by     Reginald O. Kapp


Chapter 23 - Misplaced Efforts at Understanding

23.1: Symmetrical Impermanence is Difficult to Accept but not to Understand
The many unsolved problems about gravitation reveal, it has just been pointed out, a serious gap in our knowledge of the physical world. It will be shown here that there is a good prospect that a bridge can be provided to span the gap provided the traditional hypothesis about gravitation is replaced by another one. This will be shown to meet Occam's razor better than the traditional one does and thus to be justified both by the criterion of minimum assumption and by that of maximum explanatory power. But its foundations will be different from what one might perhaps expect.

At one end of the span of the bridge the foundation will be the Hypothesis of the Symmetrical Impermanence of matter and at the other end the relativistic notion that space has physical properties. In other words it will be shown that a gravitational field around an accumulation of inert mass can be inferred as the effect on the geometry of space of the continuous origin and extinction of matter.

If both these basic notions were fully established and understood, I could proceed forthwith to build the bridge of logical reasoning that spans them. But it is not so, and anyone who rejects either of the two notions will not be inclined even to consider what inferences can be built on them. Similarly, anyone who does not properly understand either notion is likely to reach a wrong conclusion. Hence I have no choice but to allow a little time for examination of the difficulties inherent in both notions before I can begin to show how a gravitational field can be inferred from them.

Understanding a notion and accepting it are by no means the same thing. I believe that many people can understand the notion of the con- tinuous origin and extinction of matter quite easily, but I have found also that many cannot accept it. On the other hand, a majority of physicists accept today the notion that space has physical properties, but even physicists find the mathematical basis of this conclusion difficult to understand. This distinction has to be faced and appreciated. It is with the big subject of understanding that this chapter is chiefly concerned. But it will be helpful if I first give passing attention to the fact that the notion of Symmetrical Impermanence is difficult to accept. If we cannot remove the difficulties of acceptance as well as of understanding, we must at least try to come to terms with them.

What makes Symmetrical Impermanence difficult to accept is that the concept is new, unfamiliar, at variance with tradition. To some it may also appear unattractive, for if matter itself is impermanent the very foundations of science and the universe may seem to be threatened. The resultant sense of insecurity may cause some to feel uneasy. For a physicist to be influenced by such emotional considerations is, admittedly, reprehensible. But we are all human and cannot quite avoid judging a notion at least partly by the criterion of attractiveness, even when we know that this criterion has no place in science.

If, however, objections to Symmetrical Impermanence can be urged in plenty, I do not think that incomprehensibility is among them. Incredible' is a more probable epithet from those who do not like the notion. It may be difficult to believe that an elementary component of the material universe originates and becomes extinct without cause, but the idea is not difficult to understand.

For Symmetrical Impermanence it is thus acceptability and not comprehensibility that needs to be achieved before attention can be given to my new theory of gravitation. How can this be done? Acceptance cannot be urged by reference to authority, for orthodox physics accepts, as though it were proved and irrefutable fact, that the future duration of every component of the material universe is infinite and that its past duration dates from some moment that occurred between the beginning and the completion of the Creation. To suggest, as I have done, that there is a half-life for matter in the sense in which there is a half-life for a radio-active element is today regarded by authority as a heresy.

The justification for my suggestion is, as has been explained in earlier chapters, not to be found in tradition. It is that it meets the two criteria of minimum assumption and maximum explanatory power, as has been demonstrated already. It has been shown by closely reasoned steps that one can infer many observed facts about the nebulae from Symmetrical Impermanence and not from any of the more orthodox, rival hypotheses about the duration of matter. This alone should suffice to gain serious consideration for Symmetrical Impermanence; and a further justification will, I am claiming, be found in its ability to explain those most recalcitrant phenomena connected with gravitation that were enumerated in Chapter 22.

23.2: Relativity is Difficult to Understand
But if Symmetrical Impermanence is unorthodox relativity theory is, as I have said above, a part of established physical science. Early disbelief has had to yield to acceptance. Incredible' is no longer the right epithet for the statement that space has physical properties. We have to believe the experts, whether we find it easy to do so or not, when they tell us that space-time can be curved, that it forms a single, indivisible physical concept, that space is not a container but a constituent of the physical universe, that matter and space are conceptually inseparable, that space expands. But I fear that 'incomprehensible' still remains a justifiable epithet for all this. The meaning of what the relativist tells us about the nature of space is as hard to understand today as it was half a century ago when the theory first startled the scientific world.

This is the situation with which we have to come to terms. To do so something less will suffice than the degree of understanding that a specialist in relativity theory requires. The specialist's services will be required, of course; but not until later. It will be for him to help test the reasoning by which my new theory of gravitation has been reached. But the reasoning must be presented by myself and followed by many who are not specialists before it can usefully be tested, and for this purpose it will not prove necessary to make the same effort at understanding relativity theory by which physicists satisfied themselves half a century ago about the soundness of Einstein's conclusions. (This is fortunate, for those who are today fully conversant with relativity theory are no longer numerous.) But the non-specialist who would follow my reasoning must, at least, appreciate what kind of understanding can be achieved and what kind of effort must be made in order to achieve it.

This would be easy if the word 'understand' always meant the same thing and always called for the same kind of effort. But it is far from so. There are several different kinds of understanding and quite a different kind of effort is required for each. 'Understand' is one of the vaguest of words, and one can only come to terms with the difficulty inherent in relativity theory if one appreciates this. I therefore make no apology for entering once again the realm of the philosophy of science and for delaying for a short while the promised new theory of gravitation.

23.3: Different Meanings of 'Understand'
Of the several meanings that the word 'understand' can have, only two have a place in physics. These will be discussed below, but it will be helpful if I first say a little about those meanings that do not have a place in physics.

Psychological understanding is one of these. It has an obvious and important place in the humanistic disciplines. It calls for the kind of effort that one makes when one pictures oneself in the situation of someone else. By this effort one is able to imagine oneself having a similar experience to the other person and thus understanding how he feels and why he acts as he does. It is thus, for instance, that one may achieve understanding of Hamlet's inability to perform the action to which his conscience prompts him.

No one believes for a moment nowadays that understanding in physics is of this kind. But it has not always been quite so. There was a time when it seemed that understanding of the mercury barometer depended on an effort to appreciate Nature's horror of a vacuum. In those days, and perhaps even later, those whose training had been wholly humanistic must have found difficulty in abandoning the notion that rivers follow an urge when they flow seawards.

Teleological understanding is another kind that has no place in physics, although it has an important place in other disciplines. In seeking to understand a thing one often seeks to discover its purpose. To say that one understands why a particular law has been enacted usually means that one knows its purpose. It is similar with many other human actions. To reveal their purpose is to make them comprehensible.

This kind of understanding is of decisive importance in engineering. In a well-designed machine every feature serves a purpose and an understanding of the machine follows from knowing what the purpose of each feature is. As, moreover, a living organism can aptly be described as a machine, one should expect the same kind of teleological understanding to have a place in biology. But those who study the mechanisms that operate in plants and animals, and who should be in the best position to appreciate the purpose of the component parts, often deny with some vehemence that the kind of teleological effort at understanding that an engineer brings to his machines applies to a living machine. Which is odd.

In ethics, again, understanding means something not quite satisfactorily included in any of the above categories. The word may be applied in ethics to the kind of understanding that leads to knowledge of the difference between good and evil. In the days when some things and substances were thought of as good and others as bad this kind of understanding seemed to help towards an appreciation of the physical world. It seemed easy in those days to understand the smoothness and beauty of planetary orbits when one thought of the planets as among the very best of the good things.

Further, there is aesthetic understanding. It is very different from the other kinds and calls for a different mental effort. We make this effort when we try to understand a piece of music that is written in an unfamiliar idiom. It is only after listening repeatedly and with concentrated attention that we succeed in recognizing the pattern of the notes, the form of the melodies, the structure of the whole, the relation between the harmonies, the nature of the progressions, the pulse of the rhythms. Until this has happened the piece appears as a meaningless jumble of unrelated noises. But when we have appreciated the order we say that we understand the piece.

It would be idle further to elaborate the catalogue of meanings of the word 'understand' that have no place in physics. It is arguable that some of the above uses are really misuses and are to be regretted. But that would only confirm the contention that only too often insufficient care is taken to define what is meant by the word.

I should not have thought it necessary to insist on this if the word always meant the same thing in physics. In that case the warning that care must be taken would be redundant for there would be no risk that an effort at understanding would ever be misplaced. But in fact the word may have one of two quite different meanings, both appropriate to physics, and it does at times happen to all of us that we inadvertently direct our effort towards the one when it ought to be directed only towards the other.

As names are needed I shall call these two kinds respectively 'deductive' and 'representational' understanding. Each will now be described and discussed in turn.

23.4. Deductive Understanding
This calls for an effort at deductive reasoning and the method is applied to statements in mathematics as well as to those in physics. The word is used in this sense when one says that one understands the rule that relates the squares on the sides of a right-angled triangle to each other. To say this means that one can follow the reasoning by which the statement is arrived at. But this kind of understanding is not confined to mathematics.

To say that one understands the principle of the lever, for instance, does not mean that one understands the psychology of this device, or the purpose that it serves, or its moral status, or its aesthetic significance. It simply means that one knows how to infer, by deductive reasoning, the ratio of the forces that are simultaneously applied to its two arms. Similarly, a claim to understand the parabolic path of a projectile simply means that one can show by deductive reasoning how the forces that act on the projectile cause successive positions to lie on a parabola.

The same kind of deductive reasoning was brought by Newton to the elliptical paths of planets. It is brought to the rise and fall of the tides, to the movement of mercury in a barometer, to the helium synthesis from which the sun derives the energy that it radiates, to the formation of a cloud from super-cooled water vapour. I have tried to show in preceding chapters how one can understand the occurrence and structure of the nebulae by making the same kind of deductive effort.

When a relativist assures us that he understands why space has physical properties, he means that he has achieved this kind of deductive under- standing. He has successfully made the necessary effort and has been able to infer from certain known facts those properties of space that cause the track of an inert mass in space-time to be curved. The reasoning by which he arrives at the conclusion is, of course, far more difficult than the reasoning that leads to an understanding of the principle of the lever, but it is a quantitative and not a qualitative difference.

All this may be called rather obvious. I think it is. But it leads to an important question. When those of us who are not mathematical experts say that we cannot understand what the relativists tell us about the physical properties of space, do we mean no more than that we are unable to follow the reasoning by which these properties have been inferred? Should we be satisfied that we understood relativity if we knew how to set up and solve the equations? We know that mathematical ability is the key by which the door to the relativist's world is opened. It is the door labelled 'deductive understanding'. But is necessarily this the door that we wish to pass through? Would deduction give us the kind of understanding for which we crave? Do we not suspect that if this door were opened for us it would only lead on to a narrow passage with another closed door at the far end?

The metaphor must not be pressed too far. But this is, I think, how many of us feel about relativity and much else in modern physics. We are prepared to take the results of deductive reasoning, mathematical or otherwise, on trust. If we could be gently guided through that reasoning, it would make no great difference to our state of mind. Our uneasiness about those modern discoveries in physics that are so difficult for us to understand does not arise from any doubt as to their logical justification. It arises from our inability to achieve a different kind of understanding. This is the kind that I propose to call representational. It is the key to the door bearing this name that we are often seeking; and we should go on seeking it even though the door labelled 'deductive understanding' stood wide open before us. But I shall show in a moment that we must often seek in vain.

23.5: Representational Understanding
Representational understanding has nothing to do with deduction but calls for an effort of the imagination. It contributes substantially to the work of both the physicist and the engineer and is often complementary to deductive understanding.

Both kinds are used, for instance, when we attempt to understand the principle of the lever. We do not then rest content with the reasoning by which the ratio of the forces on the two arms is deduced. With an effort of the imagination we also conjure up this device before the mind's eye. We should not be satisfied that we fully understood the principle unless we could add a mental picture to the algebraic symbols.

In the example of the lever the representational effort is slight. On other occasions it may be considerable. One can achieve deductive under- standing of gyroscopic action with the help of mathematical symbols. Some of these are operators defining a direction; and in three-dimensional space the direction for any one of them is at right-angles to the direction of the other two. But the logic of the symbols, irrefutable though it be, leaves us unsatisfied. If we are to feel happy about our understanding of the gyroscope we must also succeed in imagining the spatial relations of the system; we have to represent to the mind's eye the forces and movements that occur in all three dimensions. It is not altogether easy.

The slide valve system of a steam engine provides an even more cogent example. The components of the system include devices known as eccentrics, sliding members that move in a complicated way relative to each other, ports that are open to the passage of steam at certain moments and closed at other moments. These ports begin to admit steam to the cylinder when the piston is in a certain position and cut the steam off when it is in another position. In yet another position of the piston they allow steam to be discharged from the cylinder. Some of the various moving parts are in circular, others in reciprocating motion. The complexities of the system extend in all three dimensions.

For this intricate piece of kinematics the deductive effort at understanding is rather easy, the representational effort is quite difficult. But no engineer would claim to understand the action of a slide valve unless his representational effort had proved successful.

23.6: Representational Understanding is Sometimes Impossible
It is only natural to wish to understand every statement in physics in the representational as well as in the deductive sense. As has been seen from the examples of the lever and the gyroscope, we often succeed. But it is not always so. The human imagination has its limit as regards representational understanding and many accepted statements in physics lie beyond this limit.

Statements about the electron provide an example. When this particle is mentioned we try to visualize it, and each of us forms, no doubt, his own different picture. Some may think of it as a hard little sphere, others as more like a ball of loosely-tangled wool; to some its surface is perfectly smooth and featureless, to others rough enough to make the spin perceptible; to some the boundary is definite, to others the electron carries with it a sort of misty nimbus; to some it is black, to others yellow.

On occasion a fact forces itself on our attention that causes us to revise whatever private picture we may have formed. The electron consists of waves, we are reminded, and its field extends into its surroundings: forthwith the little hard sphere turns in our imagination into the tangle of wool and is surrounded by the extensive misty nimbus. But the electron also finds room in the tiny atomic nucleus: the hard sphere comes back and the nimbus is shed. The electron spins, we recall: and we imagine some surface markings to feature successive angular displacements. But one electron is so like every other that it is meaningless even to say that two electrons ever change places: gone are the surface markings.

So it goes on. No one picture is any nearer the truth than any others. Any picture that the imagination can conjure up must be false. And yet, how hard it is to prevent the imagination from intruding. What would the electron be like, we feel impelled to ask, if it were magnified to the size of a tennis ball? It would then have to be either hard or soft, rough or smooth, provided with either a clear or a fuzzy outline, be either black, or white, or coloured. Which of all the conceivable possibilities would it be?

If we are honest, we have to admit how difficult it is always to remember that these questions are silly. If we have adequate understanding of the deductive kind we know they are silly; we know that the association between the size and the other properties of the electron is not the same as it is for tennis balls. While a tennis ball of non-standard size may have all the same properties as a tennis ball of standard size, an electron of a different size would not retain a single one of its properties.

Knowing all this most of us still persist, be it confessed, in forming our mental picture of the electron. Our urge towards understanding in the representational sense is so strong that we like to pretend to ourselves that we have achieved it even when we know that we have done nothing of the sort. We then have no choice but to imagine a picture that we know to be false.

Even such poor comfort as may be obtained by this self-deception is denied us when we are seeking to understand what relativists have discovered about the physical properties of space. Space-time, expanding space, curved space, space with any features at all defy the imagination. We cannot conjure up even a false picture of it!

23.7: Objectivity is the Enemy of Representational Understanding
The reason for this inability is as simple as it is profound. When one makes an effort at representational understanding one tries, it has been pointed out already, to represent something to the imagination. One tries to see it with the mind's eye, to hear it with the mind's ear, to feel it with the mind's sense of touch. One associates it, in other words, with one's own personal, subjective capacity for experience. But it will be shown in a moment that the physicist's aim is to find aspects of reality that cannot be thus associated. What he can say about these aspects is independent of any particular observer; it is truly objective. This is why it is axiomatic that objectivity, in the physicist's sense of the word, and representational understanding are irreconcilable.

This very fundamental fact about physics needs to be elaborated a little.

In physics colour can be defined in terms of wave-length, as can also pitch of sound; temperature can be defined in terms of the average momentum of the molecules in a substance and taste in terms of chemical constitution. Why is this done?

The answer can take a variety of forms and one of them is to say that this way of defining properties gives them a more universal meaning. To say that a surface is red has meaning only for a person whose eyes can distinguish colours; it means nothing to a colour-blind person. But the information that the surface reflects radiation of such and such a wave-length conveys something to the colour-blind man, and indeed as much as it does to the one who has had the experience of distinguishing between a red and a green surface.

The same universalizing process extends into all aspects of the objective world. The physicist can tell us things about sound that have a meaning for a deaf man, some things about light that have a meaning for a blind one. He can say things about temperatures so high that no man could experience them and live, about particles too small to be perceived by any of our sense organs. The physicist thus aims at finding statements that would take the same form if people had different sense organs and a different nervous system.

Therein lies the justification, or at least one of the justifications, for the generalizations of physics. They aim at abstracting from the whole world of reality that part that is truly objective in the sense that it is independent of any particular observer. What can be said about this aspect must, by definition, have the same meaning for every receiver of the information whatever his physiological and psychological constitution may be. For this reason the statements that are regarded in physics as the greatest generalizations are those said, in technical language, 'to eliminate the observer'.

Such statements are, of course, incomplete, for the observer is still there; subjective experience is a reality that cannot be annulled by saying nothing about it. But the incompleteness is deliberate. This conceptual distinction between objective and subjective reality is one of the greatest achievements of our Western civilization.

Having made it we have to appreciate the consequences. One of them is that the widest generalizations in physics cannot be expressed in terms of sense data. If a statement about light means as much to a blind man as to one who can see it cannot refer to the experience of seeing and it cannot be presented to the visual imagination. If the observer has been eliminated, one cannot regard him as still using his organs of sense perception. The objective generalizations that the physicist seeks to find are just those that the observer could not become aware of by using his five senses. To represent something to the mind's eye is to imagine that one is observing it, that one has not been eliminated. Hence any effort at representational understanding of truly objective statements in physics must fail by the nature of the subject.

All this means that in some branches of physics there is no key to representational understanding. We are separated from it, not by a door, but by a blank wall. With his acute deductive understanding the physicist has discovered things that are, and must always remain, beyond this kind of understanding. It is an understatement to say that efforts at representational understanding are then misplaced. They are also misleading. They are efforts at replacing true concepts by false ones.

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