Reference: The Nature of the Physical World

This paper presents Chapter V (section 5) 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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The Scientific Reaction from Microscopic Analysis

From the point of view of philosophy of science the conception associated with entropy must I think be ranked as the great contribution of the nineteenth century to scientific thought. It marked a reaction from the view that everything to which science need pay attention is discovered by a microscopic dissection of objects. It provided an alternative standpoint in which the centre of interest is shifted from the entities reached by the customary analysis (atoms, electric potentials, etc.) to qualities possessed by the system as a whole, which cannot be split up and located—a little bit here, and a little bit there. The artist desires to convey significances which cannot be told by microscopic detail and accordingly he resorts to impressionist painting. Strangely enough the physicist has found the same necessity; but his impressionist scheme is just as much exact science and even more practical in its application than his microscopic scheme.

Increase in entropy means increase in equilibrium, implying greater structure, and therefore, greater quantization. Maybe we can measure quantization by measuring entropy. But this needs to be researched.

Quantization explains the nature of both material and field “particles”. It is, therefore, a concept more basic than any understanding that can be attained from a microscopic dissection of objects.

Thus in the study of the falling stone the microscopic analysis reveals myriads of separate molecules. The energy of the stone is distributed among the molecules, the sum of the energies of the molecules making up the energy of the stone. But we cannot distribute in that way the organisation or the random element in the motions. It would be meaningless to say that a particular fraction of the organisation is located in a particular molecule.

There is one ideal of survey which would look into each minute compartment of space in turn to see what it may contain and so make what it would regard as a complete inventory of the world. But this misses any world-features which are not located in minute compartments. We often think that when we have completed our study of one we know all about two, because “two” is “one and one”. We forget that we have still to make a study of “and”. Secondary physics is the study of “and”—that is to say, of organisation.

Thanks to clear-sighted pioneers in the last century science became aware that it was missing something of practical importance by following the inventory method of the primary scheme of physics. Entropy became recognised although it was not found in any of the compartments. It was discovered and exalted because it was essential to practical applications of physics, not to satisfy any philosophic hungering. But by it science has been saved from a fatal narrowness. If we had kept entirely to the inventory method, there would have been nothing to represent “becoming” in the physical world. And science, having searched high and low, would doubtless have reported that “becoming” is an unfounded mental illusion—like beauty, life, the soul, and other things which it is unable to inventory.

Study of individual elements of a system does not necessarily lead to the understanding of how the whole system ‘becomes’ and operates. It requires the study of the organization of the whole system. That is where the concept of entropy comes into picture.

I think that doubts might well have been entertained as to whether the newcomer was strictly scientific. Entropy was not in the same category as the other physical quantities recognised in science, and the extension —as we shall presently see—was in a very dangerous direction. Once you admit attributes of arrangement as subject-matter of physics, it is difficult to draw the line. But entropy had secured a firm place in physics before it was discovered that it was a measure of the random element in arrangement. It was in great favour with the engineers. Their sponsorship was the highest testimonial to its good character; because at that time it was the general assumption that the Creation was the work of an engineer (not of a mathematician, as is the fashion nowadays).

It would be interesting to look into the concept of entropy in light of the fundamental discovery of quantization.

Suppose that we were asked to arrange the following in two categories—

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.

Entropy is associated with the number of random microstates consistent with macroscopic state of the system. Entropy increases as a system spontaneously evolves toward thermodynamic equilibrium, and the system settles into an increasingly complex configuration. This shall also mean that the system is becoming increasingly quantized. Thus, we may find a quantitative measure of quantization by studying entropy.

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.

Entropy relates to the complexity of arrangements within the system, whereas, quantization relates to the macroscopic structure of the system.

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 analyzed 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.

The macroscopic picture emerging from microscopic complexity of entropy is quantization. Both entropy and quantization can be viewed objectively. There is nothing subjective about them.

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Reference: The Nature of the Physical World

This paper presents Chapter V (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.

.

Objectivity of Becoming

In general we should describe the familiar world as subjective and the scientific world as objective. Take for instance our former example of parallelism, viz. colour in the familiar world and its counterpart electromagnetic wave-length in the scientific world. Here we have little hesitation in describing the waves as objective and the colour as subjective. The wave is the reality—or the nearest we can get to a description of reality; the colour is mere mind-spinning. The beautiful hues which flood our consciousness under stimulation of the waves have no relevance to the objective reality. For a colour-blind person the hues are different; and although persons of normal sight make the same distinctions of colour, we cannot ascertain whether their consciousness of red, blue, etc. is just like our own. Moreover, we recognise that the longer and shorter electromagnetic waves which have no visual effect associated with them are just as real as the coloured waves. In this and other parallelisms we find the objective in the scientific world and the subjective in the familiar world.

The categorization, “Familiar world is subjective and the scientific world is objective,” is arbitrary. Comments in the previous section describe the criterion of objectivity and subjectivity as follows.

1. The essential criterion of objectivity is consistency, harmony and continuity among all observations.
2. Subjectivity is the degree to which one fails to observe the consistency, harmony and continuity of the universe.

Based on this criterion, the familiar world can be objective and the scientific world can be subjective. There can also be degrees of objectivity and subjectivity.

But in the parallelism between entropy-gradient and “becoming” the subjective and objective seem to have got on to the wrong sides. Surely “becoming” is a reality—or the nearest we can get to a description of reality. We are convinced that a dynamic character must be attributed to the external world; making all allowance for mental imagery, I do not see how the essence of “becoming” can be much different from what it appears to us to be. On the other side we have entropy which is frankly of a much more subjective nature than most of the ordinary physical qualities. Entropy is an appreciation of arrangement and organisation; it is subjective in the same sense that the constellation Orion is subjective. That which is arranged is objective, so too are the stars composing the constellation; but the association is the contribution of the mind which surveys. If colour is mind-spinning, so also is entropy a mind-spinning—of the statistician. It has about as much objectivity as a batting average.

Just because something is mentally perceived, does not necessarily make it subjective.

Whilst the physicist would generally say that the matter of this familiar table is really a curvature of space, and its colour is really electromagnetic wavelength, I do not think he would say that the familiar moving on of time is really an entropy-gradient. I am quoting a rather loose way of speaking; but it reveals that there is a distinct difference in our attitude towards the last parallelism. Having convinced ourselves that the two things are connected, we must conclude that there is something as yet ungrasped behind the notion of entropy—some mystic interpretation, if you like— which is not apparent in the definition by which we introduced it into physics. In short we strive to see that entropy-gradient may really be the moving on of time (instead of vice versa).

Time exists because of change. Entropy provides the reason for change to occur in terms of equilibrium.

Before passing on I would note that this exceptional appearance of subjective and objective apparently in their wrong worlds gives food for thought. It may prepare us for a view of the scientific world adopted in the later chapters which is much more subjective than that usually held by science.

Subjectivity implies that there are inconsistencies, disharmonies and discontinuities present that need to be fully sorted out.

The more closely we examine the association of entropy with “becoming” the greater do the obstacles appear. If entropy were one of the elementary indefinables of physics there would be no difficulty. Or if the moving on of time were something of which we were made aware through our sense organs there would be no difficulty. But the actual combination which we have to face seems to be unique in its difficulty.

Suppose that we had had to identify “becoming” with electrical potential-gradient instead of with entropy-change. We discover potential through the readings of a voltmeter. The numerical reading stands for something in the condition of the world, but we form no picture of what that something is. In scientific researches we only make use of the numerical value—a code-number attached to a background outside all conception. It would be very interesting if we could relate this mysterious potential to any of our familiar conceptions. Clearly, if we could identify the change of potential with the familiar moving on of time, we should have made a great step towards grasping its intrinsic nature. But turning from supposition to fact, we have to identify potential-gradient with force. Now it is true that we have a familiar conception of force— a sensation of muscular effort. But this does not give us any idea of the intrinsic nature of potential-gradient; the sensation is mere mind-spinning provoked by nervous impulses which have travelled a long way from the seat of the force. That is the way with all physical entities which affect the mind through the sense organs. The interposed nerve-mechanism would prevent any close association of the mental image with the physical cause, even if we were disposed to trust our mental insight when it has a chance of operating directly.

Regardless of what is changing, it is the fact of change that brings about the sense of time. ‘Becoming’ is whatever we sense to be there both physically and mentally.

Or suppose that we had had to identify force with entropy-gradient. That would only mean that entropy-gradient is a condition which stimulates a nerve, which thereupon transmits an impulse to the brain, out of which the mind weaves its own peculiar impression of force. No one would feel intuitive objection to the hypothesis that the muscular sensation of force is associated with change of organisation of the molecules of the muscle.

How we perceive something proceeds from the animation of atoms and molecules that form the body and its organs. This is whole another subject to be explored.

Our trouble is that we have to associate two things, both of which we more or less understand, and, so far as we understand them, they are utterly different. It is absurd to pretend that we are in ignorance of the nature of organisation in the external world in the same way that we are ignorant of the intrinsic nature of potential. It is absurd to pretend that we have no justifiable conception of “becoming” in the external world. That dynamic quality—that significance which makes a development from past to future reasonable and a development from future to past farcical—has to do much more than pull the trigger of a nerve. It is so welded into our consciousness that a moving on of time is a condition of consciousness. We have direct insight into “becoming” which sweeps aside all symbolic knowledge as on an inferior plane. If I grasp the notion of existence because I myself exist, I grasp the notion of becoming because I myself become. It is the innermost Ego of all which is and becomes.

How we become aware of the actuality of what is there deals with filters and their removal. It is whole another subject.

The incongruity of symbolising this fundamental intuition by a property of arrangement of the microscopic constituents of the world is evident. What this difficulty portends is still very obscure. But it is not irrelevant to certain signs of change which we may discern in responsible scientific opinion with regard to the question of primary and secondary law. The cast-iron determinism of primary law is, I think, still widely accepted but no longer unquestioningly. It now seems clear that we have not yet got hold of any primary law—that all those laws at one time supposed to be primary are in reality statistical. No doubt it will be said that that was only to be expected; we must be prepared for a very long search before we get down to ultimate foundations, and not be disappointed if new discoveries reveal unsuspected depths beneath. But I think it might be said that Nature has been caught using rather unfair dodges to prevent our discovering primary law—that kind of artfulness which frustrated our efforts to discover velocity relative to the aether. I believe that Nature is honest at heart, and that she only resorts to these apparent shifts of concealment when we are looking for something which is not there. It is difficult to see now any justification for the strongly rooted conviction in the ultimate re-establishment of a deterministic scheme of law except a supposed necessity of thought. Thought has grown accustomed to doing without a great many “necessities” in recent years.

What frustrated our efforts to discover velocities relative to the aether was the assumption that a substance of no inertia could be at rest. The truth is that a substance must be of infinite inertia to be at rest. Such assumption is an example of a filter that distorts our observations. Another filter is the “particles in void” perspective. As we recognize such filters and remove them, we gradually become aware of actuality. That is the function of science.

One would not be surprised if in the reconstruction of the scheme of physics which the quantum theory is now pressing on us, secondary law becomes the basis and primary law is discarded. In the reconstructed world nothing is impossible though many things are improbable. The effect is much the same, but the kind of machinery that we must conceive is altogether different. We shall have further glimpses of this problem and I will not here pursue it. Entropy, being a quantity introduced in connection with secondary law will now exist, so to speak, in its own right instead of by its current representation as arrangement of the quantities in the abandoned primary scheme; and in that right it may be more easily accepted as the symbol for the dynamic quality of the world. I cannot make my meaning more precise, because I am speaking of a still hypothetical change of ideas which no one has been able to bring about.

Associating increasing randomity, instead of equilibrium, with entropy may be another filter.

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