The nature of the physical world

by Sir Arthur Stanley Eddington

distance, mass, electric force, entropy, beauty, melody.

I think there are the strongest grounds for placing entropy alongside beauty and melody and not with the first three. Entropy is only found when the parts are viewed in association, and it is by viewing or hearing the parts in association that beauty and melody are discerned. All three are features of arrangement. It is a pregnant thought that one of these three associates should be able to figure as a commonplace quantity of science. The reason why this stranger can pass itself off among the aborigines of the physical world is, that it is able to speak their language, viz. the language of arithmetic. It has a measure-number associated with it and so is made quite at home in physics. Beauty and melody have not the arithmetical pass-word and so are barred out. This teaches us that what exact science looks out for is not entities of some particular category, but entities with a metrical aspect. We shall see in a later chapter that when science admits them it really admits only their metrical aspect and occupies itself solely with that. It would be no use for beauty, say, to fake up a few numerical attributes (expressing for instance the ideal proportions of symmetry) in the hope of thereby gaining admission into the portals of science and carrying on an aesthetic crusade within. It would find that the numerical aspects were duly admitted, but the aesthetic significance of them left outside. So also entropy is admitted in its numerical aspect; if it has as we faintly suspect some deeper significance touching that which appears in our consciousness as purpose (opposed to chance), that significance is left outside. These fare no worse than mass, distance, and the like which surely must have some significance beyond mere numbers; if so, that significance is lost on their incorporation into the scientific scheme—the world of shadows.

You may be inclined to regard my insistence that entropy is something excluded from the inventory of microscopic contents of the world as word-splitting. If you have all the individuals before you, their associations, arrangement and organisation are automatically before you. If you have the stars, you have the constellations. Yes; but if you have the stars, you do not take the constellations seriously. It had become the regular outlook of science, closely associated with its materialistic tendencies, that constellations are not to be taken seriously, until the constellation of entropy made a solitary exception. When we analyse the picture into a large number of particles of paint, we lose the aesthetic significance of the picture. The particles of paint go into the scientific inventory, and it is claimed that everything that there really was in the picture is kept. But this way of keeping a thing may be much the same as losing it. The essence of a picture (as distinct from the paint) is arrangement. Is arrangement kept or lost? The current answer seems inconsistent. In so far as arrangement signifies a picture, it is lost; science has to do with paint, not pictures. In so far as arrangement signifies organisation it is kept; science has much to do with organisation. Why should we (speaking now as philosophers, not scientists) make a discrimination between these two aspects of arrangement? The discrimination is made because the picture is no use to the scientist—he cannot get further with it. As impartial judges it is our duty to point out that likewise entropy is no use to the artist—he cannot develop his outlook with it.

I am not trying to argue that there is in the external world an objective entity which is the picture as distinct from the myriads of particles into which science has analysed it. I doubt if the statement has any meaning; nor, if it were true, would it particularly enhance my esteem of the picture. What I would say is this: There is a side of our personality which impels us to dwell on beauty and other aesthetic significances in Nature, and in the work of man, so that our environment means to us much that is not warranted by anything found in the scientific inventory of its structure. An overwhelming feeling tells us that this is right and indispensable to the purpose of our existence. But is it rational? How can reason regard it otherwise than as a perverse misrepresentation of what is after all only a collection of atoms, aether-waves and the like, going about their business? If the physicist as advocate for reason takes this line, just whisper to him the word Entropy.

Insufficiency of Primary Law. I daresay many of my physical colleagues will join issue with me over the status I have allowed to entropy as something foreign to the microscopic scheme, but essential to the physical world. They would regard it rather as a labour-saving device, useful but not indispensable. Given any practical problem ordinarily solved by introducing the conception of entropy, precisely the same result could be reached (more laboriously) by following out the motion of each individual particle of matter or quantum of energy under the primary microscopic laws without any reference to entropy explicit or implicit. Very well; let us try. There’s a problem for you—

[A piece of chalk was thrown on the lecture table where it rolled and broke into two pieces.]

You are given the instantaneous position and velocity[12] of every molecule, or if you like every proton and electron, in those pieces of chalk and in as much of the table and surrounding air as concerns you. Details of the instantaneous state of every element of energy are also given. By the microscopic (primary) laws of motion you can trace the state from instant to instant. You can trace how the atoms moving aimlessly within the lumps of chalk gradually form a conspiracy so that the lumps begin to move as a whole. The lumps bounce a little and roll on the table; they come together and join up; then the whole piece of chalk rises gracefully in the air, describes a parabola, and comes to rest between my fingers. I grant that you can do all that without requiring entropy or anything outside the limits of microscopic physics. You have solved the problem. But, have you quite got hold of the significance of your solution? Is it quite a negligible point that what you have described from your calculations is an unhappening? There is no need to alter a word of your description so far as it goes; but it does seem to need an addendum which would discriminate between a trick worthy of Mr. Maskelyne and an ordinary everyday unoccurrence.

The physicist may say that the addendum asked for relates to significance, and he has nothing to do with significances; he is only concerned that his calculations shall agree with observation. He cannot tell me whether the phenomenon has the significance of a happening or an unhappening; but if a clock is included in the problem he can give the readings of the clock at each stage. There is much to be said for excluding the whole field of significance from physics; it is a healthy reaction against mixing up with our calculations mystic conceptions that (officially) we know nothing about. I rather envy the pure physicist his impregnable position. But if he rules significances entirely outside his scope, somebody has the job of discovering whether the physical world of atoms, aether and electrons has any significance whatever. Unfortunately for me I am expected in these lectures to say how the plain man ought to regard the scientific world when it comes into competition with other views of our environment. Some of my audience may not be interested in a world invented as a mere calculating device. Am I to tell them that the scientific world has no claim on their consideration when the eternal question surges in the mind, What is it all about? I am sure my physical colleagues will expect me to put up some defence of the scientific world in this connection. I am ready to do so; only I must insist as a preliminary that we should settle which is the right way up of it. I cannot read any significance into a physical world when it is held before me upside down, as happened just now. For that reason I am interested in entropy not only because it shortens calculations which can be made by other methods, but because it determines an orientation which cannot be found by other methods.

The scientific world is, as I have often repeated, a shadow-world, shadowing a world familiar to our consciousness. Just how much do we expect it to shadow? We do not expect it to shadow all that is in our mind, emotions, memory, etc. In the main we expect it to shadow impressions which can be traced to external sense-organs. But time makes a dual entry and thus forms an intermediate link between the internal and the external. This is shadowed partially by the scientific world of primary physics (which excludes time’s arrow), but fully when we enlarge the scheme to include entropy. Therefore by the momentous departure in the nineteenth century the scientific world is not confined to a static extension around which the mind may spin a romance of activity and evolution; it shadows that dynamic quality of the familiar world which cannot be parted from it without disaster to its significance.

In sorting out the confused data of our experience it has generally been assumed that the object of the quest is to find out all that really exists. There is another quest not less appropriate to the nature of our experience—to find out all that really becomes.