The Analysis of Matter

of the careful records inspired by superstition. This evidently happened with the Egyptian priesthood, who learnt to predict eclipses, and probably only then ceased to regard them with awe. Gradually, the view that there must be some law according to which strange things happened became more widespread. Dr Whitehead, in his Science and the Modern World[50] traces the belief in natural laws to various sources, such as: Fate in Greek tragedy, the supremacy of Roman law, and the rationality of God in mediæval theology. In effect, however, he regards the belief as having only acquired a firm hold of the scientific mind at the renaissance. Everything that he says on this subject is so excellent that it is unnecessary to cover the ground again. Although the belief in the universality of natural law was, at the time of the renaissance, a bold faith going far in advance of the evidence, it has since been so successful that it is now[Pg 231] possible to defend it on inductive grounds. But there is some difficulty in deciding what we are to mean by it. I have dealt with this subject before,[51] and shall now consider it only briefly. The regularities which we first observe, and in which we first believe, are of the simple form: " is always accompanied (or preceded or succeeded) by ." But all such regularities are capable of having exceptions, and science soon seeks laws of a different kind. We arrive in the end (possibly not at the very end) at differential equations. I think that these are of two kinds, those expressing persistence, and those expressing accelerations (in a generalized sense). The former are concealed, more or less, by the assumption of permanent substance; but this is a topic which I shall consider in the next chapter. The latter are the ordinary differential equations of the second order which occur throughout mathematical physics. But in addition to these, in order to produce observed macroscopic results, there must be statistical laws governing quantum changes and radio-active disruptions of atoms. I want to inquire whether we are saying anything significant in assuming that there are laws governing the course of the physical world, or whether any set of percepts must be amenable to law by a sufficiently liberal use of hypothesis. It is by no means clear that the accepted laws of physics make certain imaginable series of percepts impossible; still less that the mere existence of laws would have this effect. Take, e.g. continuity. Changes which appear sudden (e.g. explosions) can be resolved into a number of continuous though rapid changes: per contra, situations in which there appears to be no change (e.g. a steadily glowing gas) are resolved into a number of discontinuous changes. Thus we can neither infer the absence of physical continuity from the absence of[Pg 232] continuity in percepts, nor the presence of physical continuity from the presence of continuity in percepts. Again: if percepts change in unexpected ways, we infer unperceived matter; and by a sufficient amount of unperceived matter almost any series of percepts could be explained. Of course a particular law is strengthened when it enables us to predict percepts, but this belongs to the arguments in favour of such-and-such laws, not to the arguments in favour of laws in general. We can have evidence in favour of such-and-such a law without having evidence for laws in general. But here we must make some distinctions. Evidence in favour of a particular law is evidence that a certain class of phenomena are subject to a rule which we have succeeded in discovering. If so, they are sure to be also subject to other rules sensibly indistinguishable from the one for which we have evidence; but these will in general be more complicated than the rule which we adopt. Complication may be of two kinds: it may be in the formula, or in the amount of hypothetical matter needed to make the rule work. The great merit of Newtonian gravitation was that it was simple in both respects. But clearly any set of observations on planetary motions could have been fitted into the Newtonian formula by postulating a sufficient number of invisible bodies or a sufficient complication in the law of attraction. For any given set of observations, there would have been many such possible methods of bringing harmony between observation and theory; most of these would not have been compatible with a fresh set of observations, but some of them would have been, given sufficient mathematical ingenuity. What is remarkable, therefore, is not the reign of law, but the reign of simple laws. If the transfer of energy were subject to laws as complicated as those governing the transfer of English land, we should never succeed in discovering them: there would always remain a number of possible codes, all of which would fit all known relevant facts.[Pg 233] The principle of induction, as practically employed, is the principle that the simplest law which fits the known facts will also fit the facts to be discovered hereafter. This principle, in all its naked simplicity, has come to the fore in Einstein's theory of gravitation, which consists in taking the simplest available tensor equation in preference to the others that are mathematically possible. It may be said that the principle of simple laws is purely heuristic, and of course this is true to a considerable extent. No sensible mathematician would test a complicated formula before testing a simple one. But the remarkable thing is that the simple formula so often turns out right. From the trend of physics, it seems as though complication were geographical rather than legal. Organic compounds have an immensely complicated structure, but there is no reason to suppose that their fundamental laws are other than those which govern the hydrogen atom. Professor J. B. Haldane, it is true, thinks otherwise, and so do all varieties of vitalists. But, to a layman, their arguments seem inconclusive, and they are rejected by many competent authorities. It is therefore at least a tenable hypothesis that all matter is governed by very simple laws. This is so remarkable that it almost suggests some relation to Mr Keynes's "principle of limitation of variety," and seems to confirm his hint that Nature may be really like the urn containing white and black balls which plays such a prominent part in the theory of probability. Some Mendelians would make us think of human beings in this way. Suppose there were a hundred pairs of characters, , , , , , , etc., such that every human being possessed by inheritance one but not both of the characters in each pair. This would make the number of differing human embryos —i.e. about . If this is thought too few, we can take more pairs of characters. Views of this sort cannot be rejected out of hand, and they are strongly suggested by the success of[Pg 234] induction and the prevalence of simple laws. Let us, therefore, ask once more: What evidence is there that simple laws prevail, and how much reason have we to be surprised by the degree of their prevalence? As I have pointed out on a former occasion, it would be fallacious to argue inductively from the simplicity of the laws we have discovered to the probable simplicity of undiscovered laws. For, if some laws are simple and some complicated, we are likely to discover the simple laws first. We have toi proceed more cautiously. First, is it surprising that there are any simple laws? Secondly, have we any ground for believing, as was suggested just now, that all phenomena are governed by simple laws? Simplicity is best established at the two opposite extremes of size: astronomy and the atom. The latter, however, is much more significant for our inquiry, since the simplicity of astronomy may result from averaging. As we saw in Part I., the theory of the atom amounts, broadly, to this: An atom is composed of electrons and protons, the latter being all in the nucleus, the former partly in the nucleus (except in hydrogen), partly planetary. The number of protons in the nucleus gives the atomic weight; the excess of the number of protons over that of electrons in the nucleus gives the atomic number. When the atom is unelectrified, the number of planetary electrons is equal to the atomic number. If the quantum theory is correct, an atom has a certain number of characters, each measured by integers called quantum numbers, which are always small. It has also a property called energy, which is a function of the quantum numbers; and in connection with each of the quantum numbers there is a periodic process which is subject to quantum rules. Each quantum number is capable of changing suddenly from one integer to another. When the atom is left to itself, these changes will only be such as to diminish the energy, but when it is receiving energy from[Pg 235] elsewhere the changes may increase the energy. All this, however, is more or less hypothetical. What we really know about is the interchange of energy between the atom and the surrounding space; here there are simple laws as to the form the radiant energy will take. But there are at present no laws determining when quantum changes will take place in the atom, though the changes that are possible are a definite known set. As we are only considering how far simple laws can account for the phenomena, we may accept the view of the atom as a miniature solar system, governed, except as to quantum changes, by attractions and repulsions among its electrons. Nevertheless it remains a fact that the atom only indicates its presence when it suffers a quantum change, and that we know of no laws determining why, at a given moment, such a change takes place in some atoms rather than in others. The laws governing the intensity of the light emitted by a gas are statistical laws. This suggests a world in which the number of possibilities is finite, but the choice among possibilities is left purely to chance. We might suppose, as Poincaré once suggested, and as Pythagoras apparently believed, that space and time are granular, not continuous—i.e. the distance between two electrons may be always an integral multiple of some unit, and so may the time between two events in the history of one electron. This, together with the fact that the number of electrons is finite, would give a finite number of possible situations for each electron. And it may be that the choice among possible situations is wholly a matter of chance. In that case, the apparent regularity of the world will be due to the absence of laws. I think it improbable that such a view could be developed satisfactorily, but at least we must take account of it before we attach undue importance to the appearance of law in the world. The real objection to a philosophy founded upon such a[Pg 236] theory of the universe as we have been considering is that, after all, we still need statistical laws, which will involve a "random distribution," or something of the kind. Such laws are still laws, though they differ from others by seeming a priori probable instead of improbable. To this extent, it is a gain if we can base science upon them; but it would not be correct to say that, in that case, science would have succeeded in doing without laws. We could no longer say, however, that the laws of science were surprising; on the contrary, we should be surprised by their failure. There is another question to be considered, and that is as to the scope of simple laws. It cannot be pretended that we know the laws governing the hydrogen atom to be sufficient to account for all that happens to matter, especially to organic matter. This is at present merely a hypothesis. All science uses laws based