SOURCE: "The Philosophic Dialectic of the Concepts of Relativity," in Albert Einstein: Philosopher-Scientist, revised edition, edited by Paul Arthur Schlipp, The Library of Living Philosophers, 1970, pp. 565-80.

[Bachelard was an influential French philosopher and critic. Many of his writings focus on poetic imagery and its relation to the creative process, and their approach is characterized by an emphasis on psychoanalytic theory. Unlike Sigmund Freud, who regarded dreams as manifestations of an individual's motivations, Bachelard, like Carl Jung, considered dreaming to be a revelation of the collective unconscious. Bachelard thus looked to dreaming, or reverie, for certain primitive archetypes—especially the traditional elements of earth, air, fire, and water—and studied representations of each in poetic imagery. In the following essay, Bachelard discusses the ways in which Einstein's relativity created "upheavals" among many of the fundamental principles of science and philosophy.]

I

Philosophers have removed the great cosmic drama of Copernican thought from the dominion of reality to the dominion of metaphor. Kant described his Critical philosophy as a Copernican revolution in metaphysics. Following the Kantian thesis, the two fundamental philosophies, rationalism and empiricism, changed places, and the world revolved about the mind. As a result of this radical modification, the knowing mind and the known world acquired the appearance of being relative to each other. But this kind of relativity remained merely symbolic. Nothing had changed in the detail or the principles of coherence of knowledge. Empiricism and rationalism remained face-to-face and incapable of achieving either true philosophical co-operation or mutual enrichment.

The philosophic virtues of the Einsteinian revolution could be quite differently effective, as compared to the philosophic metaphors of the Copernican revolution, if only the philosopher were willing to seek all the instruction contained in relativity science. A systematic revolution of basic concepts begins with Einsteinian science. In the very detail of its concepts a relativism of the rational and the empirical is established. Science then undergoes what Nietzsche called "an upheaval of concepts," as if the earth, the universe, things, possessed a different structure from the fact that their explanation rests upon new foundations. All rational organization is "shaken" when the fundamental concepts undergo dialectical transformation.

Moreover, this dialectic is not argued by an automatic logic, as is the dialectic of the philosopher too often. In relativity, the terms of the dialectic are rendered solid and cohesive to the point of presenting a philosophical synthesis of mathematical rationalism and "technological" empiricism. This, at least, is what we would like to show in the present article. First, we will present our view in respect to the "shaking" of some isolated concepts; then, we shall endeavor to show the value of the philosophical synthesis which is suggested by Einsteinian science.

II

As we know, as has been repeated a thousand times, relativity was born of an epistemological shock; it was born of the "failure" of the Michelson experiment. That experiment should contradict theoretical prediction is in itself not a singular occurrence. But it is necessary to realize how and why a negative result was, this time, the occasion for an immense positive construction. Those who live in the realm of scientific thinking doubtless do not need these remarks. They are nonetheless polemically indispensable for assessing the philosophical utility of relativity.

For this notion of the negative quality of experiment must not be allowed to subsist. In a well-performed experiment, everything is positive. And Albert Einstein understood this fact when he pondered over the Michelson experiment. This pseudo-negative experiment did not open upon the mystery of things, the unfathomable mystery of things. Its "failure" was not even a proof of the ineptitude of rationalism. The Michelson experiment proceeded from an intelligent question, a question which had to be asked. Contemporary science would be hanging "in mid-air," if the Michelson experiment had not been conceived, then actualized, then meticulously actualized in the full consciousness of the sensibility of the technique; then varied, then repeated on the floors of valleys and the peaks of mountains, and always verified. What capacity for self-doubt, for meticulous and profound doubt, for intelligent doubt, was contained in this will to test and measure again and again! Are we sure that Michelson died with the conviction that the experiment had been well performed, perfectly performed, with the conviction that the negative bases of the experiment had been reached? Thus, instead of an universal doubt, an intuitive doubt, a Cartesian doubt, technological science yields a precise doubt, a discursive doubt, an implemented doubt. It was as a consequence of this explicit doubt that the mechanistic dogmatism was shattered by relativity. To paraphrase Kant, we might say that the Michelson experiment roused classical mechanics from its dogmatic slumber.

For the negative aspect of the Michelson experiment did not deter Einstein. For him, the experimental failure of a technique thus scientifically pursued suggested the need for new theoretical information. It became indispensable to hope for a minute "Copernican revolution" in which all philosophy of reality and of reason must begin a new dialectic. In order that this dialectic may possess its full instructive value for the philosopher, it is necessary to beware of sweeping philosophical designations. It is not highly instructive to say, with Meyerson, that Einstein is a realist. Without a doubt, Einstein submits to experience, submits to "reality." But must we not inquire: to what experience, to what reality? That of the infinitesimal decimal upon which the Michelson experiment turned, or that solid reality of the whole number, of solid, ordinary, common, gross verification? It would seem that the philosopher who acknowledges the lessons of relativity must at the very least, envisage a new reality. And this new reality enjoins him to consider reality differently.

Where, then, must the philosophy of science find its initial convictions? Must it give precedence to the lessons to be found in the beginning of experience, or in the end of experience? By building upon the first structures or upon the final structures? We shall see that the latter is correct, that it is l'esprit de finesse which reveals the foundations of l'esprit geometrique.

III

Which, then, are the concepts that are "shaken"? Which concepts undergo at the rational level, in the superb light of rational philosophy, a Nietzschean transmutation of rational values?

They are the concepts of:

• absolute space,
• absolute time,
• absolute velocity.

Is so little required to "shake" the universe of spatiality? Can a single experiment of the twentieth century annihilate—a Sartrian would say "neantiser"'—two or three centuries of rational thought? Yes, a single decimal sufficed, as our poet Henri de Regnier would say, to "make all nature sing."

Upon what, in fact, did the notion of absolute space rest? Did it rest upon an absolute reality or upon an absolute intuition of the Kantian variety? Is it not philosophically strange that absoluteness could be attributed as well to a reality as to an a priori intuition? This double success of a raw realism and an over-simple intuitionism seems spurious. This twofold success makes a double failure. Therefore, it is necessary to investigate this double possibility of philosophical interpretation from the standpoint of the precision of modern scientific experiment. Uncriticized experience is no longer admissible. The double philosophy of the experience of space—realistic philosophy and Kantian philosophy—must be replaced by a dialectical philosophy of space, by a philosophy which is at once experimental and rational. In short, the philosophy of ultra-refined experience and the philosophy of physical theory are firmly coupled in relativity. The new philosophy of science will prove to be a critical philosophy more subtle and more synthetic than was Kantian philosophy in respect to Newtonian science. Relativistic criticism does not limit itself to a revolution of means of explanation. It is more profoundly revolutionary. It is more génial.

Thus, we come face-to-face with the fundamental assertion of Einstein: the position of an absolute space as the affirmation of a kind of materialization of immobility and as the residence of an unconditioned subject in the center of all the conditioned relations, is a position without proof. Therefore, one must—Copernican revolution at the level of an unique concept—formulate the essential relativity of the intuition of localization and the experience of localization, which simultaneously destroys two absolutes: first, the intuition of an observer has no absolute character; and secondly, the extension of an objective world has no absolute character. The essentially discursive method of reference will, therefore, always have to be explicitly considered in relation to the real phenomena studied in the extremity of scientific precision. Extreme experimental dexterity will underlie any knowledge of space. The Michelson experiment, at first sight so particular in character, will form the basis of the most far-reaching generalization.

It is, moreover, quite striking that the Michelson laboratory was, properly speaking, cosmic. There, the most artificial physics imaginable was referred to the space of the world. The decimal which they wished to reveal by means of the interferometer, the decimal which is of the order of three-fourths of the wavelength of a vibration of light, was related to the orbital speed of the earth, a speed of the order of eighteen miles per second. The precision of such a question posed by this technique in respect to the space of the world, this attempt to experience the immobility of space in its cosmic significance, ought to set the metaphysicians thinking who study the place of man in the world; if only these metaphysicians would give their attention to the lengthy discursive processes which lead science to build new intuitions.

IV

The new intuitions of time likewise demand lengthy preparation. They must struggle against the blinding clarity of common intuitions, and against the equally over-hasty formulation of Kantian criticism.

Here, the concept which experiences the "Nietzschean upheaval" is that of simultaneity. In regard to this concept, so evident, so familiar, the Einsteinian claim is pregnant. This claim collides with common sense; it is contrary to common experience; it puts in question again the very basis of classical mechanics. It demands therefore, a decisive intellectual mutation which must reverberate among the most fundamental philosophical values. More precisely, if the notion of simultaneity, which was not criticized by Kant, must receive a neo-critical examination, empiricism and rationalism must, at the same time, be rectified and related to each other in a new way.

To formulate a doubt concerning the notion of simultaneity is, in our opinion, to transcend the hyperbolic doubt of Cartesian philosophy. A doubt attaching to so simple, so positive, so direct a notion no longer bears the marks of a formal doubt, an universal doubt. As long as one remains within the horizons of Cartesian doubt, one is in the contingency of doubt. The Einsteinian revolution demands a necessary doubt regarding a notion which has always passed for fundamental. Concomitantly, the putting in doubt of a rational and realistic notion cannot remain provisional. Such a doubt will always carry with it a decisive pedagogical effect. It will remain an imprescriptible cultural fact. Whoever, for the rest of time, would teach relativity would have to put in doubt the absolute character of the notion of simultaneity. This necessity constitutes, in some sense, an electro-shock for rationalistic philosophies and hardened realistic philosophies.

Granting a renunciation of the right to posit an absolute space, what is the Einsteinian claim in regard to the simultaneity of events which occur at two different points in space? Einstein demands that one define a positive experiment, a precise experiment expressible in well-defined scientific terms. There is no longer any question of retreating into the intuition of internal sensibility, whether this intuition be Kantian or Bergsonian, formalistic or realistic. One must be able to describe and institute objective experiments which enable one to verify this simultaneity. Immediately, a metaphysical nuance appears which the philosopher too often neglects. Here we have a verified reality in place of a given reality. Hereafter, if an idealist must make an initial declaration, he will be forced to do so from a point one step closer to a rationalism which is linked with reality. He cannot be satisfied with repeating after Schopenhauer: "The world is my representation"; he must say, if he is to assume the full extent of scientific thought: "The world is my verification."

More precisely, the objective world is the aggregate of facts verified by modern science, the world rendered by the conceptions verified by the science of our time. Further, experimental verification implies the coherence of the experimental method. Since a science is founded upon the Michelson experiment, this Michelson experiment must be comprehended in the very definition of simultaneity. To be sure, we are concerned with the Michelson experiment as it is, not as it was for a long time thought to be. The Michelson experiment, as it is, then, must assign reality at the outset to the convention of signaling.

Without a doubt, any number of conventions of signalling could have been adopted. One could create a metaacoustics based upon a simultaneity verified by the transmission of sounds. But physics would gain nothing from such specialization. Hereafter, physics is cosmic. The most rapid and reliable signals which are both human and universal are light signals. The Michelson experiment discloses a privileged character which accrues to these signals. They require no support; they are not conditioned by a medium, by a transmitting ether. They are independent of the relative movements of the observers who utilize them. They are truly the most "reasonable" ("rationalisables') of all signals. Thus, one would define the simultaneity of two events which occur in two different places in terms of an exchange of light signals and of the result, henceforth regarded as positive, of the Michelson experiment which justifies the following postulate: the velocity of light is the same in all directions irrespective of the observers who measure it, regardless of the relative motion of these observers.

This operational definition of simultaneity dissolves the notion of absolute time. Since simultaneity is linked to physical experiments which occur in space, the temporal contexture (contexture) is one with spatial contexture. Since there is no absolute space, there is no absolute time. And it is due to the solidarity of space-experiments and simultaneity-experiments that a reconstitution of space and time must accompany any thorough examination of space and time. Therefore, from the standpoint of philosophy, it is evident that scientific thought requires a rebuilding of the notions of space and time in terms of their solidarity. As a consequence of this necessity to provide a new basis for space and time, relativity will emerge philosophically as a rationalism of second order (rationalisme de deuxieme position), as an enlightened rationalism which necessitates a new departure.

But before building, one must destroy. One must convince oneself that any analysis which from the outset separates spatial characters and temporal characters is a crude analysis. Doubtless, such an analysis is valid for common knowledge, and no less valid for an enormous quantity of scientific thought. But for its denunciation one need only note that it masks certain well-defined problems. Looking to the new synthetic notion of space-time, henceforth indispensable for a grasp of electromagnetic phenomena, one can perceive the philosophical weakness of any attempt at vulgarization. It is not a matter of basing a synthesis upon an analysis. One must conceive the a priori synthesis which underlies the notion of space-time. All the tales of passing trains which signal an observer standing in a station, of aviators who smoke cigars in lengthened or contracted periods of time—to what purpose are they?—or, more precisely, for whom are they designed? Surely not for those who have not understood the mathematical organization of relativity. And those who have understood the mathematical organization of relativity require no examples. They install themselves in the clear and certain algebraism of the doctrine. It is on the basis of the synthesis of algebraism and scientific experiment that one may correctly designate the rationalistic revival implied in the doctrines of Einstein. Let us demonstrate this neo-Kantian aspect. It did not escape Leon Brunschvicg, who wrote: "The advancement on Kant (effected by these new doctrines) consisted in transporting the a priori synthesis from the region of intuition to the region of intellect, and this is decisive for the passage to physics."

And, in fact, any Kantian philosophy holds that space is not a concept drawn from experience of the external world, since the intuition of space is a sine qua non condition of experience of the external world. A similarly inverted formulation is enunciated in respect to time, which is given as the a priori form of internal sensibility. The sine qua non is the pivot of the Copernican revolution of intuitions of space and time.

And, in the same manner, in the same philosophical fashion, if one would determine the epistemological function of the space-time notion in relativistic science, one must say that the space-time algebraic complex is a sine qua non condition of the general validity of our knowledge of electromagnetism. Knowledge of electromagnetic phenomena during the nineteenth century was co-ordinated by the laws of Maxwell. Reflection upon these laws led to the conviction that they must remain invariant for any change of reference system. This invariance defined the transformation [formulas] of Lorentz. It established a Lorentz group which possesses the same philosophical significance for relativity geometry which the group of displacements and similitudes possesses for Euclidean geometry. Thus, it is the Lorentz transformation which underlies the notion of space-time, and the Lorentz group which forbids the separation of spatial co-ordinates and temporal coordinates. The notion of space-time takes shape in a perspective of necessity. To see in it a mere linguistic structure, a mere condensation of means of expression, would be to underestimate its philosophical significance. It is a conception, a necessary conception. If the rôle of the philosopher is, as we believe, to think thought, then he must think space-time in the totality of its functions, in its algebraic nature, and in its informing value for scientific phenomena.

If one adds now, that due to the operational definition of simultaneity the velocity of light enters into geometrical-mechanical references, and if one recalls that light is an electromagnetic phenomenon, one reaches the conclusion that the notion of space-time is hereafter a basic notion for an ultra-precise understanding of phenomena.

Thus, the concept of space-time, as suggested by Lorentz, as achieved by Einstein, appears as an a priori form, functionally a priori, permitting the comprehension of precise electromagnetic phenomena. It is of little importance, philosophically, that this form occurs tardily in the history of science. It is installed as functionally primary by the enlightened rationalism which constitutes one of the most clear-cut aspects of the theory of relativity. Once having aligned oneself with this enlightened rationalism, one sees that there is a naïve rationalism in the same sense that there is a naïve realism. And if one would reap all the philosophical benefits of scientific culture, one must realize psychologically the soundness of the new foundations; one must abandon the old points of departure, and begin again. At the close of the eighteenth century, in his history of astronomy, Bailly maintained that calculated astronomy procured a peace of mind in contrast to any theory of imaginative astronomy. Newtonian thinkers, he said, "chose to adopt the notion of attraction to fasten their imagination, to rest their thoughts."

The function of Einsteinian rationalism is likewise salutary. The algebraic notion of space-time rids us of vulgarizing images. It frees us from a falsely profound reverie upon space and time. In particular, it precludes the irrationalism associated with an unfathomable duration. The mind rests in the truth of its constructions.

Once the algebraic nature of the Einsteinian formulation is realized, one is prepared for a philosophic inversion of the abstract and concrete characters of scientific culture; or, to speak more precisely, one accedes to the abstract-concrete character of scientific thought. One may well say that the concept of space-time is more concrete, despite its intellectual character, than the two separate notions of space and time, since it consolidates two perspectives of experience. Naturally, the notion of space-time will, whenever necessary, be divided and analyzed so as to reinstate those separate functions of time and space, in view of the simplifications which are useful in classical mechanics. But relativity will be on guard against all simplifications. It rests upon the summit of its synthesis. From this vantage point, it judges confidently all analytical perspectives.

How shall philosophers be led to this summit? But philosophers no longer care, it seems, for synthetic thoughts. They do not wish to found knowledge upon its highest achievement. They claim to cut Gordian knots at a time when science is striving to knit together the most unforeseen relations, at a time when physico-mathematical science resolutely declares itself abstract-concrete.

Rather than to return ceaselessly to the base of common knowledge, as if what suffices for life could suffice for knowledge, we have the means, by pursuing Einsteinian science, to develop a terminal rationalism, a differentiating rationalism, a dialectical rationalism. This differentiation, this dialectic appears in knowledge at a second stage of approximation. In short, there occurs an inversion in [the order of] epistemological importance. The first approximation is only the opening move. Common knowledge regards it as basic, though it is only provisional. The structure of scientific understanding emerges only from refinement, through an analysis as thorough as possible of every functionality.

One may, in application, limit these functionalities, cognizant that a potentiality remains unrealized, that a sensibility is smothered. One would recognize that in quantum mechanics in numerous cases there occurs degeneration ("degenerescence'), that is to say, extinction of a structural possibility. But the new theories yield the whole hierarchy of rationalistic and empiricist values. Classical science and common knowledge have their [respective] places in the system of epistemological values. The dialectic of relativistic mechanics and classical mechanics is an enveloping dialectic. It seems that relativity risked everything which lent certainty to the classical conception of reality, but, having risked all, lost nothing. It has retained all that was scientifically known during the last century. A shift of the finer structures reveals the ancient bonds. Thus, relativity permits a retrospective re-enactment of the entire history of mechanistic rationalism.

V

This possibility of recurring to simplified philosophies will be better understood if we can now show the notably firm nature of the coupling of rationalism and realism effected by relativity. To this end, it will suffice to consider the algebraic form, space-time, in its ordering functions in mechanics and electromagnetism.

Space-time is not merely a simple epistemological necessity evoked by reflection upon the conditions of invariance stipulated by the Maxwell equations. This initial synthesis propagates its ordering power. The notion of space-time conditions quadrivectors which accentuate the synthetic character of the relativistic [mode of] organization.

For example, by extending the classical conception of mechanical impulsion, which is a vector of three-dimensional space, relativity attains the conception of the impulsion of the universe as a quadrivector of four-dimensional space. This impulsion has the three components of classical momentum as its spatial component, and energy divided by the velocity of light as its temporal component. But the quadrivector of the impulsion does not consist of a simple juxtaposition of the momentum- and energy-aspects. So powerful a conceptual fusion is achieved that the principle of the conservation of momentum and the principle of the conservation of energy are summated. In an isolated material system, the geometric sum of the quadrivectors of the impulsion remains constant when applied to different bodies in the system. Recalling that Descartes formulated his mechanics in terms of the notion of momentum whereas Leibniz advanced the notion of mechanical energy, one would perceive, from the summit of this synthesis, the historical recurrence as a profound synthesis of Descartes and Leibniz achieved by Einstein.

This same inspiration led to Einstein's discovery of the algebraic homogeneity of energy and mass. This discovery of mathematical, rationalistic origin had considerable realistic import. The mass-energy amalgam, first established for kinetic energy, clearly extends to all forms of energy. Doubtless the philosopher who thinks in words, who believes that scientific concepts have an absolute root in common notions, is shocked by the phrase "inertia of energy." And yet it is this concept of the inertia of energy which marks Einsteinian science as a new science, as a conceptually synthetic science.

In effect, the realistic aspect of this mass-energy amalgam consists in none other than the union of the so different classical principles of the conservation of mass and the conservation of energy. Considered in their historical evolution, the concepts of mass and energy appear bereft of an absolute. Now it is necessary to establish between them a profound relation, an ontological relation.

In other words, in order to realize this relativization of so realistic a principle as that of the conservation of mass, one must accept once more the Copernican revolution of relativity, one must install mathematics at the center of experience, one must take mathematics as the inspiration of scientific experiment. For, after all, experiments as precise as those of chemistry cast no doubt upon the principle of Lavoisier. Chemistry was, in this respect, the recital of an immense success. Chemistry codified the absolute character of a materialism of balances. Scientific realism was, on this point, on a par in conviction with naive realism. Let us firmly underscore that efficacious thought proceeds in the direction of rationalism s → realism. Primacy belongs, not to the principle of conservation (in realistic fashion), but to a principle of invariance (in rationalistic fashion). It is the conditions of invariance in the mathematical expression of the laws which permit a definition of the meaning and validity of the true principles of conversation. Insofar as it was thought possible to characterize the philosophy of relativity by the too-simple label of "realism" from the sole fact that relativity substantiates principles of conservation, this epistemological evolution must be the more definitively formulated. For our part, we are of the opinion that the manner of conserving is more important than what is conserved. To conserve mass and energy in a single formula is not really to ground one's faith in the reality conserved but, rather, to become conscious of the rationalistic power of the invariance of the laws.

Doubtless, experiment in its most refined, meticulous forms sanctioned the ingenious views of Albert Einstein; consequently, [the concept of the] inertia of energy possesses hereafter an undeniably realistic character. But these very conceptions were original and inspired; they were not psychologically natural and they led to scientific experiments which were quasi-supernatural. For example, the entirety of nuclear physics falls within the jurisdiction of the principle of inertia of energy. And the power of nuclear physics has been sufficiently emphasized, perhaps to the neglect of its ultra-phenomenal character. The scientist has already smashed more uranium nuclei in the space of five years than Nature in a millennium. The laboratory technician has succeeded in implementing by means of the atomic pile the Einsteinian principle of inertia of energy. The reality which slumbered in his materials was provoked by mathematically-founded experiments. Seen from the nuclear level, one might well say that matter evokes a neomaterialism in which substance and energy are interchangeable entities. Reality is no longer nature pure and simple. It must be wrought to become the object of scientific experiment. Thus, the philosophy of contemporary science as it issued from the revolutions of the beginning of the century appears as a dialectic of enlightened rationalism and elaborated realism. In order to lose none of the philosophical implications of science the two concepts of invariance and conservation must be synthesized in an abstract-concrete philosophy by introducing an additional unifying trait in the form of an invariance-conservation. Here is a philosophical doublet which would be mutilated by an unilateral philosophical interpretation, whether rationalistic or realistic. Science requires hereafter a bicertitude. It must satisfy the requirements of mathematical coherence and minute experimental verification.

VI

We have followed rapidly a development of relativistic thought to a synthetic center of the science of mechanics. The synthesis on the side of electromagnetism was not less important. The components of the two tri-dimensional vectors by which classical physics defined separately the electric field and the magnetic field are recognized by relativity as the components of a single tensor. This fact endows the Maxwell-Lorentz equations with an extreme generality which goes hand in hand with an extreme algebraic condensation.

It is not the least paradoxical character of general relativity to find in the development of its doctrine this dialectic of rational condensation and extension of empirical significations. When enlightened rationalism takes hold of reality by such condensed symbols, one experiences, there too, a great peace of mind. Tensor calculus, Paul Langevin liked to say, knows relativity better than the relativist himself. Tensor calculus becomes, in some manner, charged for us with subaltern thought; it is our guarantee of forgetting nothing; it arranges for particular analyses. These symbols are in no way mystical. They are translucent to the mathematician and they render the physicist perspicacious. The unifying formulas of general relativity are philosophical syntheses which reunite rationalism and realism.

VII

If we were to consider dialectically the principle of equivalence of inert mass and heavy mass, the principle which founded general relativity, we would be led to the same philosophical conclusions.

In effect, to reunite inert mass and heavy mass in a single concept amounts to amalgamating inertia, a quality inhering in a given body, and weight, a quality whose seat is, in some manner, external to the body in question. Thus, we have a prime example of the correlation of a force and a structure of space-time. This correlation inscribed in the Einsteinian principle of equivalence is greatly extended in the development of the doctrine.

Here, again, the philosopher may find instruction; for the principle of equivalence constitutes a denial of the [supposed] logical priority habitually assigned to force over against its manifestations. In fact, force is contemporaneous with phenomena. There is no circuit of being which assigns being to matter, then to its forces, then to the deformations of matter. As Eddington said [in Space, Time and Gravitation], "Matter is not a cause, it is an index." All exists together as the structure of space-time.

Relativity, therefore, seems to us to modify philosophically the principles of "causalism" in quite as thoroughgoing fashion as those of realism. Abstract-concrete philosophy will have to be formulated in terms of a new trait of metaphysical union and will have to think of scientific phenomena as cause-functions. There occurs an endosmosis of mathematical consequences and physical causes.

Thus, relativity ceaselessly calls scientific thought to a philosophical activity which is both central and dialectic. The traditional problem of the dualism of mind and body is posed in a precise central locus, with the benefit of an extreme sensibility. Here the most rigorous mathematician and the most meticulous physicist agree. They understand each other. They instruct each other. Thought would become empty, experience would become obscure, if one were not to accept, in the regions in which relativity functions, the synthesis of enlightened rationalism and elaborated realism.