside stars. This enabled nuclear reactions to take place. Protons and neutrons interacted with each other to form large numbers of deuterons, which are the nuclei of heavy hydrogen atoms and consist of a proton combined with a neutron. The deuterons in turn could combine to form nuclei of the element helium, and there were also large numbers of electrons, photons and neutrinos around. As the universe expanded, the energy density and temperature decreased and the nuclear interactions stopped. Eventually the electrons could attach to the atomic nuclei so as to form atoms, mostly of hydrogen and helium at this stage.

The universe continued to expand and cool down, and by the time it was 400,000 years old, the atoms were no longer continually torn apart by collisions with other atoms. In general, things had become much more stable. The photons were no longer continually absorbed by collisions with atoms and electrons but could travel uninterruptedly through space. Many of the photons have survived until now; they have turned into the so-called cosmic microwave background radiation, having been stretched to very much longer wavelengths by the continued expansion of the universe.

After about 400 million years, the hydrogen and helium were able to condense by gravitational attraction so as to form the first generation of stars. In the interiors of stars made mainly of hydrogen, nuclear reactions occur in which hydrogen nuclei—that is, protons—combine together and form heavier elements. In so doing they generate a great deal of energy, which is how stars produce their power. The first stars were very much more massive than our sun, and such stars burn themselves up relatively quickly. After a few million years, which is a much shorter lifetime than that of stars like the sun, these ultra-massive stars consumed all their hydrogen fuel, became unstable and exploded as supernovae. The supernova explosions propelled all the produced material into space as a kind of atomic debris. Much of this was now in the form of atoms of elements such as carbon, oxygen, iron and indeed all the elements that are now found in planetary objects such as our own Earth.

With plenty of material floating around and attracted together by gravity, galaxies were gradually able to form. This happened over a timescale of a billion years after the Big Bang. With our telescopes, we are able to observe back to about this point by detecting very distant and ancient galaxies whose light has taken many billions of years to reach us. Inside the galaxies, more stars formed from the condensing material. These stars were of various sizes but overall much smaller than the first generation of giant stars. Planets of all sizes also formed and were captured by the gravitational attraction of the new stars. These processes have been going on ever since the formation of the galaxies. Some 8.7 billion years from the start of it all, our own sun formed, along with the solar system containing the planet Earth.

BASIC REQUIREMENTS FOR PLANETS WITH ADVANCED LIFE

With the complex history of the universe kept in mind, we are in a position to write a basic “shopping list” of conditions that would allow a planet with advanced life to form. This list is not claimed to be complete, but it shows that the requirements are by no means trivial or few in number. One proviso should be made: we know only about life forms such as occur on Earth, which consist of organic materials, that is to say carbon-based chemistry. No convincing case has been made that other types of chemistry could be a basis for life, although much of what follows here would still be the same.

Some of life’s basic necessities arise from the structure of the universe and from elementary particle physics. Three space dimensions are necessary. Two are too few to give sufficiently rich physical possibilities for life. Four space dimensions would have different physical properties from three, so that gravitational orbits of planets would not be stable: planets would either fly away from their stars or spiral into them. All four known kinds of physical force seem to be needed. Gravity is essential to form stars and planets, while the strong nuclear force is needed for protons and neutrons to form and to bind into nuclei. Electromagnetic forces make possible the existence of atoms and molecules, while the weak nuclear force enables hydrogen to burn in stars like our sun. All these forces must have appropriate strengths, as we shall see.

A further condition for a workable universe is that it must contain more matter than antimatter—or vice versa. The problem here is that theories usually predict that equal quantities of particles and antiparticles will be formed in the initial processes. These would be likely to annihilate each other to form nothing but photons and neutrinos, with no matter left that can form atoms. We know of processes that are weakly asymmetric between particles and antiparticles, but at present there is no real understanding of how the universe should have turned out the way that it has. One thing that does appear to be necessary is the presence of at least three families of elementary particles, to provide enough mathematical flexibility in the equations to generate the possibility of matter-antimatter asymmetry.

With these basic conditions satisfied, there are still a considerable number of further requirements:

1. a sufficiently long-lived universe

2. the ability to form galaxies

3. a suitable quantity of hydrogen

4. the ability to form heavier elements in stars

5. first stars that explode properly

6. a suitable population of later-generation stars

7. suitable planets

8. organic chemistry

In other words, for the formation of life of any kind, and advanced life in particular, quite a large set of circumstances must be right. How easily can this be achieved? The following sections will attempt to summarize a great deal of material on this subject. More details have been given by a number of authors, especially Martin Rees, Paul Davies, Robin Collins and Luke Barnes, [2] in addition to the text by Barrow and Tipler already mentioned.

A SUFFICIENTLY LONG-LIVED UNIVERSE

From what has been said so far, it is clear that a universe must be in existence for a very long time if it is to generate life of the kind that we know. A second generation of stars must be able to form, and these must provide a home for planets of a suitable kind. Once primitive life has formed, evolutionary processes will take billions of years to form creatures at the level of human beings, if our experience on Earth is typical. The numbers are uncertain, but it is reasonable to take our own history as providing an approximate indication of the timescales that are needed.

According to general relativity, the behavior of a universe depends on the overall density of energy and matter in it, conventionally denoted by the Greek symbol Omega (Ω). The value is usually quoted in units such that if Ω is precisely 1, the universe will expand forever—but only just. If Ω is greater than 1, the gravitational attraction of the energy and matter will pull the universe back on itself so that it will eventually collapse and come to an end. The larger the value of Ω, the shorter the lifetime of the universe. With Ω less than 1, the universe will expand indefinitely. If Ω is too large, the universe will not survive long enough for galaxies, stars, planets and life to form, but if Ω is too small, then the universe expands too quickly, and the gravitational pull of the matter in it will not be sufficiently strong for the matter to condense and form galaxies. There is a comfortable region within which galaxies will form in a long-lived universe.

The value of Ω can change as the universe expands. Theoretical calculations state that in the present era, Ω must be in the numerical range of approximately 0.9 to 1.1, if life-giving planets are to have formed. In fact, it is found to be equal to 1 to within better than 0.1 percent. At the start of the universe the requirements are much more stringent; for example, after one second Ω must equal 1 to a precision of one part in 10^15, which was no doubt the case. This means that space must not be appreciably curved: the universe must be geometrically close to being flat, to an extraordinarily high level of precision. In principle there is no reason why this should be. The best theoretical reason on offer is that a process called “cosmic inflation” took place during the earliest fraction of a second after the Big Bang. This involves a sudden dramatic expansion of the universe by reason of the behavior of quantum fields that were initially present, according to this theory, and it would produce a very flat universe after the expansion stopped, almost irrespectively of what the curvature might have been before the inflation started.

Cosmic inflation is still a controversial idea, because although it solves problems concerning why the present universe is found to be uniform in all directions and also very flat, it introduces theoretical complexities and difficulties of its own. It may be that the physical parameters of the inflation process itself need to be finely adjusted if it is to start and finish in an appropriate way. At present it is safest to regard this area as “under study.” We do not really understand the earliest instants of the universe well enough yet. But it would be a remarkable coincidence if an inflating universe turned out to be just what was needed to generate life later on!

The quantity Ω, then, is the first example of a physical number that has to be “just right,” and is so, when it in principle might have been very different.

EINSTEIN’S “COSMOLOGICAL CONSTANT”

As he put together his theory of general relativity, Einstein realized that the equations required the presence of two fixed numerical quantities. The first of these represents the strength of the gravitational force, as originally defined by Newton. The second does not affect the workings of the theory except on very large-distance scales. It is called the cosmological constant, and it can behave like a source of “cosmic antigravity,” affecting the behavior of the universe as a whole. Recent observations have revealed that within the universe there is a kind of “dark energy” whose source is unknown. This dark energy will affect the value of Einstein’s cosmological constant. It also contributes to the value of Ω.

We can measure the cosmological constant experimentally by observing the properties of very distant galaxies. It is numerically small and positive and it has the effect of making the universe expand in such a way that in the distant future the expansion will become ever faster, and the universe will never contract again. But if the value of the cosmological constant were too large, the universe would have been expanding too fast at the beginning of time, and matter would never have been able to condense gravitationally to form galaxies. If its value were more than about ten times what it is, then galaxies, stars and planets could not have formed.

What makes the situation perplexing is that we believe that the universe is full of quantum fields in their unexcited state—these are the fields that can be excited so as to form elementary particles. Each field ought to contribute to the observed value of the cosmological constant, with an effect that should be enormous, perhaps making the total cosmological constant as much as 10^120 greater than the value actually found. There are theoretical arguments that can reduce the total from this order of magnitude but nothing at all capable of giving the observed small value. [3] So the fields seem to be canceling each other with amazing precision. If the actual value were “merely” ten times what it is, this would be fatal for us. Somehow, some extremely large numerical quantities, given by the fields individually, are apparently canceling each other out almost exactly, but there is no known reason why they should. This looks like an amazing cosmic coincidence.

One might naturally suspect that the present theory must be wrong and that a correct theory of elementary particles and their fields would predict the cosmological constant to be close to zero. Obviously, this thought has occurred to the world’s best theoreticians, but up to now nobody has been able to propose any convincing physical reason for the small value of this constant. [4] There is no known property of elementary particle fields that would connect them with gravity in this way. This suggests that the constant may well be small for a non-theoretical, anthropic reason, for if it were much larger than it is, we would not be present to observe it.

GALAXY FORMATION

The term parameter means a numerical quantity that can affect other things, and we have just mentioned two cosmological parameters that must be right if galaxies are to form out of dispersed material in the universe. The next parameter that must be taken into account refers to the ability for the dispersed matter in the universe to condense by gravitational attraction into galaxies. Although the galaxies formed relatively late in the history of the universe, their proper formation depends on small irregularities in the density of energy in the universe at the earliest times, deviations from perfect smoothness in the distribution of matter. These have been called “ripples.” Where the energy is slightly denser, more matter is found, and the force of gravity eventually makes this condense into stars and, later on, into galaxies, which are larger structures and take longer to form. If the ripples were too weak, the effects of the expansion of the universe would overcome the gravitational attraction of the matter, and stars and galaxies would not then form. If the ripples were too strong, the gravitational condensation would occur too strongly and massively and it would result in black holes rather than stars and galaxies.

The quantity that must be “right” is the size of the ripples relative to the overall density of energy, and it should have a value of approximately ten parts in a million. The theoretical uncertainty on this value is approximately a factor of ten, which sounds generous. However, it could in principle have any value at all from zero up to one, or possibly even up to ten thousand, and so there are very many more ways for it to be wrong than right. The value is generally attributed to “quantum fluctuations” in the fields present in the early stages of the Big Bang. We do not know enough about this to explain why the ripples should have had the size that they did, but it appears that if they come from inflation, the model for inflation must be chosen “with great care.” [5] If a physical reason were found, then this would presumably just push the questions back one step.

ENTROPY IN THE UNIVERSE

The physical quantity entropy is a measure of disorderliness in a system, as we explained in chapter two. In a system that consists of smaller things, such as atoms, large-scale order will tend to degrade into small-scale disorder. Entropy applies to the universe just as to anything else, but with some subtleties. The cosmologist Roger Penrose pointed out that the initial state of the universe after the Big Bang appears to have been one of extraordinarily high order, and this is something that really ought to have an explanation. The orderliness of the very early universe consisted of the matter in it being spread out unusually evenly over the volume of the universe. This is reflected in the cosmic microwave background being very nearly the same in all directions.

At first, one might suppose that a universe with a very uniform distribution of particles was in the final degraded stages of its thermodynamic “heat death,” with maximum entropy. What changes the situation is the action of gravity, through which material becomes attracted together so as to form galaxies and stars—things clump together. The gravitational energy then tends to convert into heat, which is why stars are hot enough for thermonuclear reactions to occur. The ultimate state would in fact be a universe in which all the material had clumped into one black hole. In short, evaluating entropy with gravity included changes the picture drastically. At a random time in its later history, a universe has all sorts of gravitationally induced unevennesses—such as galaxies, stars and so on, none of which were present originally in our universe. Entropy has increased as these objects were formed.

The question, then, is whether the initial very smooth state requires explanation. As we will see later, if our present universe derived from a previous one, then it should almost certainly have more entropy than it has. The observed smoothness must depend on whatever initiated the Big Bang and is associated with the small size of ripples in space, discussed above. One could call the low entropy value a fine tuning, or else say that the universe started out in a special state that might be natural in a given theoretical or even theological understanding. However, it was very special with regard to the overall set of possibilities, and there were an enormous number of ways in which it could have been different.

HYDROGEN AND THE HEAVIER ELEMENTS—THE STRONG FORCE

Life requires chemistry of a suitable kind, with planets to provide an appropriate environment. The formation of chemical elements started with hydrogen and helium in the earliest stages of the universe. The hydrogen fueled the first generation of super-massive, short-lived stars, within which heavier elements formed. An important requirement for life is that these processes should be possible and should take place.

The size of the strong nuclear force is the first quantity that must be right. Rees quotes a physical parameter that measures this and has a value 0.007. This number as such is not of absolute importance for us here; what matters is how precisely it needs to equal the value that it has. This is a question of nuclear physics. On the way to the formation of helium and other elements, protons must first be able to form nuclei of deuterium, which consist of a proton and a neutron bound together. The deuterium nuclei then form helium nuclei, and through a series of further reactions in the later stages of the star’s life the heavier elements can be formed.

It has been calculated that if the strong force parameter were less than 0.006, then the proton and neutron would not bind together and deuterium would be unstable. This would severely hamper the production of heavier elements. On the other hand, if the strong force parameter were too high, quite a lot of a new kind of helium nucleus could form, consisting of just two protons bound together. A normal helium nucleus has two protons and two neutrons, and a helium nucleus with just two protons would decay into deuterium. The normal hydrogen would tend to be used up and disappear; there is some debate about how harmful this would be, but to be safe, the strong force parameter should probably be less than about 0.01. This question is examined at further length by Barnes and Collins, who quote calculations from other theoretical astronomers. The possibilities for different physics are complex, but there are many more ways for the strong force to be wrong than right.

A crucial life-essential factor is the need for the element carbon to be produced plentifully in the giant first-generation stars, and this provides further constraints on the strong force. The most important production mechanism consists of nuclei of helium merging with other nuclei to form heavier ones. For example, two helium nuclei can collide to form the isotope beryllium-eight, which can then take a further helium nucleus to form carbon-twelve, which can then turn into oxygen-sixteen and so on. These numbers refer to the total number of protons and neutrons in the respective nucleus, its “atomic weight.” The relevant helium nucleus is helium-four, otherwise known as an alpha particle, with two protons and two neutrons. In each of these processes, a high energy photon is emitted to take away excess energy.

The nuclear reactions take place at a certain rate, but much more quickly if they produce excited states of the new nuclei. When these states exist, they are formed first, and then they immediately decay into the new stable nucleus. The unstable excited states are called “resonances” because of their strong ability to absorb energy at certain precisely determined values, just as a violin string will vibrate strongly only at fixed frequencies. It turns out that such a resonance is present in carbon at just the right energy to amplify strongly the production of carbon from beryllium; however the corresponding resonance in oxygen is not at the right energy to enable further alpha particles to convert the carbon equally strongly into oxygen. A good amount of oxygen was still generated from the carbon, but fortunately much of the carbon was retained. What makes all this remarkable for us is that the beryllium-eight nucleus is very unstable, and little carbon would have been formed if the beryllium-to-carbon process were not amplified in this way. This amplification enabled good quantities of carbon and oxygen to be produced in the first stars so as to be dispersed into space when the stars exploded.

These processes were worked out in the 1950s by Fred Hoyle, together with colleagues, and the physical existence of these resonances at precisely the right energies persuaded him that something strange was going on. More recent calculations have indicated that if the nuclear strong force were different from its actual value by as much as 0.4 percent, either the amount of carbon in the universe would be seriously depleted or else there would be insufficient oxygen, also important for life. The final stages of burning of stars may produce further amounts of carbon, but it appears that the strong force is tightly selected to optimize the main production process.

HYDROGEN AND HEAVIER ELEMENTS—THE WEAK FORCE

We have seen that to generate planets that can bear life, the earliest stages of the universe must provide the elementary ingredients of matter, in particular protons and neutrons. The neutrons on their own are unstable, but they can be preserved when bound into atomic nuclei, and of these the helium nucleus is very important, since it can become transformed into nuclei of heavier elements. It is not altogether easy to get the relevant processes right, and at the start of the universe they happened in two stages, one lasting for about one second after the Big Bang, and the next lasting for about one hundred seconds.

Originally, protons and neutrons were formed in closely equal numbers out of the primeval quarks and gluons. During the first second after the Big Bang, the neutrons and protons tended to transform into each other, radiating and absorbing neutrinos and electrons in order to do this. The interaction with the neutrinos depends on the weak nuclear force, which acts more strongly at high energies. Things now played out in the following way. The universe initially was extremely hot but cooled rapidly as it expanded; at first the neutrinos interacted relatively strongly with the protons and neutrons, but after a second they could do this no more. The numbers of neutrons and protons were now approximately fixed, with more protons than neutrons since protons are slightly lighter. The remaining neutrons then combined with protons to form deuterium, if they could do this without decaying first. The combination process took place over the next hundred seconds or so. The half-life of the neutron is about nine hundred seconds, again governed by the strength of the weak nuclear force. So this was long enough to allow the formation of large amounts of deuterium and from this, helium. This assisted the production of heavy elements subsequently, although it is not clear that the helium at this stage was essential for the later formation of life. It should be remembered that here we are just talking about the atomic nuclei of deuterium and helium since electrons have not yet joined with them to form atoms.

Each neutron takes one proton in forming deuterium and helium. A proton is a hydrogen nucleus, and a good excess of protons must still be left so that stars can be powered and chemical compounds such as water can form later on planets. After the first second, the proton-to-neutron ratio was about six to one, which is evidently satisfactory for life. If the weak nuclear force had been significantly weaker, the neutrinos would not have been able to generate a sufficiently large excess of protons during the first second.

The weak force also played an important part in the explosions that terminated the existence of the first generation of very massive stars. It turns out that the production of large numbers of neutrinos inside the star is important here, despite the weakness of their interaction with matter. If the interaction is too weak, then the outer layers of the star will not be blown off and there will be no explosion. If it is too strong, the neutrinos are absorbed in the central regions of the star and there is no explosion. So the dispersal of the heavier elements into space depends on the strength of the weak force as carried by the neutrinos. A stronger weak force would also make the star use up its hydrogen fuel more quickly, decreasing the lifetime of a star of given mass, since the conversion of hydrogen into deuterium takes place by the weak force.

Roughly, a weak force a factor of ten or so stronger would have been bad or even a small fraction weaker. Perhaps this sounds not very constraining, but the weak force could in principle have any strength at all, as far as we know, and so there are wide ranges that would not have allowed life to form as we know it.

HYDROGEN AND HEAVIER ELEMENTS—THE MASSES OF QUARKS

We have mentioned that for heavier elements to form in stars, it is essential that the hydrogen nuclei—that is, protons—should interact to produce deuterium as the first step. The deuterium nucleus therefore has to be stable. One way to express this, as we have seen, is in terms of the strong force. A parallel condition is that the quarks that make up the neutron must not be too much heavier than those that make up the proton, or else neutrons will decay even when they are bound into deuterium nuclei. The up and down quarks have masses of approximately 2 and 5 of the usual units (million electron volts, or MeV). The neutron has an extra down quark, and the proton has an up quark, making the neutron a few MeV heavier than the proton when the electric charge of the proton is taken into account.

According to calculations, the masses of the up and down quarks and the electron must be tightly constrained for everything to work. [6] If the down quark were about 1 MeV heavier still, relative to the up quark, the deuterium nucleus would not be stable, making heavy-element production almost impossible. If it were an MeV lighter, protons in atomic nuclei could absorb electrons in the atoms, and heavier elements would become unstable. If the electron mass were more than about twice its actual light value of 0.5 MeV, both of these disasters could occur.

To put these light up and down quark masses in perspective, the other quarks are very much heavier, the “top” quark weighing in at 175,000 MeV. We do not know why the quarks have the masses that they do, nor the electron. To say that the difference in mass between down and up quarks has to be within an MeV or so of its actual value, even with some uncertainty, implies a significant constraint relative to the overall range of possibilities.

STABLE STARS AND GRAVITY

As a star burns its hydrogen as fuel, the heat and radiation produced in the heart of the star balance the gravitational weight of its outer layers and prevent the star from collapsing, so long as the hydrogen burning continues. The strength of gravity must therefore be right—too strong and the star will collapse, too weak and nothing much can happen in the universe. This constrains the star-giving and hence life-giving range of values of the constant of gravity. Gravity is very feeble, compared to the other forces, and there is no known reason in principle for it not to be stronger, even as strong as the nuclear force as a plausible upper limit. There is also nothing in principle to prevent gravity from being zero in a hypothetical universe, although such a universe would be very boring.

Stable stars could still exist if gravity were somewhat stronger than it is, but not too strong. Barnes estimates that when the electromagnetic force is also included in the calculation, a fraction of about 10-39 of the possible range of gravitational strengths is suitable. [7] Needless to say, our universe occupies a place inside this minuscule region.

PLANETS AND LIFE

The “human-friendliness” of the universe is usually presented in terms of the physical quantities discussed above, but there are other factors. The chemistry of biological organisms requires that the electromagnetic force be sufficiently strong to hold atoms together in complex organic molecules, but too strong chemical binding would inhibit the processes that life requires. The electron mass comes into the calculation and must be no heavier than about 10 MeV. Such a heavy electron would already have been damaging to the necessary nuclear physics. While this is much heavier than the actual electron, heavy electrons are perfectly possible and the set of known elementary particles includes unstable “heavy electrons.” The next lightest (the so-called muon) has a mass of 106 MeV, and it is not known why the electron should be as light as it is. In general, the requirements for suitable chemistry are similar to but less strong than those needed for the nuclear-physics processes to take place satisfactorily. These are a different set of constraints, however, and it is not obvious why the two sets should be even compatible.

The strength of gravity must again be about right. For complex reasons, the temperature of the surface of stars would be significantly different for a different gravitational constant, making it difficult for light radiated from stars to power biochemical processes on planets. If gravity were too strong, large animals would not have the strength to function physically. These conditions are not very precisely determined, but even quite an approximate permitted range would still be significant since in principle the strength of gravity might be anything from zero up to at least the strength of the strong nuclear force, a factor of 10^38 times greater than its actual value. Rees has outlined some of the disastrous consequences for living creatures if the gravitational constant were a mere million times its actual size. [8] This again seems very generous, but it still represents a tiny fraction of the overall possibilities. Collins discusses this further, along with conditions involving the lifetime of stars, and reduces Rees’s factor of one million to a few thousand. [9] There is a need for plate tectonics, which again is constrained by strength of gravity. Perhaps one part in 10^36 of the conceivable range of values of the gravitational constant is suitable for advanced conscious life on planets. Fortunately, this is the same range that makes stars work.

The special nature of our planet Earth has been widely discussed in the scientific literature. To provide suitable conditions for advanced life, a planet must be the right distance from the right kind of stable star; it may well need an unusually large moon around it to stabilize its rotation; and it probably needs a large protective planet farther out (like Jupiter) to divert comets and asteroids, preventing too many from striking it. From our point of view, such a planet needs plate tectonics (namely, a suitable crust) to provide both dry land and sea. The fraction of planets in the universe with suitable properties is unknown, and while some researchers believe there could be many of them, others feel that we are lucky to have even one. This is an area of ongoing astronomical research.

We have briefly mentioned biochemistry. A few general requirements have been listed, but this is an area that deserves much more attention. On the one hand, the chemistry of life appears to be amazingly flexible. On the other hand, many of the elaborate and complex processes are extremely delicate. One suspects that it might not work if the chemistry of carbon or water were very different, but this is largely an open question. Terrestrial life forms higher than bacteria will not function if they are given heavy water rather than normal water, but perhaps heavy-water life might be able to evolve? These are questions that deserve future study.

SUMMARY

We have just outlined a list, which is not at all exhaustive, of conditions that must be fulfilled by a universe in which advanced life should be able to develop. Of particular importance are the basic physical structure of the universe and the features of the nuclear processes that contribute to the formation of stable matter in the form of atoms that can have suitable chemical properties. The conditions involve all the physical forces that are known in nature, as well as various physical constants whose values are not known to be determined by laws. We absolutely cannot take for granted that a randomly constructed universe will generate advanced life; the exact opposite turns out to be the case.

EIGHT

IMPLICATIONS OF A UNIVERSE “FINE-TUNED” FOR US

Our present discussion is very much in disagreement with the views of religiously skeptical writers who assert that the universe appears purposeless and meaningless. For example, Richard Dawkins has written, “The universe we observe has precisely the properties we should expect if there is at bottom no purpose . . . nothing but blind, pitiless indifference.” [1] Clearly, this is untrue. Given the factors described in the previous chapter, together with further arguments that are more technical or speculative, there is widespread agreement among astronomers, cosmologists and other theoretical physicists that our universe is in a very real sense “fine-tuned” for our human existence. A substantial number of physical parameters—that is, numerical quantities—have values that are “right,” when there are very many more ways that their values could be “wrong.” This certainly looks like purpose.

Some words of caution are needed, however. The first is that to define fine-tuning in a precise mathematical way is difficult. This would require a confident statement that a given parameter might in principle be in a certain wide range of possible values, with a particular set of prior probabilities, while advanced life requires it to be in a much narrower range within which it is found. Defining the wide range of “possible” values is likely to be approximate and uncertain, and the relevant prior probabilities may just have to be assumed.

For some parameters, a simple range of possible values is relevant. For others, it might be better to use the scale of the parameter, that is, how many powers of ten the parameter might be divided by or multiplied by. This reduces the apparent significance of anthropic requirements. For example, if a parameter might be multiplied by up to a factor of ten and still remain suitable for life, and the conceivable range of scales were a “mere” 10^9 larger, then one-ninth of this range of scales is permitted. On the other hand, if the absolute range of values is relevant, then only ten parts per billion of it are permitted, which is very much more restrictive. Varying the scale is not valid if the parameter might in principle be zero, in which case we are obliged to consider the absolute value range. The cosmological constant is of this kind, since its value could quite well be zero, as Einstein originally thought. This means that it really does seem to lie within something like one part in 10^120 of its “possible” range. In fact, most if not all of the parameters we have considered are of the absolute-range type.

A further complication is that the effects of different parameters might combine together. It would be misleading to say that a variation of 1 percent on parameter A is disastrous for life, and also on parameter B, if a variation on parameter A could be compensated by choosing a new value for B. So one must be careful. Most random combinations of A and of B would still be bad, and the value of B still needs to be tuned to 1 percent, whatever the value of A might be. So the small likelihood that B is life-giving remains, but a tuning of A should not be included as well. A better way is to consider combinations of the two parameters. In fact, to evaluate the overall degree of fine-tuning of the universe, one ought to consider variations of all possible parameters taken together—a challenging task. Barnes has given some multi-parameter results that point toward how this may work in practice. The conclusion remains that our universe is set up in a surprisingly favorable condition. We have simplified the present discussion by considering the physical requirements separately, but this does not seem seriously to affect the conclusions. Most of the parameters do not appear to be strongly interconnected and so they provide a good case for “fine-tuning” on their own.

For these reasons, I have not attempted to provide a precise value for the “probability” of a human-friendly universe, although by any considerations it would appear to be extremely small for this to happen by chance. The only way to evaluate such a quantity with rigor would be to formulate a complete theoretical model of possible universes and see how many of them could generate advanced life. There have been attempts in this direction, but it is not clear that they yet add very much to the conclusions given here. Taking everything into account, there seem to be enormously more ways that the universe could be wrong for life than right.

EXPLANATIONS FOR FINE-TUNING

Although its numerical quantification is difficult, the apparent fine-tuned state of our universe for advanced life is something that is widely agreed to be extremely unlikely. [2] We normally feel that a very unlikely fact that is nonetheless “significant” requires an explanation. This is because we have a general conviction that our universe is set up on rational principles and that there ought to be a reason for its important features. Four main reasons are commonly put forward for the fine-tuning phenomenon:

1. The fine-tuning is real and significant. An arbitrarily set up universe would be most unlikely to support advanced life, and a creative purpose is therefore indicated. We or others like us were meant to be here.

2. It is a matter of chance. There are enormously many universes—a so-called multiverse—and of course we must be living in one of a small fraction of them that can support us, just as we live on one of the minority of hospitable planets in our galaxy.

3. There is nothing that needs to be explained. Advanced life is indeed a complex phenomenon, but it is of no real significance. It is merely one physical possibility among many. The cosmic tea leaves just chanced to fall this way.

4. Only one set of laws and parameters of physics is logically possible, and it has a number of consequences, very much as the axioms of mathematics have their consequences. Advanced theorems of mathematics can be sometimes very interesting, but they just arise from the basics. Life likewise arises out of a basic “theory of everything” in physics. We do not know this theory yet.

We now discuss these options in more detail.

A PURPOSEFUL CREATOR

From the point of view of the traditional faiths, the idea that God has created this universe is perfectly natural, as is the idea that this was done in a way designed to generate life. The traditional teaching that human beings are in some sense “in the image of God” enables us to connect the kind of intelligence attributable to a Cosmic Designer with the kind of intelligence that we ourselves can understand, but on a far greater scale.

A design argument in itself says little about the nature of the Designer, the means used by the Designer or the Designer’s motivation apart from creating advanced conscious life, although this could be important. Objections are sometimes made that surely God would not do things this way. These are theological claims, of course. A Cosmic Designer might in principle be God as traditionally understood, a race of superintelligent beings in another cosmos or a deity very different from our normal conception. More theological input is needed, but a traditional God would seem to be a perfectly reasonable supposition if this option is taken.

A MULTIVERSE

One way of accounting for the existence of a special and significant phenomenon without postulating that it was planned or designed is to suggest that it is one of a large and varied set of phenomena, and happens to be the one that we can observe. An everyday example of this was suggested by the philosopher John Leslie, who imagined an angler with a net that will catch fish only of a certain size. [3] If the angler catches a fish, it is reasonable to assume the existence of a large shoal of fish of varying sizes, such as to give a good chance of making a catch with that net. Otherwise the very unlikely occurrence of a catch is inexplicable, unless someone deliberately placed this fish in the lake. So maybe there is a large collection of universes, such as to give one of them a chance of generating life forms. This large hypothetical collection of universes is known as a “multiverse.”

A few comments need to be made about this analogy. The first is that to propose a shoal of fish is very reasonable, because we know that fish often occur in shoals. The proposal would be less convincing if it were a type of fish that never swam in shoals. So we have to ask about the basic reasonableness of a multiverse. The hypothesis can be criticized on the grounds that something more complex is being introduced to explain something less complex. To be sure, advanced life is already complex enough, but the vast set of universes that is needed to account for it may seem more complex and unconvincing. The solution is worse than the problem.

A further point is that a purely “statistical” explanation—that is to say, our example is a selection from a much larger population of fish, universes or whatever—is not in itself very explanatory. A good explanation for something will take our understanding back one stage. Take, for example, the question “Why did the London murderer Jack the Ripper kill his victims?” There could be a causal explanation along the lines of “He was emotionally deranged following a broken love affair,” or a statistical explanation such as “It had to happen in a place like London, because in such a large city there will always be one or two people who behave that way.” Both these statements might be true, but the causal explanation is much more enlightening.

Therefore, in order to gain conviction, a multiverse hypothesis needs to be founded on a more basic theory that could account for multiverses. Such theories are claimed. The best known is the theory of superstrings, which are hypothetical quantum objects that exist in a large number of space dimensions and possibly form a basis for a quantum theory of elementary particles and physical forces. The theory is controversial because of its lack of experimental confirmation so far and its extreme mathematical complexity. Also, it seems to require a further and more general theory to embed it in, which goes by the name of M-theory, but which has not yet been fully formulated. The theory of superstrings started out as an attempt to generate a theory of everything starting from a small number of very basic assumptions, but in the end it has turned into the most mathematically difficult physical theory yet devised and is still incomplete.

One interpretation of superstring theory is that it might provide an extremely large number of ways of setting up a quantum universe, and any or all of these could occur within the framework of a larger cosmos with suitable properties. The number of possible different universes is colossal, of the magnitude of ten to the power five hundred, in a cosmos that could be any size—surely enough to make some that will generate advanced life! This proposal requires a suitable cosmological theory, which is very much a matter of speculation. In principle, this theory should generate a way of calculating a mathematical probability for a universe to be fine-tuned for life such as ours, provided that the necessary mathematics can be worked out. For example, a theory of “inflating bubble universes” has been put forward, more about which will be given in the next chapter.

The multiverse hypothesis has some more general problems, however. Such proposals “over-explain,” especially if the number of proposed universes is infinite. Having an infinite set of random universes means that any possibility will occur an infinite number of times. There is, then, no need to explain anything in the physics of our own universe, because whatever we find could have just occurred by chance. So those who are seeking explanations for the values of parameters such as the masses of elementary particles, or the strengths of physical forces, could be wasting their time. If even our own universe is infinitely large, then there will be an infinite number of planets closely like our own planet Earth, containing populations that include people closely resembling you and me, who made choices in their lives the same as yours and mine, or differing in arbitrary ways. Anything with a small probability to happen will occur somewhere, indeed an infinite number of times. “Impossible” events might occur with nominally zero probability but still a finite number of times. It becomes hard to determine whether anything is truly impossible.

Suggestions such as these stretch our notion of what is reasonable far beyond normal limits. They are not forced upon us by observation, needless to say, but by theoretical ideas that are considered by their proposers to be attractive! The quantum theorist Max Born once wrote, “Intellect distinguishes between the possible and the impossible, but reason distinguishes between the sensible and the senseless. Even the possible can be senseless.” [4] We need to think very hard about the criteria for judging concepts that are logically consistent but which seem to destroy understanding rather than extend it, or even destroy the need for understanding.

The choice at this point, then, is whether a given type of proposed multiverse amounts to a more preferable hypothesis than a Designer. Or perhaps one can have both; maybe this is how the Deity chose to make the necessary large set of universes, which might not need to be actually infinite. Conceivably, a multiverse needs less divine intelligence than does the design of a single universe with unique properties. However, the life-giving success of the project would still need to be assured, since the probability for advanced life is not automatically guaranteed to be high in any given scheme. The basic laws of quantum physics still need to be set up by the Designer, together with the cosmological framework, and the mathematical structure of superstring theory is formidable.

IS AN EXPLANATION REALLY NEEDED?

It is perhaps a matter of taste to define whether a fact that appears to be significant, and requiring of an explanation, really is so. We are all familiar with coincidences that are no more than just that. To a true skeptic, advanced life might be of no more significance than a curious rock formation on a seashore. However, one aspect of advanced life really would appear special, and that is the occurrence within it of consciousness such as our own. In a later chapter we will discuss consciousness in more detail, arguing that it lies outside the science of physics. It is only through having conscious minds that we can discuss these subjects in the first place, one might obviously add.

The simple conclusion is that the occurrence of advanced life cannot reasonably be considered as a mere happenstance of nature. Advanced life is a physical phenomenon that is specifically able to support another completely different and highly important kind of phenomenon, namely consciousness, the existence of which is not at all logically implied by the physics of atoms and molecules as such. This makes advanced life something special. The situation is surely of great significance, and we are certainly entitled to ask for an explanation for it.

WOULD A THEORY OF EVERYTHING BE SUFFICIENT?

If a theory of everything were able to account for the whole of physics uniquely, its discovery would be the most remarkable intellectual achievement ever made by the human race. It would be even more remarkable if such a theory were the only one that could account for a universe, and this universe contained advanced life, and this advanced life could be conscious. It would mean that our universe is governed by a unique theoretical structure that just happens to be conducive to life, as a byproduct. A truly remarkable coincidence! Clearly, no one has yet discovered such a theory.

Einstein once asked whether God had a choice when creating the universe, and this is indeed a key question. We know of no reason that there could be only one conceivable theory of everything, or if any such theories can be formulated at all. Einstein’s general theory of relativity, despite its mathematical complexity, is seen as the simplest type of theory that can fulfill the task of generating gravity out of space-time curvature. It has two undetermined physical parameters (“constants”), namely, Newton’s gravitational constant and the cosmological constant. These quantities are not part of the logic of the theory and have to be measured experimentally. It is possible to elaborate Einstein’s theory by introducing more complexities so as to form extended theories, although these new theories so far are experimentally disfavored compared to Einstein’s original. So if even general relativity is not unique one may seriously doubt whether a unique theory of everything can be possible and, if it were possible, whether it would really have no undetermined physical parameters.

Of course, a universe generated according to such a theory and also generating conscious life could be seen as a truly divine construction, the product of a Mind, and one would still ask why it should actually exist. To judge from the past, one can expect further progress in theoretical physics in the future. Some of the anthropic coincidences outlined above may turn out to be connected with the structure of an improved theory, even if not with a unique theory of everything. In that case, the coincidences will now refer to the improved theory happening to be right, in place of the physical parameters happening to be right.

INTELLIGENT DESIGN IN BIOLOGY

In these chapters we have examined many pieces of evidence that our universe is particularly suited to human existence. This state of affairs could be the result of purposive action by a Creator, but even a multiverse requires laws of nature that will work, which is far from trivial. One can legitimately claim that either way, the universe considered as a whole shows evidence for design by an intelligent mind.

It has taken many millions of years for advanced conscious life to develop on our planet, and there is an overwhelming scientific consensus that the processes by which this has happened were in general terms “Darwinian.” That is, mutations of various kinds have a tendency to occur in the genetic material of living creatures, and those that improve their possessors’ chances of surviving and reproducing will be passed on preferentially to subsequent generations. In due course, new species can be formed. The processes by which this can happen are now acknowledged to be much more complex than Darwin himself was able to know about, and they are still far from fully understood. The general ideas of evolution, however, have been vindicated by a great deal of experimental evidence.

In the Darwinian picture, the occurrence of mutations is through random processes. It may well be questioned whether the mutations must always be small, as Darwin and others envisaged, or can be large, but this is a technical matter. Most mutations do not benefit their possessors, and they result in death or fewer offspring, or else they are neutral in their effects. However, if a change in the living creature’s environment later occurs, this may result in neutral mutations turning out now to be beneficial. The success of natural processes such as these in generating new kinds of creatures has been remarkable.

The original opposition to Darwin’s ideas came not especially from the church but from fellow scientists who were at the time not fully convinced. Some modern skeptics have expressed the view that they are still not convinced, believing that aspects of living creatures could not have been produced this way. They point to Darwin’s requirement that evolution must take place step by step and that each step must be beneficial or at least not harmful. Some aspects of living creatures appear to require a coordinated set of changes to have taken place simultaneously. This, they argue, requires intervention by an external intelligence (which may or may not have been God), since if the set of changes were to take place step by step, the intermediate developments would have been harmful; only the complete set of changes actually confers benefit.

Much of evolutionary biology is well enough understood, and the kinds of development mentioned above represent “gaps” in our present scientific knowledge. In the past, more such “coordinated developments” in biological species could have been pointed out, but believable evolutionary pathways have been proposed over the years. The eye is a notable example of a biological feature that looks to have been designed, but biologists can suggest ways and means by which it can have developed in stages through an evolutionary process. Even the complex biochemistry in the retina, by which the signal from a few photons can be amplified manyfold into a signal in a nerve leading to the brain, is believed to be explicable. It may sometimes be that a complex component can evolve unproblematically to perform a particular biological function, and then it may become evolutionarily adapted to perform a different function, which is the final result that is now found. It now looks as if the final component has appeared suddenly; in fact, it evolved perfectly normally but mainly in a different context.

The complexities of the evolutionary process are such that in some cases it might never be fully demonstrated whether a given organ or biochemical process could or could not have arisen naturally. The difficulty with the “intelligent design” position in biology is that it relies on an intuitive assessment of the biological impossibility of a given development, when such intuitive assessments have been proved wrong in the past and may continue to be disproved in the future. It is very dangerous to argue strongly from scientific ignorance in a particular situation. For these reasons, biological intelligent design does not form part of the argument of this book.

It is a different matter when considering the universe as a whole, because it is not clear that the properties of the universe as a whole are something that is amenable to scientific explanation. We shall discuss the nature of explanations in a later chapter. Biological questions, on the other hand, are specific matters that do invite scientific explanations, although a few caveats should be mentioned.

A particular problem with biological intelligent design is that the instances where it is claimed to be likely do not have any clear particular rationale behind them but are apparently just “difficult cases” at present. It would be more plausible if some specific a priori reason were given to justify the employment of a design argument. One such case might be the beginnings of life on our planet, where at present we have hardly any real idea as to what happened. If there were any situation where a miraculous intervention might be expected, it could be here. This is why searches for life on other planets, such as Mars, are of exceptionally great interest, and not just so as to help us feel less lonely in the universe. If we succeed in finding life elsewhere, then it is probably a common occurrence as a natural process in the universe. At present, however, we cannot exclude the possibility that life-producing circumstances might be extraordinarily rare and that we might even be the universe’s only inhabited planet. If that were the case, we would probably never know the natural cause that first gave rise to life, assuming that there was one. We would choose to believe in it or not, according to our personal inclination and judgment.

Questions might also be asked about the function of the conscious mind in evolution, to which we will return later. Many higher animals may have conscious minds, although it is hard to be sure. If God communicates by means of the mind, then this could provide an orderly way for the higher stages of evolution to be “guided” toward the development of creatures with advanced intelligence, if that were the Creator’s aim. I am not arguing either way on this here, but our ignorance of this area is profound, and further research would seem very welcome.

CONCLUSIONS

We human beings are conscious forms of advanced life, and maybe similar beings exist on other planets. The universe appears to have characteristics that are well matched for such life forms, requiring a sizable number of physical parameters to have values within limited ranges, sometimes very limited indeed compared with what might be possible in principle.

It seems a remarkable coincidence. As we have said, there are very, very many more ways for a universe to be unsuitable for advanced life than suitable. An intelligent Designer with a purpose to create advanced life forms through an evolutionary process would no doubt create a universe with a set of features that achieve this end, and so the existence of these features naturally points toward such a Designer. An enormously large multiverse might also contain some universes with suitable features, and so this is another possibility, but it is a very elaborate and uneconomical one. Of course, God could decide to create conscious advanced life by means of a multiverse. The choice between which of these options is more believable is a matter of personal judgment, but even a multiverse system would need to have overall physical features and laws that enable the desired set of universes to emerge.

We take it for granted that the universe is complex, but it is surely quite amazing that such a complex structure should exist and function at all, let alone produce living creatures. This takes us back to the first topics of the previous chapter, where the very basic elements of a universe need to be right in order for it to function. The complex structure of biological life forms of even a rather basic kind is even more amazing. Perhaps we should not be surprised if a long process of evolution could be the best way for God to create all this.

The nature of the Designer is not strongly constrained by these arguments, a point raised long ago by the eighteenth-century skeptical philosopher David Hume, who argued that a design argument was inadequate as a sole argument for God. [5] We would wish to know more than this kind of argument can tell us, and so it needs to be supplemented by further arguments and sources of information. One important point can be made, however. If it were indeed the case that our human consciousness is a significant factor in a designed creation, then this would imply that the Designer knows about consciousness and therefore must also possess a conscious mentality of some kind, no doubt vastly more powerful than our own. Conscious beings relate to each other, and so we may infer that the Designer is in some way personal and can relate to us. This is God in the traditional understanding. How the relationship may work out in practice is not something that science is in a position to discuss. Here we are definitely in the realm of revealed religion.

NINE

GOD AS FIRST CAUSE

An Argument That Seems to Hold

At a wedding reception in the 1970s in the north of England, I was in conversation with the host, a charming and civilized university academic in an arts subject. He was evidently not a religious believer. On learning that I was a physicist, he asked with interest about the state of current opinion on the origins of the universe. The Big Bang theory had by that time become firmly established, supplanting the Steady State theory in which the universe has always been the same, and this was something that saddened him. “I very much prefer the Steady State theory,” he said, “and always have. The trouble with the Big Bang theory is, it will have us all going back to church again!”

This gentleman was reluctantly voicing, in a very basic way, the so-called Kalam cosmological argument for the existence of God. The original Kalam argument came from ninth- to eleventh-century Islamic scholars and in its simplest form states that anything that comes into existence must have a cause. Our physical universe has come into existence, if it had a beginning in time. Its initial cause must therefore lie outside it. This would be something outside the domain of physics, and the obvious candidate for such a cause is God.

To succeed in this way, the argument requires good confidence in believing that the universe had a beginning in time. Over later centuries, many astronomers and scholars came to assume that the universe had always existed, although the earth had a finite age. The situation changed dramatically, however, with the twentieth-century discovery that the universe is expanding and apparently originated in an event some fourteen billion years ago known as the Big Bang. Arguments of the Kalam type have now become relevant again, and the philosopher William Lane Craig is especially associated with reviving modern interest in this area. [1] Of course, it is entirely possible for astronomers to adhere strictly to the scientific practice of their work and ignore any metaphysical implications that it might have. Craig asked a professional astronomer to consult a group of her colleagues about the matter on his behalf. Her reply was that their reactions were the same as her own—“no relevance.” [2] Stephen Hawking would perhaps disagree. “A point of creation would be a place where science broke down,” he is reported as saying at a conference in honor of his seventieth birthday. “One would have to appeal to religion and the hand of God.” [3]

The modern presentation of the Kalam argument focuses on the question of whether our universe had an absolute beginning in time, or whether it has had an infinite past history. This leads into an extensive discussion of cosmology (the study of the universe as a whole), and a great deal of the scientific material in this area is very technical. The intended hope of the present chapter is to examine this complex subject in a way that is accessible to non-specialists. The interested reader can find more details in accounts given by Craig and his fellow writers, Sinclair, Spitzer and Gordon. [4]

CAUSATION IN PHYSICS

The main premise of the simple Kalam argument is that anything that comes into existence has a cause. To give a good basis for this, it would be useful to identify classes of physical objects that come into existence, owing to causes, for otherwise the argument will be about only one object, the universe. This task is not completely straightforward, because most objects in physics have a permanence of existence, although they may well change their physical state. Two possible examples come to mind: elementary particles and compound physical systems. The problem with elementary particles is that while they do indeed make sudden appearances in particle interactions, what is happening is that quantum fields in space are being lifted from their “ground” state, which is normally not physically noticeable, into a new state that corresponds to a particle. So whether something “comes into being” is perhaps a debatable question, although the quantum fields certainly do change their state. In a similar way, it might be argued that a compound physical system is not a new thing coming into being but merely a new arrangement of the already existing parts. If a car is manufactured from its components, does it come into being? Most people would probably affirm that it does, but some might argue that its parts existed all along and nothing has really come into being, although the form of the car certainly has.

Issues like these can be avoided if we re-express the Kalam argument in a more general way, by saying that a cause is required for any physical object or system to be in the state that it is in, where the state it is in comprises its intrinsic features at the time, including the fact that it exists. Some situation must have given rise to this, and there are two logical possibilities—the cause can act either from earlier in time or else from outside time. We do not believe that causes in physics act from the future. But if the cause is associated with an earlier physical state of something, then the latter in turn requires a cause, or perhaps a set of causes. If we attempt to take a purely physicalist viewpoint, then causes from outside time are excluded, and so we find ourselves tracing a chain or stream of physical causes back to the beginning of time, if that can be identified. But at that point only a cause from outside time is available, by which the system and indeed the entire universe came into being, and so the physicalist viewpoint will not do after all. A first cause from outside time invites identification with a Creator, which supports the idea of God as the First Cause.

In philosophical discourse, the concept of a “cause” is a notoriously tricky topic. It would appear that everyone knows what a cause is until they start to think about the matter, and the more they think about it, the less clear it becomes! It would take us far out of our way to try to discuss this much-debated subject here. I take the question to be metaphysical, and one where our basic intuitions are likely to be as good a guide as anything. Causation is something that we will here accept as a given, a priori fact of existence. However, it is necessary to say a few words about how it operates in the context of physics.

When the state of a physical object changes, this is usually because a force has acted. In classical physics, which means physics before quantum mechanics, a force is an interaction between two objects. So the cause for the first object’s later state is this force, arising from the presence of the second object. In classical physics, state changes—for example, changes of an object’s velocity—and forces can operate continuously, and the processes are deterministic. New material objects do not come into being, although waves can be radiated. However, objects can be rearranged to form new physical systems. For example, dissolved atoms in a solution may come together to form a crystal, and in such a case we might say that a new system has come into being because of various inter-atomic forces that have acted.

Quantum physics changes the situation in two particularly important ways. The first of these is that state-changing quantum events occur discontinuously in time. In other words, events suddenly happen. Second, there is wide agreement that the occurrence of a quantum event is not fully deterministic. This means that which quantum event happens out of a set of possibilities, or where or when it happens, is affected by random chance. To a certain extent, these details are uncaused. Does this mean that we can no longer trace chains of caused events back to the beginning of time?

The answer to this question is no, because quantum events must have a well-defined physical context in order to occur. So, for example, while the decay of one radioactive nucleus into another occurs randomly on the timescale of the half-life of the nucleus, the basic reason for its occurrence is that certain nuclear forces are acting. Also, something must have produced the first nucleus. A common type of radioactive decay is called “beta-decay” and is due to the weak nuclear force, in whose absence the decay would not occur. So the new nuclear state has a cause, namely, the weak nuclear force acting on the previous nuclear state. This is true even though the precise details of the decay event are only partially causative. To take another example, the state of an atomic particle may be such that it could be detected in any one of several particle detectors. Which of them detects it is random. But the fact that a detection happens at all still has its cause in the exposure of the particle to the detector system, without which it would not occur.

The central point here is that when a new physical state occurs through a quantum process, this is due to the previous circumstance that gave it a certain probability to happen. A backwards set of physical causes is still part of quantum physics. It can be traced back to the beginning of the universe as before, if the universe had a beginning. Causation is still relevant, and the Kalam argument can still be used. Full determinism is not needed for this argument.

Classical physics always had a degree of difficulty in identifying what causation really means, because Newton’s second law of motion is symmetric with regard to time. In other words, the forces and accelerations still look correct if time is viewed in reverse. The mathematician Pierre Laplace famously stated that a perfect intelligence could predict the entire future of the universe from its state in the past. This works in both directions: one could equally well calculate the universe’s entire past given a perfect knowledge of its state in the future. In thermodynamics there is a law that disorder, or entropy, can only increase with time, and this is often invoked to define an “arrow of time.” But this depends on the universe having started in a state of low entropy and high order—an interesting fact in itself, as we have seen. A universe that ended up in a state of low entropy could still obey the laws of dynamics in the normal way, but it would have to start off in an astonishingly well-tuned initial state in order to achieve this.

The concept of physical causation may actually be somewhat clearer in the quantum context. An object now acquires what could be called a “disposition” to change its state, with a certain probability. [5] The term cause seems very appropriate to apply to the physical reason for this state-changing disposition, and the situation is not time-reversible: a direction of time is implied whenever we talk about quantum probabilities. [6] The quantum point of view therefore introduces an “arrow of time” that seems intrinsic to the basic processes of physics.

By now the reader might be tempted to protest that this discussion has become a little complicated. Why not just bypass all the physics and simply assert that the universe must have had an external cause for its coming into being? The point is that for a First Cause argument to work, we do need to establish the principle of prior physical causation in time. To be sure, the effect of the First Cause may differ from that of subsequent physical causes. The First Cause is responsible for something new coming into existence—acquiring a physical state in the process—while the later physical causes often just produce changes to existing physical states. There are some interesting issues here, but they do not really affect the argument. Do new elementary particles come into existence in “creation” processes, or are they merely excitations of quantum fields? Do new quantum fields come into existence as the universe expands? Should the structural form of a system be taken as a concrete reality? Whatever the answers to questions such as these, the premise that a physical state requires a cause would seem to cover all the options.

One possible objection should be addressed. Although everything in the universe must be caused, does this apply to the universe as a whole? There is, after all, a well-known philosophical error, which is to assume that the whole has the same properties as its parts. This need not be true: every sheep in a flock might be small, but the flock as a whole might be large. However, this does not apply in our present case. If each member of the set of physical objects and systems in the universe can be causally traced back to an origin in time, then each needs an external cause at this point, and therefore so does the set of all of them, which is a physical system in its own right. The Kalam argument holds both singly and collectively. It is incorrect to assert that the universe “as a whole” is different in kind from its constituents. The universe is a physical system, and physical systems of any size must be caused.

THE BIG BANG AND ITS IMPLICATIONS

Our universe is expanding, which means that the galaxies and everything else in it are moving away from us and from each other. Strictly speaking, the galaxies that are nearest to us form a group known as the local cluster of galaxies, and these tend to stay together. But for a more distant galaxy, the further away from us it is, the faster it is receding from us. As explained in chapter three, this effect is believed to be due not to movement of the galaxies themselves but to the expansion of the actual fabric of space between ourselves and the distant galaxies.

Tracing this expansion backwards in time leads to the conclusion that there was an initial instant when the universe had small or zero size, and that this occurred at a definite time in the past—about 13.7 billion years ago. The explosive-like expansion of the universe at that point in time is the so-called Big Bang. It is strongly suspected that the earliest stage of the universe was also marked by a sudden period of super-fast expansion, known as inflation, shortly after the initial Big Bang event took place.

If the Big Bang occurred at an instant that was the true start of time, then the Kalam argument can be applied. That is, a cause is required for the universe to appear in its initial expanding state. This requirement is still present if the universe were to have started in a “singular” state, such as being instantaneously infinitely dense. So since there were no earlier times, an external cause for the universe is indicated, which we may choose to identify with a Creator.

Unsurprisingly, physicalists and many scientists in general are unhappy with this conclusion. To avoid it, cosmologists have proposed a variety of schemes in which the Big Bang was preceded by an earlier physical system which by some process gave rise to our present universe. As we shall see, there is a large collection of such theoretical models. Some of the suggested ideas may seem quite far-fetched, but inventing new cosmologies is a well-established intellectual occupation for theoreticians. In the next section we will look at the main ideas that are currently considered to be reasonable [7] and attempt to see if the Kalam argument would still apply.

For clarity I will, where appropriate, refer to a Big Bang–initiated system as “a universe” and to a larger or earlier system as “the cosmos.” To some cosmologists, a desirable feature would be that the past history of the cosmos should extend infinitely far back in time so as to retain an unterminating fabric of physics and hopefully avoid a First Cause. In fact, it seems that almost everyone is actually in agreement with the Kalam argument—a cause for our universe is needed! But is this to be a Creator, or can we attribute everything to preexisting physical causes?

COSMOLOGICAL MODELS

Here, then, is a summary of the major types of cosmological models that are current at present (a model is simply a term for a hypothetical theory of something). These models are not all mutually exclusive. Some of them are quite complex, and here we can do no more than give an overview of their general principles. Experimentally, it is an open situation, and any or none of these hypotheses might be true, although we will see that some of them turn out to be very unlikely. Einstein’s theory of general relativity is believed to govern the behavior of space and time in nearly all circumstances, although it cannot yet deal satisfactorily with quantum effects.

Basic Big Bang. Our universe started with the familiar Big Bang that we know of, and time also started then. [8] The Kalam argument therefore applies and indicates a transcendent agent as the cause of the universe.

Oscillating universes. In this class of theory, it is proposed that our universe is the latest of a long or infinite sequence of Big Bangs. In each case, the universe expands to a maximum size, and then it collapses in on itself, a so-called Big Crunch. After this another Big Bang occurs, and so on. This does not have to involve singular physical states at the starts of the Big Bangs. One problem with this idea is that physical entropy gradually accumulates in the successive universes, so that after a very long or infinite sequence, a thermodynamic equilibrium will have been reached and nothing much of interest can happen. But we can see that our own universe is far from being in such a state. There is also what is known as the “radiation problem.” During a collapse and reexpansion, starlight passing through space is recycled and will appear as background radiation in the next cycle of the universe. After many cycles, this background radiation will be very strong so as to overwhelmingly dominate the starlight generated in the latest new universe. Our own universe does have about a hundred times more background radiation energy than starlight energy, as measured by radio telescopes and optical telescopes. However, an infinitely old cosmos would have accumulated enormously more background radiation than this at a level that would eventually take away the energy that is needed to make stars. This has not happened, obviously.

Another difficulty is that the cycles of oscillation are believed to slow down with time. They are calculated to have been increasingly fast when traced back into the past, so much so that the entire process must have had a beginning. But present observations of distant supernovae indicate that our own universe will not re-collapse at all but will continue to expand forever. This means that if there had been a long series of oscillating universes before ours, then we must be living in the first and only one to behave in this new way. [9] That would be extremely unlikely: there is no known reason why human existence should be connected with this kind of feature of a universe.

The present conclusion is that an infinitely old, oscillating universe does not work. [10] There might be another way out. Even if the system is infinitely old and thermodynamically dead, in really rare instances it might bounce by chance into a low-entropy universe capable of generating galaxies and stars. The probability against this, in any given cycle, is enormous. The counterargument is that we seem to occupy a universe that is larger and with much smaller entropy than is really required for our existence. This would imply a random fluctuation that was vastly more improbable than it needed to be, making the hypothesis even more unlikely. There are attempts to bypass entropy problems by ascribing low entropy to pieces of an oscillating cosmos. This, however, requires the universe to be in a state of general expansion, which we now discuss.

An expanding cosmos. In general relativity, it is hard to form a possible universe that is both static and stable. The predicted universes tend to expand or contract. In devising expanding models, the problems can be avoided by making the cosmos expand indefinitely, and the proposed phenomenon of inflation is usually brought into play. Within an expanding, inflating cosmos, regions can form that can give rise to new universes through Big Bang events. The new universes generated in this way are called “bubble universes” or “island universes”; they are self-contained, and our universe is said to be one such. This means that instead of just one expanding universe—namely, just our own—there can be many others. These universes may have new and different physical laws and properties, it is proposed.

The expansion rate of our universe is given by the so-called Hubble parameter, which is believed to have been always positive, so that our universe had a beginning in time. A negative value would imply contraction. Any expanding universe or cosmos has a Hubble parameter, which does not have to be constant with time. A powerful extension of this idea has been given by Borde, Guth and Vilenkin (BGV), [11] who show that any universe or cosmos with normally behaved space and time must have had a beginning in time if its Hubble parameter is greater than zero when averaged over time. This theorem ignores possible quantum effects but comes about by requiring that relative velocities cannot be greater than the velocity of light.

The BGV theorem implies that the most popular expanding-cosmos models—probably all those in wide circulation—must involve a beginning in time and so cannot be taken as having an infinite past history. [12] The theorem is far-reaching, and it can also apply to more complicated oscillating universe models that attempt to avoid entropy problems by expanding cycle by cycle. [13]

Cosmos models with an uneventful infinite past history. In some models, the cosmos has an infinite past history that is asymptotically uneventful. This means that as we trace time back toward minus infinity, a certain state is gradually approached and all changes just die away. The BGV theorem is avoided since the average Hubble parameter may be zero overall in this scenario. At some point in time, our own universe “emerged.” There are two main obstacles to these “emergent universe” schemes. One is that a quiescent asymptotic state may in fact be unstable, either as a consequence of general relativity or through quantum effects, and it may just collapse without giving rise to a universe. [14] The other is that it may indeed turn into something, such as an expanding universe, but with a finite probability per unit interval of time. In either case, an infinite time interval with nothing happening has zero probability. In an infinite timespan, something will certainly happen, if it can, if it has any probability at all, and it would have happened long before our universe could come along, preempting our universe from happening. It appears that all the seriously proposed models of this type fail in one of these ways. In any infinitely old system, if there are any degenerative or instability-generating processes, they would have operated by now—but we see that our own universe exists in a healthy state.

Universes in which time changes its nature at the Big Bang. Stephen Hawking and his colleague James Hartle proposed a model of the universe with a perfectly “normal” appearance back to a certain point in time, which we will call time-zero. [15] Here it did not have zero size and an infinite singularity: it still had a small finite radius. Time is now extended backwards as a new kind of coordinate called “imaginary time,” [16] such that the space-time structure curves around on itself and is limited in size. The controversial question is how to interpret imaginary time, whose introduction was for mathematical convenience so as to avoid a physical singularity, which had seemed an undesirable feature in a cosmological model. Hawking himself suggests that imaginary time is like another space dimension. [17] In any case, the time dimension of the universe ceases to function in a normal time-like way as we trace it back through time-zero, and this would have to imply an inability to support causal processes. Causative time is thus not infinitely old, and we still have to ask what caused the primal physical state that gave rise to the first physically caused events in “real time.”

There are other proposals, one of which we will discuss later, in which the universe arose out of a primal “quantum state.” The Kalam argument always seems to apply in some way also to these, asking what caused the existence of the primal state, whatever its nature might be.

Contracting and expanding universes. An alternative proposal has the universe contracting to a minimum size and then reexpanding. But time also changes its direction at this juncture and somehow was running in reverse during the contraction process. [18] This, then, will not resolve the matter; we just have a pair of conjoined normal Big Bang universes, back to back. Each has a definite start to its own timescale, and the question of initial causation remains—in duplicate. In further proposals, various regions of a complex universe could have many beginnings in time. This does not seem to affect the Kalam argument, but maybe it gives the Creator a more complex task to do.

Identically repeating universe. Occasionally, it has been suggested that the same universe continually repeats itself, with no beginning or end. This idea fails because causality paradoxes would be hard to eliminate: we could arrange to do something that would prevent our own existence next time around. Also, in a repeating universe, entropy cannot always continue to increase as it has to, if it must reset itself at the start of each new cycle.

COORDINATE TRANSFORMATIONS AND SINGULARITIES

If what has been said above is true, claims that the cosmos is infinitely old are at present implausible. Nevertheless, modern cosmological theories often disregard the conceptual hazards involved with physical infinities by assigning infinite extension to space or time in a universe, or a part of one. Some of these structures may be potentially infinite rather than actually infinite. Here I outline a further possible way of dealing with this situation. These paragraphs are slightly mathematical, and the non-mathematical reader may choose to pass over them.

In many situations, the theorist can make use of what is called a coordinate transformation. By coordinate, one means quantities such as x and t, which measure space and time. Instead of working with what might be called “ordinary time,” a mathematical operation can be introduced to convert the normal time values into a different set of time values, and then one works with these instead. It is like stretching or compressing time. In general relativity, space and time transformations of this kind are entirely allowed, and the theory is designed to cope with them; in fact, one coordinate system is taken to be just as valid as any other. This is what makes general relativity “general.” The equations of physics appear different when expressed in different coordinate systems, and in any given calculation the usual idea is to seek the set of coordinates that makes the calculation simplest technically.

In this way Einstein’s methods make it quite allowable to use a different cosmic timescale from the normal one, if we so wish. [19] Let us then propose the following to deal with infinitely old cosmic times. Nothing in principle prohibits us from compressing the “normal” timescale into a new scale such that when normal time is at minus infinity in the past, the new version of time has a finite negative value; this now represents the beginning of the cosmos. The cosmos now has a finite history! The simplest case is of a cosmos with an uneventful history extending to minus infinity in time, when its state was S; this is known as an asymptotic state. After a suitable time transformation, the history of the cosmos commences at a finitely old time, where it has the same state S, and the Kalam argument posits that the universe at this point required a non-temporal cause. This kind of uneventful infinitely old cosmos has already been put in doubt on the grounds of physical instability, but now it seems that the Kalam argument will apply anyway. In the original time frame, where the past history was infinite, it was unclear whether or not the asymptotic state of the universe requires a cause. In the second time frame, it becomes evident that it does.

A more complex case would be of a cosmos with an infinite number of causal events in its infinite past history. If the history is transformed so as to be finite, this entire set of events becomes squashed into a singularity at the new beginning of time, which might be problematic. However, it may be valid to treat this entire structure “as a whole.” Then the simple Kalam argument can be applied to it, provided that our description of the infinite event sequence is sufficiently coherent so as to think of the singular structure in a unified way. One then asks: What caused that collection to happen? Provided that the situation is sufficiently well characterized, this question is valid. Careful evaluation is needed in any given case, but the implication is again that many infinitely old universes may still be subject to the Kalam argument. Certain oscillating universes start with a singular set of infinitely rapid oscillations, [20] and this approach would very likely apply to them.

To illustrate the argument, consider Benardete’s paradoxical infinite book, described earlier. Place it flat on a table, with page one at the top, and each of its pages supported by the page below. In fact, each page supports all the pages that lie above it. There is no final page, and the infinite sequence of supporting pages does not terminate. Nevertheless, the book exists “as a whole” with a certain thickness and weight. It still needs to be supported and it is supported by an external object, the table. “Support” plays a role here analogous to causation in the Kalam argument.

Perhaps an infinite collection of events could be completely disparate and lacking mathematical coherence, so ill-specified as to lack a good physical or mathematical description. I do not know that anyone is seriously suggesting cosmological theories of this sort. “Explanation” would probably then break down, and it is not clear that the situation is meaningful. One of the arguments of this book is that a proposed infinite physical system needs a rigorously well-defined description before it can be taken seriously. Physical infinities are not to be proposed lightly! Moreover, the second law of thermodynamics can be generalized to suggest that an infinite series of events in the past would have caused entropy to “run out” by the present time anyway. [21]

“UNIVERSE FROM NOTHING” PROPOSALS

Some cosmologists claim that the universe could have arisen “from nothing.” One example of a proposal with this nomenclature was put forward by Alex Vilenkin in his book Many Worlds in One. [22] He suggests that there existed a prior state, which I will here call the proto-universe, that turned into a new cosmos or universe, which developed into the one we live in. It is not a particularly simple theory, but it illustrates the kind of idea that modern cosmologists are proposing.

The proto-universe is initially thought of as a small, closed universe that would expand to a maximum size and then collapse again. It has its own internal space and time dimensions. We are now asked to imagine, first, that a universe is a quantum object. This means that certain kinds of quantum behavior can be attributed to it, in particular that it can make a transition into another quantum state, namely, one corresponding to the earliest stage of our own universe—also imagined as a quantum object. A second step is to imagine the dimensions of the proto-universe being mathematically reduced to zero, so that it does not possess any internal structure, even time. This state is dubbed “nothing,” although it is still said to be a quantum object and so it is not really nothing. Its transition into a “real” universe remains mathematically calculable, as a so-called quantum tunneling process. The real universe is in this way jump-started to have a finite radius, from which it can then undergo inflationary expansion without an initial singularity.

There are a number of issues here. Our universe may or may not have been initiated by this means. However, to treat a universe as a quantum object is to extrapolate quantum theory a tremendously long way from its tried and verified use. Normal quantum physics asks about different observable properties of a particle and their observation by external apparatus. A quantum universe is not subject to this, it is not at all clear how an observation could be set up, and cosmologists often take refuge in a “many worlds” interpretation in which observations do not really take place. [23] It may be better to acknowledge either that there is something important in this area that we do not understand or else that a universe cannot very safely be regarded as a quantum object.

Then there is the role of time. Quantum processes in the laboratory take place in real time, and if the transition of the proto-universe into the new universe occurred in an external time frame, the use of the quantum concepts would be more transparent. This is apparently not the case here, and the absence of time deepens the obscurities, even though the mathematics can still be set out. Another problem is that quantum gravity is ignored. Having a proto-universe with zero radius may be invalid: many cosmologists doubt that any distance smaller than the Planck radius is possible. [24] Quantum-field effects have also been argued as preventing the proto-universe from having zero radius. [25]

But in any case we may still ask how this “nothing” object could exist, even if it is outside time. As a physical object, it needs a cause, clearly also from outside time, and mathematical laws of nature are still required. In his book, Vilenkin himself is indeed quite willing to imagine God as a celestial mathematician whose creative act gives rise to all this. [26]

Similar responses can be made to the ideas presented by Lawrence Krauss in his book A Universe from Nothing. [27] A major problem with his writing is a shifting definition of “nothing,” which could refer either to unoccupied space-time within which a new universe is generated by quantum effects, possibly involving vacuum fields, or else to “true nothing.” [28] In the first case, the reply is that the previously existing space and its vacuum fields, together with relevant laws of nature, cause the universe to appear—but they are obviously not “nothing,” and they too need a cause. The arguments and models presented in previous sections would still apply to this situation.

On the other hand, to say that a universe appears “from” true nothing makes no sense, because true nothing does not exist to be the source of anything, such as a universe; the term nothing is being inappropriately reified. Dropping the misleading terminology, proposals of this latter kind are merely saying that the universe had a beginning in time. Medieval scholars, it must be granted, had often used the Latin phrase ex nihilo (literally, “out of nothing”), but for them it always really meant “not out of something.”

The ultimate cause of the universe in such scenarios is often claimed to be “laws of nature.” The first thing to say here is that laws of nature, as the term is normally used, are laws of nature. They act on what is there, and “nothing” does not exist to be acted on! Laws causing a universe to appear as if from nothing would surely require an external existence—they certainly cannot be associated with the non-existing nothing. Does this imply a Platonic world of eternal ideas? But then, creative power must also be present. All this is effectively indistinguishable from the mind and creative power of a deity, and one may well feel that God is being brought in incognito through the backdoor. Whether such a deity is personal is another question, of course, and one that cosmology is not in a position to discuss.

SOME FINAL WORDS

Cosmology is a surprisingly complex subject, where experts may disagree and absolute proofs are lacking, and all that can be done is to summarize as well as possible the latest position. There is no generally accepted quantum theory of gravity at present, and the biggest “known unknown” is how such a theory would affect the situation. Acting at small times and distances, a quantum theory would in general be expected to remove singularities in its account of the physics of space-time. This is because a physical singularity must occur at a precise, definite time value, which the quantum theory would most likely not permit. [29] The quantum approach would introduce randomness into the theory, but only partially, for complete randomness would destroy the theory.

A serious general problem in this area is that all pre–Big Bang cosmological models are conjectural and speculative, some much more so than others. An author who is willing to alter the features of physics ad lib and ad hoc can produce a cosmos with a wide choice of features. The judgment on any given model, whether it is too contrived to be reasonable, can be a subjective affair. Very little of this is subject to experimental test, and it may well be that most of these ideas will never be testable. In that case they will remain to a large extent philosophical rather than scientific. Some of the ideas may be justifiably rejected as “science fiction.” Leon Lederman, in his book The God Particle, went so far as to remark, “When you read or hear anything about the birth of the universe, someone is making it up. We are in the realm of philosophy.” [30]

If the discussion of this chapter is correct, cosmologies with an infinite past history are not easily viable at present, and so the universe seems to have had a beginning. Therefore, the Kalam argument appears to be valid. Even if the past history were infinite, it may still be valid. What the Kalam argument demonstrates, if its premises and conclusions are accepted, is that the attempt to exclude non-temporal causes ultimately fails, and that a non-temporal and non-physical First Cause for the universe (or cosmos) is required if the idea of causation is taken seriously. In his own proposal, Vilenkin sought to take the causality chain one step further back out of space-time, but that is the limit. The physics still has a starting point. [31]

A few comments need to be made, however, regarding the theological side of the discussion. Many theologians would say that the divine act of creation is continuous throughout physical time and is not confined to one instant. [32] In this perspective, the question will be whether it is better to see “creation” as the cause of the universe coming into existence or of its being in existence. If the universe were actually infinite in time, then we would surely seek a cause for its being in existence, and so God’s creative activity would be understood in a timeless way. Such a viewpoint can of course also be applied to a universe with a finite history. Is the Kalam argument, then, dispensable?

The reply is that the Kalam argument certainly does not exclude this perspective, but it should be seen primarily as a demonstration of the limitations of physicalist philosophy. Starting with a naturalistic, physical set of causes, which of course we do believe has taken place, we find that something more is implied. To say that the initial state of the universe is due to God’s activity is in no way to deny such activity at other times or in a broader sense; this is not at all the aim of the argument. There is no claim that God is not responsible for the continuous existence of the universe, or even that the first instant of the universe is necessarily different from the others. But while continuous action by God might be disregarded, initial causative action cannot be.

From here, questions open up about whether the universe can be ontologically self-subsistent—that is, whether it can exist on its own. This is the viewpoint held by materialist philosophers but disputed by many theologians, and it leads into a much wider area of debate concerning the relationship of God to the universe. These are profound issues, but here we have largely bypassed them by allowing the universe to have phenomenal self-subsistence. In other words, the universe is possessed with laws of nature and they operate. Within this framework, it seems at present that the Kalam argument is very persuasive. An external First Cause to the universe, or cosmos, is difficult to avoid. But as we have said, the argument on its own does not say much about the nature of God or indeed any other proposed transcendent First Cause. For this one must turn to other considerations than cosmology.

TEN

EXPLANATIONS AND EVIDENCE

We saw earlier how a multiple universe has been proposed as one explanation for our existence on our planet. This rather surprising suggestion invites further exploration of what makes a good explanation in science. In general, the role of science can be seen as twofold: discovery and understanding. Discovery is the observation of new facts about the world around us, while understanding involves the forming of correct explanations as to the reasons for these facts. The explanation is the intelligible human account of the matter; the reason is the objective factor in nature that has made the given facts to be as they are. The assumed intelligibility of nature means that we can indeed hope to give explanations about reasons. Certain types of explanation can be called scientific; [1] other types of explanations are needed if we wish to consider questions that science does not address, such as those of purpose and meaning. Always, an explanation is an attempt to answer the human question why.

It is useful to distinguish between proximate and ultimate explanations in science. The proximate, or immediate, explanation concerns the circumstances that form the direct reason for what we observe. For example, the pond in the garden froze because it was a cloudless winter night and heat radiated away, lowering the temperature of the pond. But we may not be content with this. These circumstances surely demand an explanation in turn, to be found in terms of the earth’s weather patterns. We may wish to go still further and try to explain the latter as a consequence of the history of the earth, or even of the solar system and the universe as a whole. The laws of physics underlie all the above. An ultimate explanation would in principle be one beyond which we cannot go, a basis for everything, but what is taken as ultimate in practice depends upon the investigators’ abilities and concerns. For everyday weather forecasting, we are probably happy to take as a basis the fairly well-understood physical behavior of the earth’s atmosphere as our planet goes around the sun. This does not amount to a truly ultimate explanation, but it is sufficient for the purposes of meteorology.

Should explanations be simple? If we are confident of our understanding of a scientific situation, then even a complex explanation will be accepted. Truth takes precedence over simplicity. Controversy is more likely to arise in situations where hypothetical explanations are offered in the absence of experimental proof. When the true explanation for a given phenomenon is not known, the complexity of a proposed explanation becomes a discussable issue. Aesthetic reasons apart, a simple hypothesis may seem to promise better understanding. But simplicity is a dubious principle to apply dogmatically in a scientific context, and it ought to become a side issue in the end. The goal is a correct explanation, however complex that may be.

EXPLANATIONS AND PROOFS IN MATHEMATICS

The subject of mathematics provides a helpful testing ground for thinking about these questions. Standard mathematical practice is to start with a set of basic statements, known as axioms, accompanied by some logical rules to allow further statements to be deduced. From these, general results, known as theorems, can be derived.

For example, the well-known theorem of Pythagoras states that in a right-angled triangle, the sum of the squares of the two shortest sides equals the square of the longest side. This fact was widely known in the ancient world, and many different types of proof of it were given over the centuries. Around 300 BC Euclid gave the first surviving recorded proof of the theorem, using a small, well-defined set of axioms about the properties of straight lines and other basic features of geometry. [2] It is not the simplest possible proof, but it has historical importance as the first that we know of and because of the logical manner of its presentation.

The essence of a proof lies in the fact that if the axioms and rules of deduction are accepted, it provides full assurance of the truth of the theorem in all conceivable cases. Before Euclid, many examples had been known of triangles satisfying Pythagoras’s theorem. The best known is that the squares of the numbers three and four add up to the square of five, and a triangle whose sides are three, four and five units is right-angled. On the basis of such examples, it is quite easy to imagine that Pythagoras’s theorem may be universally true, but Euclid’s proof converts conjecture into certainty, provided that we are prepared to accept his axioms and his use of logic. All this, in normal circumstances, appears to be common sense and difficult to doubt.

The axiomatic proof can be viewed as providing an explanation for the truth of the theorem. Explanations and proofs operate in opposite directions: the explanation answers the question why with “because,” while the proof says “therefore.” From the point of view of a proof, we start with axioms and build up, combining different proved facts until the theorem of interest is reached. From the point of view of an explanation, we start with a statement of the theorem as a believed or proposed truth, and the proof then gives us an explanation as to why it is true. Such an explanation will apply both to the general theorem and to any given instance of it, such as why Pythagoras’s theorem is true for a particular right-angled triangle.

However it is a mistake to assume that mathematicians always work by building proofs up from first principles, ending with theorems whose existence was unsuspected before the logic was followed to its conclusion. This can happen, but it is probably exceptional, because a virtually unlimited number of mathematical arguments may be constructible from a given set of axioms, and most of them will not lead anywhere very interesting. A mathematician will prefer to have at least a glimmering of the kind of theorem that may be provable, and it can happen that a theorem is asserted as a “provisionally believed conjecture” long before a proof is finally found. [3] In some cases, we are still awaiting the proof.

An example of this is what is known as Fermat’s Last Theorem, which dates from the year 1637. It states that if we have three positive integers a, b and c, and each is raised to the power n, then the equation an + bn = cn has no solutions when n is greater than two. So two squares can add up to another square, but two cubes cannot add up to another cube, nor can this occur for any other higher integer power n. Fermat did not reveal his own claimed proof, and his theorem retained the status of a conjecture, proved for special cases and generally believed to be true, until Andrew Wiles finally published a full proof in 1994. [4] Another famous conjecture that found proof only after a long period of being widely believed is the so-called four-color theorem, which states that any map on a flat or spherical surface can be painted using no more than four different colors so that no two adjacent areas have the same color. First proposed in 1852 by Francis Guthrie, a law student, its proof was eventually given in 1976 by Kenneth Appel and Wolfgang Haken. [5]

We will have more to say later about these celebrated theorems, but in their cases it was certainly a commonly believed “fact” that sought an explanation in the form of a proof that would make it certain and universal, rather than a theorem that emerged unforeseen from a deductive argument starting from some axioms.

There are a number of similarities in the ways that proofs and explanations operate in science, especially in physics, and in mathematics. After some experimental facts become known, an explanation is sought with the hope of producing a full theory that operates in the general style of a mathematical proof. A set of basic facts and laws, appropriate for the given scientific area, will play the role of axioms and logical rules, from which the scientific consequences can be deduced. The main difference is that experimental testing must be sought for any new set of proposed theoretical ideas in science.

MODES OF EXPLANATION IN SCIENCE

Science attempts to answer the question why in three important ways: historical (or causal), compositional (or analytic) and in terms of laws (nomological). [6] Historical explanations account for observed facts in terms of a set of previous causes. An example of this would be evolutionary accounts of how living species have developed over timespans of many years. In physics, as we discussed earlier, a train of causes and effects can in principle be extended back to the cosmic Big Bang.

A compositional explanation accounts for the properties of a compound system in terms of its constituent parts and their arrangement. Thus, a crystal is composed of atoms arranged in a certain regular pattern, atoms are made up of elementary particles and so on. A nomological explanation accounts for patterns of observed behavior in terms of laws of nature, and these may have an explanation in terms of more fundamental or more general laws and principles. A compositional explanation may reach a stopping point at the level of atoms or elementary particles, after which we will concentrate more on the laws of nature that govern the elementary particles. A historical explanation relies on laws of nature to govern the causal processes and may sometimes be statistical, dealing with probabilities for laws to have certain consequences. [7] In physics, in contrast to biology and cosmology, the explanations are mainly compositional and nomological. In biological systems, additional types of causes may often be ascribed to a given situation: functional, genetic and even purposive. [8]

Many aspects of explanations refer to “forms” in a very general sense: laws, causes, patterns, concepts, theories and so on. But an explanation may well also depend upon physical facts. A scientific explanation must have a starting point, and this may consist of basic concepts that are believed, or a set of accepted physical facts, or both. The initial conditions in a historical explanation are likely to be some physical facts, and the elemental entities of a compositional explanation will be some objects that factually exist. Both the formal aspects and the factual aspects of an explanation are important.

LEVELS OF EXPLANATION IN SCIENCE

Any science provides explanations, and the question then is how ultimate or basic these explanations may be. The other sciences are often regarded as reducing to physics, and physicalism is the hypothesis that only physical reasons and explanations are truly ultimate.

Well-defined branches of science have their own local assumptions and methods, and even if it were true that physics can provide a “more ultimate” level of explanation, this may not always be practicable or useful. If we are studying the behavior of bears, the context will be one of animal species and their environment, with basic principles and understandings set out at this level, and we are unlikely to feel a need to delve back into quantum physics. For practical convenience, every field operates within a limited context that facilitates its work. To probe it all back to the Big Bang or quantum field theory is unnecessary and irrelevant and probably not even feasible.

In a given area, the chain of explanations is most likely to begin with an explanation for an experimental observation in terms of some proximate reasons for it. These will eventually be explained by the basic facts and principles that are conventionally employed in the field. Such facts and principles serve as provisional “ultimate reasons” from which all the observed phenomena in the field can be derived, in analogy with an axiomatic proof in mathematics. A deeper level of explanation may exist and can be aimed for, but an explanation does not need to have this in order to be valid at its own level. In science, explanations can be usefully taken one stage at a time; an explanation does not need to have an explanation.

ULTIMATE EXPLANATIONS IN SCIENCE

Suppose we seek to take science back to a truly foundational ultimate explanation. We start with a branch of science of our choice, trace its contents back to laws and facts of everyday physics and then explain these in terms of atoms and molecules. We introduce quantum theory and take the explanation back further to elementary particles, from where we look for a more general theory that can account for all the elementary particles. Then we seek a further theory that will give rise to the ideas of this theory. The question is, how can this process terminate if we still desire to remain within the domain of science? There would seem to be a limited number of possibilities:

1. The scientific reasons go back forever with no stopping point. We human beings cannot reconstruct such an infinite sequence, however, or even necessarily know that it exists.

2. They stop at some fact or law for which there is no further explanation or reason.

3. They stop at something that is a logically necessary truth.

4. Our human minds become incapable of formulating the explanations at some stage. [9] But reasons still exist.

5. The reasons and explanations at a certain point are sufficiently different from those in the science of physics that they can no longer be called science or physics.

Here science differs from mathematics. A given area of mathematics has a clearly defined set of axioms as its starting point, which represents the “ultimate reasons” for all of the theorems in this area. There is no need for deeper axioms from which the given set can be proved. We might like to devise alternative axioms that are in some sense preferable, or we might engage in a philosophical discussion about the axioms, but none of this is actually required. No further explanations are due.

From the above list of options, we are bound to conclude that science is not capable of providing a truly ultimate explanation for the physical phenomena we observe around us. If as in (1) there is an infinite regress, then there exists no ultimate scientific reason or explanation, in much the same way that there exists no largest integer number. A possible way out could be that an infinite series of explanations might somehow be combined into a single explanatory concept. But then we would ask for an explanation for this concept! We are otherwise left with an infinitely complicated chain of reasons for everything. This kind of infinite sequence has a very questionable nature: what kind of actual infinity is this really? Is anything really explainable at all?

In case (2) it might be that the stopping situation “just happens.” Any attempt to find a further scientific explanation will fail. Science now ceases to provide the goods, so that this kind of stopping point does not comprise in any true sense an ultimate scientific explanation—merely an absence of one. It is the end of a road that might have led further: the unanswered question why can still be asked. This is the situation when people propose that our universe “just is.”

Possibility (3) is scientifically implausible, because it implies a final stage that has no logical possibility of being otherwise: for some reason, science is not now allowed to ask a further question why. Such a situation is hard to imagine, since science seems always able to propose alternative logic possibilities, the choice between which requires a reason, or else we can take issue with the nature of the logic. It does not seem at all likely that science is able to terminate in this way.

Case (4) suggests a different situation. It refers not to the mere absence of a known scientific explanation but to a situation where the very nature of the next explanation would be incomprehensible to us, whether or not we realized this. But science is a discipline that we humans construct, and if we completely lack a capacity to understand something as science, then it would not be science—whatever else it might be. The situation has diverged from what we call science and leads into possibility (5), which takes the explanations explicitly out of science’s hands. Science reaches its final limit. We may be able to understand some of the further explanations, but the true ultimate explanation, if it exists, is not of a scientific nature. We will return to this later.

Case (4), to repeat, does not refer to the possibility that beyond a certain point the physics may be unknown to us, as in case (1). Physics deals with quantities whose behavior is given by mathematical laws, which we believe we can understand in principle however far back they go. For example, even though multiple universes are scientifically problematic because of their possibly permanent unobservability, the relevant mathematical concepts still remain within our mental grasp. The mathematics of quantum physics is likewise understandable to us even though its interpretation may be unclear. A different kind of explanation, however, will not be physics, and whatever lies outside our mental scope lies outside the scope of what we would call physics.

COMPLEXITY AND SIMPLICITY

If an explanation is true, then its degree of complexity is irrelevant once it is simplified as far as possible. We might still wonder, however, whether all true reasons are in the end simpler than the facts that they explain. Here again it is necessary to distinguish between proximate and ultimate (or provisionally ultimate) explanations. It is undeniable that the proximate explanation for a simple fact can be highly complex, even if the ultimate reason might be relatively simple.

The philosopher Del Ratzsch has proposed a story to illustrate a legitimate need for complexity in certain explanations. [10] He considers the case if a geometrical metal object were discovered on Mars. Most people would immediately think that the object had been made by visiting aliens and would regard such an item as virtual proof that aliens existed, despite our total lack of knowledge about them. The proximate explanation in terms of aliens is simply the only one on offer. As an explanation it appears both complex and incomplete, but the object cannot be accounted for on the basis of natural laws and processes, and we would really like an explanation.

Fermat’s Last Theorem provides another illustration. The proof that was discovered is long and subtle even though the theorem itself is understandable by any numerate person. The four-color theorem for maps, our second example above, was proved by reducing the issue to some two thousand special cases, and the authors wrote a computer program to work its way through these. The complexity has since then been reduced a little, but an author of a later version of the proof remarked nevertheless that “the entire argument occupies about 13,000 lines, and each line takes some thought to verify. Therefore, verifying all of this without a computer would require an amount of persistence and determination my coauthors and I do not possess.” [11] So a computer had to do it. These complex proofs constitute proximate explanations for very simple mathematical statements, for which the ultimate explanation and reason lies in a simple set of basic mathematical axioms—but we cannot go straight from these to the final results. There are a number of cases of this type. [12] However, an interesting theorem often does possess a certain quality of simplicity, and in mathematics it tends to be seen as particularly “beautiful” when a simple result emerges as the outcome of a highly complex line of argument!

Other things being equal, a simple set of axioms will be preferred to a complex set, but we may find in practice that a set of mathematical axioms is not really overall any simpler than a given theorem that arises out of it. Euclid’s set of geometrical axioms, even selecting only those relevant for Pythagoras’s theorem, might seem at least as complex as the statement of the theorem itself. Some later mathematicians have argued that Euclid should have included more axioms in his set. The axioms do have a good degree of simplicity, but they much more importantly have the quality of being “basic” and of having wide application. The simplicity of an explanation is not just that of the axioms, though. The axioms of arithmetic may be fairly simple, but the proof may be highly complicated, as it is for Fermat’s theorem, and it is the proof as a whole that constitutes the explanation.

Simplicity in science can be misleading or just wrong, and sometimes complexity is unavoidable. It was simple to attribute malaria to “bad air,” but the true and complex explanation is in terms of the life cycle of a parasite of a certain species of mosquito. To demand simplicity in a given situation may or may not be appropriate. Within physics, simple phenomena with complex explanations include superconductivity and the Pauli exclusion principle. [13] Most of the known basic laws of physics are conceptually fairly simple, but to explain the physics of our universe, we still have to assemble the mathematical apparatus of quantum mechanics, field theory, quantum chromodynamics, general relativity and so on. This is not first-year university stuff! Searches for a “theory of everything” continue, and such a theory again will probably be highly sophisticated, for otherwise we might expect to have had it long ago.

Why then do we like simple explanations? Perhaps because we can easily understand them! Some further reasons are as follows. There is a fear that by making reasons sufficiently complex one can explain anything at all, as in the case of an infinite multiple universe. Complex hypotheses can have more side effects that may prove false when tested—so they are riskier hypotheses, although the falsifiability is a good scientific feature. Since all the elements of a complex hypothesis have to be true, this is rather like proposing a set of coincidences, something that seems undesirable. A complex hypothesis is likely to require more explanation at its own deeper level than a simple one. Conversely, if a simple hypothesis successfully explains a number of different facts, it connects them and pleasantly removes them from the category of coincidence. This is a compelling feature of realist laws of nature: a small number of laws can provide reasons and explanations for a large and varied amount of data.

The above considerations are reasonable in dealing with hypothetical proposals but are much less relevant when the true explanation is established. We may well wonder, given that true explanations can be extremely complex, how we are to discern when the simplicity criterion is really needed. Simplicity, perhaps, should really just be a guideline.

A further factor concerns the intrinsic likelihood or believability of a proposed explanation, and it is at this level that most arguments occur. For some people, political conspiracies provide a highly plausible explanation for many undesired events in society; for others they are improbable. For some, a multiple universe is believable; for others not. For some, the existence of God is seen as likely, while for others it is out of the question. The important thing here is to be aware of the subjective nature of many of the assumptions in this kind of discussion.

What if the choice turns out to be between an explanation and no explanation? We have seen the example of quantum events: if a particle is exposed to a piece of apparatus and a number of different outcomes could occur, then the outcome is normally believed to be random, subject to a set of probabilities given by theory. This means that there cannot be a complete explanation for the quantum event in any given instance.

This interpretational position is found unsatisfactory by a minority of physicists, who believe that all things must be physically determined and therefore explainable. Theories of “hidden variables” have been proposed, as we have seen, in which unobserved physical quantities behaves in a definite way that determines how a given quantum event will occur. So the event is not really random. All this in principle gives the explanation of the quantum event, despite a lack of experimental confirmation for the existence of the hidden variables, our lack of knowledge of their actual values, and the tendency for such theories to be somewhat complex. In practice it is the unconfirmability, more than the complexity, that leads most physicists to reject these theories, but for those who have a strong philosophical commitment to determinism, such objections have no compelling power. The primary question relates to whether a complete explanation is needed, and an a priori belief in this is given precedence over the rejection of complexity or unconfirmability.

In his books, Richard Dawkins has argued that as a reason and explanation for the universe, or at least for the presence of advanced life, the concept of God must be very complex and is therefore unhelpful. He writes: “However statistically improbable the entity you seek to explain by invoking a designer, the designer has got to be at least as improbable,” [14] where he takes complexity to be equated with improbability. [15] This is a poor argument for several reasons. It presumes to assign a statistical probability to God, on the same basis as to the universe, which is naive. Human designers certainly exist and are complex, with both biological and mental complexity. [16] Also, it is not clear how complex the initial state of the universe really was. But as we have seen, it is really no easy matter to judge when complexity is problematic in an explanation. Scientific explanations cannot be restricted to those that are simple, and the purpose of human understanding is to find truth, whether this is simple or not. In fact, an equally valid complaint might be that the concept of God is too simple. Dawkins’s argument would much more clearly hold against the multiple-universe hypothesis, where to account for our own “statistically improbable” universe a colossally complex ensemble of different universes is proposed as its explanation.

CHANGES OF PARADIGM AT DIFFERENT LEVELS

A paradigm is a basic way of understanding and thinking about a topic in terms of a particular set of reasons for things. Consider the following tale. An overseas tourist is visiting Saint Paul’s Cathedral in London and asks the tour guide how such an impressive building came to be built. “This cathedral,” the guide starts off, “was designed by Sir Christopher Wren.” But at this point the visitor suddenly becomes impatient. “Come now,” he says rather rudely, “that’s no proper answer at all! Because in that case, just tell me this: Who designed Sir Christopher Wren?”

The issue here is that the tourist assumes that the same kind of explanation goes on forever. This is wrong, because at certain stages in taking explanations back step by step, the nature of the useful questions and of their answers is likely to change, possibly quite radically. To insist on asking the same kind of question forever is simple-minded. The paradigm has to change. In the tale above, instead of the tourist’s final misconceived question, the relevant questions concern aesthetics, history and religion. It is new questions such as these that relate to the real reasons for how the cathedral came to be designed and built. An unwillingness to change paradigms is likewise the main error of those who insist on asking “scientific” questions about God, or questions such as “Who designed God?”

Ultimate explanations may well turn out to be different in kind—that is, in paradigm—from proximate explanations. Science strives to press its explanations back, step by step, but even within science there is from time to time the need for a new way of thinking. To take biological explanations back, we move to biochemistry and chemistry; to take chemistry explanations back, we move to physics. To understand physics at the atomic scale, we must use a quantum approach since classical physics will no longer do. Each step involves a different kind of reason and of understanding, a different paradigm. It is natural to try to take a successful paradigm back as far as it will go, but eventually a change will be needed.

GOD AS EXPLANATION

Given our large and complex universe, organized by a set of sophisticated physical laws, a standard explanation is that it is the creation of God. This proposal can be made either in a philosophical or in a religious context.

Two separate issues are present here that should not be confused: one is the question of simplicity, and the other is that of how explanations regress. The former we have discussed. With regard to the latter, we have seen that there may always be problems in dealing with a chain of possible scientific explanations. A point of no further scientific explanation may be encountered, and then to go further something non-scientific is needed. Likewise, if there is an ultimate explanation, we must look outside science for it. In either case we have to expect a different paradigm. God may provide such a paradigm.

Believers hold God to be the ultimate reason for the physical universe. God is usually thought of as being in some sense infinite, which might imply complexity, although this is a matter of debate. [17] However, there may be no real need for intrinsic complexity in God. Human designers can have complex thoughts, and we have already accepted the existence of complex explanations within science and mathematics, so why should a universe not derive from quite complex thoughts in the mind of God? Such thoughts may perhaps even have a simple ultimate reason in deeper thoughts within the mind of God, if it is still legitimate to think in this way in this context. There could be some analogy to simple mathematical axioms that are able to give rise to complex but rich and elegant theorems. The regress “Who designed the designer?” can be escaped by removing the demand for another agent and asking instead, “What designed the design?” since this may be easier to answer within the same agent: the mind of God. But just as with the story of Sir Christopher Wren, both questions may be misplaced. We are surely out of our depth here, not knowing how to ask about these things. [18]

When it comes to ultimate explanations, then, it might appear that theism is as challenged as science, since we are in no position to understand how these really operate within the Deity. But the explanations are at least now being taken across into something that we, acknowledging our human limitations, may reasonably accept as transcendent to ourselves. The mode of God’s ultimateness is unlikely to be open to us; we do not have good cause to expect to know or understand the answers, or even the right questions. Simplicity can be a valid criterion in comparing alternative scientific hypotheses, but it loses importance as soon as the correct explanation is found, and it becomes hard to define if we are considering a transcendent explanation. To call an atheistic absence of final explanation “simple” seems to be cheating. In any case, if an explanation is being sought that is ultimate in a genuine sense, then science cannot give it.

The objection is sometimes raised that since God can do whatever he likes, the God hypothesis does not easily allow predictions to be made, and so it cannot be tested in a scientific way. Of course, this overlooks the opposite possibility that the divine actions might be totally predictable, and then we would call them laws of nature. In fact, there is a basic fault with the objection of unpredictability. Suppose some archaeologists find on a remote island something that appears to be an artifact of a long-lost civilization. We would like to decide whether this is so. Should we object that the “civilization” hypothesis lacks predictive qualities, because after all, civilizations could do pretty well anything, we know not what? This objection is not helpful, because the civilization hypothesis is not a scientific explanation. We just need to know the possibilities, and it is perfectly reasonable to ask whether a civilization created the discovered object.

God should likewise not be regarded as a “scientific” explanation. For an explanation to be scientific, we would expect to test its consequences by controlled experiments, and although it is a common experience that faith in God does make a positive difference to human lives, there seems to be no laboratory experiment that could decide these things. Indeed, given the biblical commandment not to “test the Lord your God,” one should probably not expect any such attempt to succeed. It must be agreed that our universe may not be entirely what many of us might have constructed if we were God—there are unresolved puzzles and much that we do not understand. This, of course, can also be said about science. But rather than saying, “God cannot exist because I would have done it better!” it may be wise to acknowledge our limited understanding.

Just as an inference that an artifact was produced by an intelligent race assumes that we can understand the race at some level, we suppose a degree of human intelligibility of God at some limited level. Further information about God comes from trusted revelatory sources and from human personal experience, and this is not information of a scientific kind.

Should all explanations be scientific ones, as many physicalists would demand? This is in fact a metaphysical question and therefore one that is beyond the competence of science itself to answer. Science, it may be asserted, provides full explanations, unlike theology. But it can pretend to do this only by denying questions it is not equipped to answer, so that one ends up defining the subject matter according to the answerable questions. Science also cannot provide a truly ultimate explanation. We have to live with some kind of ignorance or mystery.

EVIDENCE FOR GOD

By evidence we mean facts that make a given proposal believable, or more believable. This means that the proposal in question must provide or contribute to a possible explanation for the stated facts. In interpreting facts as evidence, an argument must be constructed: we must say why the proposal can help to provide an explanation for the facts. Without this argument, a fact is simply a fact of a “so what” kind. Moreover, there could be alternative explanations for the facts in question, and the human assessor must form a personal judgment about which explanation has the best plausibility, taking the arguments into account.

In the case of a crime, for example, evidence consists of a set of facts, including witness statements, that help to make the proposal believable that the accused person is the criminal. In other words, these facts have a good explanation in terms of this person acting criminally, and less so otherwise. There may be forensic facts, and then the argument has to provide an understanding of how they are connected with the crime and the criminal. In the case of witness statements, the character and coherence of the witness are important for their credibility as evidence.

Even in the case of scientific experiments, an argument is required in order to turn a set of observed data into evidence for a particular hypothesis, so as to help to explain it. This argument must include a demonstrated understanding of the apparatus and how the apparatus works. A simple observation on its own is not self-interpreting.

On the basis of these understandings, we can see how various aspects of our existence in the universe may be interpreted as evidence for a Creator. We have pointed out that the existence, ingenuity and intelligibility of the laws of nature may be explained by postulating a creative Intelligence, the physical existence of a universe may be explained in terms of a creative Cause, and the apparent design of the universe may be explained in terms of a purposeful Designer. The existence of mentality in humans suggests a source in a higher mentality. These are fact-based and therefore evidence-based arguments that make belief in a deity reasonable.

Evidential arguments are not proofs, and they do not in themselves exclude other hypotheses, whose reasonableness must also be evaluated. However, it is hard to obtain evidence for a “no-God” proposal. The most natural consequences of a no-God hypothesis would be no universe, no laws of nature, no mentality, no intelligibility, no purpose—in short, nothing. None of this is the case. Unbelievers are obliged to accept a universe, since it undoubtedly exists. Likewise, minds exist, and the physical universe with its laws of nature is evidently intelligible. In practice, unbelievers are most likely to focus on an alleged absence of purpose in the universe. Purpose is a hard thing to evaluate objectively, since one cannot be sure of a Creator’s purposes. But if the purpose of the universe were to include the generation of conscious intelligent beings, then this is something that has also successfully occurred.

In short, it is very difficult to produce positive evidence for no God except along the lines of, “If I were God, I would have done things differently.” It is no doubt true that the universe contains features that are puzzling from a believer’s viewpoint, but it is hard to argue with any definiteness that God could not have done it this way. Other features, as we have seen, provide positive evidence for God. Unbelievers are obliged to argue that the no-God hypothesis is one that is capable of explaining not only an existence of no universe, obviously, but also an existence of an actual universe, one like our own. This makes the no-God hypothesis extremely unpredictive and hard to test, and unbelievers are on weak ground in criticizing the God hypothesis on this basis.

Negative claims tend to be intrinsically problematic. So usually we ask for sufficient positive evidence to justify the positive claim, without anything that amounts to a clear inconsistency. This, we have argued, is reasonably satisfied when considering evidence for God.

CONCLUSIONS

In this discussion we have followed the standard line of supposing that a set of observational facts normally has a reason accompanied by an understandable explanation. There may be a train of further and more basic reasons and explanations, stopping in practice at a point that is scientifically attainable or convenient. But science is incapable of furnishing a truly ultimate explanation for the facts around us. As regards simplicity and complexity in scientific explanations, either of these can be present at any stage; what matters is whether a proposed explanation is correct. At various stages, changes in the explanatory paradigm are to be expected, even within science.

To take God as providing the explanation for the universe means taking the explanation back to a final stage, with a final change of paradigm. This is indeed a very serious paradigm change, one that precludes scientific methodology and in particular prevents the use of concepts such as complexity and simplicity in a clearly defined way. But it does permit pointers toward a reason for the universe and ourselves, one that may be ultimate, even though the details will be surely beyond our comprehension.

It is reasonable to have deep hesitations about any kind of human intellectualizing concerning God’s inner nature, even though a few ideas perhaps need to be aired sometimes, “lest nothing be said.” But from the viewpoint of faith, this is not really needed. God is largely beyond our understanding. This is the correct theological reply to those who believe that science can solve all problems. Of course, it is a non-intellectual reply that will certainly not satisfy those who think within a rationalist paradigm.

What, then, should be asked about God, and how should we try to proceed further? Here the search changes its nature and must become a personal spiritual quest. In the next two chapters we discuss why the science of physics, while providing a number of important signposts to God, cannot take us all the way. We will first see that human nature has to be considered as extending beyond the physical. Then we will consider some aspects to human existence that extend beyond the intellectual, but which many have found relevant and useful.

ELEVEN

MENTAL REALITY

The nature and status of the mind have been the subject of deep debate throughout human history. During the late Roman and medieval periods, the church was the main guardian of scholarship in Western Europe, and discussions about the mind and the soul presented no problems. Since the seventeenth century, however, the most spectacular advances in human knowledge have taken place in the sciences. As we have noted, the boldest claim from the scientific point of view is that all existence is accountable in terms of the science of physics: the entire properties and behavior of any system arise from the physics of its component elements and their arrangement. But human beings consider themselves marked by possessing qualities such as purpose, consciousness and moral responsibility, which in no evident way have anything to do with the physics of a biological system. A rigorous belief in materialism or physicalism threatens to eliminate these qualities, leaving us to be regarded as physical and chemical automata. [1] Such a view contradicts our deepest intuitions.

The aspects of our nature that are seemingly not physical have traditionally been associated with the “mind” or “soul,” which in a poorly understood sense is associated with the brain. Receiving cognitive input through the brain, the mind exercises a degree of control over the behavior of the brain and hence the body. To many, the implication that there is a non-physical aspect to reality is highly troublesome. The connection between mind and matter is also a longstanding problem, and indeed, a great deal of human behavior that we might feel is caused by the mind is at least to a large part due to neurophysical phenomena in the brain.

THE QUESTION OF CONSCIOUSNESS

The materialist account of human nature finds its most serious difficulty in the existence of consciousness, and this is commonly referred to in the literature as the “hard problem” of neuroscience. Can consciousness be generated purely by the physics of the brain? How are we to incorporate the human belief in free will or conscious agency into our scientific thinking? Certainly, a widespread opinion exists that physicalist principles will in the end answer all such questions. It is well exemplified by Daniel Dennett: “I would have thought a historical perspective alone would make [the non-materialist view of consciousness] seem ludicrous; over the centuries, every other phenomenon of initial ‘supernatural’ mysteriousness has succumbed to uncontroversial explanation within the commodious folds of physical science.” [2] But such sentiments suffer from more than just optimism. Conscious awareness has qualities that make it radically different from anything in physics, even quantum physics, and we will argue below that it is something that the science of physics is not able to describe. None of the ideas contained within the subject matter of physics has anything to say about consciousness. This has always been the case, even though physical science itself has changed its nature considerably over the centuries.

The determined physicalist might respond to this in several ways. One is to say that at some future stage physics may expand its remit further so as to deal with consciousness, just as it has done in the past with regard to other areas. Another is to say that consciousness concerns complex physical systems, and it is in the complexity that the essence of consciousness resides. A related idea is that consciousness is about information, and that computers with enough information stored in them might become conscious, like the human brain.

A reply to the first of these points is that any new, expanded science of physics that dealt with consciousness would have to be so radically different from the present physics as to be a virtually new subject. It is difficult to see why complexity on its own should generate consciousness, even though a very complex brain may well be needed for consciousness to operate. Nothing about consciousness is implied by complexity as such. With information, likewise, no concept of consciousness is implied in the idea of a set of bits, nor in streams of bits passing through devices that convert them into other streams of bits. Bits, after all, are simply states of physical components that can have two possible settings. The meaning of the information is another matter but meaning implies a mind. The mind that gives meaning to a given pattern of bits must be associated with the agent who sets up the bits, or programs the computer, or receives the outcome of the process. In other words, a mind defines, transmits, receives and interprets information, but the consciousness is in the mind and not in the physical information as such.

WHY CONSCIOUSNESS AND PHYSICS ARE DIFFERENT THINGS

A conscious mind is an entity that can receive information, but there are also physical systems that can do that in a functional way. Imagine two physical “frames of reference,” defined by two information-processing beings, which may be robotic or human. Let the two information processors be called Arthur and Bertha, and let them be moving relative to each other on two boats sailing at different speeds on a lake. Both carry out measurements on some external object—for example, the speed and position of a bird that is flying overhead. The numerical information about the position and speed of the bird relative to Arthur, at a given time, is different from the corresponding numerical information obtained by Bertha. However, Arthur can transmit all his (or its) information to Bertha, and vice versa, and in that case each now has all that there is to know about the physical information present in the other frame of reference. This information comprises sets of numbers, which contain everything physically relevant to the object as observed in a given physical frame of reference, because physical information is essentially mathematical and numerical. For this exercise, it does not matter whether Arthur and Bertha are conscious beings or unconscious robotic devices.

Now imagine the two observers as conscious human beings exchanging information about their experiences of, say, the setting sun. Bertha relates to Arthur that she saw a red disk, and there is no doubt that the geometrical form of the disk, its size and the wavelength of the light are physical and mathematical quantities that can be objectively transmitted to Arthur just as before. However, the experience of redness is different: it cannot be communicated. It has been asserted many times over the centuries that in situations like this, Bertha’s experience of redness might perhaps be the same as Arthur’s experience of greenness, say, but that, it is impossible to know. In fact, the situation is considerably more serious: the two observers’ conscious color experiences are not only incommunicable; they are mutually incommensurable. No comparison is possible between the two different conscious experiences as such.

It does not help if we try to relate the experiences to the patterns of cells that are firing in Arthur’s and Bertha’s brains. It is known from experiment that when certain cells fire, a conscious experience is probably being had, but a bare physical description of cell activity does not describe a conscious experience, or even logically imply it. I may be tempted to say that since you are generally like me, your experiences are also like mine. But this is not only an assumption; it is strictly speaking meaningless. Only in your mental place could I really compare your experience with mine, but I cannot be in your mental place.

It should be clear, then, that physically objective information, which can be completely communicated and shared, is of a mathematical kind and qualitatively different from subjective information, which has an unshareable aspect. With regard to subjective information, all I can do is to empathize as much as possible with another person and hope that my experiences are analogous to theirs—but analogy is not the same as identity. Sometimes, I may have no way of really knowing about what you are experiencing. It is similar with animals. We feel we can empathize with cats and dogs, for example, and we infer that they are probably conscious, a bit like us. It may be otherwise with fish, and there is probably no reason to believe that insects are conscious; their brains are no more than programmed information-processing systems. But in no case can we really know for certain what the animal may be experiencing. [3]

There are several important conclusions here. First, a conscious individual defines a personal subjective worldview, which cannot be experienced from the outside. By means such as verbal communication I can correlate your experiences with my own, but I cannot experience your experiences, since to do that I would have to be you. Physics, on the other hand, deals entirely in shareable quantities that are definable and measurable, objectively and publicly. It is therefore unsurprising that physics has no conceptual equipment or vocabulary for intrinsically private things and no means of reference for the conscious sensations themselves. These are often referred to as qualia. The experiences of colors, musical notes, smells, pain, emotions and so on can be correlated with the behavior patterns of neurons in the brain, but they are not definable in terms of these or any other physical items. This is the so-called knowledge problem in debates about consciousness: knowledge of physics does not in itself provide knowledge about conscious experiences. These are different kinds of knowledge.

Physics is therefore not enough. Dennett’s logic is simplistic. Note of course his unjustified identification of non-physical with “supernatural,” a fear of which may be at the heart of the physicalist’s attitude.

THE CONSCIOUS MIND AS AN ACTIVE AGENT

There is more to the conscious mind than its cognitive aspects. Our experiential belief is that consciousness is not just a passive faculty but can also affect how we behave, a capacity often referred to as “free will.” This presents fundamental difficulties for any kind of materialist position, which would like to hold that the physical universe is causally closed, that is to say, that it cannot be affected by anything non-physical.

The aim of epiphenomenalism, as proposed by T. Huxley in 1874, [4] is to do away with this difficulty without doing away with consciousness itself. Consciousness is postulated as a side effect, or epiphenomenon, of the brain’s activity, with no effects of its own. No further details are offered. This position seems to have little real evidence for it, despite its popularity in different guises, but there are a number of arguments against it.

An objection first put forward by William James is based on Darwinian evolution and can be expressed as follows. [5] We take it that consciousness exists in humans but probably not in simple organisms; therefore consciousness must have evolved. For a biological feature to evolve successfully, it must benefit its possessor; so consciousness must have a useful function. But this means it must be a causal agent of some kind, or the means by which a causal agent acts. Therefore, the mental must be able to affect the physical. And our experience indeed suggests that consciousness aids us in acting more intelligently and efficaciously and also in the learning of new facts, ideas and skills.

A possible reply is that if consciousness were generated automatically by brain processes, it really might possess no function at all, and so the evolutionary argument would not apply. The difficulty here is in justifying the automatic generation of consciousness. It is absent from most aspects of brain operation, after all. We can do a variety of activities with little or no conscious awareness, and people do surprising things while sleepwalking. Consciousness is something we can often choose whether or not to apply—for example, to our breathing or to the feel of our clothes. So the suggestion seems weak: it is not at all evident that consciousness happens automatically. Neither is its complex and coordinated nature readily and naturally compatible with coming about as an evolutionary accident. Various kinds of conscious sensation—vision, hearing, touch and so on—are all bound into one integrated conscious experience. How come? This is the so-called binding problem: Why is there not a set of separate consciousnesses?

There is a more fundamental point. If consciousness is an epiphenomenon, how can the physical brain have knowledge of it? [6] We talk and argue verbally about consciousness—but word formation is a brain activity. How can such talk occur without there being input to the physical neurons, that is, from the conscious mind? How could the brain, acting purely on its own, possess the information that certain of its neural states are associated with consciousness? To be sure, words such as stimulus or knowledge might refer to data input and storage in the brain, but the word consciousness means something different. We are able to have debates about when, how, why or whether consciousness occurs, debates that do not make much sense if we are really referring to the other things. Moreover, the words that my brain formulates correspond with precision to my personal experience of consciousness. All this requires informative input to the brain from my consciousness, impossible if the latter were a mere epiphenomenon.

At a more general level, once the distinctive nature of consciousness is acknowledged, it is arbitrary to restrict a priori what its relationship to the physical world may be. To make a parallel, Newton’s third law of force states that if A affects B, then B will affect A. This law underlies the interactive dynamics of all physical processes. It seems artificial to suppose that in the brain-consciousness interaction, the effect is only one-way, from the brain to the conscious mind. Epiphenomenalism, in short, is a very unconvincing hypothesis.

All of this means that the horizons must be expanded. Physicalism is incorrect; physics is not all that there is. There is a mental reality whose relationship to the world in its physical aspects is hard to describe, and which cannot be understood at all if we choose to think solely in terms of physics. [7]

CONSCIOUSNESS AS AN EMERGENT PROPERTY

It is sometimes suggested that consciousness poses no real problem, because as systems become more complex, new kinds of system properties become present, known as “emergent” properties. In this case, it is suggested, the brain is a physical system that is sufficiently elaborate for consciousness to appear in it as a new phenomenon. We do not know how this comes about, but somehow it is an emergent property of the brain.

The mere use of the term emergence solves nothing, however. It is true that at a new level of complexity, physical systems can develop collective properties that a simpler system does not have. For example, atoms of matter can form different phases: solid, liquid and gas. For this, large numbers of atoms or molecules are needed, and the solid, liquid or gas has properties that are different from those of individual atoms and must be described in their own right. Electrons in a very cold metal can flow in a superconducting way, in which the electric current experiences no resistivity. Superconductivity is a quantum phenomenon in which the electrons couple in a particular way to the atoms forming the lattice structure of the metal, and it can be called an “emergent” property of the material.

Even so, these new “emergent” properties are still entirely physical and can be calculated from the physics of the elementary atoms and electrons, given sufficient understanding and computational resources. Consciousness, however, cannot be taken as an aspect of the physical behavior of even a very complex system. It is not a special type of physical process that we describe in a new way and give a name to; it is qualitatively different from a physical process of any kind. A complex system may be needed to support consciousness, but that is another matter. As we have said, “emergent” physics is still physics, and it is not possible to understand or represent the phenomenon of consciousness in purely physical terms.

There are many other theories inspired by materialism and physicalism—too many to discuss in detail here—which try to associate a “real” mind to a brain while retaining a causally closed physical universe. [8] Among these are what are known as type and token identity theories, functionalism, and supervenience theories. All suffer from the following defects. First, if the associated mind is non-physical, it is not able to affect the physical, and so it must be epiphenomenal. Second, there is still no explanation for the manifestation of a mind in a physical system, which a properly physicalist theory ought to provide. Overviews have been given by Ludwig and Chalmers, [9] and an account of many of these theories has been given by Foster. [10]

It is sometimes suggested that a sufficiently powerful computer could be conscious. This seems fanciful, but in any case even a very powerful computer would have its behavior determined solely by its physical structure and by the programs that are operating in it. If it had a consciousness, therefore, the latter could not actually affect anything and so would be epiphenomenal. Its presence would clearly be undetectable. This is certainly not a proposal of any scientific consequence.

CONSCIOUSNESS IN QUANTUM EVENTS?

In discussing the enigmatic nature of quantum events in chapter three, we mentioned that the problem is so serious that the conscious act of observation has been proposed as playing the key role in inducing the event to happen. It is time to say more about this surprising idea.

As a quantum system develops in time, the Schrödinger equation governs how this occurs and allows a well-defined wave function for the system to be calculated. This is the case even if the system is thought to consist not of one particle on its own of a particle plus a measurement apparatus. A measurement apparatus is large and complicated compared to a single quantum particle, but quantum theory still permits it to be treated in a quantum way and gives no explicit reason for not doing this. What is not included in all this is any kind of random factor; yet we believe that quantum events are random. Something that will achieve this needs to be included as a separate assumption, and the theory is unclear about how to do this. So there have been a number of different proposals, all designed to be compatible with the experimental results that are obtained in practice. Many theorists, including Einstein and Schrödinger, have been unhappy that there should be any randomness in the theory at all.

It could be said that the only stage in the measurement process where we definitely and undeniably know that a random quantum event has happened is when it is finally recorded by the conscious awareness of an observing person. We now know for certain that it has happened, and a number of prominent quantum physicists have proposed that there is something in the behavior of the quantum world such that the wave function is obliged to “collapse” when, and only when, the system is exposed to a conscious mind. The names of John von Neumann and Eugene Wigner, both preeminent quantum theorists, are especially associated with this viewpoint. Wigner argued that it is inconceivable that a conscious mind should be in an indeterminate state, and so the quantum decision is essential at this point. It might then be supposed that Schrödinger’s cat, if it is a conscious creature, can induce a quantum event and so not be in a state that is both dead and alive.

An obvious problem with this point of view is that the universe developed for long ages before conscious life appeared in it. During this time, then, the myriad of possibilities must all have just accumulated, rather like in the interpretation proposed by Hugh Everett. This cannot be disproved, but it seems philosophically cumbersome. It also invites the remarkable conclusion that conscious life must develop and appear in the universe if this is anywhere at all possible—the so-called strong anthropic principle. If the large set of alternative quantum states of the universe contain both conscious and unconscious possibilities in parallel, then the “unconscious universe” possibilities cannot perform an observation on the system; only the possibilities with consciousness can do that, and so they do. This, it seems, was Fred Hoyle’s point of view. [11] If conscious observation makes the choice happen, then it must choose an outcome in which a consciousness is present; this would be the only logical possibility. This line of thought offers an intriguing though ethically questionable possibility to test the entire hypothesis using Schrödinger’s cat experiments: only the conscious cat can make the quantum choice happen. So provided there are no external conscious onlookers until well after the action is over, the quantum observation can only be of the cat on itself, and for this the cat must always survive! It would be sufficient to anaesthetize the cat first: only the living cat could wake up to be conscious of the situation, and so it must do so. So there can be no dead cats.

These questions notwithstanding, the theorist Henry Stapp has made an interesting proposal about how an observing mind could make a physical event happen in the brain. [12] He considers that mind and matter form an integrated or at least interrelated system at the quantum level. In a class of experiments in quantum physics called the “quantum Zeno effect,” continuously repeated observations of an otherwise unstable state will always observe the state and will thereby stabilize it. The effect has been confirmed to a certain level in experiments, although these are delicate and the time needed to make the observation tends to reduce the effect in practice. Stapp suggests that constant mental concentration on one outcome of a quantum process in the brain is a kind of repeated observation and is able to stabilize a particular neural pathway so that a physical effect, such as contracting a muscle, can be achieved. [13]

None of these considerations defines the conscious mind in more basic terms, of course, but merely asserts that it is there and active. Most physicists would view this interpretation of quantum events with skepticism. What Stapp has certainly done is to make an intelligent preliminary suggestion, rightly or wrongly, on how mind and matter might conceivably interact. The present prevailing opinion, however, is that the brain is not really a quantum system and that it is very difficult to implement individual quantum processes in it, but the situation remains a matter of debate.

DUALISM AND THE POSITION OF DESCARTES

Although many aspects of mental processes have inevitably been passed over in our discussion, enough has been said to conclude that the conscious mind cannot be incorporated into the materialist paradigm. A new paradigm is needed that will include the mind. One traditional opinion has been that the human mind is an entity in some sense “residing” in the body. This view is especially associated with the seventeenth-century philosopher René Descartes and is termed dualism.

Descartes’s primary goal was to establish a method that would allow him to construct a philosophical system without any prior assumptions. [14] He began with the well-known statement, which he felt was impossible to doubt, that he thought and therefore he existed. This starting point led him to a system in which mind and matter are two distinct entities, namely, that which thinks and that which is spatially extended. The mind does not possess spatial qualities, nor does the body think. However, Descartes’s own dualism was limited. He rejected Plato’s view of a human being as a spirit that makes use of the body. The rational soul in the body is not like a pilot directing a ship, the view discused by Aristotle, [15] but is “very closely linked to [my body] and so to speak so intermingled with it that I seem to compose one whole.” [16] In reply to a critic Descartes stated, “I think I have neither proved too much in showing that mind can exist apart from the body nor too little in saying it is substantially united to the body.” [17] Here his position was not so very different from the medieval thinkers we discussed in chapter four. Unlike Aquinas, however, he insisted that the mind on its own was a “complete thing.”

The nature of the mind-body union he declined to discuss. “These are questions of which the most ignorant man might raise more in a quarter of an hour than the wisest could solve in a lifetime.” [18] Descartes refused to worry about it. All kinds of objects have very diverse physical attributes attached to them. People find no trouble with that. Why then should a mind not also be attached to a body?

Mind-body dualism is today an unfashionable viewpoint for a number of reasons. A strong distinction between mind and body has been criticized by many non-physicalists as giving the physical world too much independence, which then allows science to exclude mind and mental things entirely from its consideration while claiming all-competence. Physicalists, for their part, oppose treating the mind as anything other than an aspect of the body. Descartes identified himself personally with his mind, saying that he could imagine existing without a body but not without a mind. At the same time, he strove hard to take fully into account the laws of nature and the workings of the body, especially the brain and nervous system, and this was quite an innovation at the time.

On the physicalist side of the discussion, Dennett has expressed the view that the basic flaw in dualism is that if the mind affects the physical brain, physical energy must be supplied, which he believes a non-physical entity cannot do. [19] Further objections concern our ignorance concerning the relationship between the mind and the body. This is the “lack of a theory” objection: phenomena are more readily accepted if we think we understand what may be happening. Perhaps there are also fears about where dualism would take us, including a lingering reaction against the late nineteenth-century interest in spiritualism. Further difficulties involve how to interpret a dualistic soul when a person suffers from brain damage—for example, cases where the two halves of the brain are surgically separated or where the person suffers from severe dementia. Our personalities seem to be affected by our brains, and this is another factor to be taken into account.

None of these objections is decisive, however. Physicists, who after all have no hesitation in proposing abstract and unproven ideas about elementary particles and cosmology, are in no strong position to object to unconventional ideas in other areas. Historically, physics has had no problems with proposing new forms of energy when necessary, and if a new kind of mental or spiritual energy were shown to be acting, then this would have to be accepted. In fact, Stapp’s idea that the mind can reinforce something physical that could occur anyway, by stabilizing a chosen outcome of a quantum neural process, does not obviously lead to any non-conservation of energy.

It may be interesting to note why energy and momentum are conserved in particle processes in physics. If two particles interact with each other, and they or others emerge from the interaction, then all the particles are represented by quantum waves. The interaction does not take place at a mathematical point in space but over an indeterminate finite volume of space; in other words, we cannot specify with exactitude where it occurs. Likewise, we cannot specify with exactitude when it occurs in time. When everything is averaged over a range of space and time values, the incoming and outgoing waves will “fit together” only if momentum and energy are conserved in the interaction—a consequence of the geometry of the situation. In a completely different kind of situation, the behavior of energy might not be easy to describe without a very clear conceptual grasp of what is happening.

In proposing his law of gravity, Newton realized that it implied an action between two objects that pulled on each other gravitationally even if they were very far apart. This seemed very strange, even magical, to Newton’s colleagues, but he declared that he was putting forward no hypotheses about it, just simply stating it as a practical assumption. In any new field, situations arise where further understanding has to await further developments. What happens to the mind when we are asleep? We may suppose that a subconscious mental entity exists that experiences consciousness only when conditions are right, that is, when the brain lets us be awake. An open attitude is needed about what is not understood; there are certainly questions in these areas that may not have an easy answer.

Some very important issues concern exactly what aspects of the mind should be considered as intrinsic to the mind, when many features of a human personality are strongly conditioned by the brain. The question of whether the mind and brain should be considered as two or one may be subsidiary here; two closely coupled things may be considered as one whole for many purposes, while one object with two sets of properties may sometimes be conveniently considered as two. Is a hydrogen atom two objects—namely, a proton and an electron—or is it just one entity, an atom?

OTHER POSSIBILITIES

Another set of options regarding consciousness is known as neutral monism, which is a view that reality is both physical and mental, and can manifest both aspects of its nature. [20] The difficulty is to define with any degree of clarity what is going on, and the various philosophers who have held views along these lines have tended to hold different opinions; probably many of them would not even have used the title “neutral monism.” This position is more a starting point for individual philosophies than a well-defined philosophy in itself. It is not possible here to present the various viewpoints of this type that have been put forward, but it is important to stress that these are not physicalist philosophies, and they affirm a mental reality in nature whatever its mode of existence may be. Aquinas would have counted as a monist, but in addition he believed that the human soul survives death. [21]

Another viewpoint is panpsychism, which states that a universal mind is everywhere and in everything. This view can merge with pantheism, which identifies the universe with God or states that the universe is in a literal sense a part of God. An opposite position is deism, which states that God originally created the universe but hardly interacts with it at all. The seventeenth-century philosopher Baruch Spinoza was a pantheist with controversial theological views, since for him God was a universal presence but without any personal relationship to us. Einstein considered his views to be close to those of Spinoza. There have been many various forms of panpsychism, and one of its problems is to decide whether or not all things, even electrons, are at some level conscious. There is also the question of whether mind is a kind of “universal presence” or whether it is confined only to living beings. Along with this is the task of distinguishing between mind in general and individual minds. As we saw earlier, the astrophysicist Arthur Eddington, who was a Quaker, expressed views of a panpsychist kind and had tendencies toward idealism. Idealism is an extreme form of panpsychism; it is the polar opposite of materialist physicalism and asserts that everything is primarily mental.

Perhaps a return to a more Aristotelian approach, but in the quantum context, offers a suitable starting point. Form and matter are the key concepts, and a particle at any time consists of quantum fields whose “form” is presented by the wave function of the particle. The mathematics of the laws of physics provides a further pattern or form, at a higher level. All this implies that there is a fundamental basis of “ideas” in nature, partly in a way that Eddington might have appreciated. We are not yet talking about consciousness, however, and this is something that no purely physics-based philosophy can do. With regard to the action of the will, perhaps the best that quantum physics can offer is a way of thinking in which conscious minds can somehow formulate thought patterns that can affect wave functions in the brain. Or perhaps Stapp’s proposal might prove to be along the right lines, since it offers a rationale for consciousness and quantum events. But these are very preliminary suggestions. The conclusion at present, then, is a need for an open mind to something beyond physics, and physicalism does not constitute an open mind. No mind is more closed than one that seeks to deny its own existence.

FURTHER IMPLICATIONS

It may not be profitable to argue whether the conscious mind is a separate entity from the brain, but interleaved with it, or one part of a combined brain-mind object. A better question is whether “mind” is a universal substratum that is unconscious except where it interacts with a brain, in which consciousness appears, or whether there is only a large collection of individual mind-brain systems. If the former, then the collective subconscious proposed by the psychologist Carl Jung should be brought into the discussion. [22] According to Jung, all human minds have a collective background that supplies thematic material to our thinking in the form of “archetypes.” The archetypes are many (Jung gave them names), and they energize our conscious thoughts, where they are instantiated in specific ways. Jung justified this proposal by pointing out similarities in the way people think in various cultures around the world. The call sign of an archetypal input to our thinking is when unexpected energy or influence seems to be present in a particular type of thought. There is unfortunately no space here for further discussion of this potentially far-reaching subject.

One of Aquinas’s arguments for the existence of God was based on the proposal that anything that exists in our world is not likely to be the greatest of its type. Things find their perfection in God. At the physical level, then, the laws of nature are an aspect of the mind of God. Consciousness is something to which this argument can also be applied. We are surely unlikely to be the most conscious beings in existence, and even the possibility of conscious beings on other planets does not really resolve the matter. The existence of consciousness as a specific and identifiable characteristic in nature implies a need for a greater source and therefore points toward consciousness of some kind as an attribute of God. This argument cannot be made more precise without a fuller understanding of mind and consciousness, but the alternative is to suppose that our own conscious existence could in principle be supreme in the universe. This seems a highly presumptuous claim.

ABSTRACT THOUGHT

The biologist J. B. S. Haldane wrote that mind cannot be a mere aspect of matter: “For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. . . . And hence I have no reason for supposing my brain to be composed of atoms.” [23] This argument was developed by C. S. Lewis in his book Miracles [24] and raises a valid question. Have we here a simple knockdown argument against both physicalism and its impotent cousin, epiphenomenalism?

It is clearly evolutionarily advantageous for living creatures to have practical intelligence, whether they have conscious minds or not. This means an ability to construct solutions to problems and respond to challenging situations, since this helps creatures to survive. Some animals, such as foxes and sheepdogs, have remarkable practical intelligence. Where our understanding of the evolutionary process falters is in justifying the existence and validity of what may be called “abstract” thought. Many philosophical ideas have been set out, for example, none having an obvious connection with human survival value. The same can be said about advanced mathematics. Secular evolutionists often try to explain religious beliefs on grounds of social usefulness and survival value, but these factors have little connection with the truth of the beliefs, and so the implication is that evolved ways of thinking are not at all necessarily true! Lewis argued that physicalism undermines the validity of logical argument. [25] Logic is essential for abstract thought and has a metaphysical basis of its own; physical processes that are merely causal cannot reliably incorporate it. If abstract thought is based solely on physical causation or even on usefulness, its truth-giving reliability is quite uncertain.

The situation is perhaps a little more subtle than Lewis stated it. In nature we may point to the cunning fox, who can apparently think correctly much of the time. We now face several options. Perhaps the fox has a mind able to think abstractly at some level, and therefore foxes are not governed by physicalism. In that case the argument is concluded. Otherwise there are two possibilities, of which the first is that the fox is not really using logic at all but just employs trained and programmed physical brain operations that work, because its brain evolved this way. We humans in that case are not like the fox but differ in an important way, because our minds can indeed use higher types of abstract logic, and so Lewis is again right: in us there exists something more than physical processes.

The other possibility is that the fox is indeed using logic like ours correctly in a purely practical situation. He knows in advance that if he pushes on the henhouse door, then the door may open, logic that has been learned by training as a result of experience in pushing things. These perfectly valid logical abilities have physically evolved in the vulpine brain, and we have evolved similar abilities too. What then is different for us? It must be in the types of concepts on which we employ the logic. It is not abstract logic that we are using but abstract concepts—universals, for example. We possess the ability to think not just about the logic of specific situations but about logic in general. Evolution has no obvious way to provide us with this kind of thing, because a physical mechanism (such as a physicalist brain) can only use trained methods that concern specific tasks, namely those on which the mechanism was trained. In this case, Lewis’s argument is not quite right as he states it, but his conclusion still holds, because there is no reason to suppose that systems of atoms and molecules can harbor abstract concepts that do not have usefulness. [26]

PERSONAL EXISTENCE

We are not merely information processors who are conscious but also personal beings, which introduces further non-physical factors that shape our existence. Beauty and value are classic examples. It’s hard to define beauty—one just recognizes it. Beauty can be purely subjective or conventional; for example, facial features that are considered beautiful by those of one ethnic group may be seen as unattractive by others. This, we must immediately add, is different from “beauty of character.” Personal characteristics such as honesty, kindness, warmth and love are considered good and valuable at the relational level, and these perceptions seem to be much more universal over the whole human race.

The kind of beauty that we perceive to be present in nature is another matter. This beauty may refer to the phenomena of nature or even to the theoretical formulas that are perceived to be embedded in nature. What is it that we respond to? What we perceive as beauty in natural phenomena appears to be a combination of variation with regularity, of surprise with a sense of inevitability and sometimes an amazement that the regularities can be permanently retained. Another factor that attracts us is the formation of complex systems that have a coherent and unified structure. In the mathematics of physical theories, beauty is found when a simple set of equations can describe an amazing number of things. Equations have simple solutions with profound consequences. The equations are actually solvable. A set of several equations can have combined solutions that indicate unexpected new things. The algebra amazingly happens to fit together.

Unfortunately, the mathematics of much of modern physics is too complex to be appreciated except by specialists. Einstein remarked that if his equations of general relativity did not apply to the real world, he would be “sorry for the Creator.” In his case, he started with a simple physical idea—that gravitational forces, as we perceive them, arise from space-time curvature induced by the presence of matter in space. Although a sophisticated idea, it can be expressed conceptually in a single sentence. The necessary mathematics is extremely complex, but at the end there is just one simplest way to do it, resulting in a single equation known as “Einstein’s equation,” which represents with exactness the basic idea of the theory. Is this beautiful? It is certainly considered elegant. Analogous stories can be told in other areas of theoretical physics.

The miracle seems to be that the universe, at least up to the limited point we have reached so far, is both comprehensible and comprehended. Since there is no clear evolutionary reason for our ability to understand so much about a universe that is so complex and subtle, we are amazed. The combination of regularity and surprise is also often part of what we identify as beauty. There is an irresistible conclusion that we are attuned to the universe in a deep way, which makes sense only if we have been given a gift of being attuned to a Creative Intelligence.

THE MORAL FACTOR

Beauty comes to us with a sense of intrinsic value, and this introduces a new element to the discussion. Two main factors are present: the evaluation of value in a given human situation, whether something is good or bad, and the question of personal moral obligation. It is beyond our present scope to analyze the nature of value in depth here, but this is not necessary. It is sufficient to say first of all that value is not a term that has any meaning in the language of physics or science in general, although scientists may attach personal value to the work they do. Value is part of our human experience and discourse. So either it is a matter of personal or social preference only, or else it has a supra-personal status, which means it is something objective and absolute. If it is the latter, which most people normally assume, then it is most naturally associated with a God who possesses personal attributes. Goodness is to do with God.

For us to take value seriously, it must make some kind of moral demands on us. Apart from a small minority who have no moral conscience, nearly all of us are aware of a sense of moral obligation that seeks to lead us into behaving in certain ways. We ought to do this, we feel, and we ought not to do that. What is the nature of this impulse? Here the physicalist has very great difficulties.

If our human nature consisted entirely of our physical nature, then the sense of moral obligation would be simply a physical phenomenon that occurs in our brains. In fact, a variety of impulses occur in our brains and tend to direct our actions. These include feelings of hunger and thirst, anger, sexual drives, care toward children and various others. They can also include effects of social pressure. Since it is an impulse that tends to impel us in some way, the sense of moral obligation must be just another one of these, if a physical phenomenon is all that it is, because there is nothing else it could be. As human beings, we have to manage all these impulses, sometimes going along with them, sometimes modifying them, sometimes resisting them.

But moral obligation, as we actually perceive it to be, is different. It is something whose intrinsic nature is more than just that of a physical impulse to be managed. It affects us personally and, once correctly identified, does not allow itself to be “managed” in the same way as the others. It operates on a different and higher level than the basic physical impulses and it directs their management—when or how we decide to exercise them. It is associated with values and with a sense that these values are objective and make objective claims on us. It also directs how we make choices of action.

If the physical is all that there is, then there really is no such thing as moral obligation as we understand it. It is illusory. Only lower-level impulses exist. In that case one might as well be honest about the matter, and treat “morality” as no more than the means by which we manage various personal impulses in a convenient way and manage our relationships with each other. It is just a type of pragmatism. In the world of business, for example, business managers of this kind will treat their employees and customers adequately well for the sake of good practice and good business. The goal will be to maximize profit and keep within the law, and employees will be instructed to think along these lines. A genuine sense of moral obligation would act on a higher plane than this, of course. It is absent in the kind of case just portrayed, and its presence would make a difference. Without it, a true physicalist, acting on a truly rational basis, would find it logical to be amoral while pretending not to be for the sake of appearances.

Pragmatism does not suffice as a replacement for moral value: it has to do with considerations such as convenience, maximizing of pleasure, avoiding trouble, manipulating others and getting what we want. It can be somewhat Machiavellian. These things are very different from what we inwardly perceive as the true nature of the moral factor that is part of our personal existence and condition. The physicalist error is based on a failure to realize that the moral factor acts through our mental nature and is a distinctive part of it. For this reason alone, moral obligation and moral values should not be considered physical in origin.

Identifying this factor more clearly is not easy. One approach might be to take the beauty that is found in nature, identify it with goodness, and try to extrapolate from this to a notion of absolute value that would cover human personal situations too. But this does not take proper account of the fact that moral issues are concerned with relationships. Historically, an awareness of moral duty seems to come from a small number of different sources: the conventions of a society, the edicts of a king and the reception of God’s will though religious leaders such as Moses or Jesus.

During the Classical period it became clear that moral conventions in different societies cannot easily be discussed without a concept of absolute moral values, since otherwise people simply talk past each other or fight for dominance. This concept requires a transcendent basis of some kind in order to be defined even in principle. The Greek philosophers began to discuss goodness as an absolute, because otherwise they would have been confined to comparing the customs of Athens, Thebes and other places, or evaluating the conflicting wishes attributed to their different deities. In today’s society, those who are unwilling to anchor moral values or standards in God, a Platonic realm or some other transcendent source often end up taking the issues into politics, relying on the common voice of their party and their friends to convince them that an absolute standard exists, and allowing the popular vote to decide which version of social morality should be actually enforced. But this in no way solves the real question, and there are many who take the more cynical line that morality is what the individual can get away with. A purely personal ethic will not suffice, since it is nonbinding and can be ignored whenever the person wishes.

Clearly, we encounter a deep problem here. If an absolute standard for moral values exists, how do we establish what it is? But if it does not, then in the end anything goes. As Dostoyevsky wrote, “If there is no God, all things are permitted.” Without a genuine transcendent origin for moral values, a pragmatic social attitude may be the best that can be achieved, but this policy has several defects. It has no real place for ideals; the pragmatic attitudes still have to be evaluated; selfish people will flout convention if they can. Nobody will really believe it. This is a very serious situation. Of course, an unbeliever can be “moral.” Indeed, moral in any way one likes! But if you choose not to be moral and can get away with it, who has any objective grounds to argue with that?

If human beings possess a mental and personal nature, then we are in this respect different in kind from physical systems such as computers. It then follows that non-physical principles are needed to deal with the questions that arise, particulary in the area of values and moral obligation. Purely physical systems are disconnected from such matters, and computers just do what their programs tell them. A lack of an absolute in moral values may result in moral ambiguity that can have disastrous consequences both for individuals and societies. For this reason alone it makes sense, if one is in any doubt, to take seriously the presence of a Transcendent, which in our tradition means God.

TWELVE

MYSTERY AND IGNORANCE

Through the earlier chapters, we showed that the sciences of physics and astronomy can give clear pointers toward God as Creator and Designer of the universe. In chapter ten, we asked whether an ultimate explanation for the universe could be scientific and concluded that this is not to be expected, even in principle. We may believe in an ultimate reason for existence, and we may identify this with God, but God will be in many respects beyond our understanding. In chapter eleven, we saw that there are important aspects of human existence that demand to be considered in ways that go beyond physical science. Physics has its limits. We now take this further and examine the limitations of the intellect, a line of thought that can give further openings toward the Transcendent.

When faced with something that is not amenable to intellectual knowledge or is not expressible in words, we are dealing with an instance of what will here be referred to as mystery. This is to be contrasted with ignorance, which is an absence of knowledge where knowledge can in principle be obtained. The methods of science, for example, are well able to reduce and sometimes eliminate ignorance, but mystery can remain when all the scientific facts are known. There are questions that cannot be addressed by scientific means or even by means of the intellect more generally. As we will see, confusion between mystery and ignorance may be a significant factor contributing to the perceived opposition between religion and science. The popular usage of these two words tends not to make much distinction between them; in daily language, mystery and ignorance mean roughly the same thing. Here I assign different meanings, in order to point to some important areas of how we interact with the universe around us and with God.

Mystery can carry religious connotations, but this is by no means always the case. Our entire lives are in fact permeated in mystery, but this does not devalue the role of rationality. These will be the themes of the present chapter.

STRONG MYSTERY

What may be called a “religious impulse” is seemingly built into human nature. It comes as a yearning for something more than the immediate, a seeking for something “beyond.” The official atheism of the communist states failed to eradicate it in their citizens. It shows up in diverse ways—sometimes arriving by surprise, sometimes willingly accepted, sometimes resisted and suppressed. It is found more strongly in less developed societies than in the more developed, but it is not a primitive impulse in the manner of a physical hunger or other bodily urge. It can be sensed as an element missing from ordinary life, and it resembles an aspiration more than an appetite.

Albert Einstein did not hold conventional religious views, but he still regarded himself in his own way as religious and certainly not as an atheist. As a basic expression of his beliefs, he wrote,

The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. . . . It was the experience of mystery—even if mixed with fear—that engendered religion. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms—it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man. [1]

This is an important example of what we are referring to here as mystery, but declarations of this kind may elicit many reactions. One is to view them as expressing a genuine and authentic spiritual awareness. Another is to consider them as fine and noble sentiments, hinting at a religious statement, but inadequate as they stand. At the other extreme, such declarations may be regarded as purely subjective emotions, lacking in any real significance at all—but this does not seem to do justice to the situation. Even many who would call themselves agnostics or atheists can experience feelings akin to those quoted above, which relate to an intuition of something greater than oneself and extending beyond our own rational understanding. They generate a sense of humility. I will call this a perception of strong mystery, but it could equally well be called “transcendent mystery.”

There is no shortage of statements by scientists and others in which this type of experience is expressed, in varying degrees of strength. They come from religious believers and unbelievers. The astronomer Carl Sagan wrote, “Every aspect of Nature reveals a deep mystery and touches our sense of wonder and awe.” [2] The physicist Marcelo Gleiser put it as follows: “We look at the cosmos with a mixed sense of awe and wonder, of terror and devotion. And we want to know. How can something come from nothing? What is the origin of all things? Can order emerge by itself, without a guiding hand? Is beauty a mere accident of Nature, or is there a deeper meaning to it? Why do we crave beauty, as junkies a drug?” [3] These are religiously oriented questions, and gazing up at the stars at night seems to be a typical way to open the door to them. At its most intense, a sense of strong mystery requires language as uncompromising as that of Einstein. Here is something that verges on a profound spiritual experience, pushing words beyond their limits.

Other encounters with mystery make less forceful assertions. A lesser type of awe might be aroused by an experience of something almost immeasurably bigger than the human observer, but physically rather than in a spiritual sense. At a lower level, it could be a strong sense of amazement that there is so much we still do not know. In this kind of transition, we can trace even with strong mystery a gradual movement between our two main topics here of mystery and ignorance. The feelings associated with the two qualities can merge into each other, with a potential for confusion between them.

EVERYDAY MYSTERY

Mystery, we have said, is not a mere absence of intellectual knowledge. It refers to whatever the rational intellect is unsuited to deal with, and when we have a direct perceptual awareness of such a quality, this awareness is not of a rational kind. We do not need to go to the cosmos for mystery, however, because it is to be found all around us.

What I will term everyday mystery relates to questions of ordinary existence and personal experience and even extends into the scientific realm. Let us try to ask what something “is.” One approach is by a method of subdivision. We can ask a question such as “What is water?” and be told that water consists of oxygen and hydrogen atoms. We can then ask what the atoms are and obtain an answer in terms of elementary particles. But unless the subdivision goes on forever, which would be both unexpected and unprovable, we will eventually arrive at some kind of fundamental objects, which at present might be quarks, gluons and electrons, or quantum fields. What then can we say that the most fundamental things are? No rational reply is available. What these things are—and hence what anything is—must be assigned to the category of mystery.

Theoretical physicists sometimes give a certain type of answer to this class of question that in the end will not do. Suppose, say, that the most elementary kinds of particles are claimed to be objects with certain quantum structures. We would naturally like to ask what these quantum objects are. A likely reply from a theorist would be to present the mathematical properties of the postulated entities. We will be politely told, “The fundamental physical entity is an object whose mathematics is given by the following equations, which I will write on the board for you. That is what it is!” Now it is true, let us accept, that the physical objects have these mathematical properties. It may also be that this is all we can say about them. But if the claim is made that the mathematics tells us what a particle is, then an error is made in confusing the object’s formal properties with the object as such. Even mathematical properties do not constitute what something is.

Here I have been recounting the kind of argument used two centuries ago by the philosopher Immanuel Kant in his analysis of the limitations of human reason. [4] Kant concluded that the thing-in-itself, whatever kind of thing it may be, remains always unknowable by the human intellect. We can know a thing’s properties and attributes, but not its “is-ness.” The properties can be observed and rendered within our minds, but the is-ness cannot. It remains outside, and we must simply infer it and believe in it. The intellect is not able to deal with that. It therefore falls into the kind of category I here refer to as “mystery.” Anything and everything around us, given that it is, possesses this type of mystery of existence, which can be regarded as a prime example of everyday mystery.

Definitions of terms establish conceptual relationships between ideas, but these concepts cannot address the final “is” question. A set of definitions always requires a starting point that must simply be accepted. What is an electric field? A property of a point in space, such that electric charges placed there experience a force. What then are electric charges? At some point we must just accept the basic phenomenon, without having an answer to what it is. Practical definitions can of course be made. An electron, for example, may be uniquely defined as a negatively charged particle with a certain value of its mass. Given this, we can in principle recognize any electron we come across. But definitions are still only about properties, and they do not address the unanswerable accompanying question regarding existence.

We will meet other examples of everyday mystery. Overall, one might say that strong mystery tends to point beyond our rational understandings, while everyday mystery lies in and around them, but the two categories are not completely separate. Perhaps many would prefer to avoid referring to anything as elusive as mystery and would rather drop matters when our understanding stops. For others, though, this would be deeply unsatisfying. The absence of one type of answer to a question does not preclude the possibility of other, different ways of dealing with it, as we shall see.

MYSTERY AND RATIONALISM

Rationality is a mode of thinking in which we form logical structures between ideas, drawing conclusions according to this logic. This process is central to science, where it will be valid if there is a consonance between the world and the ideas we form about it. Kant had doubts about taking this assumption too far. He proposed that we can think only in certain ways, and that these comprise a kind of conceptual filter that enables us to have correct thoughts only about those aspects of the world that match our own mental capabilities. Bearing in mind that Kant wrote before modern science had become fully developed, we might ask how his proposal could apply to science. It would say that we are able to think with scientific rationality only about certain things: chiefly, those that can be observed and measured experimentally and whose behavior is described by humanly understandable concepts and laws. Other aspects of reality, if they exist, would lie outside the capability of human science.

The suggestion that human rationality might have limitations can meet resistance. Just as there is a philosophy of physicalism that says that everything is at heart physics, and a closely related attitude of scientism that says that everything conforms to human science, so there is an ideology of rationalism that in its strictest form asserts that all valid thinking about anything should be rational. All of us have a rational element in our makeup, being by nature rational creatures, but those who would call themselves rationalists profess to take this to a very high level.

Rationalism is a word whose meaning has changed over time. In the eighteenth century, it was a philosophy that was held in opposition to empiricism. Rationalism asserted a fundamental reliance on ideas, held to be knowable in a clear and direct way, while empiricism claimed that knowledge comes solely from direct observation of phenomena in the world around us. The later philosophy of positivism said much the same as empiricism but was somewhat less open-minded. An eighteenth-century empiricist might have allowed that unobservable things could exist but would have denied that there was any way to know about them. Twentieth-century positivists attempted to deny that there was even any meaning in speaking about something that is unobservable. Unobservable things were not merely unknowable but were conceptually invalid—they could therefore have no reality even in principle. This implies a radical denial of many kinds of mystery.

Positivism has now largely lost its appeal. The realization grew that we must make sense of observations, because otherwise they are of no use, and this requires that we deploy assumptions and beliefs that are not themselves observable things but are in some sense basic and prior ideas. Raw observations, in short, do not provide their own interpretation. We must supply it, and to do this we have no choice but to be old-fashioned rationalists to some degree. Einstein was at one stage a positivist but later rejected the position for reasons of this kind. [5]

The disagreement between rationalists and empiricists was an important theme in eighteenth-century thought, and some rationalists went so far as to assert that only mental ideas are real. That would certainly seem a hard position for a scientist to take, despite Eddington’s inclinations in that direction. Kant argued against both empiricism and rationalism as absolute statements by saying that while we can think rationally about observed features of things, the unobservable thing-in-itself has existence but remains unknown.

In its modern usage, rationalism has come to stand in opposition not to empiricism but rather to any reliance on intuition, tradition, faith, authority or mystery. In particular, the new rationalism tends to be against religion, which normally contains elements of all these things. The mathematical philosopher Bertrand Russell was prominent in promoting this kind of rationalism in the first half of the twentieth century. He declared, “I am, in this age when there are a great many appeals to unreason, an unrepentant Rationalist. I have been a Rationalist ever since I can remember, and I do not propose to cease to be so whatever appeals to unreason may be made.” [6] Russell proceeded to define rationalism as the attitude of “not believing a proposition or causing others to believe it unless there is at least some reason for supposing it to be true.” This he felt was a “modest proposition.” The rational habit of mind was a rare one. However, in the short piece cited here, titled Why I Am a Rationalist, Russell provided no clear reason for his rationalist position other than a distaste for “unreason.” He apparently felt that his viewpoint was self-evident.

The obvious problem with this definition of rationalism is that in practice almost all of us are able to find reasons of some kind for the things we believe. A more typical definition of modern rationalism may be found in the online Catholic Encyclopedia: “Rationalism, in the broader, popular meaning of the term, is used to designate any mode of thought in which human reason holds the place of supreme criterion of truth.” [7] This is much stronger than Russell’s proposal, and in practice he seems to have followed something closer to this statement than to his own original. [8] A perfect rationalist would hold human reason to be the sole criterion of truth. But no one is a perfect rationalist in actual practice, and Russell portrayed perfect rationalism as a distant prospect rather than a present human achievement. In practice, those who claim to be rationalists tend to display a diversity of viewpoints, with rationalism often employed as a flag-waving word to advertise a person’s own brand of skeptical philosophy.

Between Russell’s earlier definition and the strongest later definitions, an important line can be crossed between rationalism as an epistemological statement and rationalism as an ontological statement. That is, are proponents claiming that rationality is the only valid mode of knowledge, or are they saying that the rationally knowable is all that can exist? If the former, one would have to give up attempts to know further about what is here termed mystery. If the latter, the very existence of anything in the mystery category would be denied. Individual rationalists need to know where they stand on this point. Since physics claims to be both knowable and rational, physicalism can be quite a strong form of rationalism.

Rationalism has a basic difficulty, however. To say “I believe in rationality because it is rational to do so” is a circular justification and thus invalid by rational criteria. Rationality cannot in the end rest on a foundation of rationality. It must rest either on something different or on nothing. If the former, then something important other than rationality is going on. If the latter, how is rationality justified? Note that it is not good enough to say that you believe in rationality “because it works.” That would mean that in the end you are a pragmatist rather than a rationalist!

Other people may say that other things than rationalism work for them; for example, there are those who might rely more on personal intuitions than on rationality. Few people in practice seem to be “pragmatic rationalists.” Rationality is normally taken to be valid prior to its practical application—for example, in activities such as science. We rely on an intuitive perception of the authenticity of rationality—an everyday mystery. Rationalism as an ideology therefore amounts to a belief system like others, and the existence of “perfect rationalism” is an illusion.

Mystery is not opposed to reason and should not be despised as “unreason.” It extends beyond and around human reason. In this area, a crucial difference of emotional attitude can be found between two classes of people: those for whom a recognition of mystery is quite acceptable, even attractive, and those for whom the entire notion of mystery is repellent. Opponents of mystery, possibly tagging it as “unreason,” often assert a strongly rationalistic stance with vociferous opposition to religion, desiring to co-opt science for their side. Under the mistaken impression that science opposes mystery, a number of them become scientists. But the example of Einstein shows without any doubt that an acceptance of mystery does no harm to the practice of science and is not in opposition to it.

MYSTERY AND SCIENCE

The psychologist Abraham Maslow suggested that a certain kind of “narrowed” scientific attitude, which he termed “desacralizing,” arises essentially out of fear and emotional fragility: “Orthodox desacralizing science has for various reasons tried to purge itself of these transcendent experiences. . . . This desacralization can be used as a defense against being flooded by emotion, especially the emotions of humility, reverence, wonder, and awe.” [9] But many good scientists, as Maslow goes on to say, do not show this trait. The qualities he lists are those we have associated with a sense of strong mystery, and it is clear that they are in conflict with the attitudes of narrow rationalism, not with rationality itself. The fact that mystery is not rational knowledge should not be held against it.

Another noteworthy feature of science, which we have mentioned already, is that it tends to reveal a universe possessing considerable beauty. Sometimes this beauty is of a rather esoteric kind—perhaps it may be appreciated only by mathematicians—but then, a Bach fugue also makes its own specialist demands. The fact of beauty seems to be something that defies rational analysis, another example of mystery. Not everyone seems to feel these emotions. Richard Dawkins supportively quotes an opinion that “most scientists are bored by what they have already discovered. It is ignorance that drives them on” [10]—a surprising remark from one who is so clearly enthusiastic about what has been discovered in the field of genetics. We shall find some very different attitudes in the following paragraphs.

Even those who are irreligious in the usual sense can sometimes obtain a rudimentary religious outlook from feelings of wonder evoked by science. [11] The physicist Richard Feynman was responsible for developing much of the basic theory of elementary particles. In his autobiography he related his reasons for wanting art lessons, in words that are worth quoting at length:

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It’s difficult to describe because it’s an emotion. It’s analogous to the feeling one has in religion that has to do with a god that controls the whole universe: there’s a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run “behind the scenes” by the same organization, the same physical laws. It’s an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It’s a feeling of awe—of scientific awe—which I felt could be communicated through drawing to someone who had also had this emotion. It would remind him, for a moment, of this feeling about the glories of the universe. [12]

Here is a religiously skeptical scientist’s very intuitive interpretation of what we have called mystery, expressed in a certain type of beauty. The rationality and the intellectual understanding are both there but are overlaid with a different quality, one that is “difficult to describe” and expressed by Feynman as an emotion. Far from being anti-rational, this quality is actually aided by the presence of scientific rationality.

Einstein wrote in a similar way:

The individual feels the nothingness of human desires and aims and the sublimity and marvellous order which reveal themselves both in nature and the world of thought. . . .

[The scientist’s] religious feeling takes the form of a rapturous amazement of the harmony of natural law, which reveals an intelligence of such superiority that compared with it all the systematic thinking and acting of human beings is an utterly insignificant reflection. [13]

The error of equating mystery with scientific ignorance is made completely evident here. It is fundamentally mistaken to say that mystery begins where rational knowledge stops. The biologist E. O. Wilson has written in a slightly more complex way that seems to combine wonder, knowledge, mystery and possibly ignorance: “Our sense of wonder grows exponentially: the greater the knowledge, the deeper the mystery and the more we seek knowledge to create new mystery.” [14] Overall, the sense of mystery operates within science by contemplating what we know and realizing the wonder surrounding this and the wonder of the apparent fact that there is so much beyond. Scientific knowledge itself becomes a vehicle for a sense of mystery.

MYSTERY AND IGNORANCE IN THE SEARCH FOR GOD

It should be clear by now that mystery is not to be identified with obscurantism but is something positive. Moreover, the frequent association of mystery with some kind of religious dimension cannot be honestly ignored. At the same time, science is often held to be opposed to all this. Let us explore the situation further.

There is a long-standing tendency in Western society since the nineteenth century to keep the secular and religious sides of life in separate compartments—a habit that is obviously inconsistent with a faith that is present in all of a person’s life. A common lifestyle has consisted of one day a week with God and six days without. This pattern inevitably leads to a view of the world as something that is on the whole self-subsistent, running with its own set of rules, namely, the laws of nature and of human nature—at least for six days a week.

In this way a division between the secular and the religious is easily established. People commonly perceive a rational, scientific world in which we live most of the time, together with a separate religious domain that is entered occasionally and where a different set of rules applies. This domain may even be regarded as spatially located—in a church building, for example. Meanwhile, scientific knowledge has become secularized.

From such a perspective, it would seem natural to say that religion begins where science leaves off. Existence has two sides, and science denotes the governing principle of the secular side. Those who take physicalism as their philosophy will at this point make plain their view that physical science never leaves off, and so religion should never begin. In any case, science has acquired the habit of expanding its domain. Once, comets and meteorites were seen as having direct supernatural causes, and the planets were associated with deities. Over the centuries, these phenomena have become well understood within physics and astronomy, and similar examples could be cited from the other sciences. In this way, the area of human existence once seen as a reserve of religion has had a continued tendency to shrink—like a nature park encroached by industrial zones. As science advances, religion retreats, it has appeared. Thus, six days a week without God has easily turned into seven.

In this type of thinking, we have what Charles Coulson, in a famous phrase, called the “God of the gaps.” [15] Excluding God from weekdays and from the world known by science, we locate him in regions where current scientific knowledge stops: that is to say, the “gaps.” Here we allow God to exist. But the gaps tend to shrink with time. One of the traditional ways of arguing against religion is centered on dismissing the God of the gaps. [16]

Clearly, such attitudes have always lacked logic. God has to be God of all existence and not just where science has gaps. Why should there be the irrational feeling that God is seen mainly here? God is surely enwrapped in mystery, and in directing one’s attention toward God, the acceptance of mystery is a prerequisite. However, if we fail to differentiate between mystery and ignorance, then, confusing the two, we will link them together. We will then associate the gaps in our knowledge not just with ignorance but also with mystery. In this way the skeptic, noting that the task of science is to reduce ignorance, takes science as equally reducing mystery. Science then comes to be thought of as acting against religious thought and belief.

A variant of this type of argument is more rationalistic. A true-believing rationalist will hold that everything of importance is at least in principle rationally knowable. So-called mystery is thus just another kind of ignorance or else illusory. God seems to be both invisible and unknowable and is therefore by this definition probably illusory. To gain knowledge about something removes it from the realm of darkness and ignorance into that of light and rationality. Science, in advancing, provides knowledge and takes away ignorance. This process will eventually leave no place for God to hide. [17]

An obvious objection here is that God is surely able to create things, such as a universe, that we can know about. The progress of science thus has no logical bearing on God’s existence. A further reply from believers is that God is by no means wholly unknown but has revealed to us aspects of his nature over the ages, as recorded in the Scriptures. So the presupposition of God’s total unknowability is false; in fact, Saint Paul taught that in the next life we will have a full knowledge of God (1 Cor 13:12). At the same time, the world of nature, as God’s handiwork, may also be able to suggest things about its Author. Galileo, among others, considered this world to be God’s “second book.” [18] In this volume we have also sought to indicate some characteristics of God seen from the standpoint of nature.

Mystery, meanwhile, does not know gaps. It is omnipresent. Our discussion has shown scientists referring to mystery, awe and wonder in areas where rational scientific knowledge is certainly present too, as well as where it may be absent. In other words, the rational intellect can perfectly well have a coexistence and indeed a partnership with a sense of mystery. The universe of laws can be also a universe of mystery. The rationalist argument evaporates.

A further remark: although in science much is often made of the diminishing gaps, another common theme states that the more questions science answers, the more unknown territory appears to lie beyond. While old gaps are filled, others open up. Some—and biologist E. O. Wilson may be in this category—enjoy the sense of mystery by associating it with the new scientific gaps, though in a nonreligious way. My comment would be that this is one of the weaker forms of strong mystery discussed earlier, and that it leads to confusion unless the distinction between ignorance and mystery is firmly made.

In all this, it should not be automatically assumed that mystery in nature is in itself the mystery of God. Pantheists might say so, but others would see nature instead as iconic with regard to God: it opens up the mind and heart into God’s direction. In either case, an appreciation of nature has the potential to expand our spiritual awareness and so perhaps act as a means toward God. This would be an important aspect of nature as God’s second book, and it is perhaps the true sense in which nature may be sacralized.

THE ROMANTICS

A contrary opinion on what we have been saying is typified by the views of romantic poets such as Samuel Taylor Coleridge, William Wordsworth and William Blake. For these writers, mystery and knowledge stand in mutual practical opposition, and it is knowledge that is problematic. Whenever we encounter an area of life that is new and unfamiliar to us, we begin in a state of natural ignorance. In this condition it is not possible to employ the intellect to evaluate what lies before us: a learning process is first required. Only a non-rational kind of awareness is available, and it seems to allow a relatively easy entry to wonder and awe. Later, alas, knowledge and experience supplant the original mystery-tinged mode of awareness. Ignorance and mystery thus disappear together, and so our knowledge comes at a heavy spiritual price. The romantic poets believed that young children are in this sense more spiritually privileged than knowledge-degraded adults. [19]

But if knowledge in the sciences can be accompanied by a sense of mystery, as we have seen, this cannot be the whole story. The romantics were to a serious degree mistaken. The problem evidently does not lie in knowledge itself. Perhaps it is in part due to our use of the intellect to exert control over our surroundings. In knowing about a thing, we seek to “understand” it, “grasp” it and mentally “possess” it so as to subdue it and allow its use for active designs and goals. This is a necessary part of practical life, but it strikes a discord with mystery. Mystery is associated with humility and requires a different, more self-denying, more passive, more receptive mode of the mind.

A more basic point may be that knowledge is something that resides within me, whereas mystery is not: it is associated with relating to outside things. Knowledge is an internal possession and focuses an important part of our attention inward; mystery is outgoing. So perhaps knowledge can indeed crowd out a person’s awareness of mystery, although we do not have to let it do this. [20]

A WORD OF CAUTION

At this point a general word of caution is in order. We should be alert to the fact that when different areas of human experience contain unanswered questions, a common temptation is to wish to connect all of these together by means of one all-embracing theory.

So it is sometimes hard to browse through a popular bookshop without encountering the kind of volume that takes UFOs, the Bermuda Triangle, the Egyptian pyramids or whatever is of interest to the author, and seeks to pull all the selected areas of ignorance together so as to allow one grand theory that will account for everything. This may be called a “conflation of ignorances.” In science we do not properly understand quantum events, nor do we understand much about human consciousness. Taking this approach, we might elegantly connect the two areas together and thereby reduce two areas of ignorance to one! Now there may be a connection between quantum events and consciousness, or there may not. But we should be extremely wary of assuming that a connection exists just because we currently understand neither.

Viewed charitably, such a practice might be seen as a pardonable intellectual overindulgence, like putting too much food on one’s plate at once. It is likely to be misguided, because different areas of human ignorance usually have to be sorted out one by one, each by means of its own specialist method. Archaeologists may succeed in resolving questions about the Egyptian pyramids, nautical experts about the Bermuda Triangle. In the end, we may be able to say whether or not the areas are actually connected. To attempt to bring it all together prematurely is over-bold but possibly entertaining if not taken too seriously.

This leads into the far deeper issue of mystery. To repeat, ignorance concerns questions that can in principle be answered with the rational mind, with an outcome of conceptual understanding. Mystery cannot be dealt with in this way. Better vocabulary might be brought in to talk about the matter, but the mystery is not reducible to words or intellectual ideas, even within a particular context. Now, if there is such a thing as conflation of ignorances, there is also such a thing as conflation of mysteries, where one tries to merge a number of smaller mysteries together to form one big Mystery. This might occasionally be appropriate, but more likely not. An element of mystery in astronomy may well have nothing to do with the mystery of consciousness, neither of which is necessarily connected with the mystery of beauty, or of goodness, or any other mystery. Mysteries can presumably be manifold and diverse.

To use the big word Mystery to encompass all instances of mystery is therefore simple-minded and perhaps even a little dangerous. A conflation of ignorances will in the end be sorted out with no serious consequences. The situation could be otherwise with regard to mystery.

RELATING TO MYSTERY

The human intellect copes with different types of ignorance in the same fundamental way. We investigate to uncover more facts, and we think about the subject to gain a better understanding. Such are the means to bring about the goal of replacing ignorance by knowledge.

Mysteries, on the other hand, are approached not by intellectual means but by direct human interaction on our part. Each mystery requires that we interact with it in its own appropriate way, and these different ways will involve different aspects of our personal existence. At one level, there are mysteries such as those of physical existence that we just live with, no special demand being made on us. We interact with the mystery of the basic nature of physical matter by living in contact with physical things. In this practical way we deal with its mystery. The mystery of beauty, on the other hand, demands a more conscious personal interaction, because it is in some sense able to feed our souls.

Mystery resides in almost anything. We have mentioned the mystery in the basic existence of human rationality: the scholar or scientist interacts with this implicitly by the fact of using the mind to do study and research. The mystery of God is grappled with by means of prayer. There is a human mystery in each of us, and personal relationships are our way of managing this mystery. Kicking a stone in the manner of Samuel Johnson might be a very explicit way of interacting with the mystery of the material existence of the stone. [21] Interacting with mystery is in most cases practical, relational and personal, rather than intellectual and informational. No comprehensive human faculty, analogous to the rational intellect in dealing with ignorance, can generically and globally deal with every type of mystery.

Ignorance is something negative, an absence. In the intellectual area, every specific absence of knowledge can be seen as an instance of a generic absence of knowledge, that is to say, generic ignorance. By contrast, all true mysteries have something positive about them. This in the end is the crucial difference between ignorance and mystery. The positive element in a given mystery is found by means of a suitable way of interacting with it, and it will not be the same way in each case.

Seen from this viewpoint, rationalism, if it is taken as a rejection of all that is non-rational and non-intellectual, is a life-impoverishing principle. It may protect its practitioners from certain types of erroneous belief, but this comes at a very heavy price of what is lost. It is a blinkered philosophy.

A THEOLOGICAL PERSPECTIVE

A little more should be said about mystery and ignorance in a theological context. This is a profound subject, about which many things have been written, and we can only attempt to sketch a few basic themes here. In the New Testament, the Greek word mysterion refers to things that were unknown to us before God revealed them. This has led to a church tradition of designating as “mysteries” those teachings that cannot be proved logically or deduced from worldly experience but are truths that are part of the church’s beliefs by virtue of revelation. [22] This differs from our present use of the word mystery. In neither case does the word refer to any kind of esoteric teaching known only to a select few, as in the Gnostic “mystery religions.”

The contrast that we have been examining between mystery and ignorance is found in two kinds of theology put forward around the year 500 by a writer often known as Saint Denis, or today as Pseudo-Dionysius. On the one hand, there is a familiar theology of revelation and intellectual knowledge. Here positive statements about God are made, and if we do not know them, we are ignorant. But God is not to be considered as an idea in the human mind, and a deeper relationship comes through God’s spiritual presence in our hearts. A Platonist might seek absolute Beauty through an increasingly pure mental image of beauty; God, however, cannot be ultimately sought in terms of images or mental concepts. According to the second kind of theology, then, we can relate more closely to God by setting aside attempts at mental understanding. Over the centuries a “theology of darkness,” or apophatic theology, has been a common theme in Christian contemplative practice.

Revelation removes intellectual ignorance and is an essential part of the Christian faith. Knowledge as such, however, does not make us godly—this was the error made by the Gnostics. We become godly through spiritual contact with God, and this must be driven by the heart and will more than by the mind. It is also something given as a grace from God. It corresponds to an attitude to God as mystery in the sense defined in this chapter. Note again that mystery is something positive. Followers of the apophatic tradition seek closer contact leading to union with God by an intense program of prayerful contemplation, the intellect taking a back seat.

CONCLUSIONS

We have classified two types of absence of knowledge, referring to them as mystery and ignorance. Both concern the way we relate to other things, but confusing them is a serious mistake. Ignorance is something that scientific research, in particular, can reduce or eliminate, but mystery lies outside the remit of science and its means of investigation. As science advances, ignorance retreats! But mystery remains, even deepens. There are types of everyday mysteries that we familiarly live with, with no further ado. Other dimensions of mystery have much stronger overtones associated with experiences of a deep and awesome sense of wonder, which could have a religious connection.

Although primarily non-intellectual in its functioning, the awareness of mystery can work together with the rational mind. The elimination of many historic scientific gaps of ignorance has been seen by skeptics as a death sentence for religion, but this notion comes largely from a confusion of ignorance and mystery, linked to a secularized attitude to scientific knowledge. God must be seen as God of all things, including both rationality and mystery, and certainly of science. Every scientific result that accounts for a new area in terms of laws of nature makes it more manifest how remarkable these are. As has often been said, rather than a God of the gaps we should see a God of the laws. Like all other aspects of the created order, laws of nature are capable of evoking wonder and a sense of mystery, while being at the same time supremely rational. The rational intellect must therefore be prepared to cooperate with other aspects of our personal existence and awareness including mystery. Where an element of mystery comes in, the intellect cannot expect to hold center stage on its own.

Mystery can be controversial. A characteristically dismissive opinion has been expressed by Richard Dawkins, who writes that “a quasi-mystical response to nature and the universe is common among scientists and rationalists. It has no connection with supernatural belief.” [23] Many, however, notably Einstein, have found these experiences to be powerful and intensely meaningful. Perhaps they really ought to make rationalists and others more receptive to supernatural belief. Something lies beyond the intellect. But in an experience-oriented age such as our own, interesting experiences easily become ends in themselves, and mystery cultivated for its own sake is not enough. It must be a pointer and path to something further and deeper if it is to be of real significance.

THIRTEEN

BEYOND PHYSICALISM

In the preceding chapters we have explored the science of physics so as to understand the ways in which its principles underlie the structure and behavior of the universe. It is a majestic story, a combination of rigorously well-defined processes given by strict natural laws, together with the altogether subtler behavior of matter at the quantum level, where more flexibility and freedom are possible.

But we are human beings and have an innate sense of existing in a broader context than that of physical objects behaving solely according to physical laws. Many today claim to deny this and would call themselves materialists or physicalists. In our discussion, however, we have seen that there is much more to say. It is entirely reasonable to interpret our universe as structured according to intelligent principles. The principle of causation that appears to operate at all levels in the universe points toward a First Cause that must have operated from outside the universe. Our own existence in the universe depends on a sizable collection of factors that very plausibly suggest deliberately imposed intention.

These are signposts to God. They point without amounting to rigorous proofs, but the alternative is seriously problematic. A universe pervaded by causes that are in the end without cause seems strange. A universe pervaded by mathematical structure without an originating intelligence seems paradoxical. An existence in a universe whose background might be an infinitely complex set of multiple universes seems bizarre and constitutes a picture that stretches human rationality and belief to their limits and beyond.

On top of this, the existence of mentality at the human level cannot be denied by any sane individual. It has no explanation in physical terms, and we have explored reasons for this. We have examined a series of questions about explanations whose very presuppositions are meta-scientific and therefore metaphysical. They are questions that are meaningful to us, and we presume that our minds are validly able to operate in this milieu. In other words, all existence possesses an intellectual aspect. If this were not so, then science itself would be nothing but a set of rules of thumb to enable us to live efficiently and build devices that somehow work.

Finally, we have sought to establish contact with the element of mystery that underlies and accompanies our physical existence. This is something positive rather than negative, in contrast with ignorance, which is simply a lack of knowledge.

Why then do people assert that they are physicalists, which means that they consider themselves to be merely biological robots? The limited nature of the professed vision, however strongly it may be expressed, is remarkable. Some of the voices that say this will at the same time proclaim the awesome wonders of science, or the need for justice in human affairs, even while ostensibly refusing to consider the existence of anything at all that might be beyond the remit of science.

One of the twentieth century’s most notable popularizers of science was Carl Sagan. An admitted religious agnostic, he nevertheless engaged in dialogue with religious believers while being scornful about “excesses” that he observed in popular religious practice. A key to understanding a major strand of modern religious skepticism is to be found in his book The Demon-Haunted World: Science as a Candle in the Dark. [1] Here Sagan presents a catalogue of human credulity and folly throughout the ages, not least our own. Astrology, crop circles, extraterrestrial visitors, witchcraft—these and many other weird and wonderful things come under his penetrating scrutiny. Some of these items arise from imagination that has got out of control, some come from religiously motivated extravagance, some are hoaxes and so on. Some of these flights of fancy keep people amused but do no harm, but in other cases there are damaging consequences. All are due to a human tendency to believe in things uncritically, Sagan feels.

To Sagan as to many rational-minded people, science is the key to clear vision and clear thinking, and especially so in view of the apparent prevalence of pseudoscience, exotic fantasy and superstition found even in modern-day America. It may appear hard at first to disagree with this perspective, but a few qualifications must be made.

The first is that to bring in “science” to deal with many of these issues is to brandish too big a gun. Usually, a little intelligent thinking and worldly wisdom will be sufficient. In fact, science as such is of limited help in many of the areas that Sagan describes. Most of them can be investigated by a variety of everyday methods that have more in common with police detective work than with the science laboratory. Who is making the unusual claim? Are they believable? Are there reasonable alternative explanations? Several witnesses? What does the evidence amount to? Could it be a hoax? A few of the strange phenomena under consideration can be studied using scientific techniques, but in most cases this seems unnecessary or impracticable. Plenty of critical thinking, but remarkably little actual science, is brought into play in the majority of Sagan’s skeptical discussion!

But it is attractive to have something positive to uphold, rather than merely pour cold water on everything. The hope is that science, with its claim to believe only in what can be scientifically proved, will act as a paradigm for our lives. This is how one should think and see things. Then the demons of superstition and error will never gain any hold on us and will just go away. No one will even think of taking absurd things seriously.

Up to a point this view is fine, but it is not really quite so simple. Yes, science may indeed be a candle in the dark—more like a powerful streetlight than a candle, one might well say. It can cast light on many things. But consider the well-known tale of the drunkard who is found looking for a set of lost car keys beneath a streetlight. “Why there?” he is asked. He replies, “Because this is the only place where I can possibly find them!” Science will find precisely those things that its light is able to shine on. Where there is anything that science is unequipped to deal with, it will not be able to help us. The pool of light shed by science can have its limits. Physicalists, as viewed in this picture, are clustering themselves around the streetlight of science and no doubt discovering quite a lot in its beams. If no car keys are found there, however, they will deny the existence of the car keys.

As Sagan concedes, science has made errors in the past, and scientists are both intellectually and morally fallible. The candle (or streetlight) sometimes flickers. But science also has its intrinsic limitations, which Sagan tends to ignore. His argument appears to be to let science take the credit for the use of everyday common-sense intelligence, and then claim that science is the only real light that we have. But Sagan’s own strong interests in social and political matters could hardly come under the concern of science. Clearly, there has to be more than science and more types of light than science can cast.

The second problem, which follows from this, concerns throwing out the baby with the bathwater. Most members of mainstream religions in Western societies would presumably join with Sagan in rejecting astrology, magic crystals, abduction by aliens and the like. They would not necessarily take on board his skepticism about prayer, but most of the items that he disdains would be disdained by orthodox religious believers too. (Other societies are different. There is, for example, a great deal of interest in astrology in India.) But the false does not invalidate the true—always an extremely important principle to remember—and the task is to discriminate between them. We do not reject astronomy because of the existence of astrology, and to reject all belief in God because of the excesses of certain cults and factions is equally unjustified. This is throwing out the baby with the bathwater.

The previous chapters have shown, I hope, that rational science-based argument can give good support for mainstream religious belief in God. Sagan appears ambivalent about the deepest questions, however, and he appears to believe that the avoidance of error takes precedence over all other things. In what is otherwise quite a perspicacious review of Sagan’s book, the atheist biologist Richard Lewontin expressed his own physicalist position, under the synonym of materialism, in terms that are explicit and somewhat surprising:

We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door. [2]

Is this just an extreme reaction against astrology, New Age and all that? If so, it is very crude and turns rationalism into a parody of itself. It is hardly an example of good logic. Educated people over the ages, including scientists, have regarded belief in God as perfectly reasonable, even unavoidable. No—this is axiomatic atheism, dogmatic and simple and a way of avoiding questions.

It must be granted that practicing scientists have to use a methodology related to physicalism in order to obtain experimental results that are under their control. This is known as methodological naturalism. It means that they will find what they look for, if it is there—namely, a set of natural laws and principles that operate in the chosen experimental situation. Miracles are assumed not to take place in the laboratory. Indeed, no one today is denying that the laws of physics provide the basic mechanism of the universe—although this does imply a boundary to biology. We can study which brain circuits are active when the human subject reports different kinds of conscious experience, but this says nothing about the nature of the experience. A non-physical and hence non-biological factor is present. This may be frustrating to many biologists and perhaps rather unwelcome, but in every area of existence one has to live within limitations.

However, Lewontin makes it very clear that his physicalism is in fact a personal position and not just methodological. He simply does not want God. While being much more openly critical about science than Sagan is, especially popular science, he still asserts in his review that science is “the only begetter of truth.” He is an axiomatic atheist and as such would like physical materialism to be self-validating. In later sentiments he seems to be afraid that if you believe in God, miracles might be allowed, which is something that had also disturbed Laplace two centuries earlier. [3] But miracles are by definition exceptional occurrences, and they will not interfere with our experiments. Lewontin approvingly quotes Laplace’s famous but apocryphal remark to Napoleon regarding divine intervention to assist the physical working of the universe: “Sire, I have no need of that hypothesis.” To the religious believer, however, the laws of physics themselves are a miracle, but it is one of a different kind and magnitude.

To practicing scientists who affirm a religious faith, science is a method rather than a fundamental philosophy. It is a way of obtaining answers to certain classes of question, which it does extremely competently and well. The resulting knowledge can well be a source of awe and wonder, and the scientific method is compatible with both religious belief and unbelief. It is clearly going beyond rational sense if anyone claims that an assumption of atheism is necessary in order to practice science. To that, the scientist or science student who is a religious believer simply makes the reply, “Professor, I have no need of that hypothesis!”

We have considered arguments to show that physics and astronomy are entirely “God-friendly.” Physicalism is a desperate attempt to escape from these questions—and in the end all that it does is present a deficient view of human nature. As I suggested in this book’s introduction, it is doubtful whether anyone is truly at heart a physicalist; it is time for the pseudo-physicalists to come clean on this. In acknowledging that there is more to our nature than physics, one does not have to become a New Age enthusiast or an astrologer. Many mainstream positions leave science and religious faith intact, but physicalism does not leave one’s humanity intact.

To those who might prefer a literalist interpretation of the Scriptures, I would say the same. While it has not been part of my present task to attempt to cover biblical exposition, it is perfectly possible to take all the books of the Bible seriously while allowing modern interpretations of the early creation stories. In fact, these interpretations are not altogether modern. Early writers such as Saint Jerome and Saint Augustine were already well aware of the different kinds of material contained in the different books of the Bible, and they held that the early chapters of Genesis should be interpreted figuratively.

In short, one can be intellectually satisfied both in science and in the Christian faith. A view of physics and astronomy without God is either metaphysically limited or else risks becoming constructionally and interpretationally out of control. A viewpoint that includes God in the picture is much more complete and satisfactory. Much more than science is needed to find God personally, but we do have here some signposts that can point a few steps of the way.

INDEX

acceleration, 7-9, 26, 49, 128

accident, accidentals, 52, 167, 187

agnostic, agnosticism, 69, 187, 206

Alexander, Denis, 5

alpha particle, 17, 104

anthropic coincidence, 94, 99, 100, 118, 122

anthropic principle, 93-110

final, 94

strong, 94

weak, 94

antiparticles, 19, 97

apophatic theology, 203

Appel, Kenneth, 146

Aquinas, Thomas, 40-41, 53, 54, 59, 68, 173, 176-177

archetypes, unconscious, 177

arena, Roman, 82

Aristotle, Aristotelean, 38, 40, 42-43, 48, 54, 58-59, 75, 173, 176

picture of the universe, 59

Arnold, Matthew, 84

arrow of time, 128

astrology, 87, 206, 208-209

astronomer, 27, 39, 51, 61-62, 77, 104, 111, 124-125, 187

astronomy, astronomical, 2, 4-5, 8, 39, 48, 74-92, 93, 95, 109, 185, 196, 208, 210-211

atheism, atheist, 86, 157, 160, 186-187, 208-209

atom, 14-18, 20, 24, 29-31, 33, 40-41, 52, 70, 74, 89, 95-97, 102, 106-108, 110, 117, 127, 147, 149, 169, 175, 178-179, 188, 194

atomic nucleus, 17-18, 30, 105-106

Augustine, Saint, 40-41, 92, 210

awe, 194

See also wonder

axioms, mathematical, 113-114, 144-146, 148-152, 157

bacteria, 109

Barnes, Luke, 98, 103, 108, 112, 113

Barrow, John, 94

BBC, 69

beauty, 23, 180, 181, 186-187, 186, 194-195, 200-201, 202

mathematical, 49, 152, 180, 194

Benardete’s Book, 65, 137

Berkeley, Bishop, 201

Berlin, 29, 57

beryllium, 104

beta-decay, 127

Bible, 11, 26, 80, 210

Big Bang, 26-28, 69, 89, 95-96, 101-102, 105, 124, 129-135, 141, 147

binding problem, conscious, 167

biochemistry, 108-109, 120, 156

See also chemistry

biology, biological system, 3, 6, 39-40, 108, 119-122, 147, 155-156, 162, 167, 204, 209

black hole, 26, 101, 103

black-body radiation, 29

Blake, William, 198, 199

Bohr model of atom, 30, 31

Bohr, Niels, 30, 33, 35

Bondi, Hermann, 68-69

Borde, A., 133

Borde, Guth, Vilenkin (BGV) theorem, 133

Born, Max, 116

bouncing ball paradox, 66

Bradwardine, Thomas, 60, 71

brain, 3, 53, 120, 162-169, 171-179, 181, 209

Broglie, Louis de, 30

Brookhaven Laboratory, 19

Brout, Robert, 22

Browne, Sir Thomas, 9

bubble universes, 116, 133

Buridan, Jean, 60

Buridan’s spiral, 60

Cambridge, 7, 11

Cantor, Georg, 58, 62, 63

carbon, 96, 104-105, 109

Carter, Brandon, 93-94

cause, causation, 10, 43, 46, 54, 115, 121, 124-129, 142, 147-148, 163, 178, 179, 196, 205, 209

God as cause. See First Cause

causal agent, 167

celestial spheres, 76, 86

CERN, 19, 22

Chalmers, David, 169

chemistry, 6, 96-98, 108

Christianity, 203

Cicero, Marcus Tullius, 38

Clausius, Rudolf, 14

coincidence, 153

Coleridge, Samuel Taylor, 198

Collins, Robin, 98, 103, 109, 113

Columbus, 77

compass, 10

complementarity, 31-33

complexity, 52, 194

in God, 156-157, 156

of explanations, 144, 151-155, 160, 163-164

computers, 163

conflation of ignorance, mystery, 200-201

conscious life, 109, 114, 118-119, 121-122

consciousness, conscious experience, conscious mind, 36-37, 51, 53, 117, 122, 160, 162-179, 200-201

emergent. See emergence

in animals, 165

in quantum physics, 170-172

coordinate transformation, 135

Copenhagen interpretation, 33, 35-36, 53

Copernicus, Nicolaus, 61, 77-78

Corinthians, I, 197

cosmic

design, Designer, 58, 114, 117, 122-123, 157

expansion, 132, 135

inflation, 102, 132-133

intelligence, 195

microwave background, 90, 102

models. See models

purpose, 111, 113

ripples, 101, 103

cosmological constant, 99, 101

cosmological principle, perfect, 68-69

cosmology, 89, 125, 129, 130-135,140

cosmos. See universe

Coulomb, Charles-Augustin de, 9

Coulson, Charles, 196

Craig, William Lane, 64, 125

library paradox, 64, 66

Creator. See God

curvature, space-time, 25-26, 99, 118, 134, 180

dark energy, 100

Darwin, Charles, 119-120, 199

Darwinian processes, 119

Davies, Paul, 98

Dawkins, Richard, 111, 154-155, 194, 204

Democritus, 16

Dennett, Daniel, 163, 166, 174

desacralizing of nature, 193

Descartes, René, 48, 172-174

Designer. See God

determinism, 33, 37, 46, 127, 154

as a philosophy, 128, 154

deuterium, 95, 103, 106

dimensions of space, 25-26, 28, 52, 65, 92, 97, 115, 134, 138

Dirac equation, 31, 69

Dirac, Paul, 49

Donne, John, 80

Doppler effect, 27

Dostoyevsky, Fyodor, 183

Drummond, William, 80

Dryden, 80, 87

dualism, 173-175

Duns Scotus, John, 41, 53, 55, 62

Earth (planet), 8-9, 26, 59, 61, 75-86, 89, 96, 98, 109, 116, 124

See also flat Earth

Eddington, Arthur, 28, 51, 54, 176, 191

Einstein, Albert, 9, 24-26, 29, 34, 39, 53, 56, 99, 112, 118, 136, 170, 176, 180, 186-187, 191, 193, 204

electricity, 9-11

electromagnetism, 10-11, 97

electric current, 10-11

electron, 17, 18, 20, 44, 55, 72, 95, 107-108

elementary particles, 19-22, 52, 95

standard model of, 20

elements,

chemical, 18, 27

heavy, 103-107

ellipse, elliptical, 39

emergence, 168-169

empiricism, 190-199

energy, 14-16, 18-20, 25, 28-29, 32, 35, 66, 71, 95-96, 102, 104, 131-132, 174-175

dark, 100

density in universe, 95, 98-99, 101

Englert, Francois, 22

entropy, 16, 102-103, 128, 132, 137

epiphenomenalism, 166-170

essence, 41, 54

Euclid, 48, 144-145, 152

Everett, Hugh, 36, 138-139

evolution, evolutionary, 51, 55, 98, 119-122, 147, 167, 178-179, 181, 196

existence, 188

personal, 3-5, 89, 95, 159, 163, 178-182, 188-189, 198, 201, 204, 206

of God, 70, 73, 122, 124, 154, 159, 177, 197

explanation, 143-161

proximate, 143, 148

simplicity in, 144, 151-155

ultimate, 143, 148, 149-151, 155-158

levels of, 148, 155-156

modes of, 147

proximate, 151

scientific, 121, 143-161

eye, evolution of, 120

falsifiability, 153

Faraday, Michael, 11

Fermat’s last theorem, 146, 152

Feynman, Richard, 194

field, 10, 20-22

electric, 10-11

gravitational, 10

magnetic, 10-11

See also Higgs field, quantum field

fine-tuning of universe, 103, 111-123

First Cause, 4, 70, 124-142, 159, 205

fish, fishing net, 114-115

flat Earth, 74-76

force, 7, 97

gravitational, 8, 10, 61, 96, 98, 99, 101, 107, 175, 180

strong nuclear, 18, 97, 103-105, 107

weak nuclear, 20, 97, 105-106, 127

See also electricity, electromagnetism

form, forming idea, 40-42, 51-53, 54-55

temporal, 52

Foster, J., 167

four-color theorem, 146, 152

free will, 166-168

galaxy, galaxies, 85, 90, 97, 101-102

Galileo Galilei, 8, 48, 61, 77-78, 197-198

Genesis, book of, 11, 62, 210

Gleiser, Marcelo, 187

gluon, 20

Gnostic religions, 202, 203

God, 5, 22-23, 41, 44, 47, 50, 53, 57-58, 60-61, 63, 69-73, 79, 81-92, 114, 119, 121-122, 181, 183, 185-186, 196-198, 201-203, 154-161

as First Cause. See First Cause

of the gaps, 196-198, 203

as Designer, 114, 117, 122-123, 154-155, 159, 185

as mathematician, 138

See also intelligibility of God

God particle. See Higgs particle

Gold, Thomas, 68-69

Gordon, L., 125

gravitation/gravity, 8, 20, 26, 95, 97, 98-101, 107-108, 118

gravitational constant, 108-109, 118, 139

See also force, general relativity

Guth, A, 133

Guthrie, Francis, 146

Haken, Wolfgang, 146

Haldane, J. B. S., 178

half life, radioactive, 33

“hard problem” of consciousness, 163

Hartle, James, 134

Hawking, Stephen, 53, 72, 125, 134, 138

Hawking-Hartle universe, 134

heat, 14-16

heat death of universe, 15, 102

heaven, 92

Heisenberg uncertainty principle, 32

helium, 95-96, 103-105

hell, 79, 81

Hempel, Carl, 147

hidden variables, 36, 154

Higgs, Peter, 21

field, 21-22

particle, 21-23, 45

Hilbert, David, 64

Hilbert’s Hotel, 64, 66-67

Holder, Rodney, 58

Hoyle, Fred, 68-70, 104, 171

Hubble, Edwin, 27

Hubble parameter, 27-28, 133

Hume, David, 42, 122

Huxley, T. H., 162, 166

hydrogen, 18, 27, 30, 95-97, 103, 106, 175, 188

antihydrogen 19

ignorance, 185-204

imaginary time, 134

impossibility, 25, 44, 66-67, 71, 91, 107, 116, 120, 165, 168

infinity, infinite, 57-73, 136

infinite sequence, 149-150

infinite space, 60-62, 81-82

infinity of universes. See multiverse

actual, 58-59, 63

continuous, 62

countable, 62

paradoxes of, 64-67

physical, 63-68, 72

potential, 58-59, 63

See also universe

inflation, cosmic, 99, 102, 130, 132, 135, 138

information, 94, 163-165, 179, 201

intelligence, 114, 128, 167, 178, 208

apparent in nature, 23, 56, 114, 117, 181, 195

“intelligent design” in biology, 119-121

intelligibility

of nature, 143, 159

of God, 158, 181, 195, 205

intuitions, 193

James, William, 167

Jerome, Saint, 10, 210

Jesus, 183, 197

John of Bassols, 61

Johnson, Samuel, 201

Joule, James, 14

Jung, Carl, 177

Jupiter, 77, 109

Kalam argument, 124, 142

Kant, Immanuel, 54, 188-190

Kelvin, Lord, 14, 24

Kepler telescope, 87, 88

Kepler, Johannes, 39, 78

Kepler’s laws, 39

knowledge problem in consciousness, 166

Koran, 76

Krauss, Lawrence, 139

Laplace, Pierre, 128, 21

Large Hadron Collider, 22

laws

as descriptions, 42-47

higher-level, 39-40

of nature, 38-56, 140, 142, 195, 203

of motion. See Newton

of physics, 39, 56, 144, 194, 210

Ledermann, Leon, 22, 23, 141

Leibniz, 58

Lemaître, Georges, 27

Leslie, John, 114

Leucippus, 16

Lewis, C. S., 34, 77, 178-179

Lewontin, Richard, 208-209

life, 41, 87, 88, 93, 110

advanced life 4, 58, 93, 96-98, 111-123

light, 11-13, 96

particles of. See photons

reflection and refraction of, 12

speed of, 12-13, 24-26, 91

waves, 12

Linde, Andre, 72

logic, 178-179

London, 11, 24, 86, 155

Louis IV of France, 82

Lucretius, 16

Ludwig, K, 169

magnetism, magnet, 9-10

malaria, 153

M-theory, 115

Major, John, 60

many-worlds interpretation, 36, 138

Mars, 78, 121

Maslow, Abraham, 193

materialism. See physicalism

mathematics, 55-56, 164, 180, 188

and beauty, 180

and logic, 178

in nature, 47-51, 78

mathematical laws, 151

mathematical proofs, 144-146, 148

school of intuitionism, 63

matter, 53-55

Maxwell, James Clerk, 11

Maxwell’s equations, 11, 13, 34, 44

Mayer, Robert, 14

meaning, 164

measurement. See quantum measurement

medieval scholars, philosophers, 40-42, 54, 58, 140

medieval thought, 51

medieval universe, 82, 90

mentality, mind, 2, 4, 22, 50-51, 56, 162, 168, 184

See also conscious mind

meteorology, 144

methodological naturalism, 209

Middle Ages, 74, 76

Milky Way, 79

Milton, John, 79-81, 85, 87, 88, 92

mind. See mentality

mind and body. See dualism

miracles, 48, 55, 56, 107, 197, 209-210

model, physical, 46, 102

cosmological, 61, 71, 113, 130-135, 138, 141

standard. See elementary particles

See also Bohr model of atom

moon, 8, 77, 86, 109

moral obligation, 181-184

morality, moral value, 162

Moses, 183

multiverse, multiple universe(s), 58, 113-117, 122, 151, 153

mysterion, 202

mystery, 185-204

everyday, 188-189

relating to, 201-202

strong, 186-187

myth, 89-90

myth, social, 1-2

Nagel, Thomas, 165

Narlikar, Jayant, 69

natural philosophy, 78, 80

necessary being, 157

Nernst, Walter, 57

Neumann, John von, 171

neutral monism, 175-176

neutrino, 19, 20-21, 95, 97, 105-106

neutron, 18-20, 30, 95, 97, 103-107

Newton, Sir Isaac, 7, 12-13, 48, 50, 58, 61, 70, 78, 118

laws of motion, 7-8, 34, 38-40, 128, 168

Principia, 78

law of gravity, 8, 39, 61, 175

Nietzsche, Friedrich, 83-84, 87

nominalism, 41-44, 45-47

nothing, 139, 140

nuclear forces. See force

nuclear resonance, 104

nucleus. See atomic nucleus

Ockham, William of, 41, 43

Oersted, Hans Christian, 10

Olbers, Heinrich, 90

Olbers paradox, 68, 90

Omega (cosmic constant), 98

Oxford, 42, 60

oxygen, 96, 104-105, 188

panpsychism, 176

pantheism, 198

Papineau, David, 2

paradigm, 155-156, 16

Paradise Lost. See Milton, John

Paris, 60

Pascal, Blaise, 81-82, 85-86

Paul, Saint, 197

Pauli exclusion principle, 152

Penrose, Roger, 102

personal existence, 179-181

phases of matter, 169

photoelectric effect, 29

photon, particles of light, quanta, 12, 20, 29, 95, 104

physical existence, 201

physicalism, physicalist, materialism, 2-4, 37, 46-47, 126, 133, 142, 148, 158, 162-163, 168-169, 173-174, 176-179, 181-182, 190, 192, 196, 205-211

physics, 4, 6-23, 161, 163-166, 196

classical, 33, 128

quantum, 30-37

Planck radius, 138

Planck, Max, 29-30

planets, 39, 48, 75, 87-88, 96, 98-99, 108, 109, 121, 177

elliptical orbits, 78

orbits of, 8

Ptolemaic system, 76-78

plate tectonics, 109

Plato, 42, 173

Platonic ideas, Platonism, 40, 42, 202

poets

and astronomy, 79-81, 84

romantic, 198-199

positivism, 190-119

positron, 19

possibility, 44

pragmatism, 182, 193

primary matter, 40-41, 55

probability, 44, 52, 128

proton, 18, 44, 55, 72, 95-96, 103-107

Psalm 8, 86, 92

Pseudo-Dionysius, 202

Ptolemy, Claudius, 76, 85

See also universe

purpose

human, 143, 155, 162

in universe, 111, 113, 114, 122, 159-160

Pythagoras, 47, 50

theorem of, 144-145, 152

quanta. See photon

quantum

gravity, 139-140

chromodynamics (QCD), 20

events, 34, 127, 138, 154, 170-172, 177, 200

fields, 21, 53-55, 88, 100, 126, 148

fluctuations in early universe, 101

measurement, 32-33, 35-37, 53, 170

mechanics, physics, theory, 21, 30-37, 52

quarks, 20, 188

masses of, 106-107

radiation problem, 131

Ramanujan, Srinavasa, 50

randomness

in nature 14-16, 85, 102, 110, 116, 119, 132

in quantum physics, 33-37, 52, 127, 139, 140, 154, 170

rationalism, rationalist, 190-193, 197, 202, 204

rationality, 204

Ratzsch, Del, 151

realism, 42-47

reason, sufficient, 43

reasons, 143-161

Rees, Martin, 71, 98, 108-109

regularism, 42

relativity

general theory, 9, 25-26, 27-28, 39-40, 98-99, 118, 131-132, 134, 136

special theory, 24-25

religion, 1-2, 69, 84, 123, 125, 186, 194, 196-197, 208

rationalism and, 191, 193

See also rationalism, science

revelation, 202-203

ripples in space, 101

Romantic poets, 198-199

Rome, ancient, 38

Russell, Bertrand, 191-192

Rutherford, Ernest, 17

Sagan, Carl, 187, 206-208

Schrödinger, Erwin, 31, 35, 170

cat paradox, 35, 36, 171

equation, 31, 45, 46, 52, 170

science, sciences, 4-5, 6, 38-39, 42, 47, 57, 80, 125, 143, 147-148, 150, 162, 186, 190, 193, 199, 206-209

alleged conflict with religion, 1, 185, 195-196, 203

See also biology, chemistry, explanations, physics

Science and Christian Belief, 5

scientism, 190

secularism, 196

Sinclair, J. D., 125

singularity, cosmic, 134, 136-137

solar system, 78, 96

soul, 41, 57

sound waves, 12

space, 80-83

curved, 99

flat, 99

Spinoza, Baruch, 53, 176

spiritual awareness, 186

Spitzer, R. J., 125

standard model of elementary particles, 20

Stapp, Henry, 171-172, 74, 176-177

stars, 86, 96, 97, 101, 108

first generation, 96-97, 103-104, 106

Stenger, Victor, 113

strong force. See nuclear strong force

sun, 8, 11, 13, 39, 61-62, 75, 78, 80-83, 85, 96-97

superconductivity, 152, 169

supernova, 96, 132

superstition, 197, 206-207

superstring theory, 115-116

Susskind, Leonard, 58, 102

Swartz, Norman, 47

Swinburne, R., 156

Tempier, Bishop of Paris, 60, 68

theories, theory 45

of consciousness, 169

of everything, 114, 118-119

thermodynamics, laws of, 14-16, 128, 137

thing in itself (Kant), 54, 189

Thomson, J. J., 17

Thomson, William. See Kelvin, Lord

thought, abstract, 178-179

Tipler, F. J., 94

transcendence, 54, 187

Tristram Shandy paradox, 65-66

universalism, 41, 42

universality, 44, 46

universe, 4, 11, 15-16, 19, 21-22, 44, 49, 58, 60, 72, 74-92, 93-110, 111-123, 130, 187, 194

age of, 26-28, 57, 62, 68

beauty of, 23

causally closed, 169

collapse of, 98, 131-132

contracting, 135

early, 95

expansion of, expanding, 27-28, 99

from nothing, 70, 138-140

history of, 95-96

infinitely old, 61, 62, 68-70, 133-134, 136-137, 141

lifetime, 98

models of. See cosmology

origins of, 124-142

oscillating, 131

psychological attitude to, 85, 89

Ptolemaic, 74-78

rational structure of, 49, 51-53, 55-56

quantum, 138

repeating, 135

size of, 28, 59-64, 70-72, 77, 88-92

steady state theory of, 68-69, 124

unreason, 191, 193

value, moral, 181-184

velocity, 7

Venus, 77

Vilenkin, Alex, 133, 134, 138, 139

Volta, Alessandro, 9

W particle, 21

waves, 12

interference, 13, 30

electromagnetic, 13

particle waves, 30-31

quantum wave function, 35, 52, 170

weak force. See nuclear weak force

Weizsacker, C. F. von, 57

Wigner, Eugene, 48, 50, 171

Wilczek, Frank, 55

Wiles, Andrew, 146

Wilson, E. O., 195, 198

wonder, 86-87, 91, 187, 193-195, 198, 204

Wordsworth, William, 198, 199

x-rays, 30

Z particle, 21

Zeno, 63

quantum Zeno effect, 172

NOTES

CHAPTER 1: INTRODUCTION

1.

D. Papineau, “Physicalism in the Human Sciences,” in Philosophy of the Social Sciences (Cambridge: Cambridge University Press, 2009).

CHAPTER 2: THE WORLD OF PHYSICS

1.

Sir Thomas Browne, Pseudodoxia epidemica (1646), 51.

2.

Lucretius, De rerum natura (On the Nature of Things).

3.

L. Lederman with D. Teresi, The God Particle (London: Bantam, 1993).

4.

Ibid., 24.

CHAPTER 3: REVOLUTIONS IN PHYSICS

1.

Provided the observer who does the measurement is not accelerating; this would change the situation.

2.

This analogy was introduced by Arthur Eddington in 1931.

3.

C. S. Lewis, Miracles (London: Fontana, 1960), 25.

4.

See, e.g., W. Hermanns, Einstein and the Poet (Brookline Village, MA: Branden, 1983), 60.

5.

An important technical difficulty is that if the universe, or a quantum system, splits into n copies to allow n different outcomes of a measurement all to occur in parallel, it is very difficult to avoid having the apparent probability for each of these outcomes being simply 1/n. But standard quantum theory gives probabilities that can have any value between zero and one.

6.

J. Baggott, Beyond Measure (Oxford: Oxford Univ. Press, 2004) may be recommended.

CHAPTER 4: LAWS OF NATURE AND OF PHYSICS

1.

Information for these sections is drawn from E. Gilson, The Spirit of Mediaeval Philosophy (1936; repr., Notre Dame, IN: Univ. of Notre Dame Press, 1991); the online Stanford Encyclopedia of Philosophy; F. Copleston, A History of Philosophy, vol. 2 (Mahwah, NJ: Paulist Press, 1950); and original authors.

2.

T. Aquinas, Summa theologica 1.15.3; note that the term “idea” is Greek for the Latin “form” and Aquinas uses the two words rather similarly.

3.

Gilson, Spirit of Mediaeval Philosophy, 160.

4.

See, e.g., T. Aquinas, Compendium theologica, chap. 11. Today’s usage of the word, as in “almond essence,” is quite different from that of Aquinas.

5.

T. Aquinas, De principiis naturae, chap. 2.

6.

Gilson, Spirit of Mediaeval Philosophy, chap. 9, has a more extended discussion.

7.

Aristotle, Sophistical Refutations 22.

8.

M. Tooley, ed., Laws of Nature, Causation, and Supervenience (New York: Garland, 1999); F. Weinert, ed., Laws of Nature: Essays on the Philosophical Scientific and Historical Dimensions (Berlin: de Gruyter, 1995).

9.

See S. Weinberg, “Can Science Explain Everything? Can Science Explain Anything?” in Explanations: Styles of Explanation in Science, ed. J. Cornwell (Oxford: Oxford Univ. Press, 2004), 23-38. For further debate, see P. M. Churchland and C. A. Hooker, eds., Images of Science: Essays on Realism and Empiricism (Chicago: Univ. of Chicago Press, 1985) and in particular the article by C. Glymour.

10.

Many prescientific societies had no confidence at all in the regularity of nature and relied on sacrifices to deities in order to keep things going.

11.

N. Swartz, “Laws of Nature,” Internet Encyclopedia of Philosophy, www.iep.utm.edu/lawofnat/ (accessed 2015), and in Weinert, Laws of Nature, 67-70.

12.

Aristotle, Metaphysics 2.3.

13.

Galileo, The Assayer (Rome, 1623).

14.

E. P. Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications on Pure and Applied Mathematics 13 (1960): 1.

15.

P. A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American, May 1963, 45.

16.

For some viewpoints, see R. W. Howell, “The Matter of Mathematics,” Perspectives on Science and Christian Faith 67, no. 2 (2015): 74-88, and references.

17.

S. R. Ranganathan, Ramanujan: The Man and the Mathematician (1967; repr., New Delhi: Ess Ess, 2009), 88.

18.

A. S. Eddington, The Nature of the Physical World (Cambridge: Cambridge Univ. Press, 1933), 276.

19.

Ibid., 280.

20.

Ibid.

21.

Quoted in M. Jammer, Einstein and Religion (Princeton, NJ: Princeton Univ. Press, 1999), 51.

22.

I. Kant, Critique of Pure Reason (1787), section 1.

23.

T. Aquinas, Compendium theologica, chap. 71.

24.

T. Aquinas, On Being and Essence, chap. 2.

25.

F. Wilczek, “Quantum Field Theory,” Reviews of Modern Physics 71 (1999): S85.

26.

A. Einstein, “Physics and Reality,” Journal of the Franklin Institute 221 (1936): 313-48; trans. author.

27.

W. Hermanns, Einstein and the Poet (Brookline Village, MA: Branden, 1983), 64.

CHAPTER 5: DANGEROUS INFINITIES?

1.

C. F. von Weizsäcker, The Relevance of Science, Gifford Lectures 1959–60 (London: Collins, 1964), 151.

2.

L. Susskind, The Cosmic Landscape (New York: Little, Brown, 2005).

3.

See R. Holder’s anecdote in Big Bang, Big God (Oxford: Lion Hudson, 2013), 122. For a more extensive summary of Susskind’s book, see the review by M. Duff in Physics World, December 2005, 42.

4.

Information for this section has been obtained from Pierre Duhem, Medieval Cosmology, ed. and trans. R. Ariew (Chicago: Univ. of Chicago Press, 1985), and E. Grant, The Foundations of Modern Science in the Middle Ages (Cambridge: Cambridge Univ. Press, 1996).

5.

Duhem, Medieval Cosmology, 503.

6.

I. Newton, The Principia, General Scholium (1687), trans. I. B. Cohen and A. Whitman (Berkeley: Univ. of California Press, 1999), 94.

7.

See J. Barrow, The Infinite Book (London: Jonathan Cape, 2005) for a fuller account of Cantor and his work.

8.

D. Hilbert, On the Infinite (1925), in Philosophy of Mathematics: Selected Readings, ed. P. Benacerraf and H. Putnam, 2nd ed. (Cambridge: Cambridge Univ. Press, 1983), 183.

9.

W. L. Craig, The Kalam Cosmological Argument (London: Macmillan, 1979), 121.

10.

Adapted from J. A. Benardete, Infinity, an Essay in Metaphysics (Oxford: Oxford Univ. Press, 1964), 236.

11.

Adapted from M. R. Nowacki, The Kalam Cosmological Argument for God (New York: Prometheus, 2007), 254.

12.

Cf. Craig, Kalam Cosmological Argument, 97, where he argues against Bertrand Russell’s erroneous account of Tristram Shandy.

13.

Grant, Foundations, 75.

14.

For further discussion of many of the topics covered here, see H. Kragh, Cosmology and Controversy (Princeton: Princeton Univ. Press, 1996), and Kragh, Matter and Spirit in the Universe (London: Imperial College Press, 2004). Nernst had already put forward a less-developed theory of this type.

15.

F. Hoyle, Steady-State Cosmology Re-Visited (Cardiff: Univ. College Cardiff Press, 1980), 7.

16.

F. Hoyle, The Nature of the Universe, 2nd ed. (Oxford: Blackwell, 1960), 100 (originally published 1950).

17.

F. Hoyle, Home Is Where the Wind Blows (1994; repr., Oxford: Oxford Univ. Press, 1997), 338-39, 414-17.

18.

H. Bondi, “Arrogance of Certainty,” Times, May 20, 1991.

19.

F. Hoyle, Man in the Universe (New York: Columbia Univ. Press, 1966), 16. Of course, even this kind of viewpoint would be anathema to Norman Swartz, as quoted in chapter four above.

20.

F. Hoyle, Home, 416-17.

21.

Ibid., 413, 421.

22.

Why it should be matter rather than antimatter is particularly puzzling.

23.

M. Rees, Before the Beginning (New York: Simon and Schuster, 1997), 6.

24.

Quoted in C. S. Powell, God in the Equation (New York: Free Press, 2002), 249.

25.

S. Hawking, A Briefer History of Time (London: Bantam, 2005), 142.

CHAPTER 6: MODERN ASTRONOMY

1.

For a classic account, see J. L. E. Dreyer, A History of Astronomy from Thales to Kepler, 2nd ed. (New York: Dover, 1953).

2.

Q 37 (The Ranks); The Koran, trans. N. J. Dawood, 4th rev. ed. (Harmondsworth: Penguin Books, 1974).

3.

J. B. Russell, Inventing the Flat Earth: Columbus and Modern Historians (Westport, CT: Praeger, 1997).

4.

A. Van Helden, Measuring the Universe (Chicago: Univ. of Chicago Press, 1985).

5.

C. S. Lewis, The Discarded Image (Cambridge: Cambridge Univ. Press, 1964), chap. 5. This book gives a description of many varied aspects of medieval thought.

6.

Strictly, Kepler demonstrated his elliptical theory only for the planet Mars but then assumed that it held for all the planets.

7.

I have made use here of the account by M. Nicolson in Science and Imagination (Ithaca, NY: Cornell Univ. Press, 1956), particularly the essay “Milton and the Telescope.”

8.

J. Milton, Paradise Lost, bk. 7, lines 577-78.

9.

J. Dryden, Eleonora, lines 76-79.

10.

J. Donne, First Anniversary, lines 257-62.

11.

W. Drummond, Cypress Grove (1623).

12.

J. Milton, Paradise Lost, bk. 2, lines 891-94; cf. bk. 7, lines 211-12.

13.

Ibid., bk. 2, lines 438-39.

14.

Ibid., bk. 10, line 471.

15.

Ibid., bk. 7, lines 168-69. “Infinitude” might refer to God, the Deep, space, or all three.

16.

Ibid., bk. 8, lines 103-4.

17.

B. Pascal, Pensées, 194, 205, 206 (Brunschvicg). It should be remembered that much of the Pensées consists of fragments subsequently assembled by later editors.

18.

F. Nietzsche, “The Madman,” section 125 of The Gay Science (1882).

19.

For a fuller account of this area, see David Wilkinson, Science, Religion and the Search for Extraterrestrial Intelligence (Oxford: Oxford Univ. Press, 2013).

20.

J. Milton, Paradise Lost, bk. 9, lines 107-8.

21.

Dorothy F. Gurney, God’s Garden (1913).

22.

J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford: Oxford Univ. Press, 1986), 384.

23.

A qualification should be made here in that Christians have always allowed pictorial images of Jesus, while affirming that he is the incarnation of God. Of course, it is the human figure of Jesus who is portrayed; he is also in a spiritual sense the image of God (Col 1:15), which is something that cannot be apprehended visually.

24.

Augustine, Confessions, chap. 12.

CHAPTER 7: THE HUMAN-FRIENDLY UNIVERSE

1.

J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford: Oxford Univ. Press, 1986).

2.

M. Rees, Just Six Numbers (London: Weidenfeld and Nicolson, 1999); P. Davies, Cosmic Jackpot (Boston: Houghton Mifflin, 2007); Davies, The Goldilocks Enigma (London: Penguin, 2006); R. Collins, “Evidence for Fine-Tuning,” in God and Design, ed. N. A. Manson (London: Routledge, 2003), 178-99; L. Barnes, “The Fine-Tuning of the Universe for Intelligent Life,” last revised June 7, 2012, arxiv.org (arXiv:1112.4647v2 [physics.hist-ph]).

3.

For more explanation, see Davies, Cosmic Jackpot, 148.

4.

Barnes, “Fine-Tuning,” 38.

5.

L. Susskind, The Cosmic Landscape (New York: Little, Brown, 2005), 184.

6.

B. J. Carr and M. J. Rees, “The Anthropic Principle and the Nature of the Physical World,” Nature 278 (1979): 605. See also C. Hogan, “Quarks, Electrons and Atoms in Closely Related Universes,” in Universe or Multiverse?, ed. B. J. Carr (Cambridge: Cambridge Univ. Press, 2007), 221-30.

7.

Barnes, “Fine-Tuning,” section 4.7.1.

8.

Rees, Just Six Numbers, 26-27, 30.

9.

Collins, “Evidence for Fine-Tuning,” 189-90, 192-94.

CHAPTER 8: IMPLICATIONS OF A UNIVERSE “FINE-TUNED” FOR US

1.

R. Dawkins, River out of Eden (London: Weidenfeld and Nicolson, 1995), 155.

2.

Victor Stenger has disputed the existence of the apparent fine-tuning in The Fallacy of Fine Tuning: Why the Universe Is Not Designed for Us (Amherst, NY: Prometheus, 2011). His arguments and his level of understanding of the relevant physics have been heavily criticized by L. Barnes, “The Fine-Tuning of the Universe for Intelligent Life,” last revised June 7, 2012, arxiv.org (arXiv:1112.4647v2 [physics.hist-ph]), and by Collins, “The Fine Tuning Evidence is Convincing,” in Debating Christian Theism, ed. J. P. Moreland, K. A. Sweis and C. Meister (Oxford: Oxford Univ. Press, 2013). Stenger has given a defense of his position (arXiv:1202.4359).

3.

J. Leslie, Universes (London: Routledge, 1989), 9.

4.

M. Born, My Life and My Views (New York: Charles Scribner’s Sons, 1968), 154. Born made this comment in the context of human space travel, but it seems to be of much wider application.

5.

D. Hume, Dialogues Concerning Natural Religion (1779).

CHAPTER 9: GOD AS FIRST CAUSE

1.

W. L. Craig, The Kalam Cosmological Argument (London: Macmillan, 1979).

2.

Ibid., 121.

3.

Reported by L. Grossman in “Why Physicists Can’t Avoid a Creation Event,” New Scientist 2847 (January 2012): 6.

4.

W. L. Craig and J. D. Sinclair, “The Kalam Cosmological Argument,” in The Blackwell Companion to Natural Theology, ed. W. L. Craig and J. P. Moreland (Chichester, UK: Wiley-Blackwell, 2009), 101-201; R. J. Spitzer, New Proofs of the Existence of God (Grand Rapids: Eerdmans, 2010), 47-74; B. L. Gordon, “Inflationary Cosmology and the String Universe,” in Spitzer, New Proofs, 75-104.

5.

Some statistical interpretations of quantum physics might be in conflict with these statements. I do not accept them, on the grounds that quantum physics surely does apply to single quantum objects.

6.

I am referring to physical probabilities here, rather than Bayesian probabilities, which more concern the believability of an assertion.

7.

A readable and comprehensive account of this area can be found in J. D. Barrow, The Book of Universes (London: Vintage, 2012).

8.

As upheld, e.g., by Jim Al-Khalili in Black Holes, Wormholes and Time Machines, 2nd ed. (Boca Raton: CRC, 2012), 55.

9.

J. D. Barrow and M. Dabrowski (see Barrow, Book of Universes, 79 and reference) showed that oscillating universes must always eventually behave in this way in certain general circumstances.

10.

A. Mithani and A. Vilenkin, “Did the Universe Have a Beginning?” April 20, 2012, arxiv.org (arXiv:1204.4658 [hep-th]).

11.

A. Borde, A. Guth and A. Vilenkin, “Inflationary Spacetimes Are Not Past-Complete,” Physical Review Letters 90 (2003): 151301 (arXiv:gr-qc/0110012v2).

12.

A. Vilenkin, “Did the Universe Have a Beginning?” (conference talk, The State of the Universe, Cambridge, 2012), available at www.ctc.cam.ac.uk/stephen70/talks/swh70_vilenkin.pdf; Mithani and Vilenkin, “Did the Universe Have a Beginning?”

13.

Also the so-called ekpyrotic universe of P. Steinhardt and N. Turok, “Cosmic Evolution in a Cyclic Universe,” Physical Review D 65 (2002): 126003 (arXiv:hep-th/0111098v2) and further references; see Gordon, “Inflationary Cosmology,” 80.

14.

The problem with instability in a supposedly infinitely old structure is formidable. Any instability, however small, is likely to destroy such a structure and is incompatible with it. Once the possibility of instability has been plausibly raised, then the onus lies on the model builder to demonstrate that it does not apply in the given case. Vilenkin and others appear indeed to have done the former, and so the default position is to assume that such a model cannot be past-infinite.

15.

J. Hartle and S. Hawking, “Wave Function of the Universe,” Physical Review D 28 (1983): 2960.

16.

“Imaginary” is used in its technical mathematical sense, as Hawking explains in A Brief History of Time (London: Bantam, 1988), 134.

17.

Hawking, A Brief History of Time, 134, 143. For further discussion of this somewhat artificial proposal, see, e.g., R. Holder, God, the Multiverse and Everything (Aldershot, UK: Ashgate, 2004), 58-62.

18.

A. Aguirre and S. Gratton, “Steady-State Eternal Inflation,” Physical Review D 65 (2002): 083507. The same authors have presented an analogous theory in which inflationary ideas are implemented; however, from the Kalam point of view, similar comments can be made. The arrows of time diverge from a particular plane, but what then was the ultimate cause of the conditions there? Aguirre and Gratton, “Inflation Without a Beginning: A Null Boundary Proposal,” Physical Review D 67 (2003): 083515. A. Vilenkin, Many Worlds in One (New York: Hill and Wang, 2006), lists more recent examples of this kind of “no boundary” model, to which the same comment may be made.

19.

See, e.g., Craig and Sinclair, “Kalam Cosmological Argument,” 145.

20.

See, e.g., Barrow, Book of Universes, 168.

21.

A. Wall, “The Generalized Second Law Implies a Quantum Singularity Theorem,” Quantum Gravity 30 (2013): 165003 (arXiv:1010.5513 [gr-qc]).

22.

Vilenkin, Many Worlds in One, 180-86. He is rather critical of the Hartle and Hawking model (ibid., 190-91).

23.

When I asked Hawking at a conference in 1987 how quantum events occurred in his quantum universe, he replied, “That is a good question. I think a many worlds approach is needed.” But while this interpretation eliminates random choices, it does not actually tell us about how the universe splits (or seems to split) into the many versions of itself. This, just like conventional random quantum events, remains unexplained. A good account of this family of interpretations can be found in J. A. Barrett and P. Byrne, eds., The Everett Interpretation of Quantum Mechanics (Princeton: Princeton Univ. Press, 2012).

24.

The so-called Planck radius (10-35 m) is the extremely small distance (calculated in terms of the speed of light, Planck’s constant and Newton’s gravitational constant) at which quantum effects should be present in gravity. There is a corresponding Planck time, 10-43 s.

25.

J . Gott and L-X. Li, quoted in Craig and Sinclair, “Kalam Cosmological Argument,” 178.

26.

Vilenkin, Many Worlds in One, 199-202.

27.

L. M. Krauss, A Universe from Nothing (New York: Free Press, 2012).

28.

A similar lack of precision is found in Stephen Hawking, The Grand Design (London: Bantam, 2010), 179-81.

29.

A quantum theory of gravity will most importantly affect space-time at the Planck scales, which are beyond our imaginable experimental capability. Classical singularities can depend on time being infinitely precisely determined at the point where the singularity occurs, but quantum effects would tend to smear out the determinate nature of time values such as this.

30.

L. Lederman and D. Teresi, The God Particle (London: Bantam, 1993), 1.

31.

A complex-structured universe might have multiple starting points! This does not really affect the Kalam argument, however.

32.

Cf. W. E. Carroll, “Aquinas and Contemporary Cosmology: Creation and Beginnings,” Science and Christian Belief 24, no. 1 (2012): 5-18.

CHAPTER 10: EXPLANATIONS AND EVIDENCE

1.

For an overview of the function of scientific explanation, see P. Lipton, “What Good Is an Explanation?” in Explanations: Styles of Explanation in Science, ed. J. Cornwell (Oxford: Oxford Univ. Press, 2004), 1-22.

2.

Euclid’s five axioms are (1) a straight line can be drawn between any two points, (2) any straight line can be continued indefinitely, (3) a circle with any radius can be drawn with any point as center, (4) all right angles are equal and (5) just one line can be drawn through a point parallel to a given straight line (stated slightly differently by Euclid).

3.

Mathematics can sometimes resemble an “experimental science,” in which conjectures are formed and tested empirically. See J. Echeverria, “Observations, Problems and Conjectures in Number Theory—the History of the Prime Number Theorem” and references, in The Space of Mathematics, ed. J. Echeverria, A. Ibarra and T. Mormann (Berlin: de Gruyter, 1992).

4.

For an accessible account, see S. Singh, Fermat’s Last Theorem (London: Fourth Estate, 2002).

5.

K. Appel, W. Haken and J. Koch, “Solution of the Four Color Map Problem,” Scientific American, October 1977, 108-21; R. Wilson, Four Colours Suffice (London: Penguin Books, 2002).

6.

Many detailed discussions of this subject may be found in the literature. The most standard modern approach, largely followed here, is known as the deductive-nomological (DN) model and was formulated by Carl Hempel. See C. G. Hempel, Philosophy of Natural Science (New York: Prentice-Hall, 1965), 49, and Hempel, Aspects of Scientific Explanation (New York: Free Press, 1965), 335.

7.

See Hempel, Philosophy of Natural Science, 376. Statistical laws can be included in the DN model. P. Railton, “A Deductive-Nomological Model of Probabilistic Explanation,” Philosophy of Science 45 (1978): 206; reprinted in J. Pitt, ed., Theories of Explanation (Oxford: Oxford Univ. Press, 1988). For a review, see W. Salmon, Causality and Explanation (Oxford: Oxford Univ. Press, 1998), 302-19. While disagreement exists among philosophers on topics such as epistemology and causality in science (ibid., 320-29), our discussion here is not greatly affected by this. But it is important to note that historical explanations require causation to operate in some sense and not mere deducibility of one fact from another.

8.

See the articles by S. Rose and D. Hanke, in Cornwell, Explanations, 125-42, 143-56.

9.

This theme has been explored by C. McGinn in Problems in Philosophy: The Limits of Inquiry (Oxford: Blackwell, 1993).

10.

D. Ratzsch, Nature, Design and Science (Albany, NY: State Univ. of New York Press, 2001), 135.

11.

R. Thomas, “An Update on the Four-Color Theorem,” Notices of the American Mathematical Society 45 (1998): 848-59.

12.

For an account of the problems in this area, see J. Aron, “Proof of Concept,” New Scientist, August 29, 2015, 29.

13.

Superconductivity is a phenomenon found when electric currents flow in some materials at very low temperatures. All the conduction electrons flow together through the material, and there is no resistance to their flow. The Pauli exclusion principle states that two electrons, or other particles with half-integral spin, cannot occupy the same physical state.

14.

R. Dawkins, The God Delusion (New York: Mariner Books, 2008), 138.

15.

R. Dawkins, Climbing Mount Improbable (New York: W. W. Norton, 1996), 77.

16.

A different type of combined probability may be needed in this case. See R. Swinburne, The Existence of God (Oxford: Oxford Univ. Press, 2004).

17.

R. Swinburne has argued the opposite in Existence of God, where he proposes that finiteness is more complex, since it implies limitations that require information to specify. I question this argument, on the grounds that the nature of God’s assumed infiniteness cannot be evaluated by ourselves.

18.

It is for this reason that I have not stressed the traditional argument that God is a “necessary being.” Indeed this may be so, but necessity in terms that are comprehensible to us tends to imply a kind of separate and prior logic that necessitates God. This seems wrong. The necessitating logic would surely need to be built into God’s being, and we are unlikely to understand its nature.

CHAPTER 11: MENTAL REALITY

1.

A view advocated notably by T. H. Huxley. See Huxley, “On the Hypothesis That Animals Are Automata, and Its History,” Fortnightly Review 95 (1874): 555-80; Huxley, Collected Essays, vol. 1, Method and Results (London: Macmillan, 1893).

2.

D. C. Dennett, “Cog: Steps Towards Consciousness in Robots,” in Conscious Experience, ed. T. Metzinger (Paderborn, Germany: Schöningh, 1995), 471.

3.

The philosopher Thomas Nagel presented a classic discussion of this topic in “What Is It Like to Be a Bat?” Philosophical Review 83 (1974): 435-50.

4.

Huxley, Method and Results.

5.

W. James, “Are We Automata?” Mind 4 (1879): 1-22.

6.

J. Foster, The Undivided Self (London: Routledge, 1991).

7.

For further reading on what is a voluminous topic, the three Tucson conference proceedings are essential: S. R. Hameroff, A. W. Kaszniak and A. C. Scott, eds., Towards a Science of Consciousness: The First Tucson Discussion and Debates (Cambridge, MA: MIT Press, 1996); S. R. Hameroff, A. W. Kaszniak and A. C. Scott, eds., Towards a Science of Consciousness: The Second Tucson Discussion and Debates (Cambridge, MA: MIT Press, 1998); S. R. Hameroff, A. W. Kaszniak and D. J. Chalmers, eds., Towards a Science of Consciousness: The Third Tucson Discussion and Debates (Cambridge, MA: MIT Press, 1999).

8.

For a classic anthology, see S. P. Stich and T. A. Warfield, eds., The Blackwell Guide to the Philosophy of Mind (Oxford: Blackwell, 2003).

9.

K. Ludwig, “The Mind-Body Problem: An Overview,” in Stich and Warfield, Philosophy of Mind, 1-46; D. Chalmers, “Consciousness and Its Place in Nature,” in Stich and Warfield, Philosophy of Mind, 102-42.

10.

Foster, Undivided Self.

11.

F. Hoyle, Home Is Where the Wind Blows (1994; repr., Oxford: Oxford Univ. Press, 1997), 257-58, 266-67.

12.

H. P. Stapp, Mindful Universe, 2nd ed. (Berlin: Springer-Verlag, 2011), chap. 6.

13.

Ibid., 35.

14.

R. Descartes, Discourse on the Method, Meditations on First Philosophy and Objections and Replies. Page references are to Descartes, Key Philosophical Writings, ed. E. Chávez-Arviso, trans. E. S. Haldane and G. R. T. Ross, Wordsworth Classics of World Literature (Ware, UK: Wordsworth Editions, 1997). Reference in parentheses are to the standard French-Latin edition cited therein: C. Adam and P. Tanney, eds., Oeuvres de Descartes, 12 vols. (Paris: J. Vrin, 1964–1976).

15.

Descartes, Discourse on the Method, 109 (6.59); Aristotle, Of the Soul 1.1.

16.

Descartes, Mediations, 183 (7.81).

17.

Descartes, Objections and Replies, 246 (7.228).

18.

Descartes, Objections and Replies, 248 (9A.213).

19.

D. Dennett, Consciousness Explained (London: Penguin, 1993), 34-35.

20.

For further discussion, see Chalmers, “Consciousness,” 102. The online Stanford Encyclopedia of Philosophy provides a useful outline of the subject.

21.

F. Copleston, History of Philosophy, vol. 2 (Mahwah, NJ: Paulist Press, 1950), 375-87.

22.

C. G. Jung, Archetypes of the Collective Unconscious, Collected Works of C. G. Jung, vol. 9 (Princeton, NJ: Princeton Univ. Press, 1969), part 1.

23.

J. B. S. Haldane, Possible Worlds: And Other Essays (1927; repr., London: Chatto and Windus, 1932), 209.

24.

C. S. Lewis, Miracles, 2nd ed. (Glasgow: Collins, 1960), chap. 3.

25.

Ibid.

26.

Lewis argued correctly that if we reply to an opponent, “You say that merely because you are a capitalist!”—a purely deterministic cause—then we undermine the other person’s reasoning. However, this would not apply in the case of saying, “You say you need food merely because you are hungry!”—an equally deterministic reason. So we must distinguish between abstract and concrete situations.

CHAPTER 12: MYSTERY AND IGNORANCE

1.

A. Einstein, “What I Believe,” Forum and Century 84 (1930): 193-94, and Has Science Discovered God? ed. E. H. Cotton (New York: Crowell, 1931), 93-97, quoted in M. Jammer, Einstein and Religion, (Princeton: Princeton Univ. Press, 1999), 73.

2.

C. Sagan, Cosmos (New York: Ballantine, 1980), 275.

3.

M. Gleiser, “Emergent Realities in the Cosmos,” in Spiritual Information, ed. C. L. Harper Jr. (Philadelphia: Templeton Foundation Press, 2005), 147; also in The Best American Science Writing 2003, ed. Oliver Sacks (New York: HarperCollins, 2003), 102.

4.

I. Kant, Critique of Pure Reason (1787), section 1. There are of course other philosophical treatments of this topic. That of Kant, however, does provide a particularly good reference to what I am discussing here. In chapter four we compared Kant’s “thing in itself” with the unobservable medieval “primary matter.”

5.

W. Heisenberg, Encounters with Einstein (Princeton: Princeton Univ. Press, 1983), 114.

6.

B. Russell, “Why I Am a Rationalist.” Delivered to the Rationalist Press Association in 1928, this talk was reprinted in an early edition of Why I Am Not a Christian (Girard, KS: Haldeman-Julius, 1929). It is easily located on the Internet.

7.

F. Aveling, “Rationalism,” The Catholic Encyclopedia, vol. 12 (New York: Robert Appleton, 1911), www.newadvent.org/cathen/12652a.htm.

8.

By the time Russell wrote The Faith of a Rationalist in 1947, he claimed to require rational proof in order to believe anything, based on sense data, mathematics and logic. This sounds like positivism, and the standard objections could be raised to it, as well as those raised here against rationalism.

9.

A. H. Maslow, The Psychology of Science: A Reconnaissance (Chicago: Regnery, 1966), 138, 139.

10.

R. Dawkins, The God Delusion (New York: Mariner Books, 2008), 125.

11.

See, e.g., Einstein’s attitudes, quoted above, and the account given by Jammer (Einstein and Religion, 151) of the effects of Einstein’s religious statements on other people.

12.

R. P. Feynman, Surely You’re Joking, Mr Feynman (London: Unwin, 1986), 261.

13.

A. Einstein, The World as I See It, trans. A. Harris (London: The Bodley Head, 1935), 25, 28.

14.

E. O. Wilson, Biophilia (Cambridge, MA: Harvard Univ. Press, 1986), 10.

15.

C. Coulson, Science and Christian Belief (Oxford: Oxford Univ. Press, 1955).

16.

Miracles are something different: anomalies rather than gaps. But it is important to note that Jesus and his followers saw miracles primarily as signs of God’s power, not of his existence.

17.

Another traditional “ignorance” argument made by rationalists goes something like this: the peasants believe in superstitions; the peasants believe in God; therefore God is a superstition. The elementary error of logic here hardly needs pointing out.

18.

Galileo Galilei, Letter to the Grand Duchess Christina (1615).

19.

D. Newsome, Two Classes of Men, Platonics and English Romantic Thought (London: Murray, 1974), chap. 2.

20.

A well-known example of this kind of effect can be found in a letter written by Charles Darwin to a friend at a late period in his life: “Up to the age of thirty, or beyond it, poetry of many kinds, such as the works of Milton, Gray, Byron, Wordsworth, Coleridge, and Shelley, gave me great pleasure. But now for many years I cannot endure to read a line of poetry. . . . My mind seems to have become a kind of machine for grinding general laws out of large collections of facts. . . . The loss of these tastes is a loss of happiness, and may possibly be injurious to the intellect, and more probably to the moral character, by enfeebling the emotional part of our nature.” Charles Darwin: His Life Told in an Autobiographical Chapter and in a Selected Series of His Published Letters, ed. Francis Darwin (London: W. Clowes and Sons, 1892), 51.

21.

Dr. Johnson refuted Bishop Berkeley’s philosophy of extreme mental idealism, with the nonexistence of matter, by kicking a large stone with great force. James Boswell, The Life of Samuel Johnson (New York: Penguin Books, 1986), 122.

22.

For more details, see, e.g., Catechism of the Catholic Church, 2nd ed. (United States Conference of Catholic Bishops, Libreria Editrice Vaticana, 2000).

23.

Dawkins, God Delusion, 11.

CHAPTER 13: BEYOND PHYSICALISM

1.

C. Sagan, The Demon-Haunted World: Science as a Candle in the Dark (New York: Random House, 1995).

2.

R. Lewontin, “Billions and Billions of Demons,” New York Review of Books, January 9, 1997, www.nybooks.com/articles/archives/1997/jan/09/billions-and-billions-of-demons.

3.

R. Hahn, Pierre Simon Laplace, 1749–1827: A Determined Scientist (Cambridge, MA: Harvard Univ. Press, 2005), 202.

PRAISE FOR SIGNPOSTS TO GOD

“During my decades of teaching, I have carried a constant sadness about the complete ignorance and misunderstanding—by almost all secularists and many Christians—of the relationship between Christianity and science. Upon reading Signposts to God, my cloud began to lift. This book does a thorough and masterful job of showing that physics and astronomy have usually been friendly, not hostile, to Christian ideas. Peter Bussey wisely provides a user-friendly overview of the last centuries of physics and astronomy so the reader can understand the arguments to follow. If you get one book on science and religion this year, get this one.”

J. P. Moreland, distinguished professor of philosophy, Biola University

“In Signposts to God, Peter Bussey brings a useful survey of today’s science. In this book, he shows that rather than conflicting with the biblical picture of a creating God active in the universe, the discoveries of the past century and a half have moved the view of science ever closer to that unchanging biblical paradigm.”

Gerald Schroeder, The College of Jewish Studies, Jerusalem, author of Genesis and the Big Bang and The Science of God

“The spreading belief in a fundamental opposition between religion and science intensifies the need for scientists to weigh in on the question. In reader-friendly prose, Bussey presents a balanced, sober, up-to-date account of the many ways in which current physics and cosmology not only remain open to belief, but point the way to it, indicating the existence of an intelligent cause prior to the world of nature. A fine contribution to the great conversation between physics, philosophy, and faith.”

Michael Augros, author of Who Designed the Designer?

“Bussey explains that many of the physical parameters of our universe must be very close to their measured values if the universe is to be human friendly. There are many, many more ways the universe could be wrong rather than right for life. Although there is some ambiguity as to whether this situation clearly points to a creator, Bussey goes further to argue that consciousness clearly tips the balance toward the universe being created by God.”

Robert C. Bishop, associate professor of physics and philosophy, John and Madeleine McIntyre Endowed Professor of Philosophy and History of Science, Wheaton College

“Particle physicist Peter Bussey’s Signposts to God is an edifying introduction to the interaction between science and faith. One part informative discussion of modern physics, astronomy, and cosmology, one part critique of the myth of physicalism, and one part apologetic for the hallmarks of transcendence in the origin and structure of the universe and the deep mysteries of conscious existence, Bussey’s heartfelt reflections set our feet on a path well marked with signposts to God as the source and end of all things.”

Bruce L. Gordon, associate professor of the history and philosophy of science, Houston Baptist University

ABOUT THE AUTHOR

Peter Bussey (PhD, ScD, Cambridge) is a particle physicist and an honorary research fellow in the school of physics and astronomy at the University of Glasgow. He is a fellow of the Institute of Physics and previously served at Cambridge University, CERN and Sheffield University.

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Table of Contents

Title Page

Contents

1 Introduction

2 The World of Physics: A Quick Tour

3 Revolutions in Physics

4 Laws of Nature and of Physics

5 Dangerous Infinities?

6 Modern Astronomy: Where Has God Gone?

7 The Human-Friendly Universe

8 Implications of a Universe “Fine-Tuned” for Us

9 God as First Cause: An Argument That Seems to Hold

10 Explanations and Evidence

11 Mental Reality

12 Mystery and Ignorance

13 Beyond Physicalism

Index

Notes

Praise for Signposts to God

About the Author

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