... to discuss - and to some extent explore - that borderline territory between physics and philosophy which used to seem so dull, but suddenly became so interesting and important through recent developments of theoretical physics.The first part of Jeans' What is Physics? is given at this link
Here we continue with Jeans' Pictorial Representations, Geometrical Explanations of Nature, Mechanical Explanations of Nature and The Mathematical Description of Nature:-
But now the complication intervenes that our minds do not take kindly to knowledge expressed in abstract mathematical form. Our mental faculties have come to us, through a long line of ancestry from fishes and apes. At each stage the primary concern of our ancestors was not to understand the ultimate processes of physics, but to survive in the struggle for existence, to kill other animals without themselves being killed. They did not do this by pondering over mathematical formulae, but by adapting themselves to the hard facts of nature and the concrete problems of everyday life. Those who could not do this disappeared, while those who could survived, and have transmitted to us minds which are more suited to deal with concrete facts than with abstract concepts, with particulars rather than with universals; minds which are more at home in thinking of material objects, rest and motion, pushes, pulls and impacts, than in trying to digest symbols and formulae. The child who is beginning to learn algebra never takes kindly to x, y and z; he is only satisfied when he is told that they are: numbers of apples or pears or something such.
In the same way, the physicists of a generation ago could not rest content with the x, y and z which were used to describe the pattern of events, but were for ever trying to interpret them in terms of something concrete. If, they thought, there is a pattern, there must be a loom for ever weaving it. They wanted to know what this loom was, how it worked, and why it worked thus rather than otherwise. And they assumed, or at least hoped, that it would prove possible to liken its ultimate constituents to such familiar mechanical objects as occur in looms, or perhaps to billiard-balls, jellies and spinning-tops, the workings of which they thought they understood. In time they hoped to devise a model which would reproduce all the phenomena of physics, and so make it possible to predict them all.
Such a model would, they thought, in some way correspond to the reality underlying the phenomena. No one seems to have considered the situation which would arise if two different models were found, each being perfect in this respect.
Yet this situation is of some interest. If it arose, there would be no means of choosing between the two models, since each would be perfect in the only property by which it could be tested, namely the power of predicting phenomena. Neither model could, then, claim to represent reality, whence it follows that we must never associate any model with reality, since even if it accounted for all the phenomena, a second model might appear at any moment with exactly the same qualifications to represent reality.
Today we not only have no perfect model, but we know that it is of no use to search for one - it could have no intelligible meaning for us. For we have found out that nature does not function in a way that can be made comprehensible to the human mind through models or pictures.
If we are to explain the workings of an organization or a machine in a comprehensible way, we must speak to our listeners in a language they understand, and in terms of ideas with which they are familiar - otherwise our explanation will mean nothing to them. It is no, good telling a crowd of savages that the time-differential of the electric displacement is the rotation of the magnetic force multiplied by the velocity of light. In the same way, if an interpretation of the workings of nature is to mean anything to us, it must be in terms of ideas which are already in our minds - otherwise it will be incomprehensible to us, and cannot add to our knowledge. We have already seen what types of ideas can be in our minds - ideas which have been in our minds from birth, ideas which have entered our minds as perceptions, and ideas which have been developed out of these primitive ideas by processes of reflection and ratiocination. Such ideas as originated in perceptions, and so entered our minds through one or more of the five senses, may be classified by the sense or senses through which they entered. Thus the content of a mind will consist of visual ideas, auditory ideas, tactile ideas, and so on, as well as more fundamental ideas - such as those of number and quantity - which may be inborn or may have entered through several senses, and more complex ideas resulting from combinations and aggregations of simpler ideas, such as ideas of aesthetic beauty, moral perfection, maximum happiness, checkmate or free trade. It is useless to try to understand the workings of nature except in terms of ideas belonging to one or other of these classes.
For instance, the pitch, intensity and timbre of a musical sound are auditory ideas; we can explain the functioning of an orchestra in terms of them, but only to a person who is himself possessed of auditory ideas, and not to one who has been deaf all his life. Colour and illumination are visual ideas, but we could not explain a landscape or a portrait in such terms to a blind man, because he would have no visual ideas.
Clearly complex ideas of the kind exemplified above can give no help towards an understanding of the functioning of inanimate nature. The same is true of ideas which have entered through the senses of hearing, taste and smell - as for instance the memories of a symphony or of a good dinner. If for no other reason, none of these enter into direct relation with our perceptions of extension in space, which is one of the most fundamental of the things to be explained. We are left only with fundamental ideas such as number and quantity, and ideas which have entered our minds through the two senses of sight and touch. Of these sight provides more vivid and also more important ideas than touch - we learn more about the world by looking at it than by touching it. Besides number and quantity, our visual ideas include size or extension in space, position in space, shape and movement. Tactile ideas comprise all of these, although in a less vivid form, as well as ideas which are wholly tactile, such as hardness, pressure, impact and force. For an explanation of nature to be intelligible it must depend only on such ideas as these.
Various attempts have been made to explain the workings of nature in terms of visual ideas alone, these depending mainly on the ideas of shape (geometrical figures) and motion. Three examples drawn from ancient, mediaeval and modem times respectively are:
(1) The Greek explanation that all motion tends to be circular because the circle is the perfect figure geometrically, an explanation which remained in vogue at least until the fifteenth century, notwithstanding its being contrary to the facts.
(2) The system of Descartes, which tried to explain nature in terms of motion, vortices, etc. This also was contrary to the facts.
(3) Einstein's relativity theory of gravitation, which is purely geometrical in form. This, so far as is known, is in complete agreement with the facts.
We shall discuss this last theory in some detail below. In brief, it tells us that a moving object or a ray of light moves along a geodesic, which means that it takes the shortest route from place to place, or again, roughly speaking, that it goes as nearly in a straight line as circumstance s permit. This geodesic is not in ordinary space, but in an ideal composite space of four dimensions, which results from blending space and time. This space is not only four-dimensional but is also curved; it is this curvature that prevents a geodesic being an ordinary straight line. Efforts have been made to explain the whole of electric and magnetic phenomena in a similar way, but so far without success.
It is perhaps doubtful whether such a curved four-dimensional space ought to be described as a visual idea which is already in our minds. It may be only ordinary space generalized, but if so it is generalized out of all recognition. The highly trained mathematician can visualize it partially and vaguely, others not at all. Unless we are willing to concede that the plain man has the idea of such a space in his mind, we must say that no appreciable fraction of the world has been really 'explained' in terms of visual ideas.
Even if it had, such an explanation would hardly carry any conviction of finality or completeness to our modern minds. To the Greek mind the supposed fact that the stars or planets moved in perfect geometrical figures provided a completely satisfying explanation of their motion - the world was a perfection waiting only to be elucidated, and here was a bit of the elucidation. Our minds work differently. Optimism has given place to pessimism, at least to the extent that we no longer feel any confidence in an overruling tendency to perfection, and if we are told that a planet moves in a perfect circle, or in a still more perfect geodesic, we merely go on to inquire: Why? When Giotto drew his perfect circle, his pencil was not guided by any abstract compulsion to perfection - if it were, we should all be able to draw perfect circles - but by the skill of his muscles. We want to know what provides the corresponding guidance to the planets, and this requires that the purely visual ideas of geometrical form shall be supplemented by the addition of tactile ideas.
Explanations which introduce tactile ideas - forces, pressures and tensions - are of course dynamical or mechanical in their nature. It is not surprising that such explanations also should have been attempted from Greek times on, for, after all, our hairy ancestors had to think more about muscular force than about perfect circles or geodesics. Plato tells us that Anaxagoras claimed to be able to explain the workings of nature as a machine. In more recent times Newton, Huygens and others thought that the only possible explanations of nature were mechanical. Thus in 1690 Huygens wrote: 'In true philosophy, the causes of all natural phenomena are conceived in mechanical terms. We must do this, in my opinion, or else give up all hope of ever understanding anything in physics.'
Today the average man probably holds very similar opinions. An explanation in any other than mechanical terms would seem incomprehensible to him, as it did to Newton and Huygens, through the necessary ideas - the language in which the explanation was conveyed - not being in his mind. When he wants to move an object, he pulls or pushes it through the activity of his muscles, and cannot imagine that Nature does not effect her movements in a similar way. Among attempted explanations in mechanical terms, the Newtonian system of mechanics stands first. This was supplemented in due course by various mechanical representations of the electromagnetic theories of Maxwell and Faraday. All envisaged the world as a collection of particles moving under the pushes and pulls of other particles, these pushes and pulls being of the same general nature as those we exert with our muscles on the objects we touch.
We shall see later in the present book how these and other attempted mechanical explanations have all failed. Indeed the progress of science has disclosed in detail the reasons why all failed, and all must fail. Two of the simpler of these reasons may be mentioned here.
The first is provided by the theory of relativity. The essence of a mechanical explanation is that each particle of a mechanism experiences a real and definite push or pull. This must be objective as regards both quantity and quality, so that its measure will always be the same, whatever means of 'measurement are employed to measure it just as a real object must always weigh the same whether it is weighed on a spring balance or on a weighing-beam. But the, theory of relativity shows that if motions are attributed to forces, these forces will be differently estimated, as regards both quantity and quality, by observers who happen to be moving at different speeds, and furthermore that all their estimates have an equal claim to be considered right. Thus the supposed forces cannot have a real objective existence; they are seen to be mere mental constructs which we make for ourselves in our efforts to understand the workings of nature. A simple specific example of this general argument will be found below.
A second reason is provided by the theory of quanta. A mechanical explanation implies not only that the particles of the universe move in space and time, but also that their motion is governed by agencies which operate in space and time. But the quantum theory finds, as we shall see later, that the fundamental activities of nature cannot be represented as occurring in space and time; they cannot, then, be mechanical in the ordinary sense of the word.
In any case, no mechanical explanation could ever be satisfying and final; it could at best only postpone the demand for an explanation. For suppose - to imagine a simple although not very likely possibility - that it had been found that the pattern of events could be fully explained by assuming that matter consisted of hard spherical atoms, and that each of these behaved like a minute billiard-ball. At first this may look like a perfect mechanical explanation, but we soon find that if has only introduced us to a vicious circle; it first explains billiard-balls in terms of atoms, and then proceeds to explain atoms in terms Of billiard-balls, so that we have not advanced a step towards a true understanding of the ultimate nature of either billiard-balls or atoms. All mechanical explanations are open to a similar criticism, since all are of the form 'A is like B, and B is like A'. Nothing is gained by saying that the loom of nature works like our muscles if we cannot explain how our muscles work. We come, then, to the position that nothing but a mechanical explanation can be satisfying to our minds, and that such an explanation would be valueless if we attained it. We see that we can never understand the true nature of reality.
In these and similar ways, the progress of science has itself shown that there can be no pictorial representation of the workings of nature of a kind which would be intelligible to our limited minds. The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms; no other aim is possible - at least until man becomes endowed with more senses than he at present possesses. Physicists who are trying to understand nature may work in many different fields and by many different methods; one may dig, one may sow, one may reap. But the final harvest will always be a sheaf of mathematical formulae. These will never describe nature itself, but only our observations on nature. Our studies can never put us into contact with reality; we can never penetrate beyond the impressions that reality implants in our minds.
Although we can never devise a pictorial representation which shall be both true to nature and intelligible to our minds, we may still be able to make partial aspects of the truth comprehensible through pictorial representations or parables. As the whole truth does not admit of intelligible representation, every such pictorial representation or parable must fail somewhere. The physicist of the last generation was continually making pictorial representations and parables, and also making the mistake of treating the half-truths of pictorial representations and parables as literal truths. He did not see that all the concrete details of his picture - his luminiferous ether, his electric and magnetic forces, and possibly his atoms and electrons as well - were mere articles of clothing that he had himself draped over the mathematical symbols; they did not belong to the world of reality, but to the parables by which he had tried to make reality comprehensible. For instance, when observation was. found to suggest that light was of the nature of waves, it became customary to describe it as undulations in a rigid homogeneous ether which filled the whole of space. The only ascertained fact in this description is contained in the one word 'undulations', and even this must be understood in the narrowest mathematical sense; all the rest is pictorial detail, introduced to help out the limitations of our minds. Kronecker is quoted as saying that in arithmetic God made the integers and man made the rest; in the same spirit we may perhaps say that in physics God made the mathematics and man made the rest.
To sum up, physics tries to discover the pattern of events which controls the phenomena we observe. But we can never know what this pattern means or how it originates; and even if some superior intelligence were to tell us, we should find the explanation unintelligible. Our studies can never put us into contact with reality, and its true meaning and nature must be for ever hidden from us.