WE are all familiar with laws. Many are in the form of Acts of Parliament. Our daily conduct is largely governed by them. One of the simplest and commonest is the law which requires traffic to keep to its own side of the road. We take account of it almost every time we stir out of doors. In the absence of such laws things would be left to chance. Civilization would be impossible. If there were no rule of the road, the state of traffic on our highways would be chaotic.

We shall find later that all laws are not like Acts of Parliament, so we need a distinctive name for those which are. "Governmental laws" suggests itself as obviously suitable. And as a specified selection between alternatives cannot be obtained without such laws we might also call them "selective laws". This title emphasizes that they forbid certain things and demand others. We shall find several other equally appropriate names later on.

We have shown in the preceding section that in the organic world a specified selection between alternatives is obtained. In the structure and behaviour of living organisms certain things are forbidden and others demanded. So the laws of biology are of the governmental type. At first sight it may seem that all the laws of physics are of this type too. It is quite customary to speak of them as though they all were. Jeans does so when he tells us that God selected the laws of physics out of innumerable possible alternatives. In saying this Jeans expresses, we feel sure, a very prevalent belief, at least among non-physicists, and a belief implied sometimes also by physicists as when they speak of "forbidden" transitions in quantum mechanics. Singer shows this belief when he says that it is a sense of the reign of Law which the Greeks have handed down to us.

It is an excusable belief. For the true nature of the laws of physics is not immediately obvious, and their superficial resemblance to those of a country and to those of biology, is. The laws of biology are manifest in such requirements as that a tulip flower shall have three external petaloid sepals and three internal petals, that muscles shall contain glucose, that offspring shall resemble their parents, that dogs shall secrete saliva at the prospect of food. The laws of physics are manifest in such requirements as that planets shall move in ellipses, that hydrogen shall combine readily with oxygen, that carbon shall crystallize in octahedral and allied forms, that the acceleration of a particle shall be proportional to the force applied to it.

It is such lists which give the impression that those laws which govern the behaviour of substance in the organic world and those which govern the behaviour of the whole Material Universe are all fundamentally similar to the rule of the road or any other law which governs the behaviour of communities.

The laws of physics appear to be imposed on defenceless Matter just as the decrees of dictators are imposed on a defenceless people. We will consider in the present chapter whether this is true.

A moment's thought should make us suspicious, for there are differences which all would agree to be significant. Man-made laws are broken sometimes. The organic world has its failures. But the laws of physics are never broken. It would be meaningless to speak of failures in the inorganic world. An electron never makes a "forbidden" transition. A particle never fails to move with an acceleration proportional to the force apphed to it.

Man, one might say whimsically, is less obedient than Matter. Those who believe that the laws of physics have been imposed on the Material Universe as Acts of Parliament are imposed on a country could argue that Man breaks laws because he possesses Free Will, but that Matter which does not possess Free Will obeys implicitly the laws created for it. This, we shall soon find, is not the correct explanation. But some such view was undoubtedly entertained at one time. Whether it is still general, is hard to say.

In universality and permanence we have a similar distinction. Laws made by legislators vary from country to country and from year to year. The principles to which the organic world conforms have changed with every stage in evolution. But the laws and principles of physics never change and never can change. Embodied in a written statement the laws of physics, as envisaged by Jeans, would constitute a document appropriately called the Cosmic Statute Book, a document to which not a single word has been added and not a single word has been taken away since the beginning of time. Those who speak of God as the Supreme Legislator must believe that He exercised this function once only a long, long while ago.

But are we obliged to believe in a Cosmic Statute Book?

It has been suggested to us in conversation that the question is not a real one and would disappear if, instead of speaking of the laws of physics we spoke of the nature of Matter. "What are called the laws of physics", we have been told, "are really manifestations of the nature of Matter. Physicists do not really deal with laws but with observables. Their questions do not, or should not, begin with 'why' but with 'how'. There is no justification for the assumption that things which are observed need be attributed to laws."

This view seems to be gaining ground with physicists at the moment. Those who accept it would no longer speak of "forbidden" transitions for an electron. They would speak of "impossible" transitions. If Jeans accepted it he would not say that God selected the laws of physics out of innumerable alternatives. He would say, instead, that God selected the nature of Matter out of innumerable alternatives.

We, however, do not have to decide whether this view is correct or not. Whether physicists ought to ask "why" or "how" is a question, of the procedure and the obligations of physicists, not a question of scientific fact. It is hair-splitting to argue whether the laws of physics are defined by the nature of Matter or the nature of Matter is defined by the laws which it obeys. Our question remains, whichever method of procedure or way of expressing their conclusions physicists prefer to adopt.

Consider an illustration. So long as the behaviour of an electron in the atom. is expressed by saying that a law forbids certain transitions, we ask: "Is this law a specified selection between alternatives?" But if the behaviour of the electron is expressed, instead, by saying that the nature of Matter renders certain transitions impossible we formulate our question: "Is the nature of Matter a specified selection between alternatives?" It is still exactly the same question. To believe that the question does not intrude if "impossible" is substituted for "forbidden" is to adopt the policy of the ostrich. It is to believe that one can dispose of a problem by juggling with words.

The reader may, if he choose, substitute the word "observable" whenever we say "law," making such further verbal alterations as may be necessary. The sense will remain the same. He must not try to persuade himself that such verbal changes have any scientific or philosophical significance. It is true that the question whether we are obliged to believe in a Cosmic Statute Book will disappear, but only to turn up again in another form. The proper document for a collection of data such as might be called "observables" is a specification. So our question then takes the form: "Are we obliged to believe in a Cosmic Specification?"

We shall ask this question anyhow later on. But we prefer to adhere to the traditional language of physicists in which laws are distinguished from other data and to divide our investigation accordingly, treating our question concerning a Cosmic Statute Book, as part only of the more general question concerning a Cosmic Specification.

In spite of what Jeans has said we believe that most physicists are sceptical to-day of any theory of the Material Universe which implies that there has been a specified selection between alternatives. But they were not always sceptical.

A few centuries ago no one would have doubted that the laws of physics were of the governmental type. Up to the time when science had begun to free itself from the bondage of medieval superstition scientists still regarded God literally as the Divine Legislator and they believed that each and every physical law was obeyed by the Material Universe in the same way as Acts of Parliament are obeyed by the citizens of a country. In those days men might, without appearing unduly fanciful, have spoken of the Cosmic Statute Book. The task of science which was called by some a pious duty, by others an impious impertinence, appeared to be to discover from a study of the laws of physics and chemistry how the Creator's Will works.

In those days scientists' questions began with "how". They did not begin with "why". For it was taken for granted that to the question "why" only one answer could be given, namely Divine Guidance.

By abolishing a geocentric Universe, Copernicus's discovery of the solar system helped towards the emancipation of science. The change in outlook which followed was considerable and its importance is well known. But we must not forget that this change was only in the way men regarded the position of the earth in the scheme of things. Copernicus did not bring about any change whatever in the way men regarded the nature of physical laws. These were still thought of as if they were of the governmental type. A few generations had to pass before scientists came to suspect that in physics the word "law" has a different meaning.

When Copernicus's measurements of planetary paths, undertaken with comparatively crude means, led him to conclude that these paths were circles, he and those progressive contemporaries who accepted the Copernican system had no doubt but that they were being permitted to read in the skies proof that the Divine Will demands order and symmetry of celestial bodies. The only explanation for the supposed law that planets shall move in circles which was conceivable at that time was that this law represented God's selection of the most suitable path for such sublime heavenly bodies as planets. It seemed only fitting that this path should be the most perfect and symmetrical figure known to geometry.

The subsequent discovery of Kepler that the paths of planets are ellipses and not circles could not alter this survival from the medieval outlook. It merely suggested that the Divine Will had been previously misunderstood. The Creator's direct control, in the capacity of Legislator, could still be thought the cause of the planetary paths. It would not have occurred to anyone to seek another explanation. It seemed only necessary to find a justification for a geometrical figure less perfect than the circle. Kepler attempted a compromise by turning his attention from the shape of the planets' paths to their distances from the sun. By an elaborate theory he attempted to show that these distances bore the same proportions to each other as do those intervals in music which give the most perfect harmony. In those days the laws of physics were considered literally to make for order in the Material Universe just as traffic regulations make for order in our streets and biological laws make for order in every living organism. The appropriateness of Charles Singer's phrase "reign of Law" would not have been questioned.

Such theories were rendered untenable by Newton. He was not content with the question: "how". He began to ask "why". He showed that all bodies exert a pull on each other proportional to their masses and inversely proportional to the square of the distance between their centres of gravity. The law expressing this relation is called the Law of Gravitation. Newton also discovered the way in which the speed and path of any body are influenced by the pushes and pulls exerted on it, the connection between movement and applied force being defined by his famous Laws of Motion. When Newton applied these laws to the sun and planets he found that planetary orbits must inevitably be very close to ellipses. Thus Newton disposed once for all of the theory that the smooth, regular paths of heavenly bodies are due to a Divine Law or even an impersonal Cosmic Principle expressing a preference for regularity, symmetry, order or any sort of harmonious relationships.

At the same time Newton showed that the law of planetary motion is not of the governmental type. It is not like an Act of Parliament. For it does not restrict the choice between alternatives. Newton proved that for the paths of planets there are no alternatives. Other laws, namely those of gravitation and motion, preclude them. Whatever the Cosmic Statute Book may contain, we can be sure, since Newton's discoveries, that it says nothing about the way planets shall move. Provided the laws of gravitation and motion are ensured, observance of the law of planetary motion becomes automatic, even though not specifically called for.

A great many other laws are automatically ensured as well. Among these are the laws that the trajectory of a projectile shall be a parabola, that the period of swing of a pendulum shall be proportional to the square root of its length, that centrifugal force shall be proportional to the product of the radius and the square of the angular velocity. All these laws are implied in those of motion, together with hundreds of others. Newton showed that many laws relating to specific circumstances are implied in fewer general ones. The many specific laws need not be mentioned in the Cosmic Statute Book because they can be deduced from the few general ones. We will, therefore, call those laws of which the law of planetary motion is typical, "deducible" laws. This word will distinguish them from the "selective" laws.

Newton is commonly said to have brought about a great unification of science. What is meant is that the few laws which he left in the Cosmic Statute Book apply to everything in the Material Universe, in all places and at all times. Before his time it had appeared that one law was imposed on planets, another on projectiles, and yet another on pendulums. Newton showed that the behaviour of all those things is the inevitable result of a simple set of laws for all Matter. The behaviour of all things in the physical world could thereafter be attributed to the universal properties of Matter.

The unification of science achieved by Newton was, indeed, revolutionary. To many it will have appeared irreligious. For it attributed less direct and immediate control to the Almighty than had been previously supposed. But to-day physicists take this whittling away of the Cosmic Statute Book for granted. They speak of "great sweeping laws that gather together masses of apparently unrelated facts like fish into a net" ¹

Since the days of Newton a great many more fish have been gathered into the net. Successive discoveries make the Cosmic Statute Book appear ever less bulky. Among laws which have been struck out only recently are those of gravitation and motion. For more than two centuries these corresponded to nets in Professor Thornton's metaphor and not to fish; they appeared as unrelated, as absolute facts; one would have had to describe them as selective laws not as deducible ones. No one could give any reason why there is gravitational attraction, why bodies conform to Newton's Laws of Motion. One could only say that it was so. One could answer questions about gravitation beginning with "how". But one could not answer the question beginning with "why". But today these laws have been accounted for. They have been proved to correspond to fish in the above metaphor. For they have been gathered into a still wider net. This is spread by Einstein's General Theory of Relativity. The Cosmic Statute Book no longer contains the laws of gravitation and motion.

After many successive curtailments it still appeared that there was one law for tangible substance and that there were others for less tangible contents of the Material Universe, such as radiation or electricity. But further unification has obliterated any distinctions between these varied contents and has shown that the behaviour of all things in the physical world can be attributed to the same laws. Among the very wide nets is a principle called the Principle of Least Action. Eddington has pointed out² that the law of gravitation, the laws of mechanics, and the laws of the electro-magnetic field are all summed up in this principle. Perhaps it spreads so wide a net that no fish can escape. Perhaps, in other words, the whole of the contents of the Material Universe obey this one law and no other. If so, the Cosmic Statute Book need mention nothing but the Principle of Least Action.

Let us change the metaphor. According to Indian mythology the world is supported by an elephant called Testi, and the elephant stands on the back of a tortoise called Kurma. Newton showed that the law of planetary motion and many others are supported by the laws of gravitation and motion. These in turn are supported by the Principle of Least Action. We can compare this very broad generalization to the broad back of the tortoise Kurma, and call the Principle of Least Action a kurma law. All the laws which rest on it must then be called testi laws. Other names are possible. Philosophers would probably give testi and kurma laws the names reducible and irreducible. Above we have suggested the names deducible and governmental or selective. Eddington has used the terms identical and transcendental. Each pair of names has its uses, for each conveys to the mind a different aspect of an interesting and significant distinction.

The words testi and kurma remind us that everyone who is told of the Indian myth asks at once: "On what does the tortoise stand?" Similarly everyone who is told that a law A can be deduced from another more general law B asks: "From what is law B deduced?" Physicists attempt to prove that every law which is apparently a kurma law is really a testi law. They have succeeded so well that there are hardly any kurma laws left. But an end must come some time when the process of deduction can go no further. What may we expect to find then?

Does the Cosmic Statute Book contain one or two statements which require that the contents of the Material Universe shall behave thus and not otherwise? What is the fundamental law of nature which ensures the proper behaviour of planets and pendulums, of magnets and rays of light?

We can only speculate on the answer. But a brilliant suggestion of Eddington's leads to a speculation of considerable interest. He has shown that the principle of least action might also be called the principle of greatest probability. He infers that "the law of nature is that the actual state of the world is that which is statistically most probable".³ This suggestion deserves the most careful thought.

The traffic in our streets would be in the state which is statistically most probable if there were no traffic regulations. This is the state of an uncontrolled world, free from all selective principles, free from any restrictions. If Eddington's tentative suggestion is accepted, we can say what is to be found in the Cosmic Statute Book. Could we refer to it to discover how Matter is to behave, we should read but one word: "Anyhow". In this case the only law in the Cosmic Statute Book is the law that there shall be no laws.

This is, at the present stage of knowledge, pure speculation. We know that the Cosmic Statute Book does not contain much. But we cannot be sure yet that it contains nothing. And only one positive statement in that document would suffice to justify the view expressed by Jeans. Moreover, even if Eddington's surmise about the nature of the laws of physics is correct and that of Jeans is wrong, it is still necessary to define probability with care. Scattered by the monkey of chance on a billiard table a number of ivory balls all lie in one plane. The conditions imposed by circumstances limit in this instance the possible positions which the balls may occupy. Similarly the constitution of the Material Universe may meet other specified requirements which do not come under the heading "laws", and which would appear not in a Cosmic Statute Book, but in that more general document which we have called a Cosmic Specification. But before we investigate what data this may contain we will give our attention to a comparison of the attitude of physicists towards their science with that of biologists to theirs.

Notes
1 Professor Thornton, quoted in World Power of December 1937, p. 271
2 Eddington, Space, Time and Gravitation, p. 149
3 ibid, p. 178.

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