FACTS AND FAITH

THE DUAL NATURE OF REALITY

by     Reginald O. Kapp

2 - IS THERE A COSMIC STATUTE BOOK?


Ordered and Random Events
IT emerged from the first of these lectures that the dispute between monists and dualists turns on the question: What is the source of order? According to monism all order arises from the action on each other of material systems, and from nothing else. According to dualism something else is necessary, at least sometimes. The meaning of these two answers can best be appreciated with the help of a concrete example. The human brain provides a suitable one. It displays order both in its behaviour and in its structure.

When the brain is working its minute, indeed sub-microscopic, component parts act on each other in specific, co-ordinated ways; the sequence of their movements is timed with precision; they behave like the component parts of a finely constructed, very complex man-made machine. A result of this co-ordinated performance is that specific, co-ordinated messages pass to the muscles of the body and lead to specific, co-ordinated movements. If one considers any example of order in human activities and attempts to explore the path along which it came, that path will always lead to a human brain. If the behaviour of the component parts of that delicate organ were random instead of being ordered, there would be no order in our daily lives, none of those orderly things on which civilization depends, no works of art, no books or clothes, no houses. To explain the ordered performance of the brain would be to explain a great deal.

What things act on the brain? What is done to it that its component parts may behave in an ordered manner? It is not in doubt that other physical systems act on it. There are a vast number of such systems and together they form the environment. The action of the environment on the brain is largely effected through the channel of the organs of sense perception. Through these the brain is continuously receiving stimuli from the outer world. Sights, sounds, smells, tactile sensations, all contribute in great number; they arrive from a great variety of sources, some near, some far distant. In this example, as throughout the material universe, matter certainly acts on matter. That is obvious. But it does not suffice to explain order in the brain. Far from solving the mystery, it raises it; and in this way.

One very significant statement can be made about all the stimuli that reach the brain. They are not co-ordinated. They may arrive from anywhere. They are random events, unselected, most of them the result of pure chance. And yet the response of the brain to these stimuli is not random. Selection, discrimination, guidance, control, do occur. Where, when, how?

Only about the 'where' and the 'when' can one say anything at all definite; the 'how' presents the great baffling problem. Co-ordination occurs after the stimuli have been received and before the brain has sent its controlling messages to the muscles. In this example the puzzling problem that divides monists and dualists can be pinpointed at the junction between stimulus and response.

Monists and dualists offer quite different solutions. Monists find theirs wholly in the specific structure of the brain and in the laws of physics. (I use the expression ‘laws of physics' here to cover those of chemistry as well as all the others that belong to the physical sciences.) According to monism the nature of matter, which is defined by the laws of physics, constrains the component parts to behave as they do when they find themselves in the particular kind of configuration that constitutes a human brain.

Dualists deny that the structure of the brain and the nature of its component particles suffice to explain the behaviour of the particles. They deny that the stimuli provided by the environment are the only things that act on the brain. They claim that in addition a diathete, mind, acts. Thus they regard the brain as being simultaneously subjected to two kinds of action, one from matter and the other from a diathete and they attribute the ordered behaviour of the component parts of the brain to the selecting, discriminating, guiding, co-ordinating, control of the diathete. In short, monists say that the source of order is matter, dualists that it is a diathete.

For some inexplicable reason monists always insist that a living organ such as the human brain is in all essentials analogous to a man-made machine. They often construct models in the hope thereby of proving their hypothesis. And dualists rather vehemently reject the analogy. But a moment's thought shows that neither can have thought matters out very clearly.

Monists say that the impact of random events causes the brain to behave in an ordered manner, because it is in the nature of its component parts to do so. But it is not the impact of random events that causes the ordered behaviour of a man-made machine. Its component parts do not behave selectively because it is in their nature to do so. The reason is that a machine operator is in control. The random events do occur in the environment. What a motor-car does depends certainly on the twists and turns of the road, on the incidence of patches of slipperiness, on the random succession of vehicles that must be avoided. But the car would not behave as it does if it were driverless.

Servo-mechanisms provide another example and it is worth mentioning because they are nowadays quoted very often in support of the monist's contention. These devices, too, are subjected to the random influence of their environment and yet their behaviour is not random. And again the reason is that they are subjected, in addition, to control by an operator. In servo-mechanisms a principle is employed that is very old in engineering, though it seems only recently to have been noticed by philosophers. It is called feed-back. The parts of the mechanism in which this principle is incorporated are so adjusted by the operator that the desired performance is maintained. Without such adjustment the servo-mechanism would come to grief as surely as a driverless motor-car. Motor-cars, servo-mechanisms, electronic computers, and all other man-made devices depend for their ordered behaviour on the supply of two commodities, energy and control. They are all equipped with devices such as steering wheels, a clutch, gear levers, brakes, settings for feed-back adjustment, by means of which the operator ensures the intended performance. By what twist of perverted logic then can anyone find here proof that living machines do not depend on a supply of the second commodity, control? How does the analogy of a living machine to a servo-mechanism prove that the living machine is not equipped with devices for adjusting the quantity of feed-back? If monists said that they maintain their faith in the ability of living machines to function without being controlled in spite of the inability of lifeless ones to do so, one could appreciate their reasoning. Every one of us (intellectual honesty forces the admission) holds some articles of faith that seem to be refuted by facts. But when anyone says that he believes a living machine not to need controlling because it resembles a lifeless one that does, one must conclude that he has made little effort to distinguish between what in his philosophy is based on faith and what is based on facts. If those on both sides were logically minded, monists would insist that the machine analogy was mischievously misleading and dualists would insist that it was apt. But those who are most vocal on both sides have, I fear, not faced the problem squarely even though they are so ready with their solution. It does after all take more intellectual effort to understand a problem than to invent a theory.

Law and Order
Let us leave the example of the brain and consider in more general terms what is necessary that order may result. In human affairs one of the necessary things is law. This is why the words law and order are often coupled. The rule of the road provides an illustration. It has legal sanction and without it the behaviour of traffic in our streets would be chaotic. Here the law requires a selection between two simple alternatives, left and right. Some laws are more complicated. The Factory Acts, for instance, are concerned with many possible ways of building and running a factory; they require some ways and prohibit others. Some laws again are not codified. They constitute what is called the unwritten law. This governs our code of conduct in many ways and civilization owes much to it. Occasionally some of it may eventually be written down and find its place in a statute book. But whether this happens or not, all those laws that make for order in : human affairs can conveniently be described as of the statute book kind.

Are the laws of physics of the same kind? Is there, to put it concisely, such a thing as a Cosmic Statute Book? Of course I am not asking whether there is literally such a volume; I am asking whether the laws of physics are, like those in statute books, of the kind that make for order. If they are, one might say that textbooks on physics, in which these laws are mentioned, constitute a transcription into human language of the Great Statute Book by means of which the whole material universe is governed. I believe that if people were asked about it the inquiry would show opinions to be sharply, even bitterly, divided on this question. But it has not been debated as thoroughly as its great importance deserves. Its bearing on the dispute between monists and dualists is but one, and I hardly think the most important, of its many implications. But let me dwell a little on this one.

If there is a Cosmic Statute Book, it provides much stronger support for monism than the unfortunate machine analogy. That all living substance, be it in the brain or elsewhere, unfailingly conforms to the laws of physics must be agreed by both sides to the dispute. For it is by conformity to these laws that we recognize substance as material. Matter does not cease to be matter when it acquires the epithet living. What characterizes living matter is, according to dualism, not what it is but what is being done to it. Dualists do not say that a particle changes its nature or any of its properties on entering a living body but that it then comes under a control from which it was previously free. Dualists, at least if they are logical) do not say that a particle in living substance is not subject to the laws of physics; they say that it is subject to these laws and, in addition, to the laws imposed by the diathete life. Monists say that it is subject to the laws of physics and to no others.

If a monist can prove that the laws of physics make for order he has a very strong case. These laws are, so far as can be ascertained, absolutely universal; they apply everywhere and at all times. If they make for order they must do so everywhere and at all times. And if so there can be no such thing as a random event, however much some events may seem to be random. There are many, indeed, who think so. I have often been told, particularly by pious people, that there is no such thing as chance, that there is order everywhere, that even the most insignificant event has been ordered. Anyone who believes this must consider it wrong to pinpoint the problem of order at the junction between stimulus and response, or at any other place. For he cannot think that there is any problem. If he believes that everything is subject to law and order, he believes this of the stimuli; in his view they are not random, however much they may appear to be so. The component parts of the brain behave in a co-ordinated manner, he will say, because the laws of physics ensure that the stimuli received by the brain are co-ordinated; and the fact that these stimuli seem to be unselected, unguided, uncontrolled is, in his opinion, a mere delusion arising from our incomplete knowledge of all the circumstances.

A dualist who believes in a Cosmic Statute Book has, on the other hand, a very weak case. He represents the component parts of the brain as conforming to two kinds of law and he believes that each makes for a different kind of order. He has to explain why this does not lead to some odd conflict. He will not find it easy to justify his contention that two sets of law have to be obeyed by the same particle at the same time. A monist would be fully justified in pointing out that it is irrational to invoke two sets of law when one will serve. If I were satisfied that the laws of physics do make for order I should support monism.

It is quite consistent with the paradoxical logic that pervades our theme that supporters of dualism tend, on the whole, to believe in a Cosmic Statute Book and supporters of monism to reject that notion. A person whose temperament makes him like to think that there are 'higher and better' things than mere impersonal matter also likes to think that all things, however remote and impersonal, are beautifully ordered and law abiding. And a person who feels resentful at the attacks from religion from which science has often suffered likes to cling to two hypotheses that, I am showing, cannot be reconciled: that matter is the only reality and that chance controls all events. And so dualists often clog their cosmology with too much order while monists admit too little. Neither side can reach a logically consistent view of reality without the sacrifice of a cherished conviction. The monist must sacrifice the conviction that every aspect of reality, including order, can be brought within the field of study of the physicist. And the dualist must sacrifice the conviction that law and order are omnipresent throughout the universe. Here we meet one of the occasions when the criterion of attractiveness comes into conflict with the criterion of truth. And when this happens there is always an unwillingness to face a question the answer to which might destroy one of the cherished convictions. The question whether there is a Cosmic Statute Book is of this disturbing kind. It will, I fear, prove equally unwelcome to many dualists and to many monists.

One of the least worthy reasons for clinging to belief in a Cosmic Statute Book is that it provides opportunities for some attractive rhetoric. It sounds well in a peroration when a speaker proclaims such sentences as: 'Nature's sublime plan is revealed everywhere, no less in the tiniest grain of sand than in the most distant star.' 'When I contemplate the wonders of science and the beautiful consistency of those supreme and eternal laws that are implicitly obeyed by our vast majestic universe how can I doubt that there is meaning in everything?' 'The laws of physics and chemistry, no less than those of wise governments must prove to everyone capable of understanding higher things how well everything was meticulously ordained at the very beginning of time.' 'The more profoundly one immerses oneself in the great scientific verities the more must one admire the simplicity of Nature's immutable laws.'

Believers in dualism often find comfort in phrases of the kind that I have caricatured only very slightly in the foregoing quotations. There is no harm in that if the phrases represent true facts. But if they are no more than a substitute for disciplined thinking they can do much harm. Theologians and scientists would agree about that. And I doubt whether belief in a Cosmic Statute Book can really be justified even on religious grounds. Its implications are surely too deter- ministic to be sound theology. Whether the Cosmic Statute Book is supposed to have been the work of an impersonal Nature or of a personal God it is supposed to govern every detail of the material universe. It must be hard for anyone who believes that the behaviour of every particle of matter in all its details has to conform to immutable laws laid down at the Creation also to believe that such particles can conform to the present will of a living God. To accept the Cosmic Statute Book seems to deny God's guiding hand. But the theological implications are a little confusing. For there is another side. To deny that the laws of physics make for order is to deny that they are God's work. And to do this may seem to detract from the omnipotence and ever-presence that is attributed to the Diety. However, I am not qualified to judge the theological implications of the concept Cosmic Statute Book. I have little doubt that theologians have considered them very thoroughly, be it with the use of a different set of words. All that I can ask is that you consider the question without allowing any disturbing thoughts about its implications to cloud your judgement. If I, myself, have, after long cogitation, reached the conclusion that there is no Cosmic Statute Book, it is not because I set myself the task of knocking away the strongest prop of monism. Nor is it that I wanted either to support or to defy any theological doctrine. It is that I think it of the utmost importance that some of us should try to achieve a clear understanding of physical laws, and not be restrained by fear of the consequences to our tranquillity. And to ask about a Cosmic Statute Book is my way of prompting thought about a theme that has been too much neglected. I have noticed that even scientists are by no means consistent in the way they talk about the laws of physics. The remarks of a person will often imply at one moment that he accepts the notion of a Cosmic Statute Book and at another moment that he rejects it. I am hoping that use of this term will focus attention on an aspect of the philosophy of science that needs thorough consideration.

The Laws of Physics
To ask whether there is such a thing as a Cosmic Statute Book is, of course, to tackle along new lines a subject that has its accepted place in the methodology of science. Physicists have succeeded with much labour in formulating a number of statements about the material universe; some of these statements are called laws. They are the foundation on which the magnificent edifice of Western science has been built; they have led to a profound understanding of the nature of matter; they make accurate predictions possible. It is important that we should gain insight into their meaning; we ought to know what we are doing when we formulate the laws of physics. Many of man's greatest achievements in this field have been reached intuitively. But it is as well from time to time to test intuition by the discipline of reason. Hence the value of considering carefully what is happening when a law of physics is being formulated.

The methodology of science can be approached along many different paths. It is only after much deliberation that I have decided in these lectures to follow one that tradition has not signposted. My reason is that traditional questions about the laws of physics tend to conceal conflicts of opinion in this subject and I want to show as clearly as possible how sharp a conflict there is. It is not only between rival schools of thought; it is, as I have just hinted, within the mind of every one of us. Whether we decide that there is a Cosmic Statute Book or that there is not, we have to sacrifice some theory that we find attractive. It is better to face that fact than to evade it.

From the way in which the laws of physics are often spoken of I must conclude that belief in a Cosmic Statute Book is rather more orthodox than disbelief. I think that the following fairly represents the views of many about the laws of physics: 'These laws resemble those in the statute books at Westminster in their effect, which is to make for order. This is proved by the certainty with which physicists make predictions from their laws. When one knows the laws of a country one can predict some of the things that the inhabitants will do, such as on which side of the road they will most often drive. Similarly it is because physicists know the laws of the material universe that they can predict how a particle of matter will behave in given circumstances. But the laws of physics differ from those in man-made statute books in five ways. They are more ancient. They are more detailed. They are completely unalterable. They are completely binding. They are implicitly obeyed.'

Only on the reason why a particle of matter implicitly obeys the laws of physics may there be difference of opinion between a theologian and his atheistic opponent. The theologian might say it was because matter does not possess Free Will and cannot therefore sin against the laws that the Creator has ordained for the material universe, while man, on the other hand, does possess Free Will and so does some-times sin against God's moral law. The atheist might object that the laws of physics were not ordained by God but by Nature and that a particle of matter obeys them implicitly because it is made in Nature's image and cannot do otherwise. But that matter would behave differently if the laws of physics were different would be agreed by many theologians and many atheists.

Those who think thus picture the physicist as analogous to an explorer who seeks to discover the laws of a foreign country. Should he want to know what the rule of the road was he could place himself at a street corner and watch the traffic. After he had observed a sufficiently large number of vehicles he would know whether the law required them to keep to the right or the left. Similarly, it is thought, Mr. Ohm observed electric currents in circuits. When he had measured a sufficiently large number he arrived at the conclusion that the Cosmic Statute Book contains the famous law that goes by his name. This is the view that must, I am afraid, be challenged. I think that it constitutes a danger to the methodology of science.

With the sole purpose of making my meaning as uncompromisingly clear as I can let me depart even further than I have done already from the traditional approach. Let us imagine that an explorer has visited a newly discovered, very civilized country and brings back an account of its laws. He reports that they are very ancient and established, never altered, completely binding and so detailed that his list of them fills three fat volumes. He reports on them to a learned society.

'Do the inhabitants always obey these laws?', he is asked.
'Implicitly', is the reply.
'Is there a rule of the road?'
'Certainly.'
'Does traffic have to keep to the right or to the left?'
'The law says that it must either keep to the one side or to the other.'
'Are there any building regulations?'
'There are many pages of them.'
'What does the clause say in which it is laid down in what proportions cement, sand and aggregate shall be mixed in making concrete?' 'The law says that these shall be mixed in any proportions.'

And so it goes on. The audience learns that the laws require a man to have any number of wives, to pay any proportion of his income in tax, for any number of cubic feet of space in the factories of the country to be allowed per worker. Those who hear these travellers' tales are not surprised that the laws of this strange country are obeyed implicitly.

Clauses in human statute books do not contain the word 'any'. To constitute laws the wording must imply 'thus and not otherwise'. And the prevalent belief that I am now challenging is the one that the laws of physics do in effect say 'thus and not otherwise'. Indeed those who believe that the laws of physics make for order cannot think differently. So let us review some of those phenomena held to illustrate the eternal, universal order.

Days and nights succeed each other with absolute regularity and a day and night encompass between them twenty-four hours. Does the Cosmic Statute Book contain a clause to say that it shall be so? A schoolboy can tell us that it does not. A clause is not needed to say that days and nights shall succeed each other. A more general clause to say that planets shall rotate on their axes would suffice. And a clause to say that the period of rotation shall be twenty-four hours can certainly not be there; for the period of rotation of planets is different for each. A clause about the time that a planet shall take to rotate about its axis would have to be worded 'any time'.

What can be said about the length of days and nights can be said with equal force about the length of the planetary year, about the size of stars, the height of mountains, the width of valleys, the speed of rivers, the constitution of the atmosphere surrounding a planet, the proportions in which the elements are mixed in rocks, the outline of continents, the arrangement of stars in the heavens. So long as we look only on the untouched world of lifeless things we find examples of every conceivable contour, every degree of simplicity and complexity, every mixture of ingredients, every possible size and shape of things. The rugged outline of a mountain range, the starry confusion of the heavens do provide sublime beauty. But it is not the beauty of order; it is the beauty of randomness. How then, it may be asked, can one account for such examples of regularity and pattern as may undoubtedly be observed in the untouched world of lifeless things?

There is, for instance, the roundness of stars. A star with knobs or corners is unknown. Is there, perhaps, a clause to say that stars shall be nearly spherical and may not be of any other shape? A student of elementary mechanics can tell us that no such clause is necessary. The nearly spherical shape of stars is ensured by gravitation and centrifugal force. We must look for another example.

There is the beautiful regularity of crystals. Is there a clause to require that molecules shall be drilled into serried ranks when a substance solidifies from its gaseous state or when it precipitates out of a concentrated solution? A crystallographer could tell us that no such clause is necessary. During crystal formation the molecules tumble and dart about erratically. Occasionally one of them comes near enough to the growing crystal to be held firmly in position' and to become a part of the crystal structure. Then it jostles and tilts with its neighbours until it has fallen in the only position in which it can pack firmly and not easily become dislodged. The molecules reach their regular configuration in the process of rushing aimlessly hither and thither. One need not invoke a restraining law to explain their behaviour. If the Cosmic Statute Book says that molecules may form 'any' configuration, many different configurations will be observed. Those of crystals will occur occasionally, about rarely enough to explain the high price of precious stones. Shall we then turn to the law that requires planets to move in elliptical paths, to the law of the pendulum, to the law of inertia, to the laws of the electro-magnetic field? At one time it would have been thought that each of these has its separate clause in the metaphorical volume. But Newton applied the blue pencil to many of them. He showed that the elliptical paths of the planets, the falling of apples, the law of the pendulum and much else would be ensured automatically if there were only clauses calling for the laws of gravitation and motion. He inherited from his predecessors a very detailed Cosmic Statute Book and bequeathed to posterity a very meagre volume. That is what people mean when they say that Newton achieved a great unification of the laws of physics. He showed how a very large number of special laws can be deduced from a small number of general ones. The late Professor Thornton, who gave the second series of these lectures, meant the same when he spoke in World Power of 'great sweeping laws that gather together masses of apparently unrelated facts like fish into a net'.

Since Newton's day the blue pencil has been wielded again and again; ever bigger fish have been gathered into the net. The popular notion that physicists are always adding new clauses to the Cosmic Statute Book has been belied by history. On the contrary, they more frequently find that the fruits of their work enable them to strike out some of those that they have found there. The General Principle of Relativity provides a recent example. It ensures the law of gravitation together with many others. And an even wider generalization has been achieved with the formulation of what is called the Principle of Least Action. The late Sir Arthur Eddington pointed out in his Space, Time and Gravitation that the law of gravitation, the laws of mechanics, as well as the Jaws of the electromagnetic field are all summed up in this one principle. Perhaps it spreads its net so wide that no fish can escape. If so, the Cosmic Statute Book need contain only this single clause. But it is doubtful if even this is needed.

Eddington also pointed out that another apt name for the Principle of Least Action would be the Principle of Greatest Probability. He inferred from this that 'the law of nature is that the actual state of the world is that which is statistically most probable'. This is the state in which the traffic in our streets would be if there were no rule of the road; it is the state in which all things find themselves when everything is allowed and nothing prohibited. Eddington's suggestion amounts to saying that the Cosmic Statute Book consists mainly of blank pages.

If this is so a 'thus and not otherwise' type of legislation in the physical world can apply at most to only a very few so-called cosmic constants. There is, for instance, the greatest velocity at which energy can be transmitted; it is called the velocity of light in a vacuum. There is the smallest portion of ponderable matter, called an electron. There is the smallest amount by which anything can change, called the quantum of action, or Plank's constant. So far physicists have not succeeded in showing that these three constants are the inevitable consequence of some more general principle in the sense in which the succession of days and nights is the inevitable consequence of the earth's rotation. But most of them expect eventually to be able to do so. There is good reason for examining the possibility that the few remaining facts about the material universe that have so far proved irreducible are not imposed on matter but are the consequence of the way we think about things.

Be that as it may it would take a bold man to build a doctrine of universal law and order on the slender foundation of a few cosmic constants. Those who like to believe that eternal laws govern every detail of the material universe will gain but little comfort from the thought that these few constants may, after all, prove to be irreducible. And monists, in particular, who hope to show that the ordered behaviour of the component parts of the human brain is the inevitable consequence of the ordered behaviour of all matter will need more of a 'thus and not otherwise' than a few such quantities if their hypothesis is to convince anyone.

It may, however, be objected that I have chosen my examples unfairly and that one could find in textbooks on physics another category of law that does require certain things and prohibits others. In the short time at my disposal I cannot review the whole of physics and examine every one of its laws in turn. But I can at least mention some that do seem to belong to a different category and might be quoted in support of belief in a Cosmic Statute Book. As examples I shall mention Ohm's law and the inverse square law of forces. The true nature of these can be most conveniently presented to you if I refer again to the imaginary traveller who returns from a foreign country. He is asked whether that country has any laws that are of the 'thus and not otherwise' kind.

'Oh yes', he answers. 'One of them helps to regulate traffic in the streets.'
'How is it worded?'
'It says that stationary traffic shall not move. There is a rider to define stationary traffic as traffic that does not move.'

The audience can well understand that this law, too, is obeyed implicitly. And what I want to explain to you is that Ohm's law and the inverse square law are of this kind. They say no more than what is true by definition. Let us consider each in turn.

Ohm's law does not say that the current in a circuit shall have a stated value, for the value depends on the circuit. The law does not say that the ratio of current to voltage in a circuit shall have a constant value. This only happens when the resistance remains constant and other circumstances do not affect the current. What the law does say is that the ratio of current to voltage shall equal the resistance when the resistance is defined as the ratio of current to voltage.

It might be objected that the law does say something more. For it requires that the ratio of current to voltage shall be a linear function. Expressed in the form E = IR the law prevents, for instance, the current from being proportional to the square of the resistance or to its fifth power or to any other function of the resistance. If so, Ohm's law, by requiring linear proportionality, does say 'thus and not otherwise'. True enough. But if the law occurs in this form in the Cosmic Statute Book it is nearly always disobeyed. For it would be difficult indeed to find a circuit in nature for which the ratio of current to voltage was a linear function of the circuit. In nature every conceivable function between current and voltage can be observed. And even in a laboratory it takes some care to reproduce Ohm's law, as every teacher of electricity and magnetism finds out. When he succeeds he proves that nature, wild and disorderly when left to herself, can on occasion be made to toe the line and do man's bidding. In short, one can argue that Ohm's law is no more than a definition of resistance, and one can argue that it is an invention. But one cannot argue that it is a discovery.

Much the same can be said about the inverse square law. This applies equally to gravitational, electrostatic, and magnetic fields. So it seems to have some universality. Let us consider its application to electrostatic fields. The law states that the field strength around a charged body varies inversely as the square of the distance. But if a small charged body were suspended just here in front of you and the field strength around it were measured it would not vary even remotely as the inverse square of the distance. Various objects in the vicinity of the charge would interfere too much. To demonstrate the inverse square law I should have to take sundry precautions. I might let the charge be on a small sphere and surround this by a larger concentric sphere made of a conducting material. If I made measurements of field strength in the space between the two spheres I should be able to show that the inverse square law was being obeyed. The reason is that in the field between concentric spheres the field is uniformly divergent, and the law only holds for this special condition. So the clause to ensure the inverse square law must read: In the space between concentric spheres (or alternatively 'For a uniformly divergent field') the field strength shall be inversely proportional to the square of the distance from the centre of a charged body forming the inner sphere.

But this could be predicted without an experiment. When one speaks of a force one means an influence exerted from somewhere on some object, one means the kind of effect for which, as stated in elementary textbooks, action and reaction are equal and opposite. In electricity this could be expressed by saying that every tube of unit force in our concentric spheres had one end on one of the spheres and the other end on the other sphere. It follows from this that the intensity of the force on the outer sphere is inversely proportional to its area. And as the area is proportional to the square of the radius the intensity of the force, also called field strength, is inversely proportional to the square of the radius for any sphere concentric with the one carrying the charge. In short, the inverse square law is not a statement about gravitation, or electricity, or magnetism. It is a statement about geometry. It must be observed whenever there is a uniformly divergent field and it is never observed when the field has a different shape.

So the Cosmic Statute Book need not have a clause in which the inverse square law is mentioned. It would be ensured by a clause in the section headed 'Geometry'. Such a clause would have to read: 'For a sphere the area shall be proportional to the square of the radius.' Are we then to take it that there is such a clause? The answer is 'No'. For it holds only when the geometry is Euclidian. And Nature's geometry is not necessarily Euclidian. We know from the general principle of relativity that the Cosmic Statute Book allows any geometry. There are, therefore, occasions when the inverse square law does not hold even for concentric spheres. The region within the nucleus of an atom may provide an example.

The Methodology of Physics
These considerations have led us deep into the methodology of physics. It is a profound and interesting subject and I find myself tempted to dwell on it for longer than the theme of these lectures permits. It is, however, not quite irrelevant to add the following observations.

To abolish the notion of a Cosmic Statute Book is not to belittle but to enhance the achievement of Western science. If the laws of physics were really of the 'thus and not otherwise' kind, the task of physics would be to discover by observation and experiment what this metaphorical volume contains. The textbooks on physics would then be like the reports that travellers bring back from foreign countries. Physics would be built on the solid foundation of countless irreducible facts and laws. But if there is no Cosmic Statute Book there is no such ready-made foundation. The very basis of physics has not been discovered but created by Western science; those laws that have proved of such inestimable value are all, like Ohm's law, not discoveries but inventions. If the rough untouched world of lifeless things does not present us with any order then the beautiful order manifest in the textbooks is a product of scientific methodology. If the world studied in physics is one in which anything may happen that is logically possible, then the task of the physicist in finding his way about this random world is all the harder, his achievement in introducing system into chaos all the more magnificently creative.

There, with considerable regret, I must leave a most enticing subject. A useful purpose will have been served if this study causes both those who do and those who do not believe in a Cosmic Statute Book to ask themselves how much of their belief is based on facts and how much on faith. When they have faced that question some may disagree with me about the Cosmic Statute Book. They may have good reasons, and none the worse if they are based on faith rather than on fact, for belief in this metaphorical volume. Others may agree with me that the laws of physics permit every- thing that is logically possible. But having once for all found his answer to the uncompromising and rather uncomfortable question whether there is a Cosmic Statute Book, a person will no longer be free to secure what seems to him most attractive in the implications of each answer.

Summary
Let me in conclusion remind you once again of the bearing of all this on a decision between monism and dualism. The kind of order observable in human affairs has to be explained. Examples of this kind of order occur when a house is being built or a machine constructed. The component parts are arranged to a specification. The same kind of order is manifest in the structure of the brain and in the behaviour of its component parts.

If there is order everywhere there is good reason to attribute the order revealed by houses, machines, and living substance to the principle that makes for universal order.' This principle is expressed in the laws of physics, and monists do attribute all order to it. But if there is no such principle one must attribute order, when it occurs, to something that does not operate on the whole of matter but only on those particular things that differ from the rest by revealing order. Dualists say that this is in fact so; that in those instances where order is revealed a non-material influence, a diathete, is acting on matter.

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