Bergson, Mathematics, and Creativity by Pete A. Y. Gunter Pete A. Y. Gunter is Regents Professor of Philosophy at the University of North Texas, P. O. Box 310920, Denton, TX 76203-0920. E-mail gunter@po6.cas.unt.edu. The following article appeared in
I would like to make a couple of points concerning two popular misunderstandings of Bergson. The first is the impression that this philosophy is "irrationalist. The second, often incongruously con That Bergson is an "irrationalist" is often claimed: explicitly by Benedetto Croce, Leonard M. Marsak, WalterJ. Slatoff, Gerhardt Lehmann, Egon Friedall, Raymond Bayer, Walter Bruning, implicitly by Bertrand Russell and George Santayana. As for Bergson’s "literary" aura, one seeks in vain for adequate synonyms to explicate it. "Superficial," "facile," "trendy" "poetic" help but do not go far enough. Will Durant states that Bergson’s lecture rooms became the salon of splendid ladies "happy to have their hearts’ desire upheld." Since he is not widely read in English-speaking philosophical circles, it should prove helpful, in sections two and three, to outline some fundamental features of Bergson’s philosophy. This will help us to understand some of the basic problems to be examined below. Since most of these problems involve his philosophy of mathematics, and since the mathematics with ‘which he is concerned is primarily the calculus, it will help also, in section four, to sketch, briefly, a number of its fundamental features. This will make it possible, in section five, to analyze the centrality of the calculus to Bergson’s philosophical method (hence to both his epistemology and his metaphysics). II. Bergson A Refresher Course Bergson’s philosophy sprang, he tells us, from an analysis of Herbert Spencer’s On one side, there is mathematical ("clock") time, composed of instants. each of which is entirely distinct from all others, none of which, clearly conceived, can move, transform, or change itself. Or, we have units (minutes, hours, etc.) each of which is entirely homogeneous within its boundaries and identical with all units of equal length. This is a strange sort of time indeed, made up of static parts, all the same, each entirely distinct from the others. Rather than call this real time, Bergson concluded, it would be more accurate to term it a "fourth dimension of space" (TFW 109). Meanwhile there is actually experienced time which, Bergson found, looks less like mathematical time the more one explores it. "Lived time," far from being made up of instants, is dynamic throughout. No two "segments" of it -- if there are segments -- are identical; all differ qualitatively. And, far from being separate, successive states of consciousness merge into each other without sharp boundaries. Bergson calls this inner time "duration" to distinguish it from mathematical time and to stress the fundamental endurance of each of its moments into the next. To treat duration and its continuity as a kind of calibrated spatial co6rdinate -- to spatialize and spatially segment it -- is, Bergson agrees, extremely useful. Without spatialization we would not only not have modem physics: we would not have clocks, calendars, and the kinds of organized societies they make possible. But it is a mistake to raise distinctions made for pragmatic purposes to the level of fundamental theoretical postulates without first submitting them to a critique. In this case a critique demonstrates the real time -- real duration -- is neither static nor homogeneous nor internally discrete. Real duration is dynamic, heterogeneous, and (qualitatively) continuous. This fundamental distinction, between lived time and dock time, and the insight into the character of experienced time on which it depends, mark the starting-point of Bergson’s philosophy From this base, his thought is continually broadened to include embodied human consciousness ( Creative Evolution 1907), and human history and prehistory (The Two Sources of Morality, and Religion, 1932).In each of these works one finds a tension, and a resulting conflict between two contrary tendencies: one creative, expansive, dynamic, the other conservative, repetitive, static. In Analogously, sense organs filter out of the welter of our environment all those influences that would keep us from responding effectively to our surroundings. The result is a stable, pictorial world. These joint constraints, however, make possible our focused consciousness. They allow us to deal with our ordinary affairs in ordinary ways. They also make possible those exceptional acts which, Bergson states -- echoing the fundamental conclusion of
In This sketch of the development of Bergson’s philosophy conveys neither the depth and suggestiveness of this thought nor the seriousness of the conceptual problems to which it leads. Though an extensive analysis of this sketch cannot be attempted here, some amplification of it is needed. And since the present essay concerns Bergson’s philosophy of mathematics, what follows will emphasize his concept of matter: its status, and its aptness for mathematical prediction and description. III Structures of Duration 1. Matter and Mind In This problem is rendered especially acute in
The fundamental problem, Bergson argues, is our spatial notion of the relations between mind and world: "Questions relating to subject and object, to their distinction and their union, should be put in terms of time, rather than of space" (MM 77). Throughout the eighteenth and nineteenth centuries matter had been conceived as comprised of passive, simply-located particles whose most fundamental character is their imperviousness to change. Bergson takes a contrasting view, conceiving matter as: ". . modifications, perturbations, changes of tension or of energy and nothing else" (MM 266). That is: matter is a kind of duration, a succession of "rhythms," a present which is "always beginning again." Relative to human duration ‘with its directed spontaneity, matter is inert. In itself it "lives and vibrates" (MM 270). The rhythms of human consciousness are given an elaborate analysis in There is a certain artifice involved in setting up this simple calculation, Bergson admits. It is necessary to "separate the vibrations" sufficiently to allow us to count them (which suggests as will be shown below, in section 51, that some distancing between them is already present). The result is unmistakable, however; the arithmetic relationship at with Bergson arrives here is presented by him not as illusory but as having an objective basis. Between the rhythms of consciousness and those of matter there is an element of quantitative commensurability. Indeed, there is the unmistakable suggestion that it is the indivisibility of the rhythms, of both sorts, which grounds the possibility of quantitative relations. The theory of differing breadths of duration, capable of extending over each other, and the notion of matter ‘which results from it, are further developed in Thus, in This universal "movement" of matter not only involves an expansion of the physical universe. It also helps to explain why there is an "approximately mathematical" order in nature which science "approaches in proportion to its progress" (CE 218). When a physicist validly marks an event as starting at time 2. Life and Matter The theory of matter developed in That these concepts are present in The resulting "progress," with is multiple branching, is continuous from beings that vibrate almost in unison with the oscillations of the ether, up to those that embrace trillions of these in their shortest perceptions" (CE 201). The "proportionality" between consciousness and the durations of matter outlined in The theories of 3. Notes on the Calculus The "infinitesimal calculus" was developed by Isaac Newton and Gottfried Leibniz, independently, in the late seventeenth century. Their achievement scarcely took place in a noetic vacuum. Newton was right to protest that if he saw so far it was because he stood on the shoulders of giants. Both he and Leibniz were deeply indebted to a large set of mathematicians: Archimedes, Cavalieri, Wallis, Descartes, Barrow, and Fermat among them. Nor were Newton’s and Leibniz’ achievements complete as they stood. Extensions, corrections, reorganizations of the calculus continued long after their work, leading after more than two centuries to its present, presumably rigorous, foundations. From its beginnings the calculus has consisted of two contrasting parts, each designed to solve different sorts of problems. The differential calculus was developed to deal with motion -- velocity at a point and acceleration being fundamental concepts. Quantities representing velocity are termed first derivatives, those dealing with acceleration, second derivatives. The integral calculus, by contrast, was developed to deal with areas ("areas under curves") and, by extension, volumes. Both parts of the calculus have been extended beyond their original scope. The differential calculus, though designed to deal with states of motion, can be used in fields far removed from planetary orbits or falling bodies. In the words of Edward Kasner and James Newman: "Structural engineers, concerned with the elasticity of beams, the strength columns, and any phase of construction where there is shear and stress, find first, second, third, and fourth derivatives indispensable . . ." The integral calculus, similarly, is more complex than it at first appears. This complexity is summed up in the elegant Fundamental Theorem of the Calculus, which establishes both that there are two sorts of integrals with precise equivalences and -- a quite different idea -- that there is an inverse relation between the integral calculus and the differential calculus. The two fundamental integrals are the definite and the indefinite integral. The indefinite integral is a number, while the indefinite integral is a function. In the words of David Berlinski: . . . although both definite and indefinite integrals are alike in being integrals, they are different in their most crucial respects. The definite integral denotes a specific number, something fixed, and as such belongs to Integration, from the vantage point of the indefinite integral, involves following the generation of a curve up to a point, thus finding a "changing quantity" from its rate of change. The Fundamental Theorem also demonstrates that it is possible to generate a definite integral (a number) from any indefinite integral (a function). The simplicity of this computation turns out to be a boon to mathematicians, who otherwise, to get their definite integrals, would have to go through laborious computations based on Riemannian sums. It is both interesting and important to note that in the calculus one can pass from functions to numbers, and simply. It is equally important to see that one can also pass from integrals to derivatives (from the integral calculus to the differential calculus) and then back again. The creators of the calculus knew this, That is, they understood that integration and differentiation are the "inverse" of each other, in the way that addition and subtraction stand in inverse relations. What is meant by such inverse relations can be conveyed by very elementary symbolism. By differentiating This chaining relationship can be outlined using the language of first, second, third, and, in general, n Originally the calculus was established by using, not the concept of a function but that of a limit, and of the notion of "convergence" to a limit. To the beginner the notion of convergence to a limit, with its sense of endless approximation, may appear clumsy or counterintuitive, as if one were being required to "corner" velocity or acceleration or area by endlessly patching together ever smaller (or, in the case of the integral, larger) bits of time or space. In fact, if the "bits" are understood not as It is interesting, and a bit puzzling, that this new way of thinking did not emerge until the seventeenth century. Greek mathematicians had worked out many of the concepts necessary to it. Yet they seem to have halted at the entrance. One major problem lay in their unwillingness to accept change on its own terms. According to Morris Kline, the problem was both mathematical and cultural: Another characteristic of Greek mathematics runs through the culture. Euclidean geometry is static. The properties of changing figures are not investigated. . , rather, the figures are given in their entirety and studied as is. The restful atmosphere of the Greek temple reflects this theme. Mind and spirit are at peace there." In the terms of another historian of mathematics, Salomon Bochner, there is simply an immense gap between modern "analytical variability" and "Greek stationarity." Bergson could have added a second "static" limitation of Aristotle’s thought in this regard: his refusal to countenance This was not the only difficulty. The very logical rigor which made Greek mathematics exemplary also stood in the way of introducing any idea which could not be rigorously defined. Carl B. Boyer explains: It is possible not only to trace the path of development throughout the twenty-five-hundred-year interval during which the ideas of the calculus were being formulated, but also to indicate certain tendencies inimical to its growth. Perhaps the most manifest deterring force was the rigid insistence on the exclusion from the mathematics of any idea not at the time allowing of strict logical interpretation. The very concepts which gave birth to the calculus -- those of variation, of continuity, of the infinite and the infinitesimal -- were banned from Greek mathematics for this reason, the work of Euclid being a monument of this exclusion. It is arguable that breakthroughs in the sciences require, first of all, imagination and audacity Later it will be possible to formulate the original intuition with sharp precision. This sketch of some basic concepts of the calculus and of factors involved in its creation is intended neither a complete outline nor as a technical account It is intended, rather, to set the stage for Bergson’s appropriation of the calculus as fundamental to his metaphysics and epistemology; Bergson believed that the calculus represented (and furthered) a profound shift in understanding, one which made modern science possible. This shift involved both increased linguistic precision (mathematical precision) and a deepening sense of change -- of mobility of all kinds. A renewed scientific and philosophical effort is necessary, he believed, to take account of it. 4. An Introduction to Intuition 1903 saw the publication of A thorough analysis of Our usual way of thinking, Bergson observes, starts from static concepts (points, instants, lines, etc.) "in order to grasp by their means the flowing reality" (CM 224). But, he insists, we are capable of the reverse procedure, of working away from our usual concepts and assumptions towards the "flowing reality" This will upset our categories. But it may help us to arrive at fluid concepts "capable of following reality in all its windings" (CM 224). The procedure does not end here, however. From intuition, with its fluid concepts, it is possible on Bergson’s terms This reversal has never been practiced in a methodical manner, but a careful study of the history of human thought would show to it that we owe it the greatest accomplishments in the sciences, as well as whatever living quality there is in metaphysics. The most powerful method of investigation known to the mind, infinitesimal calculus, was born of this reversal. (CM 224-225) Bergson proposes, therefore, that metaphysics adopt the "generative idea" behind the calculus and extend this to reality in general. Hence he concludes that one of the aims of metaphysics is to "operate qualitative differentiations and integrations" (CM 226). The notion of qualitative differentiations and integrations, nonetheless, will seem strange to many thinkers. Possibly it will become clearer and less arcane if Bergson’s uses of it are explored. What follows will be an examination of three of these uses: (i)differentiation and the limit concept, as applied to matter (ii) integration and the relation of wholes to parts; (iii) temporal hierarchy and the interrelations of differentiation and integration. i. Limit Concepts and Qualitative Rhythms A rigorous limit concept was not introduced into calculus until the work of Augustin-Louis Cauchy in the early nineteenth century. Until then mathematics worked -- often uneasily -- with concepts like "infinitesimal" and "motion at a point." Bergson’s qualitative calculus is not intended to replace rigorous quantitative thinking. Rather, it is intended to provide, among other things, a realistic basis not only for more mundane practical activities but also for the natural sciences, particularly astronomy and physics. His qualitative "differentiation" of matter terminates, at the limit, in rhythms which, however brief; are still rhythms, and dynamic. The extent to which physical reality can retain its durational, modal character for Bergson and yet present characteristics which justify mathematical representations can be seen by examining a passage from . . . have a minimum of time enter into the world without allowing the faintest glimmer of memory to go with it. We shall see that this is impossible. Without an elementary memory that connects the two moments, there will be only one or the other, consequently a single instant, no before and no after, so succession, no time. We can bestow on this memory just what is needed to make the connection; it will be, if we like, this very connection, a mere continuing of the before into the immediate after with a perpetually renewed forgetfulness of what is not in the immediately prior moment. There is thus, in material reality a minimal but real connection between successive events and a "forgetting" by them of their predecessors. (DS 48) One thus has a quasi-epochal theory of material duration. This account of systematically approximative character of mathematical descriptions will doubtless appear familiar to readers of Whitehead. Both Bergson and the early Whitehead conclude that, to quote Whitehead, ". . . an abstractive set as we pass along it converges to the ideal of all nature with no temporal extension, namely, to the ideal of all nature at an instant. But this ideal is in fact the ideal of a nonentity." Though Bergson did not develop an elaborate theory of extensive abstraction, it is not surprising that he should have viewed Whitehead’s ii. Integration: Real Parts in Real (Dynamic) Wholes Philosophy bristles with theories of "wholes" and "parts," theories which reach from extreme atomisms (in which there are only parts, and wholes are at best mere aggregates) to extreme monisms (in which putative parts lose their identities to the whole). Bergson’s language, which stresses the wholeness of duration against the static fragmentariness of space, leads to the suspicion that his philosophy (as is argued in a recent essay in Here, as is true more than once in this study, it is not possible to deal with an important question in depth. What can be done here is to point out the language which Bergson uses to talk about one self: that is, about parts (as opposed to mere "elements") and about "integral experience." The one-many view ‘which Bergson takes of the self will be applied by him both to biological evolution and to social organization. The self Bergson states, is mathematically neither one nor many. Seen in itself; it is Strictly speaking they do not constitute multiple states . . . . While I was experiencing them they were so solidly organized, so profoundly animated with a common life, that I could never have said where any one finished or the next one began. In reality, none of them do [sic.] begin or end; they all dove-tall into one another. (CM 192) The Bergsonian self resists fragmentation into distinct, juxtaposed parts (as is attempted in, for example, associationist psychology). Yet even though the self must be conceived as a whole, it contains (consists of real parts which "encroach upon one another" (CM 198), which "dovetail." This is not a unity which ablates its parts, it is a unity This is extremely important in understanding Bergson’s position, because the knowledge of the self by the self, is, he insists, the "privileged case" (CM 236) of his philosophy. It provides a model in terms of which other levels of reality are to be understood. Interestingly, he characterizes this kind of knowledge as "integral experience" (CM 237). Nothing could appear more qualitative than the Bergsonian self; nothing could seem more out of place with regard to it than metaphors taken from the calculus. Yet his language is clear. Intuition -- even in the case of the self -- is for him a qualitative Integration. A timeworn textbook example may be helpful here. If we are to find the area of a circle, we can circumscribe it with regular polygons with indefinitely increasing numbers of sides. By increasing the number of sides we never reach the exact area. But if integration is introduced, there is an almost-magical effect The limit of the series appears, the area is attained. So with the knowledge of the self by the self. As the patchwork of partially misleading "views" of analyses which misrepresent (yet circumscribe) it disappear, the fundamental insight is given. Without comparing many psychological analyses, Bergson insists, we cannot achieve such as insight (CM 236). But this insight, and the higher degree of temporality it achieves, follows from the integration of the parts, not from their obliteration (CE 152). This sketch is of interest as it stands. It is of equally great interest in terms of its applications (which Bergson intends to carry out) to the rest of his philosophy. A biological organism is a whole for Bergson; yet he points out that each cell is itself an organism (CE 41-42, 162) hence an organism is a whole comprised of real parts. A society, he points out in iii. Temporal Hierarchy and the "Fundamental Theorem" We have noted, in The concept of temporal hierarchy first stated in . . . the intuition of our duration, far from leaving us suspended in the void as pure analysis would do, puts us in contact with a whole continuity of durations which we should try to follow either downwardly or upwardly: in both cases we can dilate ourselves indefinitely by a more and more vigorous effort, in both cases transcend ourselves. In the first case, we advance toward a duration more and more scattered, whose palpitations, more rapid than ours, dividing our simple sensation dilute its quality into quantity at the limit would be the pure homogeneous, the pure repetition by which we shall define materiality. In advancing in the other direction, we go toward a duration which stretches, tightens, and becomes more and more intensified at the limit would be eternity. This time not only conceptual eternity, which is an eternity of death, but an eternity of life. (CM 221) This passage is two-sided. It is epistemological, describing different sorts of intuition, each correlative to the level of understanding on which it operates: "an indefinite series of acts, all doubtless of the same genus but each one of a very particular species" (CM 217). There is thus no one intuition, to which this term refers. There are many sorts of intuition, each appropriate to the rhythms and the qualities of its particular object It is metaphysical, since the different sorts of intuition are said to correspond to the different "degrees of being" (CM 217; cf. also CM 218). So far this study has isolated two factors which are fundamental to Bergson’s thought: temporal hierarchy and the calculus. It is very likely that these two factors will be interrelated in some manner. But how? The reader will recall the brief but terminologically dense sketch, above, of the Fundamental Theorem of the Calculus, with its chaining of inverse relationships between differentiation and integration. It is a central thesis of this paper that the hierarchy involved in this chaining is understood by Bergson as congruent with the hierarchy which he describes as comprised of broader and briefer rhythms of duration. That there should be a precise parallel between Bergson’s hierarchy of durations and the indefinite chaining of derivatives and integrals may seem unlikely. But closer inspection will render it plausible. From the vantage-point of his metaphysics, the goals will be, as noted above, to operative qualitative differentiations and integrations. iv. Èlan Vital as Mathematics To explore these conclusions it will be necessary to take a second look at Life, Bergson proclaims, is not reducible to physico-chemistry But if he rejects mechanistic explanations of life, he also denies another kind of reductionism, which equates life with the simple step-by-step filling in of a plan. Both mechanism and finalism presuppose that "All is given," the first through efficient causes, the second through a kind of cosmic blueprint present at the beginning (CE 39- 41,45,46) In rejecting both, Bergson insists that evolution operates within inherent limitations. Matter, with its entropic drift towards increasing disorder (CE 245-246) constitutes an obstacle. The ‘vital impetus, in turn, is not omnipotent. (CE 125, 141-142, 149) It is thus not surprising that the course of biological evolution, in its innumerable branchings, should exhibit so many dead ends (CE 107,116,129), halts (CE 104, 113, 125n, 132, 134), and regressions (CE 40,50-51, 100, 127, 131), or that is progress should be accompanied by increasing conflict (CE 103). Life on this planet has, in the context of its limitations, managed a threefold success: plant and animal life, and among the animals, arthropods (including social insects) and vertebrates (including humankind. Plants, Bergson asserts, are "societies" (CE 16; 12) whose evolution may not require a vital principle. With animals, Bergson concludes, something more than mutation and natural selection is required.
We believe that if biology could ever get as close to its object as mathematics does to its own, it would become to the physics and chemistry of organized bodies, what the mathematics of the moderns has proved to be in relation to ancient geometry. The wholly superficial displacements of masses and molecules studied in physics and chemistry would become, in relation to that inner vital movement (which is transformation and not translation) what the position of the moving object is to the movement of that object in space. (CE 32) The change in outlook which led to modern physics and its mathematics thus might, extended to biology, lead to a new, more flexible, more temporalist paradigm (and perhaps to a new mathematical understanding of biology). The creative action by which a new species is formed would involve a saltation which raises the species to a higher temporality. It would involve an integration from which, however, it would be possible to derive a derivative: And, so far as we can see, the procedure by which we should then pass from the definition of a certain vital action to the system of physicochemical facts which it implies would be like passing from the function to its derivative (i.e.. the law of the continuous movement by which the curve is generated) to the equation of the tangent giving its instantaneous direction. Such a science would be a He adds that just as an infinity of functions may have the same differential (functions which differ from each other by a constant -- the so-called "constant of integration") so the integration of physico-chemical elements (a "summation" which, inversely, proceeds from the derivative to the function) would determine the vital action only in part. A part would be "left to indetermination" (CE 33). A detailed discussion of the questions raised by these ideas would require a second article, longer than the present one. Perhaps the following comments will help explain what is meant. First, Bergson’s speculations here are not conceived by him as imaginary That is, they are understood by him in terms of the actual chemicals, energies, physical principles without which life could not exist. Second, they are understood by him as putative extensions into biolog, of fundamental insights which he believes are at the root of the paradigm shift which lead to modern physics and its mathematics. It would be consistent for him to hold that another such "inversion" could lead to a more dynamic, less reductionist scientific biology, one which could avoid strict deterministic explanations. In what sense are we to understand these speculations? Bergson believes that the chemicals, energies, and physical principles without which life could not exist are misconstrued by us as being perfectly spatial, not as possessing degrees of spatiality (i.e, as characterized by their "extensity"). It is thus easy to understand the extent to which these factors, extensive and durational, could be believed by Bergson to be brought together into forms possessing broader durations. The qualitative calculus of life can be taken as having done so on our planet -- to use one of William James’ favorite phrases -- so far forth. But can a Yet it is clear that it is in this direction -- towards a more temporalist biology, utilizing a mathematics more suited to the "sinuousities" (CE 212-213) of life -- he believed biology could most profitably proceed. v. A Mechanism for "Vitalism"; Hierarchical Integrations The present essay could halt here. Its basic contentions have been sketched out, at some length, and, I hope, in such a way as to be intelligible. But to have stressed his theses of the part which an increasing awareness of temporality has played in the genesis of modern science, and to have indicated the way in which he parallels his theory of levels of duration with the "chaining" of integration/differentiation leaves one fascinating problem unsolved: namely, that of how, given what is known of genetics, Bergson could have imagined that the "vital impetus" effects its evolutionary saltations. What follows is a speculation on Bergson’s ultimate speculation. One advantage that a broader duration will have over the briefer durations with which it is contemporaneous is its capacity to sum up Bergson was anti-Lamarckian. He rejected the ‘view that the state of the environment can influence the genes. Like the majority of contemporary geneticists, he held the opposite view the genes influence the body, and only changes in the genotype can influence the phenotype. Obviously, given what has gone before, he offers a different explanation of how the genotype is altered (mutations) than do contemporary geneticists. The two kinds of synchronization sketched above are different in kind. The first (synchronization of the perceptual object) leads to static spatiality, the second (synchronization of successive indeterminacy) to summed spontaneity. Either or both could influence the DNA double helix, systematically. It will be objected that this explanation is closer to science fiction than to science. It no doubt appears so. The main point of this essay is that this theory -- though it could well be wrong – is
Notes 1. Benedetto Croce, 2. Will Durant, 3. Jacques Monod, 4. André Gidé, 5. Henri Bergson, 6. Henri Bergson, 7. Henri Bergson, 8. Henri Bergson, 9. Henri Bergson, 10. Edward Kasner and James Newman, 11. David Berlinski, 12. Moms Kline, 13. Salomon Bochner, 14. Carl B. Boyer 15. Jean Milet, 16. Henri Bergson, 17. This account of the duration of matter is also given, in almost exactly the same terms, in "Life and Consciousness", the Huxley lecture, given in 1911 at the University of Birmingham, and published in 18. Alfred North Whitehead, 19. Richard L Brougham, "Reality and Appearance in Bergson and Whitehead," in 20. That there is for Bergson a hierarchy of durations, a scala 21. This letter is in the archives of the University Library at the University of Bristol. Provisions in Bergson’s will make it impossible to publish his previously unpublished writings, including his letters. I believe that in citing his opinion in this way, without quotes, I am not transgressing any official prohibition. 22. Another advantage of broader over briefer durations is the capacity of the former to constrain the latter. This 23. This theory is introduced by Bergson "The Soul and the Body," a lecture first given April 28, 1912, and published in Henri Bergson, 24. Benoit B. Mandelbrot, Viewed 23088 times. |