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The Physics Book.

Eddington 1927: Limitations of Physical Knowledge

September 16, 2018 – 5:55 PM
knowledge paradigm

Reference: The Nature of the Physical World

This paper presents Chapter XII (section 3) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Limitations of Physical Knowledge

Whenever we state the properties of a body in terms of physical quantities we are imparting knowledge as to the response of various metrical indicators to its presence, and nothing more. After all, knowledge of this kind is fairly comprehensive. A knowledge of the response of all kinds of objects—weighing-machines and other indicators— would determine completely its relation to its environment, leaving only its inner un-get-atable nature undetermined. In the relativity theory we accept this as full knowledge, the nature of an object in so far as it is ascertainable by scientific inquiry being the abstraction of its relations to all surrounding objects. The progress of the relativity theory has been largely due to the development of a powerful mathematical calculus for dealing compendiously with an infinite scheme of pointer readings, and the technical term tensor used so largely in treatises on Einstein’s theory may be translated schedule of pointer readings. It is part of the aesthetic appeal of the mathematical theory of relativity that the mathematics is so closely adapted to the physical conceptions. It is not so in all subjects. For example, we may admire the triumph of patience of the mathematician in predicting so closely the positions of the moon, but aesthetically the lunar theory is atrocious; it is obvious that the moon and the mathematician use different methods of finding the lunar orbit. But by the use of tensors the mathematical physicist precisely describes the nature of his subject-matter as a schedule of indicator readings; and those accretions of images and conceptions which have no place in physical science are automatically dismissed.

The theory of relativity resorts so deeply to mathematics that its real explanation is lost.

The recognition that our knowledge of the objects treated in physics consists solely of readings of pointers and other indicators transforms our view of the status of physical knowledge in a fundamental way. Until recently it was taken for granted that we had knowledge of a much more intimate kind of the entities of the external world. Let me give an illustration which takes us to the root of the great problem of the relations of matter and spirit. Take the living human brain endowed with mind and thought. Thought is one of the indisputable facts of the world. I know that I think, with a certainty which I cannot attribute to any of my physical knowledge of the world. More hypothetically, but on fairly plausible evidence, I am convinced that you have minds which think. Here then is a world fact to be investigated. The physicist brings his tools and commences systematic exploration. All that he discovers is a collection of atoms and electrons and fields of force arranged in space and time, apparently similar to those found in inorganic objects. He may trace other physical characteristics, energy, temperature, entropy. None of these is identical with thought. He might set down thought as an illusion—some perverse interpretation of the interplay of the physical entities that he has found. Or if he sees the folly of calling the most undoubted element of our experience an illusion, he will have to face the tremendous question, How can this collection of ordinary atoms be a thinking machine? But what knowledge have we of the nature of atoms which renders it at all incongruous that they should constitute a thinking object? The Victorian physicist felt that he knew just what he was talking about when he used such terms as matter and atoms. Atoms were tiny billiard balls, a crisp statement that was supposed to tell you all about their nature in a way which could never be achieved for transcendental things like consciousness, beauty or humour. But now we realise that science has nothing to say as to the intrinsic nature of the atom. The physical atom is, like everything else in physics, a schedule of pointer readings. The schedule is, we agree, attached to some unknown background. Why not then attach it to something of spiritual nature of which a prominent characteristic is thought. It seems rather silly to prefer to attach it to something of a so-called “concrete” nature inconsistent with thought, and then to wonder where the thought comes from. We have dismissed all preconception as to the background of our pointer readings, and for the most part we can discover nothing as to its nature. But in one case—namely, for the pointer readings of my own brain—I have an insight which is not limited to the evidence of the pointer readings. That insight shows that they are attached to a background of consciousness. Although I may expect that the background of other pointer readings in physics is of a nature continuous with that revealed to me in this particular case, I do not suppose that it always has the more specialised attributes of consciousness.* But in regard to my one piece of insight into the background no problem of irreconcilability arises; I have no other knowledge of the background with which to reconcile it.

* For example, we should most of us assume (hypothetically) that the dynamical quality of the world referred to in chapter V is characteristic of the whole background. Apparently it is not to be found in the pointer readings, and our only insight into it is in the feeling of “becoming” in our consciousness. “Becoming” like “reasoning” is known to us only through its occurrence in our own minds; but whereas it would be absurd to suppose that the latter extends to inorganic aggregations of atoms, the former may be (and commonly is) extended to the inorganic world, so that it is not a matter of indifference whether the progress of the inorganic world is viewed from past to future or from future to past.

Thought is a fact. Thought has substance. Thought is part of the system of Nature. Today we have computers that produce thoughts. Atoms and molecules are capable of acting as microcomputers on a natural basis as evidenced by DNA. It is, therefore, possible that there are laws to consciousness, which are yet to be discovered. Such laws shall be much more sophisticated than mathematical procedures.

In science we study the linkage of pointer readings with pointer readings. The terms link together in endless cycle with the same inscrutable nature running through the whole. There is nothing to prevent the assemblage of atoms constituting a brain from being of itself a thinking object in virtue of that nature which physics leaves undetermined and undeterminable. If we must embed our schedule of indicator readings in some kind of background, at least let us accept the only hint we have received as to the significance of the background— namely that it has a nature capable of manifesting itself as mental activity.

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By vinaire | Comments (0)

Eddington 1927: Nature of Exact Science

September 16, 2018 – 4:36 PM
science1

Reference: The Nature of the Physical World

This paper presents Chapter XII (section 2) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Nature of Exact Science

One of the characteristics of physics is that it is an exact science, and I have generally identified the domain of physics with the domain of exact science. Strictly speaking the two are not synonymous. We can imagine a science arising which has no contact with the usual phenomena and laws of physics, which yet admits of the same kind of exact treatment. It is conceivable that the Mendelian theory of heredity may grow into an independent science of this kind, for it would seem to occupy in biology the same position that the atomic theory occupied in chemistry a hundred years ago. The trend of the theory is to analyse complex individuals into “unit characters”. These are like indivisible atoms with affinities and repulsions; their matings are governed by the same laws of chance which play so large a part in chemical thermodynamics; and numerical statistics of the characters of a population are predictable in the same way as the results of a chemical reaction.

Now the effect of such a theory on our philosophical views of the significance of life does not depend on whether the Mendelian atom admits of a strictly physical explanation or not. The unit character may be contained in some configuration of the physical molecules of the carrier, and perhaps even literally correspond to a chemical compound; or it may be something superadded which is peculiar to living matter and is not yet comprised in the schedule of physical entities. That is a side-issue. We are drawing near to the great question whether there is any domain of activity—of life, of consciousness, of deity—which will not be engulfed by the advance of exact science; and our apprehension is not directed against the particular entities of physics but against all entities of the category to which exact science can apply. For exact science invokes, or has seemed to invoke, a type of law inevitable and soulless against which the human spirit rebels. If science finally declares that man is no more than a fortuitous concourse of atoms, the blow will not be softened by the explanation that the atoms in question are the Mendelian unit characters and not the material atoms of the chemist.

It seems that exact science requires less number of variables in a relationship compared to the variables present in reality.

Let us then examine the kind of knowledge which is handled by exact science. If we search the examination papers in physics and natural philosophy for the more intelligible questions we may come across one beginning something like this: “An elephant slides down a grassy hillside. . . .” The experienced candidate knows that he need not pay much attention to this; it is only put in to give an impression of realism. He reads on: “The mass of the elephant is two tons.” Now we are getting down to business; the elephant fades out of the problem and a mass of two tons takes its place. What exactly is this two tons, the real subject-matter of the problem? It refers to some property or condition which we vaguely describe as “ponderosity” occurring in a particular region of the external world. But we shall not get much further that way; the nature of the external world is inscrutable, and we shall only plunge into a quagmire of indescribables. Never mind what two tons refers to; what is it? How has it actually entered in so definite a way into our experience? Two tons is the reading of the pointer when the elephant was placed on a weighing-machine. Let us pass on. “The slope of the hill is 6o°.” Now the hillside fades out of the problem and an angle of 6o° takes its place. What is 6o°? There is no need to struggle with mystical conceptions of direction; 6o° is the reading of a plumb-line against the divisions of a protractor. Similarly for the other data of the problem. The softly yielding turf on which the elephant slid is replaced by a coefficient of friction, which though perhaps not directly a pointer reading is of kindred nature. No doubt there are more roundabout ways used in practice for determining the weights of elephants and the slopes of hills, but these are justified because it is known that they give the same results as direct pointer readings.

And so we see that the poetry fades out of the problem, and by the time the serious application of exact science begins we are left with only pointer readings. If then only pointer readings or their equivalents are put into the machine of scientific calculation, how can we grind out anything but pointer readings? But that is just what we do grind out. The question presumably was to find the time of descent of the elephant, and the answer is a pointer reading on the seconds’ dial of our watch.

The triumph of exact science in the foregoing problem consisted in establishing a numerical connection between the pointer reading of the weighing-machine in one experiment on the elephant and the pointer reading of the watch in another experiment. And when we examine critically other problems of physics we find that this is typical. The whole subject-matter of exact science consists of pointer readings and similar indications. We cannot enter here into the definition of what are to be classed as similar indications. The observation of approximate coincidence of the pointer with a scale-division can generally be extended to include the observation of any kind of coincidence—or, as it is usually expressed in the language of the general relativity theory, an intersection of world-lines. The essential point is that, although we seem to have very definite conceptions of objects in the external world, those conceptions do not enter into exact science and are not in any way confirmed by it. Before exact science can begin to handle the problem they must be replaced by quantities representing the results of physical measurement.

Perhaps you will object that although only the pointer readings enter into the actual calculation it would make nonsense of the problem to leave out all reference to anything else. The problem necessarily involves some kind of connecting background. It was not the pointer reading of the weighing-machine that slid down the hill! And yet from the point of view of exact science the thing that really did descend the hill can only be described as a bundle of pointer readings. (It should be remembered that the hill also has been replaced by pointer readings, and the sliding down is no longer an active adventure but a functional relation of space and time measures.) The word elephant calls up a certain association of mental impressions, but it is clear that mental impressions as such cannot be the subject handled in the physical problem. We have, for example, an impression of bulkiness. To this there is presumably some direct counterpart in the external world, but that counterpart must be of a nature beyond our apprehension, and science can make nothing of it. Bulkiness enters into exact science by yet another substitution; we replace it by a series of readings of a pair of calipers. Similarly the greyish black appearance in our mental impression is replaced in exact science by the readings of a photometer for various wave-lengths of light. And so on until all the characteristics of the elephant are exhausted and it has become reduced to a schedule of measures. There is always the triple correspondence—

(a) a mental image, which is in our minds and not in the external world;

(b) some kind of counterpart in the external world, which is of inscrutable nature;

(c) a set of pointer readings, which exact science can study and connect with other pointer readings.

And so we have our schedule of pointer readings ready to make the descent. And if you still think that this substitution has taken away all reality from the problem, I am not sorry that you should have a foretaste of the difficulty in store for those who hold that exact science is all-sufficient for the description of the universe and that there is nothing in our experience which cannot be brought within its scope.

I should like to make it clear that the limitation of the scope of physics to pointer readings and the like is not a philosophical craze of my own but is essentially the current scientific doctrine. It is the outcome of a tendency discernible far back in the last century but only formulated comprehensively with the advent of the relativity theory. The vocabulary of the physicist comprises a number of words such as length, angle, velocity, force, potential, current, etc., which we call “physical quantities”. It is now recognised as essential that these should be defined according to the way in which we actually recognise them when confronted with them, and not according to the metaphysical significance which we may have anticipated for them. In the old textbooks mass was defined as “quantity of matter”; but when it came to an actual determination of mass, an experimental method was prescribed which had no bearing on this definition. The belief that the quantity determined by the accepted method of measurement represented the quantity of matter in the object was merely a pious opinion. At the present day there is no sense in which the quantity of matter in a pound of lead can be said to be equal to the quantity in a pound of sugar. Einstein’s theory makes a clean sweep of these pious opinions, and insists that each physical quantity should be defined as the result of certain operations of measurement and calculation. You may if you like think of mass as something of inscrutable nature to which the pointer reading has a kind of relevance. But in physics at least there is nothing much to be gained by this mystification, because it is the pointer reading itself which is handled in exact science; and if you embed it in something of a more transcendental nature, you have only the extra trouble of digging it out again.

It is quite true that when we say the mass is two tons we have not specially in mind the reading of the particular machine on which the weighing was carried out. That is because we do not start to tackle the problem of the elephant’s escapade ab initio as though it were the first inquiry we had ever made into the phenomena of the external world. The examiner would have had to be much more explicit if he had not presumed a general acquaintance with the elementary laws of physics, i.e. laws which permit us to deduce the readings of other indicators from the reading of one. It is this connectivity of pointer readings, expressed by physical laws, which supplies the continuous background that any realistic problem demands.

It is obviously one of the conditions of the problem that the same elephant should be concerned in the weighing experiment and in the tobogganing experiment. How can this identity be expressed in a description of the world by pointer readings only? Two readings may be equal, but it is meaningless to inquire if they are identical; if then the elephant is a bundle of pointer readings, how can we ask whether it is continually the identical bundle ? The examiner does not confide to us how the identity of the elephant was ensured; we have only his personal guarantee that there was no substitution. Perhaps the creature answered to its name on both occasions; if so the test of identity is clearly outside the present domain of physics. The only test lying purely in the domain of physics is that of continuity; the elephant must be watched all the way from the scales to the hillside. The elephant, we must remember, is a tube in the four-dimensional world demarcated from the rest of space-time by a more or less abrupt boundary. Using the retina of his eye as an indicator and making frequent readings of the outline of the image, the observer satisfied himself that he was following one continuous and isolated world-tube from beginning to end. If his vigilance was intermittent he took a risk of substitution, and consequently a risk of the observed time of descent failing to agree with the time calculated.* Note that we do not infer that there is any identity of the contents of the isolated world-tube throughout its length; such identity would be meaning- less in physics. We use instead the law of conservation of mass (either as an empirical law or deduced from the law of gravitation) which assures us that, provided the tube is isolated, the pointer reading on the schedule derived from the weighing-machine type of experiment has a constant value along the tube. For the purpose of exact science “the same object” becomes replaced by “isolated world-tube”. The constancy of certain properties of the elephant is not assumed as self-evident from its sameness, but is an inference from experimental and theoretical laws relating to world-tubes which are accepted as well established.

* A good illustration of such substitution is afforded by astronomical observations of a certain double star with two components of equal brightness. After an intermission of observation the two components were inadvertently interchanged, and the substitution was not detected until the increasing discrepancy between the actual and predicted orbits was inquired into.

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By vinaire | Tagged | Comments (0)

Eddington 1927: Familiar Conceptions and Scientific Symbols

September 16, 2018 – 3:13 PM
Symbols

Reference: The Nature of the Physical World

This paper presents Chapter XII (section 1) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Familiar Conceptions and Scientific Symbols

We have said in the Introduction that the raw material of the scientific world is not borrowed from the familiar world. It is only recently that the physicist has deliberately cut himself adrift from familiar conceptions. He did not set out to discover a new world but to tinker with the old. Like everyone else he started with the idea that things are more or less what they seem, and that our vivid impression of our environment may be taken as a basis to work from. Gradually it has been found that some of its most obvious features must be rejected. We learn that instead of standing on a firm immovable earth proudly rearing our heads towards the vault of heaven, we are hanging by our feet from a globe careering through space at a great many miles a second. But this new knowledge can still be grasped by a rearrangement of familiar conceptions. I can picture to myself quite vividly the state of affairs just described; if there is any strain, it is on my credulity, not on my powers of conception. Other advances of knowledge can be accommodated by that very useful aid to comprehension—”like this only more so”. For example, if you think of something like a speck of dust only more so you have the atom as it was conceived up to a fairly recent date.

In addition to the familiar entities the physicist had to reckon with mysterious agencies such as gravitation or electric force; but this did not disturb his general outlook. We cannot say what electricity is “like”; but at first its aloofness was not accepted as final. It was taken to be one of the main aims of research to discover how to reduce these agencies to something describable in terms of familiar conceptions—in short to “explain” them. For example, the true nature of electric force might be some kind of displacement of the aether. (Aether was at that time a familiar conception—like some extreme kind of matter only more so.) Thus there grew up a waiting-list of entities which should one day take on their rightful relation to conceptions of the familiar world. Meanwhile physics had to treat them as best it could without knowledge of their nature.

It managed surprisingly well. Ignorance of the nature of these entities was no bar to successful prediction of behaviour. We gradually awoke to the fact that the scheme of treatment of quantities on the waiting-list was becoming more precise and more satisfying than our knowledge of familiar things. Familiar conceptions did not absorb the waiting-list, but the waiting-list began to absorb familiar conceptions. Aether, after being in turn an elastic solid, a jelly, a froth, a conglomeration of gyrostats, was denied a material and substantial nature and put back on the waiting-list. It was found that science could accomplish so much with entities whose nature was left in suspense that it began to be questioned whether there was any advantage in removing the suspense. The crisis came when we began to construct familiar entities such as matter and light out of things on the waiting-list. Then at last it was seen that the linkage to familiar concepts should be through the advanced constructs of physics and not at the beginning of the alphabet. We have suffered, and we still suffer, from expectations that electrons and quanta must be in some fundamental respects like materials or forces familiar in the workshop—that all we have got to do is to imagine the usual kind of thing on an infinitely smaller scale. It must be our aim to avoid such prejudgments, which are surely illogical; and since we must cease to employ familiar concepts, symbols have become the only possible alternative.

We are on familiar territory up till the understanding of the atom. But the moment we enter the atom we find ourselves on unfamiliar territory.

The synthetic method by which we build up from its own symbolic elements a world which will imitate the actual behaviour of the world of familiar experience is adopted almost universally in scientific theories. Any ordinary theoretical paper in the scientific journals tacitly assumes that this approach is adopted. It has proved to be the most successful procedure; and it is the actual procedure underlying the advances set forth in the scientific part of this book. But I would not claim that no other way of working is admissible. We agree that at the end of the synthesis there must be a linkage to the familiar world of consciousness, and we are not necessarily opposed to attempts to reach the physical world from that end. From the point of view of philosophy it is desirable that this entrance should be explored, and it is conceivable that it may be fruitful scientifically. If I have rightly understood Dr. Whitehead’s philosophy, that is the course which he takes. It involves a certain amount of working backwards (as we should ordinarily describe it) ; but his method of “extensive abstraction” is intended to overcome some of the difficulties of such a procedure. I am not qualified to form a critical judgment of this work, but in principle it appears highly interesting. Although this book may in most respects seem diametrically opposed to Dr. Whitehead’s widely read philosophy of Nature, I think it would be truer to regard him as an ally who from the opposite side of the mountain is tunnelling to meet his less philosophically minded colleagues. The important thing is not to confuse the two entrances.

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Eddington 1927: Three Types of Law

September 16, 2018 – 2:32 PM
VLT image of the cometary globule CG4

Reference: The Nature of the Physical World

This paper presents Chapter XI (section 4) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Three Types of Law

So far as we are able to judge, the laws of Nature divide themselves into three classes: (1) identical laws, (2) statistical laws, (3) transcendental laws. We have just been considering the identical laws, i.e. the laws obeyed as mathematical identities in virtue of the way in which the quantities obeying them are built. They cannot be regarded as genuine laws of control of the basal material of the world. Statistical laws relate to the behaviour of crowds, and depend on the fact that although the behaviour of each individual may be extremely uncertain average results can be predicted with confidence. Much of the apparent uniformity of Nature is a uniformity of averages. Our gross senses only take cognisance of the average effect of vast numbers of individual particles and processes; and the regularity of the average might well be compatible with a great degree of lawlessness of the individual. I do not think it is possible to dismiss statistical laws (such as the second law of thermodynamics) as merely mathematical adaptations of the other classes of law to certain practical problems. They involve a peculiar element of their own connected with the notion of a priori probability; but we do not yet seem able to find a place for this in any of the current conceptions of the world substratum.

If there are any genuine laws of control of the physical world they must be sought in the third group—the transcendental laws. The transcendental laws comprise all those which have not become obvious identities implied in the scheme of world-building. They are concerned with the particular behaviour of atoms, electrons and quanta—that is to say, the laws of atomicity of matter, electricity and action. We seem to be making some progress towards formulating them, but it is clear that the mind is having a much harder struggle to gain a rational conception of them than it had with the classical field-laws. We have seen that the field-laws, especially the laws of conservation, are indirectly imposed by the mind which has, so to speak, commanded a plan of world-building to satisfy them. It is a natural suggestion that the greater difficulty in elucidating the transcendental laws is due to the fact that we are no longer engaged in recovering from Nature what we have ourselves put into Nature, but are at last confronted with its own intrinsic system of government. But I scarcely know what to think. We must not assume that the possible developments of the new attitude towards natural law have been exhausted in a few short years. It may be that the laws of atomicity, like the laws of conservation, arise only in the presentation of the world to us and can be recognised as identities by some extension of the argument we have followed. But it is perhaps as likely that after we have cleared away all the superadded laws which arise solely in our mode of apprehension of the world about us, there will be left an external world developing under genuine laws of control.

I believe that all scientific laws that are determined and stated in an objective manner are a discovery of Nature’s own intrinsic system of government.

At present we can notice the contrast that the laws which we now recognise as man-made are characterised by continuity, whereas the laws to which the mind as yet lays no claim are characterised by atomicity. The quantum theory with its avoidance of fractions and insistence on integral units seems foreign to any scheme which we should be likely subconsciously to have imposed as a frame for natural phenomena. Perhaps our final conclusion as to the world of physics will resemble Kronecker’s view of pure mathematics.

“God made the integers, all else is the work of man.”*

* Die ganzen Zahlen hat Gott gemacht; alles anderes ist Menschenwerk.
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Eddington 1927: Selective Influence of the Mind

September 16, 2018 – 1:52 PM
Molecular Thoughts

Reference: The Nature of the Physical World

This paper presents Chapter XI (section 3) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Selective Influence of the Mind

This brings us very near to the problem of bridging the gulf between the scientific world and the world of everyday experience. The simpler elements of the scientific world have no immediate counterparts in everyday experience; we use them to build things which have counterparts. Energy, momentum and stress in the scientific world shadow well-known features of the familiar world. I feel stress in my muscles; one form of energy gives me the sensation of warmth; the ratio of momentum to mass is velocity, which generally enters into my experience as change of position of objects. When I say that I feel these things I must not forget that the feeling, in so far as it is located in the physical world at all, is not in the things themselves but in a certain corner of my brain. In fact, the mind has also invented a craft of world-building; its familiar world is built not from the distribution of relata and relations but by its own peculiar interpretation of the code messages transmitted along the nerves into its sanctum.

Accordingly we must not lose sight of the fact that the world which physics attempts to describe arises from the convergence of two schemes of world-building. If we look at it only from the physical side there is inevitably an arbitrariness about the building. Given the bricks—the 16 measures of world-structure—there are all sorts of things we might build. Or we might take up again some of the rejected lumber and build a still wider variety of things. But we do not build arbitrarily; we build to order. The things we build have certain remarkable properties; they have these properties in virtue of the way they are built, but they also have them because such properties were ordered. There is a general description which covers at any rate most of the building operations needed in the construction of the physical world; in mathematical language the operation consists in Hamiltonian differentiation of an invariant function of the 16 measures of structure. I do not think that there is anything in the basal relation-structure that cries out for this special kind of combination; the significance of this process is not in inorganic nature. Its significance is that it corresponds to an outlook adopted by the mind for its own reasons; and any other building process would not converge to the mental scheme of world-building. The Hamiltonian derivative has just that kind of quality which makes it stand out in our minds as an active agent against a passive extension of space and time; and Hamiltonian differentiation is virtually the symbol for creation of an active world out of the formless background. Not once in the dim past, but continuously by conscious mind is the miracle of the Creation wrought.

The role that mind plays in world building is bringing the criterion of continuum of substance by ensuring consistency, harmony and continuity.

By following this particular plan of building we construct things which satisfy the law of conservation, that is to say things which are permanent. The law of conservation is a truism for the things which satisfy it; but its prominence in the scheme of law of the physical world is due to the mind having demanded permanence. We might have built things which do not satisfy this law. In fact we do build one very important thing “action” which is not permanent; in respect to “action” physics has taken the bit in her teeth, and has insisted on recognising this as the most fundamental thing of all, although the mind has not thought it worthy of a place in the familiar world and has not vivified it by any mental image or conception. You will understand that the building to which I refer is not a shifting about of material; it is like building constellations out of stars. The things which we might have built but did not, are there just as much as those we did build. What we have called building is rather a selection from the patterns that weave themselves.

This criterion brings about the element of permanence and the law of conservation of substance.

The element of permanence in the physical world, which is familiarly represented by the conception of substance, is essentially a contribution of the mind to the plan of building or selection. We can see this selective tendency at work in a comparatively simple problem, viz. the hydrodynamical theory of the ocean. At first sight the problem of what happens when the water is given some initial disturbance depends solely on inorganic laws; nothing could be more remote from the intervention of conscious mind. In a sense this is true; the laws of matter enable us to work out the motion and progress of the different portions of the water; and there, so far as the inorganic world is concerned, the problem might be deemed to end. But actually in hydrodynamical textbooks the investigation is diverted in a different direction, viz. to the study of the motions of waves and wave-groups. The progress of a wave is not progress of any material mass of water, but of a form which travels over the surface as the water heaves up and down; again the progress of a wave-group is not the progress of a wave. These forms have a certain degree of permanence amid the shifting particles of water. Anything permanent tends to become dignified with an attribute of substantiality. An ocean traveller has even more vividly the impression that the ocean is made of waves than that it is made of water.* Ultimately it is this innate hunger for permanence in our minds which directs the course of development of hydrodynamics, and likewise directs the world-building out of the sixteen measures of structure.

* This was not intended to allude to certain consequential effects of the waves; it is true, I think, of the happier impressions of the voyage.

The element of permanence is expressed through the process of quantization.

Perhaps it will be objected that other things besides mind can appreciate a permanent entity such as mass; a weighing machine can appreciate it and move a pointer to indicate how much mass there is. I do not think that is a valid objection. In building the physical world we must of course build the measuring appliances which are part of it; and the measuring appliances result from the plan of building in the same way as the entities which they measure. If, for example, we had used some of the “lumber” to build an entity x, we could presumably construct from the same lumber an appliance for measuring x. The difference is this—if the pointer of the weighing machine is reading 5 lbs. a human consciousness is in a mysterious way (not yet completely traced) aware of the fact, whereas if the measuring appliance for x reads 5 units no human mind is aware of it. Neither x nor the appliance for measuring x have any interaction with consciousness. Thus the responsibility for the fact that the scheme of the scientific world includes mass but excludes x rests ultimately with the phenomena of consciousness.

The above is an example of maintaining consistency.

Perhaps a better way of expressing this selective influence of mind on the laws of Nature is to say that values are created by the mind. All the “light and shade” in our conception of the world of physics comes in this way from the mind, and cannot be explained without reference to the characteristics of consciousness.

The world which we have built from the relation-structure is no doubt doomed to be pulled about a good deal as our knowledge progresses. The quantum theory shows that some radical change is impending. But I think that our building exercise has at any rate widened our minds to the possibilities and has given us a different orientation towards the idea of physical law. The points which I stress are:

Firstly, a strictly quantitative science can arise from a basis which is purely qualitative. The comparability that has to be assumed axiomatically is a merely qualitative discrimination of likeness and unlikeness.

Secondly, the laws which we have hitherto regarded as the most typical natural laws are of the nature of truisms, and the ultimate controlling laws of the basal structure (if there are any) are likely to be of a different type from any yet conceived.

Thirdly, the mind has by its selective power fitted the processes of Nature into a frame of law of a pattern largely of its own choosing; and in the discovery of this system of law the mind may be regarded as regaining from Nature that which the mind has put into Nature.

Mind is part of the same system as rest of Nature. So the laws of Nature are not arbitrarily influenced by the mind. Consciousness in Man is the product of evolution. It is subject to the laws of Nature. We have not yet become fully aware of the laws that apply to consciousness.

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By vinaire | Tagged | Comments (1)