CHAPTER X

DISCONNECTED SUGGESTIONS

Conditionality and Unconditionality of Physical Laws.--Conception of Temperature.--Grain of Sand and Universe.--Are Laws unalterable?--Paradoxes of Science.--Rejuvenation by Motion.--Gain of a Second.--Deformed Worlds.--Atomic Model.--Researches of Rutherford and Niels Bohr.--Microcosmos and Macrocosmos.--Brief Statement of the Principle of Relativity.--Science with reduced Sense-Organs.--Eternal Repetition.--Higher Types of Culture.

IN all branches of reasoning, no word and no conception has played a more important part than that of _law_. Physical laws denote the barrier that separates strictly chance and arbitrariness from necessity, and it seems to us that the region of the latter must ever extend so that finally nothing will be left of the former, which will have become amalgamated with necessity. We shall be constrained to believe more and more in a supreme law that will be a complete expression of all the

## partial laws which science presents to us as more or less permanent

results of individual researches.

Our conversation was centred about these individual laws, such as those that are taught in the theory of gases, optics, etc., and that are associated with the names, Boyle, Gay-Lussac, Dalton, Marriotte, Huyghens, Fresnel, Kirchhoff, Boltzmann, and others. In connexion with these I asked Einstein whether he regarded the laws as things unconditioned in themselves, and capable of proof under every set of circumstances; and whether absolutely valid laws existed or could exist.

Einstein's answer was essentially in the negative. "A law cannot be final, if only for the reason that the conceptions, which we use to formulate it, show themselves to be imperfect or insufficient as science progresses. Let us consider, for example, an elementary law such as Newton's Law of Force. From our more recent point of view we find the conception of direct action at a distance to be inexact in Nature. For it has been shown that action at a distance is not an ultimate factor, but must be resolved into a multiplicity of actions between immediately neighbouring points (The Theory of Action by Contact or Contiguous

## Action). Another example is provided by the conception _Temperature_.

This conception becomes meaningless if we endeavour to apply it to molecules: it leads to no result if we try to impose it on the smallest parts of matter as such. The reason is that the state, the velocity, and the inner energy of the individual molecules fluctuates between very wide limits. The conception 'temperature' is applicable only to a configuration composed of many molecules, and even then it is not applicable quite generally. For let us picture to ourselves an extremely rarefied gas contained in a closed receiver. Two opposite walls are to be at different temperatures, the one being cold and the other being hot In a gas at such very low pressure the molecules come into collision so seldom that, practically, we have to take into account only the collisions of the molecules with the confining walls. The molecules that rebound from the hot wall have greater velocities than those coming from the colder wall, and hence the conception of temperature becomes untenable for this gas."

"Would the temperature-scale on the thermometer then denote nothing?" I asked. "The greater or lesser degree of warmth of a body, in this case of the mass of gas, depends on the more rapid or less rapid motion of its smallest parts. The motions are in any case present, so what would a thermometer indicate?"

"It would betray only that it had nothing to indicate. If a thermometer that is blackened on one side were inserted into the vessel containing the gas, then _different_ temperatures would be recorded if the thermometer were gradually turned about its own axis; and this signifies that the conception of temperature has become meaningless for this configuration of molecules. And passing beyond the quoted examples, I should maintain that all our conceptions, however subtly they may have been thought out, are shown in the course of progressive knowledge to be too rough hewn, that is, too little differentiated."

* * * * * * * *

We spoke of the "Properties of Things," and of the degree to which these properties could be investigated. As an extreme thought, the following question was proposed:

Supposing it were possible to discover _all_ the properties of a _grain of sand_, would we then have gained a complete knowledge of the _whole universe_? Would there then remain no unsolved component of our comprehension of the universe?

Einstein declared that this question was to be answered with an unconditional affirmative. "For if we had completely and in a scientific sense learned the processes in the grain of sand, this would have been possible only on the basis of an exact knowledge of the laws of mechanical events in time and space. These laws, differential equations, would be the most general laws of the universe, from which the quintessence of all other events would have to be deducible."

[This thought may be spun out in yet another direction. Every piece of research, however specialized it may appear and of whatever minor importance it may be, retains a relationship with researches into the universe, and may prove to be valuable for this latter task. If we accept the view that science is capable of realizing perfection, then every contribution to knowledge, even the most insignificant, is essentially indispensable for attaining this goal.]

* * * * * * * *

Can a physical law alter with time? In more precise language, can time, as such, enter explicitly into laws, so that, for example, an experiment that is carried out at different times leads to different results? This question has been treated several times, among others, by Poincaré, who answered it with an emphatic "No!" but also by others to whom the invariability of physical laws did not seem to hold for all eternity. If my memory does not play me false, Helmholtz once expressed faint doubts about the constancy of laws.

Einstein answered this question with a decided negative. "For a law of physical nature is, by definition, a rule to which events conform wherever and whenever they take place. Thus, if we were to be compelled as a result of experience to make a law dependent on time, it would be a necessary step to seek a law independent of time, which would include in itself the law dependent on the time as a special case. The latter would be excluded from the category of physical laws, and would henceforward play the part only of a result deduced from the law which is independent of the time."

* * * * * * * *

What attitude should we adopt if, in studying a scientific doctrine, we encounter paradoxical results even though the inferences have been drawn correctly--that is, if we meet with a deduction to which our reasoning powers object, although no fallacy is discoverable in the argument?

Before we deal with cases which seem to me, personally, to be interesting, let us hear what is Einstein's attitude in general. "As soon as a paradox presents itself, we may, as a rule, infer that inaccurate reasoning is the cause, and should thus examine in each

## particular case whether an error of logic is discoverable, or whether

the paradoxical result denotes only a violent contrast with our present views."

Let us first take examples from an entirely modern science, from the _Theory of Aggregates_ founded by Georg Cantor of Halle. We shall follow the argument by the only possible method for this book, namely, by rough indications that will serve our purpose and do not claim to be accurate in expression or in sense.

If we take an aggregate of three objects, for example, an apple, a pear, and a plum, we may, by definition, form six partial aggregates, namely:

the apple the pear the plum the apple and the pear the apple and the plum the pear and the plum.

The aggregate of the partial aggregates, which contains six elements, is thus greater than (actually twice as great as) the original aggregate, in which only three elements occur.

If the original aggregate contains an additional element, for example, a nut, the following partial aggregates may be formed:

the apple the pear the plum the nut the apple and the pear the apple and the plum the apple and the nut the pear and the plum the pear and the nut the plum and the nut the apple, the pear, and the plum the apple, the pear, and the nut the apple, the plum, and the nut the pear, the plum, and the nut.

Thus, in this case, the aggregate of the partial aggregates is already considerably greater than the original aggregate. This numerical excess increases rapidly with each successive increase in the original aggregate, so that if we apply the same reasoning to an infinite aggregate, the aggregate of partial aggregates becomes an infinity of a _higher order_. This is expressed by saying that the infinite aggregate of partial aggregates has a greater _potentiality_ than the infinity of the elements of the original aggregate.

So we see that the one infinity is, in popular language, much more comprehensive, more powerful than the other. Our minds do not find it impossible to grasp this. But in a definite imaginary experiment it is found that this theorem of progression not only fails in its application, but leads to flagrant contradiction.

For if we start from the primary aggregate of "all conceivable things," its infinity can certainly not be transcended by any other infinity. But according to the above theorem the "aggregate of all partial aggregates" would have a greater potentiality, although it itself cannot extend further than to the conception of the maximum of all conceivable things. We thus arrive at an insoluble paradox, a typical example of how, in the system of conceptions involved, something is insufficient or not in conformity with logical thought. And this sceptical view receives support from various remarks of Descartes, Locke, Leibniz, and

## particularly Gauss, who, long before the advent of the Theory of

Aggregates, raised a protest against inexact definitions of infinity.

In another case, however, the same theory seems to arise by perfectly logical processes, although it again leads to a statement that does not seem correct to "common sense." For it shows by a very subtle and ingenious method that all the surface-points of a surface infinitely extended in all directions may be brought to correspond in a reversible single manner to the linear points of a line, however small; so that to every point of the unlimited plane there corresponds a definite point of the line, and vice versa. The same theorem may be extended to three-dimensional space, with the result that we have to reconcile ourselves with the incredible fact that, expressed in popular language, a straight line of however small length exhibits the same potentiality with regard to the number of its points, as all the points in the universe.

For my own part, I must confess that no means suggests itself to me to make this paradox intelligible. But the _sacrificium intellectus_ comes within dangerous proximity. Einstein, who values and marvels at the theory of aggregates as a science, or perhaps more as a work of art built up from the materials of science, gives whole-hearted support to the proof. He refuses to accept the notion of a paradox--that is, he recognizes a contradiction not in our process of reasoning, but only in a habit of thought that is open to correction. I should give much to discover the means of correction!

* * * * * * * *

A third example arises out of the special theory of relativity. It has a mysterious paradoxical character that vanishes when a clear view of the relationships involved has been obtained.

According to this theory the rate at which events happen alters according to the state of motion of the system under consideration. Let us now consider two twins A and B, that, although born at one place on the earth, are immediately separated, B remaining at rest, whilst A rushes out into space at an enormous rate, describing what, viewed from the earth, is an inconceivably great circle. In this way the rate of happening of all events is reduced very considerably for A in a manner that may be calculated. If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still.

The first introduction to this flight of imagination naturally causes profound perplexity. Nevertheless, we are dealing not with a realm of miracles, but with something that is within the range of comprehension.

"In the case of these two twins," Einstein declared, "we have merely a paradox of _feeling_. It would be a paradox of thought only if no sufficient ground could be suggested for the behaviour of these two creatures. This ground, which accounts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations. A proper grasp of the reason is furnished only when we adopt the _general_ theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life."

It certainly requires a prodigious mechanism to allow the moving twin to gain even only one second of time. If he were to spend a year in a merry-go-round whose circumference were about 19 milliard miles in length, he would have to travel in it at the rate of over 600 miles per second if he is to gain a second on his brother.

This inevitable result that is immediately apparent to a trained scientific mind throws light on the nature of "common sense," the validity of which, as an ultimate criterion, Kant too has refused to recognize, in so far as this "common sense" is incapable of passing beyond the examples offered in its own experience. It circulates, as Einstein says, in the "realms of feeling and analogy." It finds no analogy for a phenomenon like that described above, and since it can apply rules only concretely, many things appear to it paradoxical that, in the light of intensified abstraction, appear logical and necessary.

* * * * * * * *

Let us speculate on the following question. If all things in the universe should increase or decrease enormously in dimensions, and if, at the same time, in a manner totally concealed from us, certain physical conditions should become changed, we should lack all means of discovering the difference between things before and after the change. For since all measuring-rods, including those furnished by our senses, would have become changed in the same proportion, the two conditions could not be differentiated from one another. It may easily be shown that this would necessarily occur, if an extramundane power were non-uniformly to displace, deform, compress, or bend all things in the universe, provided that our instruments and senses participated in this transformation. Accordingly it is permissible also to regard the universe known to us as one that is deformed, and one that is derived from another, the original form of which will ever remain a secret to us.

Is there any connexion between this grotesque speculation and the theory of relativity?

We can establish only one that is negative and that arises _e contrario_. "These deformations," said Einstein, "are in themselves abstractions that are physically meaningless. Only _relations between bodies_ have a physical meaning, for example, the relation between measuring-rods and the objects they measure. Therefore, it is reasonable to talk of deformations only when we are dealing with the deformations of two or more bodies with respect to one another, whereas the conception of deformation has no sense, unless a real object is specified, to which it is referred. The philosophical merit of the general theory of relativity, as compared with previous views of physics, consists in the fact that the former avoids entirely these meaningless abstractions with respect to space and time."

[According to this, it is not purposeless to enter on these grotesque trains of thought, even if they are untenable physically. For since the new physics teaches us to avoid these false tracks, it seems of value to know what it is that is to be avoided. Just as we must study scholastic thought if we wish to grasp thoroughly the philosophy which sprang up after the scholastic fetters were burst. Moreover, these reflections on concealed universes are not without a certain attraction, reminiscent of the sorcerer's wand, if they pursued any other goal than that of making universes distorted. It is true that they hold out latent temptations that may in some cases lead us on to dangerous ground, in encouraging us to venture on analogies beyond the scope of geometry and physics. Would it be possible to enter suddenly into a world that is distorted and deformed with respect to its ethics, its culture, and its reasoning intellects, without our observing the difference? Are we ourselves perhaps living under such deranged conditions, of which we cannot become aware, because our perceptual organs have likewise become deformed? I must frankly confess that I do not regard it as quite inconceivable that this argument of deformation may be spun out in this direction, but I must add that Einstein rejects absolutely all such extensions, since, as he emphasizes, they lead to regions that are merely fields for the exhibition of "verbal gymnastics."]

* * * * * * * *

The question whether Nature makes leaps or not is very old. In the theory of descent it forms the foundation of the difference between revolutionists and the evolutionists, who uphold the axiom _natura non facit saltus_, with all its consequences. Recently attempts have been made, particularly by psychologists, to propound and justify a natural principle of discontinuity. They assert that our own perceptions and sensations are discontinuous in themselves, and that the mechanism of every perception is akin to that of a cinematograph with its extremely rapid interruptions. If this should actually be the case, we should scarcely have a means of solving definitely the question whether continuity reigns, or not, in Nature.

Einstein does not recognize the possibility of this alternative for a moment. If a doubt had ever arisen, the researches of Maxwell would in themselves have been sufficient to dispel it. Our universe that is to be described in terms of differential equations is absolutely continuous.

"But," I interjected, "does not modern physics offer a certain support to the assumption of a discontinuity? Does not the Quantum Theory point to an atomistic structure of energy, and hence also of events that are to be imagined as happening in jerks and as involving relations expressible in whole numbers?"

Einstein gave an answer of epigrammatic brevity and flavour. "The fact that these phenomena are expressible in whole numbers must not be construed into an argument against continuous happening. Just imagine to yourself for a moment that beer is sold only in whole litres; would you then infer that beer, as such, is discontinuous?"

* * * * * * * *

What achievements are to be expected of astronomy in the present era?

This question would have a special meaning if it were assumed that the astronomer who works in observatories is surrounded by solved problems, and can no longer hope to solve problems having the universal significance of those of Copernicus or Kepler. This assumption, however, would not be in agreement with the actual state of affairs.

Einstein indicated to me a number of fundamental problems that present themselves to modern astronomy, and the solution of which he expected of future times.

Above all, the geometrical and physical constitution of the stellar systems will, in the main, become revealed.

At present we do not yet know whether Newton's Law of Attraction holds, at least approximately, for configurations of the type of the Milky Way and of the spherical clusters of stars--that is, in extents of space in which the influence of space-curvature would become appreciable. The rapid progress of recent astronomy justifies our great hopes that the solution of this universal problem will be found within the coming decades.

In distant connexion with this we also touched on the question of the habitability of other worlds. This theme of Fontenelle, "la pluralité des mondes habités," which has again become a centre of public interest, owing to investigations of Mars, has evoked a storm of discussion. We hear the noisy war-cries of geocentric scientists who wish to regain for the earth her shattered supremacy in astronomy, and who claim the existence of organic forms as the sole prerogative of our planet. It is scarcely necessary to mention that Einstein rejects the motives of these human and all-too-human individuals as small-minded and short-sighted. Creatures in distant worlds are derived from, and are subject to, conditions of organic nature, of which we can form no idea by deductions from the world which we inhabit. But to deny their existence on numberless constellations, or to demand an ocular proof of their presence, is no better than to assume the point of view of an infusoria to whom there is no life other than that in a dirty drop of ditch-water.

* * * * * * * *

The idea of the atom as the ultimate structural element involves a philological as well as a conceptual contradiction. For _atomos_ signifies the indivisible, the no-further-divisible, whereas the idea of a body, however small, an element of structure differing from zero, demands, at least geometrically, further divisibility. Even the original founders of the theory of atoms, Leukippus, Epicurus, and Democritus, assigned definite forms to the ultimate components, and we may read in the splendid work of Lucretius how he infers from the nature of substance that the ultimate particles are smooth, round, or rough, or have the shapes of hooks and eyes. The further analysis pressed forward, the more the simplicity of the original idea vanished. Microcosms came to be regarded as copies of macrocosms, and the atoms of present-day science actually exact from us that we should regard them as worlds in themselves.

Einstein acceded to my request that he might give a sketch of the latest achievements of science sufficient to provide an approximate idea of the _atomic model_. According to the researches of Rutherford and Niels Bohr, we are to picture it as a planetary system.

The central body of this system is represented by a positively charged nucleus, which constitutes almost the whole mass of the atom, surrounded by a certain number of electrons, negative charges, that move in uniform circular or elliptic orbits about the nucleus. There is thus a certain analogy that allows us to regard the nucleus as the sun, and the electrons as the planets of this system.

The number of these electrons varies between the limits 1 and 92, according to the chemical constitution of the element. The smallest number occurs in the case of helium (in which there are two), and of the hydrogen atom, in which only one electron-planet describes its circular path about the nucleus. In other atoms there are probably more complicated orbits, although they are more or less approximately circular. According to this still very new theory, which is supported by very convincing facts, the electrons are to be imagined as arranged in concentric shells (like the layers of an onion), among which the innermost shell plays a distinctive part inasmuch as the number of the electrons arranged in it decides the chemical character of the atom in question. It sometimes occurs that electrons spring, under external influence, from one orbit to another; when the electron jumps back to the original orbit, light is emitted. An essential fact is to be noted: Whereas any arbitrary orbits of any arbitrary radius may occur in a planetary system of the celestial regions, the manifold of these orbits in the case of the electrons is restricted, in that only certain orbits are possible, namely, those that are determined mathematically by the quantum condition.

"Perhaps," I interrupted, "the whole analogy may be inverted. If the atom is considered analogous to a planetary system in the model, it should be admissible to regard our true planetary system as a cosmic atom. And then, long after we have become accustomed to regard our earth as playing the part of a grain of sand, the sovereignty of the sun, too, would be past. The whole majesty of the solar system as far as the orbit of Neptune would then shrink to a configuration compared with which the world of a grain of sand would be infinitely complex."

"This fantastic inversion is permissible up to a certain extent," said Einstein, "but we must not lose sight of the fact that there is a cardinal difference. If we disregard the enormous disparity in dimensions, the analogy is far from exact owing to the circumstance that the atom is only an element of structure, whereas the true planetary system is an extraordinarily complex structure in itself. Thus the difference between a simple thing and one that is very highly complex still remains."

"But, Professor, may not a similar complexity yet be discovered in the atom? It may be merely a difference of philosophical view from the primary idea to that of regarding the electrons as circulating like planets. May we not conjecture that in each successive step we are merely carrying out a true _regressus in infinitum_?"

"That seems highly improbable," he replied, "although, of course, structural investigations can never cease. At first they are directed at the more remote object of finding out why certain atoms are radioactive, that is, exhibit a tendency to disintegrate. It has already been established that this tendency is a property of the positive nucleus, of which little is as yet known. This means that the nucleus is not simple, yet it does not open up the possibility of an unending regression. Our aim must be to get a clear insight into the constitution of the nucleus, as regards the positive and negative charges, and it is my opinion," he concluded, "that beyond this there will be no further subdivision of matter."

When Goethe writes of the immovable pole in the flux of phenomena, we recognize that his beautiful remark pronounces an elegy to the possibility of attaining ultimate simplicity. Einstein's utterance, if I understand him aright, converts this elegy into a song of hope. If the subdivision of matter actually has an end somewhere, then we are now on the threshold of ultimate things, we are near the immovable pole, which we are capable of reaching.

* * * * * * * *

"Every new truth of science must be such that, in ordinary writing, it may be communicated completely within the space of a quarto leaf." Kirchhoff made this remark, and gave a sufficient, if not literal, demonstration of its truth. When Bunsen and he published the first notice about spectral analysis, they compressed their publication into the small space of three printed pages.

But what is to happen if the new truth should be built up of very comprehensive materials, when it requires many links, of which none can be omitted if the truth is to be made intelligible? Would Kirchhoffs quarto page still be sufficient?

"Certainly," said Einstein, "provided, of course, that it is addressed to a reader who has already mastered what went before--that is, to one who is so far acquainted with the older facts that he has to learn only the really new part of the new truth."

"That sounds very hopeful," I remarked, "for then it should also be possible to describe very briefly the theory of relativity."

"Let us rather say its essentials--the heart of the matter. Well, then, get your Kirchhoff page ready. We shall see whether we can set out on it the special theory of relativity."

The totality of our experience compels us to assume that light travels with a constant velocity in empty space. Likewise, our whole experience in optics compels us to recognize that all inertial systems are equivalent; these are systems that are produced from an allowable one by means of a uniform translation. An allowable system is one in which Galilei's and Newton's Law of Inertia holds. (This law states that a moving body that is left to itself retains its direction and velocity permanently.)

Now, the law of the constancy of light propagation seems to conflict with the classical principle of relativity, according to which the velocity of a ray of light assumes different values in the moving system according to the direction of the ray.

This apparent incompatibility arises from the following unproved assumptions:

(_a_) If two events are simultaneous with regard to one inertial system, they are also simultaneous with regard to any other inertial system.

(_b_) The length of a measuring-rod, the shape and size of a rigid body, and the rate of a clock are independent of their motion with respect to the system of reference used, provided this motion is rectilinear and non-rotational.

These assumptions must be discarded if this disagreement is to be eliminated. If we substitute for them the assumption that all inertial systems are equivalent and that the velocity of light _in vacuo_ is constant, we get:

(1) That the dimensions of bodies and the rate of clocks have a functional relation to the motion.

(2) That the equations of motion of Newton require to be modified; this modification leads to results that, for rapid motions, differ appreciably from those of Newton.

This is, in a very compressed form, the meaning of the special theory of relativity.

As there is still some space left on our quarto page, we may add a remark that, it is hoped, will make a little clearer the above-mentioned discrepancy.

Let us choose as our system of reference an express train 18 miles long. There are two passengers--Mr. Front, right at the front of the train, and Mr. Back, at the extreme end of the train, so that a rigid distance of 18 miles separates the two passengers. The carriages are transparent, so that the two passengers can signal to one another. They are, moreover, furnished with ideal clocks that run at exactly the same rate.

First, suppose that the train is at rest. Back is just opposite milestone 100, whilst Front is opposite milestone 118. By means of a flash, Back signals to Front his time, exactly 12 o'clock. It takes light very nearly ¹⁄₁₀₀₀₀ second to traverse the length of the train--18 miles; hence the flash will reach Front at 12 o'clock ¹⁄₁₀₀₀₀ second. Exactly the same result would have come about if Front had signalled his time to Back. Light makes no difference in travelling forwards and backwards. If the train moves at a great speed, the two travellers can conduct the same experiment as when the train was at rest. They will then set the time that light takes to travel from Back to Front equal to the time that it takes to traverse the same way in the reverse direction. But this phenomenon will assume a different aspect if viewed from the railway embankment. An observer on the latter would affirm that light does not take the same time in travelling the length of the train in one direction as it does when travelling in the opposite direction.

For the ray of light moving in the forward direction has to traverse not only the distance between Back and Front, but also the very short distance that Front has moved forward during the interval that the light has been moving; whereas, inversely, the flash sent out by Front to Back will traverse a distance that is correspondingly less than that between the passengers, since Back is moving towards the signal.

Thus the duration of the two phenomena of light propagation is the same or different, respectively, according as it is judged from the train or from the embankment. In other words, _the judgment of the length of time depends on the state of motion of the observer_.

All further pronouncements of the special theory of relativity are based on the preceding arguments of the relativity of time.

* * * * * * * *

Would Man be able to construct a Science if he possessed one sense less than at present--for example, if he were deprived of sight? Let us apply this to a definite case. In the new physics the velocity of light plays a decisive part as a world-constant. At first sight it would appear impossible for us to determine it and recognize its importance, if we had not at our disposal some organ which enabled us to become aware of optical phenomena.

But, as Einstein explained to me, even under such difficult circumstances, it would be possible to build up a science, for the reason that phenomena, as far as they are perceptible, may be transformed so that they become manifest to other senses if one sense should be absent. For example, the electrical conductivity of selenium is strongly influenced by the amount of illumination that falls on it. Thus light acts on a selenium cell, causing changes of current intensity, which in their turn may be perceived by feeling, or by chemical action on the mucous fluid of the tongue. Ultimately we are concerned only with a differentiation that enables us to refer identical experiences to identical events. We should certainly encounter enormous difficulties in endeavouring to form a physical picture of our surrounding world if the number of our senses should become less than the organs with which we actually operate. Yet, in principle, we should be able to overcome all difficulties by means of much lengthened and complicated lines of research, even if we should have only a single sense left, or if we had only one at the very outset. The construction of a Science would then be possible, and would give the same results, although it might be propounded only after a delay of perhaps millions of years.

[It is naturally assumed that the intellect is retained, as this is the necessary condition for all scientific research. Since the degree of understanding depends on the senses--_nihil est in intellectu, quod non prius fuerit in sensu_--we may conjecture that a human being with only one sense organ would work with a minimum degree of understanding, which would be insufficient for the acquirement of any knowledge whatsoever. This transcendental question, which lies almost beyond the bounds of discussion, was not touched on in our conversation, as the subject was restricted so that it should not drift into metaphysical regions.

Nevertheless, I should like to mention that a speculation of this kind is recorded in the history of science. Condillac, in a study teeming with ideas, investigates the behaviour of a "Statue," that he represents as a human being, with the assumption that there is at first no idea in the soul of this statue-person. This living creature is enclosed in a marble envelope, the sole exterior organ of which is at first the organ of smell. He then shows that by means of this single sense all manner of sensations and expressions of will may develop in his "statue." Condillac does not, however, undertake to give a convincing proof that this creature, restricted to the organ of smell, would be able to discover physically the relationships that hold in physical nature, and thus to build up a scientific system. Thus Einstein, in his discussion, goes considerably further than the author of this statue.]

* * * * * * * *

Has the "eternal repetition," as outlined by Nietzsche, any meaning?

The sage of Sils-Maria tells us that this revelation came to him midway between tears and ecstasy, as a fantasy with a real meaning. The crux of his idea is a finite world built up of a finite number of atoms. From the fact that the present state emerges out of the immediately preceding one, the latter from the one just before, and so on, he concludes that the present state exhibits repetition both forwards and backwards. All becoming recurs and moves in a multiple cycle of absolutely identical states.

Let us discard for the moment all philosophical objections, above all this, that the recurrence of the same disposition of atoms may not necessarily entail the recurrence of the same psychical states. Furthermore, let us suppress the cynical thought that in the return to the same state the world would have reason to enjoy extreme happiness only for moments, but to lament for aeons. Then we are left with the comparatively simple question: Is this repetition, from the point of view of physics, conceivable and possible?

It would be the death-knell of Nietzsche's idea if the answer of a great physical research scientist were entirely in the negative. But Einstein still allows it a small measure of life. "Eternal repetition," so he expressed himself, "cannot be denied by science with absolute certainty." The disciples of Nietzsche will have to rest satisfied with this very small concession. For what, in Nietzsche's eyes, is a logical necessity becomes transformed by Einstein's supplementary remark into a vague assumption, the product of fantasy. From the point of view of physics the recurrence of the same condition is to be regarded as "enormously improbable." This statement is founded chiefly on the famous second Law of Thermodynamics, according to which the processes of Nature are in the main irreversible, so that a one-sided tendency is expressed in natural phenomena. The fact that the course of phenomena is in only one sense or direction speaks in favour of the view that the events of the world are to be regarded as occurring only once.

So that when Nietzsche, in contradistinction to this, vigorously supported the doctrine of repetition, he contradicted at least one important recognized theorem of physics. The fact that he did not become conscious of this contradiction, but that, on the contrary, he regarded his idea as the most important event in the development of his intellect, may be regarded as an example of a _docta ignorantia_. But it is allowable, too, that philosophic fantasies that complete the poetical picture of the universe should be given expression. And Nietzsche would presumably have been deprived of a degree of pleasure if he had been aware of this second law.

"Truth is the most expedient error"; this statement may be traced back to a sequence of thought developed by Nietzsche. But the Eternal Repetition is shattered by just this remark, for judged by its consequences it would be a very inexpedient error.

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Supposing we should succeed in exchanging thoughts with the inhabitants of distant worlds and should, through them, acquire the elements of a civilization _superior to our own_, would this knowledge prove a blessing to us or the reverse?

The word "superior" must, of course, be treated circumspectly. It is to denote only that, relatively, this distant civilization bears somewhat the same relation to our civilization of to-day as our own bears to that of an Australasian negro or an anthropoid ape. There are fanatics of progress whose wishes plunge headlong and without restraint into the future, and to whom nothing could be more desirable than the sudden appearance of a civilization that, as they opine, would at one stroke carry us "forward" many thousands of years.

But the view of these magicians with their seven-league boots is untenable. Let me cite a mere outline of the many opposing arguments in a few words of Einstein. "Every sudden change in the conditions of existence, even if it occurred in the form of a higher development, would come upon us like a doom, and would probably annihilate us, just as the Indians succumb to the civilization that has outstripped them. The tragedy of our own highly civilized times is that we cannot create the social organizations that have become necessary as a consequence of the technical advances of the last century. This has given rise to the crises, impasses, and senseless competition between nations, and to the impoverishment of defenceless individuals. These deplorable conditions would become inconceivably accentuated if we were to be invaded by extra-mundane technical sciences of a higher order."

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Nevertheless, there is still a possibility that the "superior civilization" might contain indications of the organizations which we lack. Instead of entering on the question of this Utopia, we confined ourselves to comparing past conditions in our world with present ones. Did we not have the most promising preliminaries for an organization that was devoid of friction and tended to reduce the competition between nations in the numerous international institutions that drew together a great section of the intellectual world to work in co-operation? Are there hopes that this international coalition will be resumed?

Einstein expressed himself optimistically, not to do homage to an organization artificially formed, but to extol the world-wide mastery of intellect. "Even if international congresses were to be swept away," he said, "international co-operation would not be abolished, as it effects itself automatically." I should venture to assert that if all these congresses were to cease, we should not even have cause to fear that there would be an appreciable diminution in the combined effort of research. If certain developments are hindered by political conditions, it is only due to the resulting economic hardships affecting individuals in their work and robbing them of their intellectual freedom. The real friends of Truth have always clung together, and do so actually now; indeed, many feel the tie to be closer than that connecting them to their own country. In spite of all obstacles and boundaries they will never cease to find contact with one another!

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