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Eddington 1927: Dynamic Quality of the External World

September 6, 2018 – 6:49 PM
All-sky illustration of all Hubble observations as of 27 June 20

 Reference: The Nature of the Physical World

This paper presents Chapter V (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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Dynamic Quality of the External World

But for our ulterior conviction of the dynamic quality of time, it would be possible to take the view that ”becoming” is purely subjective—that there is no “becoming” in the external world which lies passively spread out in the time-dimension as Minkowski pictured it. My consciousness then invents its own serial order for the sense impressions belonging to the different view-points along the track in the external world, occupied by the four-dimensional worm who is in some mysterious way Myself; and in focussing the sensations of a particular view-point I get the illusion that the corresponding external events are “taking place”. I suppose that this would be adequate to account for the observed phenomena. The objections to it hinge on the fact that it leaves the external world without any dynamic quality intrinsic to it.

From the “continuum of substance” perspective the UNIVERSE is a single system that is intrinsically continuous, harmonious and consistent. Therefore, the essential criterion of objectivity is consistency, harmony and continuity among all observations.

Subjectivity is the degree to which one fails to observe the consistency, harmony and continuity of the universe. Thus, physical perceptions of the external world that are not consistent with each other are suffering from subjectivity. And mental perceptions that are consistent within themselves and with physical perceptions are objective.

Many believe that if a perception is mental then it must be subjective. This error comes from the “particles in void” perspective. The viewpoint of ‘time’ and ‘becoming’ is not necessarily subjective. It can be objective if it is consistent with surrounding observations.

It is useful to recognise how some of our most elementary reasoning tacitly assumes the existence of this dynamic quality or trend; to eradicate it would almost paralyse our faculties of inference. In the operation of shuffling cards it seems axiomatic that the cards must be in greater disarrangement at a later instant. Can you conceive Nature to be such that this is not obviously true? But what do we here mean by “later”? So far as the axiomatic character of the conclusion is concerned (not its experimental verification) we cannot mean “later” as judged by consciousness; its obviousness is not bound up with any speculations as to the behaviour of consciousness. Do we then mean “later” as judged by the physical criterion of time’s arrow, i.e. corresponding to a greater proportion of the random element? But that would be tautological—the cards are more disarranged when there is more of the random element. We did not mean a tautology; we unwittingly accepted as a basis for our thought about the question an unambiguous trend from past to future in the space-time where the operation of shuffling is performed.

It is an assumption that ‘later’ is always a greater proportion of random element. The random element is subjective because it is being viewed relative to some past condition. The concept of ‘later’ could be understood in terms of sequence of changes, or greater equilibrium.

The crux of the matter is that, although a change described as sorting is the exact opposite to a change described as shuffling we cannot imagine a cause of sorting to be the exact opposite of a cause of shuffling. Thus a reversal of the time-direction which turns shuffling into sorting does not make the appropriate transformation of their causes. Shuffling can have inorganic causes, but sorting is the prerogative of mind or instinct. We cannot believe that it is merely an orientation with respect to the time-direction which differentiates us from inorganic nature. Shuffling is related to sorting (so far as the change of configuration is concerned) as plus is to minus; but to say that the cause of shuffling is related to the cause of sorting in the same way would seem equivalent to saying that the activities of matter and mind are related like plus and minus—which surely is nonsense. Hence if we view the world from future to past so that shuffling and sorting are interchanged, their causes do not follow suit, and the rational connection is broken. To restore coherency we must postulate that by this change of direction something else has been reversed, viz. the trend in world-texture spoken of above; “becoming” has been turned into “unbecoming”. If we like we can now go on to account, not for things becoming unshuffled, but for their unbecoming shuffled—and, if we wish to pursue this aspect further, we must discuss not the causes but the un-causes. But, without tying ourselves into verbal knots, the meaning evidently is that “becoming” gives a texture to the world which it is illegitimate to reverse.

The direction of time is the direction of increasing equilibrium. Each condition has its own equilibrium organization. By changing the condition from A to B, we can trigger a sequence of changes. Then by changing the condition from B to A, we can reverse that sequence of changes. We may call this a reversal of local time per the definition above.

To reverse the universal time we must know the original condition that existed at the beginning of the universe. The universe must then be convinced to be in that original condition to establish the reversal of time.

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Eddington 1927: Linkage of Entropy with Becoming

September 6, 2018 – 10:21 AM

Reference: The Book of Physics

Linkage of Entropy with Becoming

Please see the original text at the link above.

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Summary

This is a universe of change. From the universal viewpoint, all these changes are in a near equilibrium. But from a local viewpoint, one only sees the system changing in a certain direction. The symbolic world of physics represents the universal viewpoint that gives us the primary law that applies uniformly. Our familiar world of experience represents the local viewpoint that gives us the time’s arrow of growing and becoming. This local viewpoint appears as the secondary law of entropy in the symbolic world of physics.

Thus, the change in entropy represents the moving on of time familiar to our minds. Scientifically, the system is reaching for a local equilibrium under the prevailing conditions. Mentally “becoming” is reaching toward some goal. Here we are in the domain of thought beyond physical. We feel time passing as we move toward the goal, or see the system move toward the equilibrium. Mathematically, we see it as the random element increasing steadily in the direction of the grain. Mentally, we feel all the variables in life lining up with some natural goal.

The scientific method has the purpose of ensuring continuity, consistency and harmony among all observations. As we observe more closely, the ideas in our mind lose their fixation and become more random. The application of scientific method brings that randomness into an “equilibrium” of continuity, consistency and harmony. We can intuitively sense the degree of equilibrium. Thus, when it comes to thought, we move beyond physical measurements into an intuitive sense of equilibrium defined by the degree of continuity, consistency and harmony, or oneness, that is present.

This summary is giving words to what Eddington is expressing only as a feeling. Time seems to provide a sense of movement toward equilibrium in the physical world; and a sense of movement toward oneness in the spiritual, or the thought, world. Physical measurements only extend the precision of our senses in the physical world. Similarly, an intuitive sense of oneness extends the precision of our senses in the spiritual (thought) world.

The equilibrium in the universe is moving from lower to higher complexity as represented by symbols for matter to symbols of energy to symbols of thought that represents life.

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Comments


The entropy (randomness) is increasing in the universe; but always within the constraints of continuity, consistency and harmony. We can feel the equilibrium among all thought due to its continuity, consistency and harmony. We measure this degree of “oneness” intuitively.

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Eddington 1927: Are Space and Time Infinite?

September 5, 2018 – 2:56 PM

Reference: The Book of Physics

Note: The original text is provided below.
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Summary

It is difficult to answer any question about space unless we understand what space is. According to Einstein’s theory, space is “finite but unbounded.” But,  that still does not define space. It just ties the space up with geometry, or some abstract shape. The features of space which we discover by experiment are extensions, i.e. lengths and distances. So space is like a network of distances.

Eddington says, “Distances are linkages whose intrinsic nature is inscrutable.” But distances are measured on some substance. Therefore, distances are comprehensible only in the context of substance. They have no meaning in themselves. If the surface of an object is curved it would affect the distance accordingly.

Eddington is defining space in terms of linkages between mathematical points. In reality, we have solid particles instead of mathematical points. As we cut these particles into smaller and smaller particles they ultimately reduce to a field of force without any particles. This field of force at first appears as the thick electronic field around the nucleus of an atom. As this thickness (consistency) of the field reduces it appears like an energy field, such as, light. As the consistency reduces further it appears as a field of thought. Volume increases as consistency decreases. The largest volume will be for the field of thought. Beyond thought there shall be a lack of substance, and, therefore, a lack of awareness.

Eddington is defining time as the view through a small window of a moving train. One sees sequence of events passing with a before and after. But if one climbs on the roof of the train, one sees the whole terrain laid out before one, with different elements having different durations. Science always uses a broad, universal viewpoint. From this viewpoint, time reduces to duration of substance. The duration of the substance decreases as its consistency decreases. The least duration shall  be for the field of thought. Beyond thought there is no substance; therefore, there is no awareness of duration or time.

All confusion arises because the definitions of substance, space and time are not stated with scientific precision. The universe, as a whole, may have a certain volume and a certain duration, which defines the limits of its space and time. Beyond those limits there is no substance and no awareness. The universe may cycle through awareness and non-awareness.

Eddington says, “Travelling backwards into the past we find a world with more and more organisation.” That is just what appears in consciousness from a narrow viewpoint. That is not the case when one is looking from a universal viewpoint (see the train example above). From the universal viewpoint one sees a universe made up of matter, energy and thought, each with its different volume and duration. The substance has a spectrum, and so does space and time. It is a complex affair in a certain state of an overall equilibrium. That state of equilibrium is itself evolving. The subject of physics is an outcome of the evolution of thought. The current shortcoming of Physics is that it has yet to include thought as a substance in its considerations.

Materialism is a matter-centric viewpoint. This viewpoint is represented by the subject of physics as it stands today. There is a crack in this viewpoint as Einstein’s  theory introduces energy as a substance. According to this theory, matter de-condenses into energy. Eddington is not happy with the idea that the universe started with a bang, but he doesn’t see that the idea of “Creator” alludes to thought being treated as a substance too, if physics has to gain a universal viewpoint.

The second law of thermodynamic seems to be limited as it does not include the influence of thought. Much still needs to be learned about thought as a substance. Ultimately, the conservation as well as the equilibrium of substance must include thought too. It is thought that must provide the counter-process by which radiation collects in space, evolves into electrons and protons, and begins star-building all over again.

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Comments

Space is defined by shape, or geometry as in mathematics. It is the shape of some substance. Similarly, Time is the duration of some substance. Both space and time have no relevance in the absence of substance. Without substance, there is no awareness either. Presence of space and time implies the presence of substance; and the presence of substance implies the presence of awareness.

Space and time are primary sensations that extend from the presence of substance. They make up the sense of awareness. As we look at substance as something substantial enough to be sensed, we discover that matter is not the only substance. Einstein extended the definition of substance to include energy. Now we are looking at the inclusion of thought as substance as well.

Once we do that we discover the spectrum of substance from matter to energy to thought that has wonderful implications as expressed in the summary above. We also discover that gravity is but the tendency of substance to align itself with surrounding substance according to its relative consistency.

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Original Text

I suppose that everyone has at some time plagued his imagination with the question, Is there an end to space? If space comes to an end, what is beyond the end? On the other hand the idea that there is no end, but space beyond space for ever, is inconceivable. And so the imagination is tossed to and fro in a dilemma. Prior to the relativity theory the orthodox view was that space is infinite. No one can conceive infinite space; we had to be content to admit in the physical world an inconceivable conception—disquieting but not necessarily illogical. Einstein’s theory now offers a way out of the dilemma. Is space infinite, or does it come to an end? Neither. Space is finite but it has no end; “finite but unbounded” is the usual phrase.

Infinite space cannot be conceived by anybody; finite but unbounded space is difficult to conceive but not impossible. I shall not expect you to conceive it; but you can try. Think first of a circle; or, rather, not the circle, but the line forming its circumference. This is a finite but endless line. Next think of a sphere—the surface of a sphere—that also is a region which is finite but unbounded. The surface of this earth never comes to a boundary; there is always some country beyond the point you have reached; all the same there is not an infinite amount of room on the earth. Now go one dimension more; circle, sphere—the next thing. Got that? Now for the real difficulty. Keep a tight hold of the skin of this hypersphere and imagine that the inside is not there at all—that the skin exists without the inside. That is finite but unbounded space.

No; I don’t think you have quite kept hold of the conception. You overbalanced just at the end. It was not the adding of one more dimension that was the real difficulty; it was the final taking away of a dimension that did it. I will tell you what is stopping you. You are using a conception of space which must have originated many million years ago and has become rather firmly embedded in human thought. But the space of physics ought not to be dominated by this creation of the dawning mind of an enterprising ape. Space is not necessarily like this conception; it is like—whatever we find from experiment it is like. Now the features of space which we discover by experiment are extensions, i.e. lengths and distances. So space is like a network of distances. Distances are linkages whose intrinsic nature is inscrutable; we do not deny the inscrutability when we apply measure numbers to them—2 yards, 5 miles, etc.—as a kind of code distinction. We cannot predict out of our inner consciousness the laws by which code-numbers are distributed among the different linkages of the network, any more than we can predict how the code-numbers for electromagnetic force are distributed. Both are a matter for experiment.

If we go a very long way to a point A in one direction through the universe and a very long way to a point B in the opposite direction, it is believed that between A and B there exists a linkage of the kind indicated by a very small code-number; in other words these points reached by travelling vast distances in opposite directions would be found experimentally to be close together. Why not? This happens when we travel east and west on the earth. It is true that our traditional inflexible conception of space refuses to admit it; but there was once a traditional conception of the earth which refused to admit circumnavigation. In our approach to the conception of spherical space the difficult part was to destroy the inside of the hypersphere leaving only its three-dimensional surface existing. I do not think that is so difficult when we conceive space as a network of distances. The network over the surface constitutes a self-supporting system of linkage which can be contemplated without reference to extraneous linkages. We can knock away the constructional scaffolding which helped us to approach the conception of this kind of network of distances without endangering the conception.

We must realise that a scheme of distribution of inscrutable relations linking points to one another is not bound to follow any particular preconceived plan, so that there can be no obstacle to the acceptance of any scheme indicated by experiment.

We do not yet know what is the radius of spherical space; it must, of course, be exceedingly great compared with ordinary standards. On rather insecure evidence it has been estimated to be not many times greater than the distance of the furthest known nebulae. But the boundlessness has nothing to do with the bigness. Space is boundless by re-entrant form not by great extension. That which is is a shell floating in the infinitude of that which is not. We say with Hamlet, “I could be bounded in a nutshell and count myself a king of infinite space”.

But the nightmare of infinity still arises in regard to time. The world is closed in its space dimensions like a sphere, but it is open at both ends in the time dimension. There is a bending round by which East ultimately becomes West, but no bending by which Before ultimately becomes After.

I am not sure that I am logical but I cannot feel the difficulty of an infinite future time very seriously. The difficulty about A.D. ∞ will not happen until we reach A.D. ∞, and presumably in order to reach A.D. ∞ the difficulty must first have been surmounted. It should also be noted that according to the second law of thermodynamics the whole universe will reach thermodynamical equilibrium at a not infinitely remote date in the future. Time’s arrow will then be lost altogether and the whole conception of progress towards a future fades away.

But the difficulty of an infinite past is appalling. It is inconceivable that we are the heirs of an infinite time of preparation; it is not less inconceivable that there was once a moment with no moment preceding it.

This dilemma of the beginning of time would worry us more were it not shut out by another overwhelming difficulty lying between us and the infinite past. We have been studying the running-down of the universe; if our views are right, somewhere between the beginning of time and the present day we must place the winding up of the universe.

Travelling backwards into the past we find a world with more and more organisation. If there is no barrier to stop us earlier we must reach a moment when the energy of the world was wholly organised with none of the random element in it. It is impossible to go back any further under the present system of natural law. I do not think the phrase “wholly organised” begs the question. The organisation, we are concerned with is exactly definable, and there is a limit at which it becomes perfect. There is not an infinite series of states of higher and still higher organisation; nor, I think, is the limit one which is ultimately approached more and more slowly. Complete organisation does not tend to be more immune from loss than incomplete organisation.

There is no doubt that the scheme of physics as it has stood for the last three-quarters of a century postulates a date at which either the entities of the universe were created in a state of high organisation, or preexisting entities were endowed with that organisation which they have been squandering ever since. Moreover, this organisation is admittedly the antithesis of chance. It is something which could not occur fortuitously.

This has long been used as an argument against a too aggressive materialism. It has been quoted as scientific proof of the intervention of the Creator at a time not infinitely remote from to-day. But I am not advocating that we drew any hasty conclusions from it. Scientists and theologians alike must regard as somewhat crude the naive theological doctrine which (suitably disguised) is at present to be found in every textbook of thermodynamics, namely that some billions of years ago God wound up the material universe and has left it to chance ever since. This should be regarded as the working-hypothesis of thermodynamics rather than its declaration of faith. It is one of those conclusions from which we can see no logical escape—only it suffers from the drawback that it is incredible. As a scientist I simply do not believe that the present order of things started off with a bang; unscientifically I feel equally unwilling to accept the implied discontinuity in the divine nature. But I can make no suggestion to evade the deadlock.

Turning again to the other end of time, there is one school of thought which finds very repugnant the idea of a wearing out of the world. This school is attracted by various theories of rejuvenescence. Its mascot is the Phoenix. Stars grow cold and die out. May not two dead stars collide, and be turned by the energy of the shock into fiery vapour from which a new sun—with planets and with life—is born? This theory very prevalent in the last century is no longer contemplated seriously by astronomers. There is evidence that the present stars at any rate are products of one evolutionary process which swept across primordial matter and caused it to aggregate; they were not formed individually by haphazard collisions having no particular time connection with one another. But the Phoenix complex is still active. Matter, we believe, is gradually destroyed and its energy set free in radiation. Is there no counter-process by which radiation collects in space, evolves into electrons and protons, and begins star-building all over again? This is pure speculation and there is not much to be said on one side or the other as to its truth. But I would mildly criticise the mental outlook which wishes it to be true. However much we eliminate the minor extravagances of Nature, we do not by these theories stop the inexorable running-down of the world by loss of organisation and increase of the random element. Whoever wishes for a universe which can continue indefinitely in activity must lead a crusade against the second law of thermodynamics; the possibility of re-formation of matter from radiation is not crucial and we can await conclusions with some indifference.

At present we can see no way in which an attack on the second law of thermodynamics could possibly succeed, and I confess that personally I have no great desire that it should succeed in averting the final running-down of the universe. I am no Phoenix worshipper. This is a topic on which science is silent, and all that one can say is prejudice. But since prejudice in favour of a never-ending cycle of rebirth of matter and worlds is often vocal, I may perhaps give voice to the opposite prejudice. I would feel more content that the universe should accomplish some great scheme of evolution and, having achieved whatever may be achieved, lapse back into chaotic changelessness, than that its purpose should be banalised by continual repetition. I am an Evolutionist, not a Multiplicationist. It seems rather stupid to keep doing the same thing over and over again.

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Eddington 1927: Thermodynamical Equilibrium

September 5, 2018 – 11:54 AM
equilibrium 5

Reference: The Book of Physics

Note: The original text is provided below.
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Summary

Our method of measurement of entropy emphasizes the antithesis of chance. It is a measure of the organization element. The scientific name for a fortuitous concourse of atoms is “thermodynamical equilibrium”. In a thermodynamical equilibrium no increase in the random element can occur. An example of this would be a region in the deep interior of a star.

As we divide the particles into smaller particles, more shuffling (increase of random element) becomes possible. With infinite divisibility there can be no end to the shuffling. The experimental fact that a definite state of equilibrium is rapidly reached, means energy is not infinitely divided. Time recycles but does not progress.

Nothing in the statistics of an assemblage can distinguish a direction of time when entropy fails to distinguish one.

When there is a thermodynamic equilibrium, there is no net change since all processes at microscopic level act as if they are reversible, and they are occurring in either direction at the same rate.

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Comments


A cycle includes time. A cycle is not random if its sequences are known. At thermodynamic equilibrium, all changes are cyclic, and there is no net change. Thus, there is no evolution unless a new postulate is generated. 

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Original Text

Progress of time introduces more and more of the random element into the constitution of the world. There is less of chance about the physical universe to-day than there will be to-morrow. It is curious that in this very matter-of-fact branch of physics, developed primarily because of its importance for engineers, we can scarcely avoid expressing ourselves in teleological language. We admit that the world contains both chance and design, or at any rate chance and the antithesis of chance. This antithesis is emphasised by our method of measurement of entropy; we assign to the organisation or non-chance element a measure which is, so to speak, proportional to the strength of our disbelief in a chance origin for it. “A fortuitous concourse of atoms”—that bugbear of the theologian—has a very harmless place in orthodox physics. The physicist is acquainted with it as a much-prized rarity. Its properties are very distinctive, and unlike those of the physical world in general. The scientific name for a fortuitous concourse of atoms is “thermodynamical equilibrium”.

Thermodynamical equilibrium is the other case which we promised to consider in which no increase in the random element can occur, namely, that in which the shuffling is already as thorough as possible. We must isolate a region of the universe, arranging that no energy can enter or leave it, or at least that any boundary effects are precisely compensated. The conditions are ideal, but they can be reproduced with sufficient approximation to make the ideal problem relevant to practical experiment. A region in the deep interior of a star is an almost perfect example of thermodynamical equilibrium. Under these isolated conditions the energy will be shuffled as it is bandied from matter to aether and back again, and very soon the shuffling will be complete.

The possibility of the shuffling becoming complete is significant. If after shuffling the pack you tear each card in two, a further shuffling of the half-cards becomes possible. Tear the cards again and again; each time there is further scope for the random element to increase. With infinite divisibility there can be no end to the shuffling. The experimental fact that a definite state of equilibrium is rapidly reached indicates that energy is not infinitely divisible, or at least that it is not infinitely divided in the natural processes of shuffling. Historically this is the result from which the quantum theory first arose. We shall return to it in a later chapter.

In such a region we lose time’s arrow. You remember that the arrow points in the direction of increase of the random element. When the random element has reached its limit and become steady the arrow does not know which way to point. It would not be true to say that such a region is timeless; the atoms vibrate as usual like little clocks; by them we can measure speeds and durations. Time is still there and retains its ordinary properties, but it has lost its arrow; like space it extends, but it does not “go on”.

This raises the important question, Is the random element (measured by the criterion of probability already discussed) the only feature of the physical world which can furnish time with an arrow? Up to the present we have concluded that no arrow can be found from the behaviour of isolated individuals, but there is scope for further search among the properties of crowds beyond the property represented by entropy. To give an illustration which is perhaps not quite so fantastic as it sounds, Might not the assemblage become more and more beautiful (according to some agreed aesthetic standard) as time proceeds? (In a kaleidoscope the shuffling is soon complete and all the patterns are equal as regards random element, but they differ greatly in elegance.) The question is answered by another important law of Nature which runs—

Nothing in the statistics of an assemblage can distinguish a direction of time when entropy fails to distinguish one.

I think that although this law was only discovered in the last few years there is no serious doubt as to its truth. It is accepted as fundamental in all modern studies of atoms and radiation and has proved to be one of the most powerful weapons of progress in such researches. It is, of course, one of the secondary laws. It does not seem to be rigorously deducible from the second law of thermodynamics, and presumably must be regarded as an additional secondary law.  (The law is so much disguised in the above enunciation that I must explain to the advanced reader that I am referring to “the Principle of Detailed Balancing.” This principle asserts that to every type of process (however minutely particularised) there is a converse process, and in thermodynamical equilibrium direct and converse processes occur with equal frequency. Thus every statistical enumeration of the processes is unaltered by reversing the time-direction, i.e. interchanging direct and converse processes. Hence there can be no statistical criterion for a direction of time when there is thermodynamical equilibrium, i.e. when entropy is steady and ceases to indicate time’s arrow.)

The conclusion is that whereas other statistical characters besides entropy might perhaps be used to discriminate time’s arrow, they can only succeed when it succeeds and they fail when it fails. Therefore they cannot be regarded as independent tests. So far as physics is concerned time’s arrow is a property of entropy alone.

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Eddington 1927: Primary and Secondary Law

September 5, 2018 – 8:11 AM
yinyangUniverse

Reference: The Book of Physics

Note: The original text is provided below.
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Summary


Primary laws are deterministic. Secondary laws are probabilistic. But for all its completeness, a primary law does not answer every question about Nature. Secondary law results from a different, and rather more practical, conception. At the bottom of all the questions settled by secondary law there is an elusive conception of “a priori probability of states of the world.” It involves an essentially different attitude to knowledge from that presupposed in the construction of the scheme of primary law.

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Comments


Primary laws apply more to the rigid matter. Secondary laws take into account the fluidity of energy and thought.

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Original Text

I have called the laws controlling the behaviour of single individuals “primary laws”, implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing. Some things never happen in the physical world because they are impossible; others because they are too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws. It has been the conviction of nearly all physicists (There are, however, others beside myself who have recently begun to question it) that at the root of everything there is a complete scheme of primary law governing the career of every particle or constituent of the world with an iron determinism. This primary scheme is all-sufficing, for, since it fixes the history of every constituent of the world, it fixes the whole world-history.

But for all its completeness primary law does not answer every question about Nature which we might reasonably wish to put. Can a universe evolve backwards, i.e. develop in the opposite way to our own system? Primary law, being indifferent to a time-direction, replies, “Yes, it is not impossible”. Secondary law replies, “No, it is too improbable”. The answers are not really in conflict; but the first, though true, rather misses the point. This is typical of some much more commonplace queries. If I put this saucepan of water on this fire, will the water boil? Primary law can answer definitely if it is given the chance; but it must be understood that “this” translated into mathematics means a specification of the positions, motions, etc., of some quadrillions of particles and elements of energy. So in practice the question answered is not quite the one that; is asked: If I put a saucepan resembling this one in a few major respects on a fire, will the water boil? Primary law replies, “It may boil; it may freeze; it may do pretty well anything. The details given are insufficient to exclude any result as impossible.” Secondary law replies plainly, “It will boil because it is too improbable that it should do anything else.” Secondary law is not in conflict with primary law, nor can we regard it as essential to complete a scheme of law already complete in itself. It results from a different (and rather more practical) conception of the aim of our traffic with the secrets of Nature.

The question whether the second law of thermodynamics and other statistical laws are mathematical deductions from the primary laws, presenting their results in a conveniently usable form, is difficult to answer; but I think it is generally considered that there is an unbridgeable hiatus. At the bottom of all the questions settled by secondary law there is an elusive conception of “a priori probability of states of the world” which involves an essentially different attitude to knowledge from that presupposed in the construction of the scheme of primary law.

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