Rhuthmos

Edgar Morin and the Rhuthmoi of Nature – Part 1

Pascal Michon — 2020-02-02T10:18:00Z

Sommaire

The very same year, 1977, Edgar Morin published La Méthode. La nature de la nature – Method: Towards a Study of Humankind: The Nature of Nature (trans. J.-L. Roland Bélanger, 1992). This essay was the first installment of a long series designed to establish a new scientific paradigm: “the paradigm of complexity.” The latter stood as a challenge to the fragmentary and reductionist spirit dominating the scientific enterprise and advocated a dynamic and productive interpenetration of disciplines based on the concepts of “permanent reorganization,” “information” and “loop.” In order to be able to perceive the universe in its true “nature,” i.e. as a “complex expanding whole,” or as “one single physico-bio-psycho-socio-cultural system,” physics, biology and social science should overcome their separation and work tightly together. Six volumes were published between 1977 and 2004 [1].

In volume 1, Morin approached the paradigm of complexity mainly under its physical aspect, while volume 2, 3 and 4 were respectively dedicated to discussions of the contributions of life science (1980), anthropology of knowledge (1984), and theory of beliefs and ideas (1991). However, he explained later that he had first written a draft in four parts that had been eventually developed into four volumes, and that all four subjects had actually already been introduced in the first one (see Preface in 2008, pp. 13-14). Since the volumes 5 and 6, dedicated to the relation between species, individual, and society, and to ethics, were added retrospectively in 2001 and 2004, we are therefore legitimate in limiting ourselves here to the first volume, even if further studies, extended to the following installments, would certainly be welcome.

Rhythmologically speaking, Method presented a paradoxical contribution. On the one hand, contrary to Lefebvre's, Barthes', and Serres' essays, it never referred directly to the concept of rhythm. Although Morin knew of a large number of disciplines and even, as we will see, was personally acquainted with some of the proponents of rhythmology and rhythmanalysis in his days, rhythm never became part of his vocabulary. But, on the other hand, not only Morin shared, as we will see, many ethical and political ideas with most members of the rhythmic constellation of the 1970s, but a significant part of the concepts he was manipulating was clearly related with the most recent science whose rhuthmic roots Serres' study had so powerfully illuminated. As we will see by following step by step his argumentation, somehow, his contribution replicated what Serres had done for the ancient materialist thought: it presented a complete rhuthmic worldview rooted in the latest scientific knowledge.

Concerning biographical data, we may limit ourselves to a few facts. As soon as 1940, Morin had become a member of the French Resistance and, the next year, had joined the Communist Party. However, like Henri Lefebvre, Morin had been quite critical concerning the post-war evolution of his party and was finally expelled in 1951. It is therefore no accident that in 1968, he succeeded Lefebvre at the University of Nanterre and passionately followed the student revolts for the daily Le Monde.

We do not know of any close collaboration with Michel Foucault, of whom he seems to have read only The Order of Things (see index, 2008, p. 2452), which did not fit, as we shall see, in his own dialectic or better yet, hermeneutical perspective. Likewise, whereas Discipline and Punish painted a disciplinary world in which individuals had almost no autonomy, Morin preferred to concentrate on their creativity and imagination, on everything that could derail the regulated course of events.

In a significant contrast, from the beginning of the 1960s, he had worked with Roland Barthes within the “Center for the Study of Mass Communication” established in 1960 at the École Pratique des Hautes Études by the sociologist Georges Friedmann, his mentor at the CNRS. In 1973, this center evolved into the “Center for Transdisciplinary Studies. Sociology, Anthropology, Semiology” and was codirected by Barthes and himself until 1977.

Finally, Morin was close to Michel Serres with whom he shared not only sympathetic views on the 1968 revolt, but also a renovated materialist perspective based on the latest progress of physical, life and computational science in the 20^th century. At least in the first volume, he cited extensively Serresʼ reflections on the history of science (see index, 2008, p. 2461).

Concerning now Morin's theoretical position, as we will see, the whole project of founding a “complex thought” was motivated by the deep ontological turn of science that had occurred around the middle of the 20^th century. Like Serres' reconstruction of the ancient physical “fluid paradigm,” Morin's opposition to the simplification of classical science and his project of “en-cyclo-peding” knowledge were heavily influenced by the remarkable return of the Ancient idea that everything from physical nature up to human societies and cultures, through living beings, was entirely supported and propelled by a fundamental and general creative dynamism.

We may therefore quite legitimately associate Morin's alternative worldview and epistemology with the previous rhythmic contributions we have studied hitherto. If the term “rhythm” was not part of his vocabulary, the subject “rhythm” itself was in fact at the center of his concerns—provided, naturally, it was taken in its pre-Socratic sense as “way of flowing.” Of course, the relationship with Serresʼ thought will appear more obvious than with those of Lefebvre, Foucault or Barthes. But we will see that some hidden links, even with the latter, quickly emerge as soon as we consider them from a rhythmological perspective. And that, while Morin's essay receives surprising new colors from its confrontation with the latter, reversely, it certainly sheds some light on them and their specific limitations.

Modern Rhuthmic Ontology

We can have some hints of Morin's proximity to his contemporaries' interest in rhythm by first looking at some of his intellectual sources of inspiration.

In an instructive survey on the multiple origins of the complexity paradigm, Michel Alhadeff-Jones has luminously emphasized its Bachelardian lineage (2008). Gaston Bachelard (1884-1962), as we have already noticed in chapter 1, was involved at the beginning of the 1930s in a debate with Henri Bergson (1859-1941) on the nature of duration, which opened the way to his founding of rhythmanalysis. But, in the very same years, he was also the first philosopher who legitimized the role of complexity as an ideal for contemporary science—and this is in my opinion no accident. In his famous book Le Nouvel Esprit scientifique (1934) – The New Scientific Spirit (1985), he formulated for the first time a “non-Cartesian” approach to science. While, he noticed, Cartesian epistemology reduces any complex phenomenon to the analysis of its components, understood as simple, absolute and objective, non-Cartesian epistemology favors a dialectical approach that apprehends phenomena as tissues of relations.

There is no simple idea, because, in order to be understood, a simple idea [...] must be inserted in a complex system of thoughts and experiences. (Bachelard, The New Scientific Spirit, 1934/ed. 1978, p. 152 – quoted by Alhadeff-Jones, 2008, p. 68)

As Alhadeff-Jones put it, “Bachelard's recognition of complexity appeared therefore at the root of a new type of scientific explanation” (2008). But we should add that just as duration was not, as Bergson claimed, a linear and unified line similar to a melody, but composed of an intertwined bundle of instants—and therefore liable for a rhythmanalysis—scientific thought flow was not, as Cartesian philosophers had it, a linear intellectual process progressing from one simple fact to the next, but was composed of an intertwined and dynamic bundle of ideas. Bachelard did not mention rhythmanalysis in this instance but we must keep this proximity in mind when reading Morin. “Rhythm of duration” or “complexity of scientific thought” were actually two sides of the same concern. Although the former belonged to the philosophy of time and the latter to the philosophy of knowledge, each shed light on the other under a common concern for the organization of the flow of experience. Rhythm appeared as a complex organization of time, and complexity as a rhythmic organization of thought.

A second hint of Morin's proximity to the “rhythmic” concerns of his contemporaries can be found in the opening chapter of Method. Borrowing heavily from a famous article on “Science and Complexity” published in 1948 by Warren Weaver (1894-1978), who elaborated further, on his own, some of the epistemological ideas already introduced by Bachelard (Alhadeff-Jones, 2008), Morin started his inquiry with a long section dedicated to the “invasion of disorders” into the classical physical worldview that happened from the mid-19^th century and the paradigm change it finally triggered (pp. 29-38).

Imbued with the inherited ancient principles of order, balance, and measure, classical modern physics was based on a mechanistic and determinist perspective. The world was compared to a clock, run by immutable laws, and excluding any disorder.

Order, Master-Word of classical science, reigned from the Atom to the Milky Way. [...] From Kepler to Newton and Laplace, it is established that the innumerable nations of stars obey an inexorable mechanism. [...] This clockwork Universe marks time and crosses time unalterably. Its texture, everywhere the same, is an uncreated substance (matter) and an indestructible entity (energy). The laws of physics, except for the strange exception of the second law of thermodynamics, know no dispersion, wear, and degradation. The self-sufficient Universe maintains itself perpetually. The sovereign order of the Laws of Nature is absolute and immutable. Disorder is excluded, from the beginning, forever. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 29-30)

However, due to the introduction by Rudolf Clausius of the second principle of thermodynamics and the concept of “entropy,” or irreversible loss of energy, and the discovery of the relation of this loss to the increase in the internal molecular disorder by Ludwig Boltzmann (1850-1880), due as well to the introduction of disorder and probability into micro-physics by Max Planck (1900-1910), and finally due to the recognition of a genetic unregulated expansion of the cosmos by Edwin Hubble and others (1920-1970), the Platonic, Aristotelian, Thomistic, Galilean, Cartesian, Newtonian world, based on stability, order, hierarchy, general determinism, and laws became obsolete or, at least, was to be re-founded on principles utterly foreign to it.

After its collapse during the first half of the 20^th century, this world was replaced, from the 1950s, by a new world based on becoming, disorder, multiplicity, chance encounter that clearly emulated that of the ancient materialists.

As Serres, Morin first noticed that this new perspective presupposed a critique of straight determinism. Just as declination appeared in Lucretius in the laminar flow of atoms “incerto tempore, incertisque locis,” the universe was now conceived as “constituting its order and its organization in turbulence, instability, deviance, improbability, energy dissipation” (p. 38 – Morin's italics).

But he also noticed that, although the probability to produce lasting beings was infinitesimal—Serres referred for his part, one remembers, to phenomena “statistically of extreme rarity”—the universe had witnessed and still did the relentless “constitution,” “organization,” “emergence” of new beings. In other words, in this new perspective, organization, order, and laws did still exist but only as emergent and impermanent phenomena. Instead of being the overarching physical norms, order and determinism became the impermanent results of both a generalized disorder and an infinity of random processes of organization.

Contrary to what had been concluded as early as Clausius from the second principle, the new development of thermodynamics initiated by Ilya Prigogine (1917-2003) showed that the universe was not merely doomed to an unavoidable thermic death and a maximal entropy (p. 32). There was actually not exclusion but “complementarity between disordered phenomena and organizing phenomena” (p. 37).

A similar revolution had occurred during the same period, Morin remarked, in life science thanks to John von Neumann (1903-1957), Heinz von Foerster (1911-2002) and Henri Atlan (1931-), who conceived of the living respectively as “function[ing] with disorder,” as “constructed with disorder,” or merely as resulting from “chance as organizer” (p. 38).

Even cosmo-physics had adopted this perspective. The big bang theory supposed that “a concentrated state of infinite density would have been at the source of the Universe, which would have been born in and by an explosive happening” (p. 39). But nothing intelligible according to our common space-time physical standards could be concluded from it because it presupposed that there was properly no time and no space “before” the big bang, i.e. no “before.” It was therefore “useless to look for spatio-temporal or logomorphic figuration concerning the state or the being which precedes our universe” (p. 40). The question of the origin had to be tackled with purely theoretical tools.

Opportunely, mathematician and topologist René Thom (1923-2002) had recently proposed a mathematical representation of the notion of “catastrophe” (1972), which Morin defined as “change/rupture of the form in condition of irreducible singularity” (p. 40), and which gave us the necessary means to address the problem.

The fundamentally complex and rich idea that Thom brings is to tie all morphogenesis or creation of form to a rupture of form or catastrophe. It allows us, therefore, to read disintegration and genesis in the same processes. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 40)

And that mathematical revolution concerned not only the “absolute beginning” of the Universe but also “the whole metamorphic process of transformations which disintegrate and create.”

Different from the big bang which is a concentrated moment in time and which becomes a cause separated from the processes which triggered it and which it has triggered, the idea of catastrophe, while welcoming the idea of an explosive happening, is identified with the whole metamorphic process of transformations which disintegrate and create. Now, this process is still going on today. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 41)

To explain this genuine generative power of the being, much further in the book, Morin hypothesized that it existed, associated with “the causal determinism which governed classical science” and with the newer “probabilitary causality of a statistical character” (p. 305), an “endo-causality” resulting from the retroaction of the effect on its cause. This causality did not any longer connect, on a general basis called natural law, one cause with one particular effect, but introduced a “causal autonomy” that could strongly transform the expected result.

Just the idea of retroaction affects, and much more profoundly than it seems at first sight, the simple, external, anterior, imperial, classical idea of causality. Retroaction returns to the loop, that is to say to the organizational autonomy of the machine-being. Organizational autonomy determines a causal autonomy, namely creates an endo-causality, not reducible to the “normal” play of causes/effects. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 257)

This particular causality was responsible for the emergence of totally new beings possessing new “selves” or identity principles.

Endo-causality implies production-of-self. In the same movement in which the self is born from the loop, there is born an internal causality which generates itself by itself, that is to say a causality-of-self producing original effects. The self is, therefore, the central figure in this internal causality which generates and regenerates itself by itself. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 259)

The being was thus deeply temporalized, that is, not only inserted in a linear duration but considered as “active” and “organizing” by itself. “Everything [was] interactions, transactions, retroactions, organization.”

In nature, activity is a total organizational phenomenon. Everything is active in an active system, and all the more so since it must support and maintain stationary states. Activism is generalized: flux, disequilibrium, instability, turnover, reorganization, regeneration, disorder, antagonisms, disorganizations, looping, variations, fluctuations. Everything is interactions, transactions, retroactions, organization. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 231)

As we can see, there was no fundamental difference with the Ancient atomist ontology as reconstructed by Serres: there was no fixed beings interacting according to fixed laws; rather, the physis was a flowing chaos, yet relentlessly generating and destroying, by chance encounters and retroactions, greater or smaller pockets of impermanent order. Thus, even if Morin never referred to the concept of rhuthmos, his ontological reflection clearly prolonged the Ancient rhuthmic paradigm into a remarkable extension based on the latest discovery of modern science and mathematics.

Order, disorder, organizing potentiality must be thought of together, both in their well-known antagonistic character and in their unknown complementary character. These terms shuttle from one to the other and form a sort of moving loop. In order to conceive this, we need more than a theoretical revolution. A revolution of principle and of method are called for. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 41)

As a matter of fact, in the general conclusion of the book, Morin explicitly compared his view with that of the pre-Socratic thinkers. What will be described, in a following section, as the fundamental “event-ness” and “generativity” of the universe did only but resume the Ancient dynamic conception of the physis.

We have henceforth an immanent principle of organization, properly physical. Thereby physis recovers the generic plenitude which the pre-Socratics had attributed to it. It is this reanimated and regenerated physis that can be generalized, that is to say reintroduced into everything living, everything human. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 377)

Modern Rhuthmic Physics and Space-Time Theory

The same theoretical proximity can be observed in Morin's presentation of the latest progress of physics and Space-Time theory in the following sections in which he summarized the scenario of cosmogenesis as it had been reconstructed since Georges Lemaître's (1894-1966) and Edwin Hubble's (1889-1953) studies in the 1920s and 1930s.

Morin painstakingly described the first cloud of photons that rised up and dilated after the big bang, the extreme heat, the “original fire,” the decrease of temperature because of expansion, the materializing of the first particles (electrons, neutrinos, neutrons, protons), the “chance encounters” by which protons and neutrons, “bouncing in all directions,” “aggregated” to constitute nuclei of deuterium, helium and hydrogen, the “turbulences” that provoked inequalities at the heart of the fast expanding cloud, the first “atomic compounds,” the reinforcement of these first atomic nuclei by gravitational attraction of particles that reinforced in turn their fast-rising gravitational attraction, the “dissociation of the cloud” into proto-galaxies and of those proto-galaxies into proto-stars, the ignition of local thermonuclear chain reactions triggered by the multiplication of collisions between particles due to the increase in density, the balance reached, sometimes, between explosion and gravitational rush to the heart of the newborn stars, the general decrease and local dramatic increase of temperature due to the ignition of these thermonuclear machines, finally the constitution of planets circulating around the stars (pp. 44-46).

Not only most of Democritus' and Lucretius' atomist concepts were here already mobilized, but at the very root of these processes, Morin found, consistently with his “creative ontology,” the “capital” role played by what he called successively “inequality,” “deviation, even minute,” “minimal inequality,” “minute variations,” which clearly constituted modern versions of Lucretius' foundational concept of “clinamen.”

The universe is born in extreme heat, and this heat includes these forms of disorder: agitation, turbulence, inequality of process, chance character of interactions, dispersion. The idea of inequality is capital. The general recooling is not homogeneous: it includes its zones of unequal character and its local moments of reheating. [...] Inequality of development has as starting point the thermic character of the initial catastrophe. Beginning there, and no matter how minimal, there is inequality in the very emission of the cloud. Now, and this is what undermines in its very foundations the previous deterministic vision of the world, which was a vision of ice and not of fire: any deviation, even minute, which is constituted in the emitting source tends to grow and be amplified in an extraordinary way in the course of the process of diffusion. The minute variations which are produced in the very first conditions of dispersion are going to lead subsequently to extreme and extraordinary varieties. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 44-45)

In the same Lucretian vein, Morin emphasized, in the second part of the book, the genesic power of “the whirling form” which was “the primordial Form of being, existence, productive organization.”

We now understand why the whirling form has signaled to us everywhere, in the galactic skies, the circulating air and water, the flaming fire. It is the form in and by which turbulence is transformed into loop. It carries in itself the quasi-indistinct presence of chaos and genesis, all the while remaining the [primordial Form] [la Forme première] of being, existence, productive organization. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 224, my mod.)

The emergence of order and organization out of disorder and chaos was then allowed by the “agglutination” of atoms according to a modern analogon of the “congruence of figures, magnitudes, positions and orders” as Simplicius put it (see above, chap. 4), which consisted in various types of “interactions,” strong interactions bonding protons and neutrons, gravitational interactions accelerating the concentration of galaxies and condensation of stars, or electro-magnetic interactions binding electrons to nuclei and atoms into molecules (p. 48).

As a matter of fact, a few pages below, Morin paid homage to Heraclitus by clearly mixing, and therefore somehow equating, ancient and modern views on the “original fire.”

The cosmos was formed in a genesic fire: everything which was formed is a metamorphosis of fire. It was in the fiery Cloud that particles appeared, that nuclei were bonded. It was in the fury of fire that stars lit up and atoms were forged. The idea and the image of Heraclitian fire belching, rumbling, destructive, creative is surely that of the original chaos whence logos arises. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 54 – same idea p. 82)

Naturally, Morin used also concepts that had been elaborated only recently as the reinforcement or deterioration of a phenomenon through “retroaction,” “loop” and “positive [or negative] feedback.”

At this point we can already have the concept of positive retroaction intervene (positive feedback), which means accentuation/amplification/acceleration of a deviance itself. The constitution of the star is an increase of density which is increased by itself until the lighting, which triggers a counter-process. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 44)

Morin coined in the second edition of volume 1 (1980) the word “Chaosmos” to render this tight interrelation of chaos and cosmos (pp. 26, 53). His conclusion was again both a dismissal of classical physics and a clear homage to ancient Atomists. The current cosmic “order” and the apparently “universal and eternal laws” of physics were actually born from chaos, events, and singularities.

I will have the opportunity to illustrate this indefensible paradox in the old vision of the world: it is the singular and event-full character [Fr. événementialité] of the cosmos which is at the source of its universal laws! (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 46)

What is more, chaos, events and singularities were still currently happening. “Genesis [had] not stopped.” The universe was still “disintegrating and self-organizing in the same movement.”

Now, we must give in to new evidence. Genesis has not stopped. We are still in the expanding cloud. We are still in a universe where galaxies and suns are being formed. We are still in a universe which is disintegrating and self-organizing in the same movement. We are still in the beginning of a universe which has been dying since its birth. It is this permanent and working presence of chaos which we must make people see. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 55)

In this “Chaosmos,” space and time were not universal and homogeneous. Space, as it appeared through the lastest physics, had no unique “structure.” It was expanding, “polycentric” like a “drifting set of archipelagoes” and, therefore, could not be represented as a unique sidereal room.

The universe inherited from classical science was centered. The new universe is acentric, polycentric. [...] What constituted the armature and architecture of the universe becomes [a set of archipelagoes] adrift in a dispersion without structure. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 58, my mod.)

Similarly, time was not anymore determined and measured by the eternal functioning of the cosmos. It had become external to the universe which was therefore “dereified”—Morin said also ‘historicized” by comparison with human societies.

The old universe was a perfectly regulated watch. The new universe is an uncertain cloud. The old universe controlled and distilled time. The new universe is carried away by time: galaxies are products, moments in a contradictory becoming. [...] The new universe is dereified. This means not only that now everything is in process or transformation. It also means that the universe is simultaneously, perpetually in childbirth, in genesis, in decomposition. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 58)

Due to “the great meta-Copernican, meta-Newtonian revolution, which had been making its way subterraneanly from Carnot and Boltzmann to Planck, Bohr, Einstein, and Hubble,” there was neither “a center” of space nor “a non-equivocal axis of time.”

There is no longer a center of the world, be it the earth, the sun, the galaxy, a group of galaxies. There is no longer a non-equivocal axis of time, but a double, antagonistic process stemming from the same and only process. The universe is, therefore, simultaneously polycentric, acentric, decentric, disseminated, diasporating... (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 80)

The “universal order” was therefore not any longer universal. It was not “stretching out boundlessly in time and space” but had been born “in time” and “sandwiched in space.” However, if it was not any more “an absolute,” it had become “capable of development.”

Universal order, stretching out boundlessly in time and space, has henceforth been born in time, sandwiched in space between micro-physical chaos and diasapora. It is no longer general, but provincial. It is no longer unalterable, but degradable. Nevertheless, if it loses as an absolute, it gains as a process [Fr. devenir]. It is capable of development. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 73)

Like Serres, Morin thus opposed two physical paradigms supported by two ontological options that had fought against each other ever since the Antiquity. Classical modern physics, he asserted, had based itself on classical Greek thought, ie. on Plato and Aristotle, but the latter had forgotten Heraclitus and wrongly opposed Hubris (irrational excess, madness) and Dike (law, moderation, and equilibrium) (p. 57). Contrary to Serres, though, Morin did not insist on the ancient opposite view, common until the 1^st century BC, which based science on a fluid perspective but compared the world not with fire but with water. Surprisingly, he quoted Lucretius only twice in the whole book (pp. 29, 385).

Anyway, the physical nature of the world was not that described by classical physics; it was not “perpetual order, moderation, equilibrium.” On the contrary, it was composed of “irreversible movements, order mixed with disorder, expenditure, waste, imbalance.”

We must change worlds [nous devons changer de monde]. The universe inherited from Kepler, Galileo, Copernicus, Newton, Laplace was a cold, chilling universe of celestial spheres, perpetual order, of moderation, equilibrium. We must swap it for the warm universe of a flaming cloud, balls of fire, irreversible movements, of order mixed with disorder, of expenditure, waste, imbalance. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 58)

Next chapter

[1] The whole work has been republished in French in 2008 with a new preface.

Edgar Morin and the Rhuthmoi of Nature – Part 2

Pascal Michon — 2020-02-02T10:00:00Z

Sommaire

Previous chapter

Modern Rhuthmic Theory of Becoming

Morin envisaged then the vexing theoretical problems raised by both these new ontology and new physics. What kind of concept would enable us to grasp the essentially temporal reality they were referring to? As a matter of fact, they obliged us to make “the most contradictory terms to cling together” with the danger of falling into sheer “mysticism.”

The old universe settled down into clear and distinct concepts of Determinism, Law, Being. The new universe isolates concepts, outstrips them, shatters them, obliges the most contradictory terms to cling together, in a mystic unity, without nonetheless losing their contradictions. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 58)

In order to rationally address the problem, Morin argued, we could however capitalize on the recent substitution by Prigogine of the cosmological conceptions concentrating only on entropy, as sheer loss of energy and disorganization, with more positive conceptions closely associating entropy and constructive organization, which were comparable with the two sides of the same coin (p. 67). As already noticed, Prigogine showed that entropy was not the only law to be taken into account, because there had been disorder before organization, which, consequently, was not the initial state. As a result, disorganization and organization had to be considered as parts in the same loop.

One sees that the second law considered order and organization as initial states because it did not know the preceding sequence: disorder → interaction → order/organization → disorder. [...] If there is a beginning (catastrophe), it carries in itself in an indistinct way, with its disorder, the law of order and the potentiality to organize, and cosmic history begins with the turning of the “tetralogical loop.” Thus, the law of cosmophysics is this very loop, and the sequence of the second law is inscribed in fact in the tetralogical loop, enriching and completing it. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 68)

This thread of reasoning resulted in a plain rhuthmic model of the becoming based on a succession of loops or, more accurately, on “an irreversibly spiraloid circuit” linking disorder to order and organization, and vice versa.

It is a matter, therefore, of an irreversibly spiraloid circuit, produced by the original thermic catastrophe, and which does not cease to take shape through the relation disorder/order/organization. [...] a) disorder produces order and organization (from initial constraints and interactions); b) order and organization produce disorder (from transformations). (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 69)

While, due to the second principle of thermodynamics, order was always subjected to decay, disordering and loss, disorder also acted as “a carpenter” [il est aussi charpentier] being “active everywhere.”

In fact, cosmogenesis shows us that disorder is not only dispersion, froth, slaver, and dust from the world in gestation; it is also carpentry [il est aussi charpentier]. The universe was not built only despite disorder, it was also built in and by disorder. [...] Disorder is active everywhere. It permits (fluctuations), nourishes (encounters) the constitution and the development of organized phenomena. It co-organizes and disorganizes alternately and simultaneously. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 71)

Morin formalized his model of becoming, which accompanied his ontological and physical model of “chaosmos,” with what he called “the tetralogical loop,” that is a loop linking disorder, interactions, order, and organization together.

The tetralogical loop signifies that interactions are inconceivable without disorder, that is to say without inequalities, turbulences, agitations, etc., which provoke encounters. It signifies that order and organization are inconceivable without interactions. No body, no object can be conceived outside of the interactions which have constituted it, and of the interactions in which it necessarily participates. [...] It signifies that the concepts of order and organization develop only in function of one another. Order develops only when organization creates its own determinism and makes it reign over its environment. [...] Organization needs principles of order intervening across the interactions which constitute it. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 52-53)

To describe this temporal logic Morin preferred the term “dialogic” to that of “dialectic” which he considered as a mere phenomenal expression of a deeper principle.

We need, then, a fundamental linking of the notions of order and disorder within the “tetralogue” disorder/interactions/order/organization. The fundamental linking must be of dialogic nature. I will be able to really define this term only later (v.2, ch.7); let us say here that dialogic signifies the symbiotic unity of two logics, which simultaneously nourish each other, compete against each other, live off each other, oppose and combat each other to death. I say dialogic, not to put aside the idea of dialectic, but to have it derive from it. The dialectic of order and disorder is situated at the level of phenomena; the idea of dialogic is situated at the level of principle, and already I am daring to promote it (but I will be able to demonstrate it only much later, in v.3) to the level of paradigm. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 77)

Another reason for rejecting dialectic was the domination of synthesis and ternary logic in the dialectic model since Hegel, whereas recent physics showed only permanent and endless opposition between a bunch of opposite principles with no synthesis sequence to reconcile them. Since there never were syntheses or moments of rests—as Simondon and Deleuze who underlined the necessity “to start from the middle”—Morin advocated starting “from the genesic, from chaos, namely, from the tetralogical loop.”

Given this, one can envisage a theory. It would start, not from zero, nor from the initial “point,” but from the genesic, from chaos, namely, from the tetralogical loop. It should not rest on order or disorder as on an ontological or transcendent pillar, but produce correlatively the notions of order, disorder, and organization. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 78)

This resulted in reintroducing “event-ness” or “happenings” into physics. Whereas the paradigm of classical science—“there is no science except science of the general”—obliged us to disregard singularity, the new physics was based both on an original “Happening” and on “cascades of happenings”—as if physics had been entirely historicized.

The old universe had no singularity in its obedience to general laws, it had no event-ness [Fr. évémentialité] in its repetitive clockwork movements, no play in its inflexible determinism... The Universe which is born here is singular even in its general character. [...] This universe a-borning [cet univers naissant] is born in Happening and is generated in cascades of happenings. Happenings, triply excommunicated by classical science (since it was simultaneously singular, aleatory, and concrete), re-enters by the cosmic front door. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 81)

In the general conclusion of the book, Morin underlined again the fundamental “event-ness” or “temporality” of the universe. Interestingly, in this instance, he cited Whitehead's philosophy of process.

The universe produces its general laws from its own particularity. It is an enriched universe: matter is not the ultimate essence of this universe, it is an aspect, which takes on consistency with organization. It is a reanimated universe, moving, acting, transforming, becoming. There is nothing in the universe which is not temporal; there is no element whatsoever, from the particle to the most stable component of a stable system, which cannot be conceived of as event, that is to say as something which happens, is transformed, disappears. The cosmos itself is an Event, which continues its course in cascades of events in which particles arose, atoms were formed, in which suns light up, stars die, life is born. All active organization is an interlacing of events which disorganize and reorganize. Communicational/ informational organization is made up of only of events which it produces, captures, utilizes, resurrects... Event, as Whitehead says, is the [unit] of real things. It is the concrete [unit] which nature gives, not the abstract [unit] which measurement gives. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 375-376, my mod.)

Moreover, whereas classical physics had considered time as “reversible,” in the sense that any given physical phenomenon could always be undone and taken back to its initial state, the new physics introduced the idea that time was actually “irreversible” since the things populating the universe as well as the universe itself could not be taken back to their initial states. “Everything was born” and “Matter ha[d] a history.” A few pages below: “There is an evolution of matter” (p. 134).

Physical order was unaware of the irreversibility of time until the second law of thermodynamics. Cosmic order was unaware of the irreversibility of time until 1965, when the universe entered into becoming. The eternity of the Laws of Nature was thus liquidated. There is no more frozen physis. Everything was born, everything appeared, everything began, once upon a time. Matter has a history. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 81)

Yet, this history should not be conceived in a neo-idealist way. Morin noticed that “the favorable hypothesis” suggested by the philosopher and Jesuit priest Pierre Teilhard de Chardin (1881-1955) according to which the universe developed its own richness only in an ascensional way, was one-sided and incomplete. Actually, order and organization had occurred, and still occurred, at a tremendously expensive cost. “Destruction and dispersion,” “fruitless expenses” and “useless agitations” were largely dominant features of the universe, while organization was utterly exceptional.

There is hemorrhage, waste, mess of which we must be conscious. The encounters produce more destruction and dispersion than organization. To constitute an organization, erect an order, keep a life alive, so many “useless” agitations, so many “fruitless” expenses, so many squandered energies, so many dispersive hemorrhages are needed! (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 83)

In fact, both kinds of history, the dispersive one derived from the second law of thermodynamics, and the ascensional one inspired by biological evolution, should be thought of as belonging to the same physical reality. The two perspectives, which were both born around the middle of the 19^th century, should be associated.

Now, each of these two times had arisen at the same moment, in the middle of the nineteenth century. The first, that of the second law, drew physis toward degradation, the first rumble announcing the great cosmic diaspora. The second, on the contrary, was that of ascensional evolution, or progress. It had penetrated society since 1789 and burst upon biology. (Darwin. The Origin of Species. 1859) But biological time was going inversely to entropic time, and as they had each arisen in a sphere hermetically closed to the other. [...] Now, we can finally break the schizophrenia between these two times which are unaware of and flee each other. They are simultaneously one, complementary, concurrent, and antagonistic. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 84)

As we shall see, the existence of “organizations,” biological as well as physical, was based simultaneously on stabilizing cycles and loops, irreversible transformations, and unexpected events. This meant that the historical time of the universe was in fact, as in Bachelard's view, “syncretic” or “complex” (p. 83).

To this already very complex time, we will have to integrate, when we examine the problem of organization, the time of reiterations, repetitions, loops, cycles, repeated beginnings, and we will see that these repetitive times are nourished and contaminated by irreversible time (cf. Part II, ch.2), just as they are perturbed by event-full time: their movement is always spiraloid and always subject to the risk of rupture... The great time of Becoming is syncretic. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 84)

Later in the book (part 2, chap. 2, sec. IV), Morin elaborated further this first view with a few considerations drawn from what he called the “fundamental dynamism” of the cosmos and its population by “active organizations.” Contrary to what most philosophers claimed, he first noticed, time was not only an incessant irreversible flow. It contained both the notion of passing and that of recursion. It was both “sequential” and “looping,” “irreversible and circular.”

Time is part of the internal definition of all active organization. Activity is clearly a phenomenon in time. But time, from the moment it introduces itself into active organization, becomes bifid, dissociates itself at entry into two times without ceasing to remain the same time and finds itself again at exit. It is sequential time, which in fact imbues and pervades the system, and it is the time of the loop which recloses on itself. This is to say that time is doubly part of the definition of active organization since it is both irreversible and circular time. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 213)

The result of this double movement was not any longer linear but “spiral-like.”

The unity of this double yet single time, associated yet dissociated, is like spiral movement, simultaneously irreversible and circular, returning on itself, biting its tail, closing itself up continuously in its re-opening, re-beginning itself continuously in its flow. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 214)

Second, Morin emphasized, this double “spiral time” was constantly interrupted by “accidents, perturbations, lapses,” i.e. “chopped up by a thousand small, worrisome events.”

This spiral time is fragile because it is tied to physical improbability and because it is at the mercy of ecological dependence. It is not the time of clockwork rigor [...] The time of the regenerative loop knows accidents, perturbations, lapses, which continuously threaten being and existence. This is to say that spiral time hauls in itself event-full [Fr. événementiel] time. It is chopped up by a thousand small, worrisome events. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 214)

Morin's conclusion was thus the same as in the first part of the book when he referred to a “syncretic” or “complex” time of Becoming. These three forms constituted “complementary, concurrent, and antagonistic times,” which together formed “the Time of life” (p. 215). In living beings, but also in societies, this complex structure of time appeared from the play between: 1. internal degradation and disorganization, aphazard external perturbations; 2. negative retroactions, regulation, intended to cope with these disorganizations and perturbations; 3. positive retroactions (accentuation, amplification, acceleration of a process by itself on itself) which could “play a genesic role.”

We are going to see that, in the biological sphere, and especially in the anthropo-social sphere, positive retroaction, while remaining disorganizing but also because it is disorganizing, can play a genesic role, namely create diversity, newness, complexity. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 218)

In the general conclusion of the book, Morin came back once more to this view. Time was not sheer “degradation, progress, sequence nor perpetual cycle” but “rich and complex” which meant “complementary, concurrent, and antagonistic.”

The universe of old physics could not cope with time, or rather, time could bring it nothing but degradation. The new universe is consubstantial with a rich and complex time: it is neither the simple time of degradation, nor the simple time of progress, nor the simple time of sequence, nor the simple time of perpetual cycle. It is, in a way simultaneously complementary, concurrent, and antagonistic, all of these diverse times, while still remaining the Same. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 376)

Modern Rhuthmic Theory of Individuation

As we saw, Morin's theory of becoming culminated in a theory of individuation he called “organization.” Disorder allowed interactions, which allowed in turn the emergence of local pockets of order and organization. The organizations, i.e. the beings, the existing things, were thus based both on a certain internal order “intervening across the interactions which consitute[d] [them]” and a certain external rule “over [their] environment” (p. 53). Naturally, the emergence of organizations caused in turn new disorder in the environment, which allowed new interactions, etc.

To specify what he meant by the term “organization,” Morin started from the concept of “system” as it had rapidly emerged in various sciences since the 1900s to oppose both the traditional views naively derived from architecture and the newest views based on sheer dispersion and probability. In micro-physics, he recalled, the particle lost all substance, all distinction, and was now defined only by “the interactions in which it participated,” and, when it was part of an atom, by “the interactions which [wove] the organization of this atom” (p. 95). It was “a Gordian knot of interactions and exchanges” (p. 95). Therefore, “the particles [had] the properties of the system much more than the system [had] the properties of the particles” (p. 95 – Morin's italics). The atom thus became the model of an “organized object or system.”

Since then, the atom steps forward as a new object, the organized object or system whose explanation can no longer be found solely in the nature of its elementary components, but is found also in its organizational and systemic nature, which transforms the characteristics of the components. [...] we see that the universe is founded, not on an indivisible unity but on a complex system! (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 95)

The same revolution had occurred in astro-physics which did not limit itself any longer to one solar system moved by a clockwork rotation of the planets around the sun, but discovered “myriads of sun-systems, organizing sets which self-maintain[ed] by spontaneous regulations” (p. 96). Similarly, modern biology introduced the idea of system to replace both the idea of living matter and that of vital principle, that had become obsolete, and give a more satisfactory account of the cell or the organism (p. 96). Finally, right from the start, sociology considered society as a system, in the strong sense of an organizing whole irreducible to its components, the individuals (p. 96).

While the Universe itself, due to its ongoing expansion and dislocation, could certainly not be seen as a system (p. 65), the concept well applied to the innumerable “islands and archipelagoes” that had formed ever since the big bang, including living organisms and human societies. The universe was “an astonishing architecture of systems.”

All the key objects of physics, biology, sociology, astronomy, atoms, molecules, cells, organisms, societies, stars, and galaxies constitute systems. Outside systems, there is only particle dispersion. Our organized world is an archipelago of systems in the ocean of disorder. All that was object has become system. All that was even an elementary unit, including and especially the atom, has become system. We find in nature masses, aggregates of systems, unorganized flows of organized objects. But what is remarkable is the polysystemic character of the organized universe. The latter is an astonishing architecture of systems built one on the other, one between the other, one against the other, implicating and dovetailing one with the other, in a grand game of masses, plasmas, fluids of micro-systems circulating, floating, enveloping the architectures of systems. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 96)

Similarly, “Nature” constituted an “extraordinary solidarity of mortised systems.”

The phenomenon is what we call Nature, which is nothing but extraordinary solidarity of mortised systems [systèmes enchevêtrés – entangled] building one on the other, by the other, with the other, against the other: Nature is systems of systems in chaplets, clusters, polyps, bushes, archipelagoes. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 97, my mod. – same idea p. 107)

According to Morin, systemic phenomena had thus become evident everywhere during the 20^th century, but the concept of system itself had not been satisfactorily elaborated. Even Ludwig von Bertalanffy (1901-1972) in his General System Theory: Foundations, Development, Applications (1968) had not gone far enough. The biologist had rightly chosen holism over reductionism, but he had not pursued the paradoxical nature of complex unity. We had to go even beyond holism and reach to the organizational circuit.

Quite remarkably, Morin then referred to Ferdinand de Saussure's definition in his Course in General Linguistic (notes from 1906 to 1911 published in 1916) as one of the best and the earliest one, since it introduced for the first time the idea of organization. We must here give credit to Morin to have recognized, against most of his contemporaries including deconstructionists, that Saussure was not a “structuralist” but a “systematist” and to, consequently, have half-opened a path between his own implicitly rhuthmic theory of complexity and the explicitly rhuthmic theory of language that was emerging since the 1950s with Benveniste and more recently Meschonnic, as we will see in another chapter.

Finally, the definition of Ferdinand de Saussure (who was a systematist rather that a structuralist) is particularly well articulated and evokes [fait surgir – brings out] especially the concept of organization by linking it to that of totality and interrelation: the system is “an organized totality, made up of interdependent elements holding together and not able to be defined except one by the other in function of their place in this totality.” (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 99, my mod.)

Limited to the sub-concepts of totality and interrelation, the concept of system was insufficient, though. It had to be enriched with that of organization, that is to be dynamized and endowed with a genuinely generative aspect.

In fact, it is not sufficient to associate interrelation and totality; one must tie totality to interrelation by the idea of organization. In other words, as soon as the interrelations between elements, events, or individuals have a regular or stable character, they become organizational and constitute [a “whole” – un tout]. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 99, my mod.)

Whereas a system was merely a “global organized unity of interrelations between elements, actions, or individuals” (p. 99, my trans.), the organization was the “arrangement of these interrelations” which “produced and reproduced” the system. The organization was a self-organizing unity.

Organization is the arrangement of relations between components or individuals which produces a complex unity or system, endowed with qualities unknown at the level of components or individuals. Organization interrelationally ties [note: by fixed and rigid dependences, by active interrelations or organizational interactions, by regulatory retroactions, by informational communications] diverse elements, events, or individuals which henceforth become the components of a whole. It assures relative solidarity and solidity to these ties, thus assures the system a certain possibility of duration despite chance perturbations. Organization, therefore: transforms, produces, binds, maintains. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 101)

However, Morin did not want to hierarchize the two concepts which had to be thought of as parts in the same loop, which moreover should include that of interrelations.

My aim here is to associate them, since system is the phenomenal and global character which interrelations take, whose arrangement constitutes the organization of the system. The two concepts are tied by that of interrelations: any interrelation endowed with some stability or regularity takes on an organizational character and produces a system. There is, therefore, a circular reciprocity among these three terms: interrelation, organization, system. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 101)

In order to clarify, as much as possible, the functioning of this loop, Morin elaborated in the following sections the concept of “unitas multiplex” or “organized complex unity” (p. 102-112).

The fact that a system was made up of elements linked to each other through an organization that regulated their interactions resulted, first, in a series of positive consequences. The arrangement produced the “emergence” of new properties at the level of the whole as well as of the parts.

We can call emergences the qualities or properties of a system which present a character of newness in respect to the qualities or properties of the constituents considered separately or arranged differently in another type of system. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 103-104)

The concept of “emergence” was important since it denoted, simultaneously, the production of radically new beings or properties, that is some sort of “events” (p. 105), and some degrees of tiering within each system, “the emergent qualities rise one on the other, the heads of some becoming the feet of others” (p. 108).

On the one hand, whether for atoms, molecules, or human societies, “the whole was always more than the sum of its parts” (p. 103). Quoting from Serres, Morin underlined the significance of the phenomenon of emergence for understanding the nature of no less than matter, life, language, and humankind. He also alluded, a few pages below, to “consciousness” (p. 108).

It is quite remarkable that the apparently elementary notions that are matter, life, meaning, humanity, correspond in fact to the emergent qualities of systems. (Serres, 1976, p. 276) (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 104)

But on the other hand, the parts were also much more than isolated parts. They were transformed and enriched by their existence within the whole. Individual aptitudes for “language, craftsmanship, and art,” for instance, were the result of positive retroaction of the whole upon the parts.

In human society, with the constitution of culture, individuals develop their aptitudes for language, craftsmanship, art, that is to say that their richest individual qualities emerge within the social system. Thus, we see systems where macro-emergences retroact as micro-emergences on the parts. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 105)

However, Morin was very critical of the substitution of a certain “reductionist blindness (which sees only the constitutive elements)” with a no less limiting “holistic blinding (which sees only the whole)” (p. 109). He particularly targeted here von Bertalanffy whom he reproached for not seeing clearly the central role of organization and complexity in systems.

Systems theory has reacted to reductionism, in and by “holism” or the idea of the “whole.” But, believing to go beyond reductionism, holism has in fact brought about a reduction on the whole: whence, not only its blindness on the parts insofar as parts, but its myopia on organization insofar as organization, its ignorance of the complexity at the heart of global unity. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 110)

Similarly as strict individualist methods, strict holism had to be overcome. In fact, systems induced also negative consequences. Each particular arrangement imposed new “constraints” and caused losses in the whole as much as in the parts.

The internal determinism, the roles, the regularities, the subordination of components to the whole, the adjustment of the complementaries, the specializations, the retroaction of the whole, the stability of the whole, and, in living systems, the mechanisms of regulation and control, systemic order in a word, are translated into so many constraints. Every association implies constraints: constraints exercised by parts interdependent one on the other, constraints of the parts on the whole, constraints of the whole on the parts. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 110)

So, a system was a “complex unity” where components were held together while remaining distinct by their function, but also abandoning themselves to the organization to ensure their sustainability. The system was only viable if the parts enjoyed sufficient room for their own action but also if the gregarious forces were stronger than the dissipative forces. It was thus based on tense loops linking its various levels or on active antagonisms.

Every system whose organization is active is in fact a system where antagonisms are active. Regulations suppose a minimum of antagonisms on guard [qu'elles refoulent – that they repress]. Retroaction which maintains the constancy of a system or regulates a performance is called negative (negative feed-back), a very enlightening term: triggered by the variation of an element, it tends to annul this variation. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 118, my mod.)

Actually the systemic constraints were so powerful that they resulted in the repression of important characters which remained obscure but always capable to reemerge if the opportunity was given to them. This was, Morin commented, the lesson given by Marx and Freud concerning the social and psychic unconscious (p. 125).

While emergences develop into phenomenal qualities of systems, organizational constraints immerge in a world of silence the characters inhibited, repressed, compressed at the level of parts. Every system includes, thus, its immerged, secret, obscure zone where suppressed virtualities stir. The duality between the immerged and the emergent, the virtualized and the actualized, the repressed and the expressed is a source of scissions and dissociations in great living and social polysystems. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 124, my mod.)

But the role of constraints entailed also a second characteristic. There were naturally various degrees of complexity from the lowest in “crystal groups,” mobilizing only similar and distinct components, to the highest in “living organisms,” composed of “billions of cells which remain differentiated, diversified, and individualized (possessing organizing autonomy)” (p. 113). Thus, every increase in complexity implied “an increase in variety” as much as “a more supple and complex direction” based, for instance, “on inter-communication and not on coercion.”

As I see it, every increase in complexity is translated by an increase in variety within a system; this increase, which tends to dispersion in the type of organization where it is produced, requires thenceforth a transformation of organization in a more supple and complex direction. The development of complexity requires, therefore, both a greater richness in diversity and a greater richness in unity (which will be founded for example on inter-communication and not on coercion). (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 114)

Morin's conclusion concerning the concepts of system and organization could be, once again, compared to Lucretius' theory of individuation, despite the time distance. Quite like, according to Lucretius, a building could stand and resist decay because of the tiny angles its apparently straight architecture was based on, systems could persist in their being thanks to the active antagonisms they were, so to speak, riding. Just as Lucretius' “building” was a dynamic cone where myriads of contrary fluxes reached for a time equilibrium, Morin's “organized complex system” was based on active internal looping antagonisms. This meant, based on the latest science, reactualizing the peculiar concept of equilibrium by disequilibrium, which, one remembers, allowed Lucretius to bridge the divide between Heraclitus and Parmenides, between flow and form, without depending for individuation on Plato's solution by “participation to ideal Forms.”

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Edgar Morin and the Rhuthmoi of Nature – Part 3

Pascal Michon — 2020-02-02T09:30:00Z

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Modern Rhuthmic Theory of Knowledge

As Lucretius, Morin finally proposed, at the end of the first part of his book, a theory of knowledge. Not unlike his forebear, who based his own theory on the association between passive perception of fluxes of infinitesimal simulacra and active recognition of the shapes they enveloped, he based his knowledge theory on a cross-involvement between “system perception” and “system conception.” What was new, however, besides the concept of system, was the use of the concept of loop to formalize this cross-involvement.

Against both “naive realism which takes a system as a real object” and “naive nominalism which takes a system for an ideal schema,” and their respective elimination of the subject or the object (p. 140), Morin proposed to associate them through a recurrent circuit going from “the observed system” to “the observer-system” and back.

Thus, the observation and the study of a system link physical organization and the organization of ideas to each other in systemic terms. The observed system, and consequently the organized physis of which it is a part, and the observer-system, and consequently the anthropo-social organization of which it is a part, become interrelationed in a critical manner: the observer is also a part of the definition of the observed system, and the observed system is also a part of the intellect and culture of the observer-system. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 141, my mod.)

Morin here alluded to the possibility to establish by this circular or, better, spiraloid process a “new systemic totality” which could become “a metasystem in reference to both.” But he immediately added, recognizing that this perspective was remote, “if it is possible however to find the meta-point of view.”

The new systemic totality which is constituted by associating the system-observed and the observer-system can, thenceforth, become metasystem in reference to both, if it is possible however to find the meta-point of view, which allows us to observe the set constituted by the observer and his observation. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 141, my mod.)

In his introduction, the translator Joseph Lucien Roland Bélanger (1925-2010), a Marist catholic priest, compared many times Morin's materialist evolutionism, quite wrongly as a matter of fact, to Teilhard de Chardin's grand evolutionism, but he was closer to the truth concerning his theory of knowledge.

Although Morin did not know anything about hermeneutics, Bélanger noticed, he was in fact close to the conclusions reached recently, on Heideggerian ontological basis, by Hans-Georg Gadamer (1900-2002). Wahrheit und Methode – Truth and Method had been published in German in 1960 and translated into French in 1976. We could add that he was even closer, as we will see, to the conclusions reached, on more philological basis, by Friedrich Schleiermacher (1768-1834) at the beginning of the 19^th century.

To put it in a nutshell, according to hermeneutics theoreticians, interpretation, whether of the Being or, less speculatively, of the Bible, needed constant loopings between the Dasein's or reader's “interpretations” and the “answers” given by the Being or the Text. The Cartesian “Method,” with its linear chains of reasons, had to be replaced by the back-and-forth of a “conversation” or by a spiraloid approach to “Truth.”

We must not give in to simplifications like idealizing or rationalizing or standardizing. There can be no linearity, only the spiral. [NN21f] Though there is no forthright mention at this point of two of the most prominent philosophical theorists of knowledge in our time, Michel Foucault or Hans Georg Gadamer, Morin clearly, in his categorical rejection of a dichotomy between object and subject, stands against Foucaldian “archeology” and for Gadamerian hermeneutics. (Translator's Introduction, J.-L. Roland Bélanger, in Method, 1992, p. xx)

However, because he speculated from a poor concept of language limited by his prioritarily ontological reflection, Gadamer concluded that since human understanding was part of inescapable loops, it allowed no exterior and overlooking viewpoint to emerge and that absolute truth was therefore unreachable. All knowledge was subjective or, at least, supported by grand collective movements of meaning that Gadamer called Wirkungsgeschichte – Effective History. As Bélanger recalled, for Gadamer, “understanding is always an interpretation” (quoted p. xxix) (on Gadamer's limitations, see Michon, 2000 and 2010a, chap. 7). And it is true that Morin sometimes indulged in this new sophisticated kind of deconstruction of science. In a following section dedicated to information, he wrote for instance, as Bélanger rightly noticed: “The real takes on substance, form, and meaning only under the form of messages which an observer/conceiver interprets. We have only translations of reality, never the original version [jamais la v.o.]” (p. 363).

Nevertheless, Morin also affirmed the possibility of finding a “meta-systemic point of view” that could bridge “the polysystemic group constituted by the conceiver-subject and his anthropo-social grounding,” and “the polysystemic group constituted by the object-system and its physical grounding.” He never accepted sheer subjectivism nor relativism, and he would have been very much opposed—had he known about it—to the subtle version lately proposed by Gadamer under the cloak of a radically temporalized ontology.

We can and must also go beyond in the search for a meta-systemic point of view: we can no longer escape the key epistemological problem which is the relation between, on one hand the polysystemic group constituted by the conceiver-subject and his anthropo-social grounding, on the other hand the polysystemic group constituted by the object-system and its physical grounding. Henceforth, it is a question of elaborating the meta-system of reference from which we might embrace simultaneously both groups which could communicate and interorganize therein. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 142)

If Morin's theory of knowledge shared some features with hermeneutics, it was rather with Schleiermacher's brand, who had, thanks to his philological approach and despite he was living at the beginning of the 19^th century, a much more precise and accurate knowledge of language than Gadamer, who in his book rarely talked of literature and knew nothing about modern linguistics. Whereas Gadamer, when describing the relation between Dasein and Being, used the term “conversation” as a vague metaphor, Schleiermacher used it, to describe his relation to the Bible text, in a much more proper sense as intertwining of two discourses.

As Schleiermacher who believed that modern readers could rightly understand the Bible, provided they read it carefully and recursively, because they share with ancient writers the same language capacity endowed by God, Morin thought that “the organizing retroaction of our anthropo-social understanding on the physical world,” i.e. progressive adequation between scientific discourse and physis, was made possible by their “preliminary organizational homology,” i.e. their similar systemic nature, based on their common evolutionary history.

The systemic articulation which is established between the anthropo-social universe and the physical universe, via the concept of system, suggests to us that an organizational character is fundamentally common to all systems. The possibility of posing, in systemic terms, the organization of physis as well as the organization of knowledge, supposes a preliminary organizational homology. This homology would allow the organizing retroaction of our anthropo-social understanding on the physical world, an understanding which has come about by evolution. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 142)

Thus, the concept of system, reshuffled through the concepts of interrelation, organization, loop between parts and whole, and antagonism, was an evolutionary universal mediator between physical, living, and human spheres, which allowed true knowledge.

[It is] a reading guide for all phenomena of physical, biological, anthropological, ideological, organization, including the theoretical system which I am beginning to elaborate here. This pilot-definition, concerning the common denominator of everything organized, has, therefore, universal value. System is, therefore, conceived here as the basic complex concept concerning organization. It is, if we may say so, the most simple complex concept. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 147-148)

Much further down in the book, Morin elaborated further this idea. World and mind were not opposed but were actually involved in a permanent loop.

This rotation leads us to physicalize our notions, then to socialize them, then to rephysica1ize them, then to resocialize them, then to rephysicalize them, then to resocialize them, and so on ad infinitum. It seems to us that this is not a vicious circle, but a productive praxis. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 288)

Rather than pose the problem in terms of the alternative idea/matter, we can attempt to bind these two antagonistic propositions in a loop: physical configurations – symbolic configurations. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 366)

The spiraloid movement of knowledge between observer and world, which forbid any “reflection” theory, resulted however in “a possible correspondence and translation” between the “physical play” of matter and the “psychic play,” that is two fluxes: that of the world and that of the thought.

In order to understand the correspondence between the organization of knowledge [Fr. connaissance] and the knowledge [Fr. connaissance] of organization, [...] it is no longer a matter of looking for the “reflection” of the real in the mind of the observer, nor for the “reflection” of the mind in the real: the organization of knowledge [Fr. connaissance] is perhaps a translation of, but not the “reflection” of, physical organization. This principle of equivalence can only be truly conceived if we conceive physis according to the fundamental “tetralogical” relation disorder/interaction/order/organization. From that moment on, there is a possible correspondence and translation between the physical [play]: disorder/interaction/order/organization (physical) and the psychic [play]: noise/information/redundancy/organization (psychic). (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, pp. 359-360, my mod.)

This possible correspondence between the two fluxes, psychic and physical, was actually allowed by their common temporal organization or their common way of flowing. Both, Morin claimed, were involving the same chain of basic elements—noise corresponded to disorder, redundancy to order, information to play of interaction, theories to organization—and the same kind of concatenation.

Thus, for the observer, noise is ignorance psychically (and thereby unknown, mysterious) and disorder physically; for the observer, redundancy is certainty psychically and order physically (invariance, law, repetition, pattern, regularity, stability); for the observer, information is knowledge [Fr. savoir] psychically acquired from events, understanding [Fr. connaissance] extracted from noise, and it is physically the event-full and diversely haphazard play of the interactions. And, just as physical play finds and produces its organization in physical systems, psychic play finds and produces its organization in theoretical systems. Just as there are, in the physical tetralogue, unceasing permutations and transformations (organization in disorder, disorder in organization, etc.) so in the tetralogue of ideas, noise/redundancy/information/systems, there are permutations and transformations: information is born from interactions between organization and noise, gives birth to redundancy at the heart of an ad hoc organization, dies in noise like this organization itself. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 360)

Knowledge was thus progressing through the “redistribution of redundancy, of information, of noise” (p. 360) but, due to the laws revealed by Brillouin, “an exhaustive observation [would] necessitate infinite information, which [would] necessitate infinite energy” (p. 362). This resulted in limiting human knowledge based not any more on the structure of subjectivity, as for Kant, but on the relation between the information and the energy that was needed to produce it.

Knowledge [Fr. connaissance] carried to the absolute is self-destructive. This proposition holds for every observation, every science, concerning every object, every phenomenon, every being, and of course, the universe as a whole. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 363)

Modern Rhuthmic Theory of Form

This leads us, finally, to Morin's theory of form. Unsurprisingly, as Lucretius and Serres, he explicitly rejected both Platonic and Aristotelian theories. Forms were not “essences” nor “mold[s] sculpturing the identity of the objects from the outside” (same idea p. 369). Forms were the “totality of the complex organized unit” once “manifested phenomenally” as a whole “in time and space.”

The object is no longer an essence-form and/or a substance-matter. There is no longer any form mold which sculptures the identity of the object from the outside. The idea of form is preserved, but transformed: form is the totality of the complex organized unit which is manifested phenomenally insofar as whole in time and space. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 121)

As both Lucretius and Serres, Morin conceived of form as product of processes of individuation based on the interaction of the internal dynamism of a particular complex unit and the constraints of its environment. No longer “essence,” form became “an idea of existence and organization.”

The Gestalt form is the product of catastrophes, of interrelations/interactions between elements, of internal organization, of the conditions, pressures, constraints of the environment. Form ceases to be an idea of essence in order to become an idea of existence and organization. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 121)

Form was therefore a byproduct of organization both as a “morphogenetic” process, transforming “a discrete diversity into a global form (Gestalt),” and as a “morphostatic” functioning, an “ordering principle which insure[d] permanence.”

Organization is both transformation and formation (morphogenesis). It is really a matter of transformations: elements transformed into the parts of a whole lose some qualities and gain new ones; organization transforms a discrete diversity into a global form (Gestalt). It creates a continuum—the interrelationed whole—where there was the discontinuous; thereby it brings about a change of form: it forms (a whole) starting from the transformation (of the elements). It is really a matter of morphogenesis: organization gives form, in space and time, to a new reality: complex unity or system. [...] Organization is, at the same time, the ordering principle which insures permanence. Permanence in the being of atoms, molecules, heavenly bodies does not correspond to inertia but to active organization. Organization is morphostatic: it maintains the permanence of the system in its form (Gestalt), its existence, its identity. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 128)

But that was not all. Actually, this initial description was valid only for “closed systems,” that is, the rare ones that did not effect exchanges with the outside. Yet, most were “open systems” which effected material, energetic and/or informational exchanges with the outside. Consequently, the concept had to be completed to fit this complex situation: form was thus the result of the looping interactions between morphogenetic process and morphostatic functioning, on the one hand, and, on the other hand, the environment dynamics. It thus resulted from a relentless “re-form” activity. In other words, in those cases, the form was properly in a fluid state. Although it maintained a certain consistency, it was ceaselessly “re-forming.”

Active organizations of systems called open insure the exchanges, the transformations which nourish and effect their own survival: the opening allows them to ceaselessly [re-form] themselves [à se re-former sans cesse]; they are [re-formed] [ils se re-forment] by closing, by multiple loops, negative retroactions, recursive uninterrupted cycles. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 133, my mod.)

Morin was here very close to the ancient idea of rhuthmos as “particular manner of flowing.” Each system had a specific form that was actually determined by its randomly acquired specific way to re-produce itself through its exchanges with the environment, a way that Morin called, for the time being, “qualities,” and that he was soon to call “self of the system.”

We must also, given the improbability and ever greater fragility of what becomes complex, understand evolution starting from the consolidation of fragility and improbability in and by organizational order, in and by the acquisition of emergent qualities (among them, more subtle organizational qualities, more and more apt to resolve phenomenal problems), in and by the aptitude to form organizational relations with other systems. Thus, the universe of organization, born by chance encounters, is maintained by order, necessity, but also qualities, making what otherwise should have been dissolved and dispersed survive and perdure. (Method, vol. 1, 1977, trans. J.-L. Roland Bélanger, 1992, p. 135)

On the whole, Morin's theory of knowledge and theory of form were consistent with his ontology, his physics, his model of becoming, and his theory of individuation: they were de facto rhuthmic theories based, as all other parts of his thought, on “recurrent spiraloid loops.” But they only indirectly alluded to “specific ways of flowing” whose concept was not yet completely elaborated. Contrary to Serres', the concept of rhuthmos was absent of his reflection. Remarkably, though, Morin did not stop at these first conclusions. He developed a full theory of “dynamic organization” that was his particular way of addressing the very same issue. Let us see now how far he went in this direction.

As the reader may have noticed, up to now Morin's reflection covered exactly the same subjects as Serres'—and it is not merely an artifact of my presentation. Moreover, his perspective was often very close, if not similar, to the Ancient materialist thought brilliantly revealed by Serres. For both reasons, we may legitimately consider Morin not only as a member of the rhythmic constellation of the 1970s-1980s but also as one of the most articulate contributors to an emerging rhuthmic worldview. Probably without realizing it, Morin was part of a powerful but unnoticed trend.

Next chapter

Michel Serres and the Rhuthmoi of the Flow – Part 1

Pascal Michon — 2019-12-22T06:00:00Z

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Michel Serres (1930-2019), who had made, in the 1960s, the acquaintance of Foucault at the Blaise-Pascal University in Clermont-Ferrand, briefly joined with him the post-1968 experimental Vincennes University, and was eventually appointed to a chair in the history of science at the Sorbonne. In 1977, he published La Naissance de la physique dans le texte de Lucrèce : fleuves et turbulences – The Birth of Physics (2000, trans. Jack Hawkes) in which he argued that the Ancients had all necessary mathematical resources to formulate an adequate picture of a flowing Nature; that their model of atomic matter was essentially a fluid one; that their most important concept was therefore that of dînos or dínê – whirl or turbulence; and, last but not least, that these concepts were direct sequels of that of rhuthmos. The recognition of these facts shed light on the subterranean relationship between the newest disciplines of chaos and complexity, and the ancient physics initiated by the first Atomists Leucippus (early 5^th century BC) and Democritus (c. 460-c. 370 BC), elaborated further by Archimedes (c. 287-c. 212 BC) and beautifully summarized in Lucretius' De rerum natura (c. 99-c. 55 BC).

Rhuthmós as Whirl?

Like Barthes, Serres cited Benveniste's study on “The concept of “rhythm” in its linguistic expression” (1951/1966) but, surprisingly, he first strongly opposed his interpretation. “The linguist,” he argued with a bit of philosophical haughtiness, had not recognized the true nature of the pre-Platonic rhuthmos, which was, according to him, a “vortex in the flow,” a form “adopted by atoms in conjunction in the first dinos.”

The linguist, like Heraclitus, Montaigne and the rest, had never sailed in fresh water. Nothing flows as they thought. Direct physical experience, simple practice, reveal the rhuthmos in the rhein, or the vortex in the flow, or the reversible in the irreversible. Rhythm is a form, yes, it is the form adopted by atoms in conjunction in the first dinos. In the beginning is the cataract, the waterfall: here is the reversibility to this irreversibility: thus rhuthmos. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 154)

This harsh and surprising critique of Benveniste's contribution was actually supported by very little evidence, if any (I will here limit myself to a rapid philological survey, for a more detailed analysis see Michon, 2018a). Michel Serres was obviously projecting posterior concepts on Democritus' atomism. “The cataract,” “the waterfall,” the “clinamen,” and the “vortex” were borrowed from Lucretius (c. 99 BC-c. 55 BC) and applied to older atomist doctrine. Theoretically speaking, this was naturally not a problem and Serres was legitimate in elaborating these concepts as he wished. But philologically, he was clearly mistaken and this came at a certain theoretical cost. All those terms were posterior even to Epicurus (341-270 BC) and probably dated back to the end of the 3^rd century BC.

The declination or clinamen is a term not found in any of Epicurus' texts that have been preserved to us. Everything leads us to believe that this term was forged and introduced by the successors of Epicurus in their polemics against the Stoic Chrysippus (ca. 280-ca. 206 BC) on destiny and liberty. (Dumont, 1991, p. 887, my trans.)

Moreover, in all the texts presenting the atomist dînos or dínê, the term rhuthmόs was utterly absent. Diogenes Laërtius (3^rd cent. AD), for instance, recalled the role played by the cosmic whirl in Leucippus' and Democritus' physics, but he never used the term rhuthmόs to name it.

The worlds are formed when atoms fall into the void and are entangled with one another [καὶ ἀλλήλοις περιπλεκομένων – kaì allêlois periplekoménôn]; and from their motion as they increase in bulk arises the substance of the stars. [...] In a given section many atoms of all manner of shapes are carried from the unlimited into the vast empty space. These collect together and form a single vortex [δίνην ἀπεργάζεσθαι μίαν – dínên apergázesthai mían], in which they jostle against each other and, circling round in every possible way, separate off, by like atoms joining like. And, the atoms being so numerous that they can no longer revolve in equilibrium, the light ones pass into the empty space outside, as if they were being winnowed; the remainder keep together and, becoming entangled, go on their circuit together, and form a primary spherical system. (Lives of Eminent Philosophers. Leucippus, 9.6-31, trans. R.D. Hicks)

The same observation could be made concerning most of the texts presenting or alluding to the atomistic primordial dînos: Aristotle (384-322 BC), Physics, 2, 4, 196a; Epicurus, (341-270 BC), Letter to Pythocles, quoted by Diogenes Laërtius, Lives, 10, 88-90 ; Diodorus Siculus (1^st cent. BC), Bibliotheca historica, I, 7 ; Aetius of Antioch (1^st or 2^nd cent. AD), Opinions of the Philosophers, 1, 4, 1-4; Sextus Empiricus (ca. 160-ca. 210 AD), Against the Mathematicians, 9, 113; Hippolytus of Rome (170-235 AD), Refutation of All Heresies, 1, 12; Simplicius (ca. 490-ca. 560). Among Latin writers, in his De rerum natura, 5, 621 sq., Lucretius (99 BC-ca. 55 BC) naturally referred many times to turbinatio but never linked it with rhythm or numerus either.

A fundamental reason why Serres was here misled is that the coming-to-be of the atomic clusters that constituted the existing cosmic bodies as the earth, the moon or the sun, were said, both by Leucippus and Democritus, to be resulting indeed of enormous rotating movements, whirls or vortices. But most of the smaller bodies were just clumping of atoms occurring by chance after shocks, disorderly bouncing and movements spreading in all directions.

This was quite clear in Aristotle's accounts of Democritus' physics. The atoms “act and suffer action wherever they chance to be in contact.” Consequently, all things “are generated by their interlocking and bouncing in all directions.”

The “many” move in the void (for there is a void): and by coming together they produce “coming-to-be,” while by separating they produce “passing-away.” Moreover, they act and suffer action wherever they chance to be in contact (for there they are not “one”), and they generate by being put together and becoming intertwined. (On Generation and Corruption, I, 8, 325a, trans. H. H. Joachim)

The primary masses, according to them [Leucippus and Democritus], are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by [their interlocking and bouncing in all directions] [συμπλοκῇ καὶ περιπλέξει – sumplokêi kaì peripléxei]. (On the Heavens, 3.4, 303a, trans. J.L. Stocks, my mod.)

Dionysius of Alexandria (190-265 AD), who as a committed Christian criticized the Atomists but did not lack accuracy, reported their belief that

these atoms, as they are borne along casually in the void, and clash all fortuitously against each other in an unregulated whirl, and become commingled one with another in a multitude of forms, enter into combination with each other, and thus gradually form this world and all objects in it. (Dionysius of Alexandria, On Nature, in Eusebius, Praepar. Evangel. 14, 23-27, trans. S.D.F. Salmond)

The stochastic nature of the atomic movements was also suggested by Simplicius' Commentary on Aristotle's On the Heavens (c. 490-c. 560 AD) which explained that

in the unlimited void the atoms, separated from each other and differing in size, position, and order, move in a vacuum and, after meeting each other, collide with one another, bounce in the direction in which chance launches them, while the others agglutinate according to the congruence of figures, magnitudes, positions and orders, and remain together to complete in this way the generation of compounds. (Simplicius, Commentary on Aristotle's On the Heavens 242.15, my trans.)

As far as the Atomists' dînos was concerned, all available evidence thus supported Benveniste's view and not Serres'. But this was the same with the texts referring to the notion of rhuthmόs in which that of dînos never appeared.

In Metaphysics, Aristotle made it clear that rhuthmόs meant shape in Leucippus as well as in Democritus. He even criticized the atomists for not paying enough attention to motion. This was evidently untrue and related with his polemic against their conception of motion devoid both of prime mover and final cause. In any event, the Democritean rhuthmόs did not appear as a vortex. Aristotle explicitly equated it with skhêmá, as that of a letter: “Rhythm [ῥυσμὸς – rhuthmόs] means shape [σχῆμά – skhêmá] [...] e.g. A differs from N in shape [σχήματι – skhêmati].” (Metaphysics, 1.4, 985b, trans. Hugh Tredennick, my mod.)

In On Generation and Corruption, Aristotle repeated the same idea. For Leucippus and Democritus, the atoms

differ from another according to their “shapes” [μορφάς – morphás] and the compounds they form to “the elements which constitute them”—hence to their variable shapes—their “positions” and “groupings.” (On Generation and Corruption, I, 1, 314a, trans. H. H. Joachim, my mod.)

However, further down, while discussing Democritus' conception of “coming-to-be,” “alteration,” and “passing-away,” Aristotle referred to the atoms by using directly the term “figures” (skhêmata), as if their figure or shape was one of their most essential features. (I, 1, 315b) Whence a very simple fact: in On Generation and Corruption, the terms morphê or skhêmá were clearly used instead of what was called rhuthmόs in Metaphysics. Since the atoms were hard and unbreakable entities, their shape could not change. Therefore rhuthmόs meant here, without a shadow of a doubt, fixed form, shape or figure. Besides, the same kind of use equating rhuthmόs with skhêmá was found in his famous psychological essay On the Soul.

The spherical atoms are identified with soul because atoms of that [rhythm – shape] [τοὐς τοιούτους ῥυσμοὺς – tous toioútous rhusmoùs] are most adapted to permeate everywhere, and to set all the others moving by being themselves in movement. (On the Soul, 1, 2, 404a 1, trans. J.A. Smith, my mod.)

Thus, this second series of evidence confirmed once again Benveniste's interpretation and contradicted Serres'. In the Atomists, just as the dînos was not called a rhuthmόs, the rhuthmόs was never termed a dînos, a whirl, but a shape.

There was however something in Serres' misplaced critique that remained enlightening because it hinted at an important point in the older Atomist doctrine—precisely that one which Benveniste had been the first to reveal.

There were indeed a few good reasons to believe that rhuthmόs was also used to denote the changing forms, shapes or figures of the atomic compounds themselves. In these cases, the term was probably employed according to the common pre-Platonic meaning of “impermanent form” and—but this is only a guess—maybe sometimes philosophically “remotivated”—as Saussurean linguists would say—according to the etymological structure of the word as “way of flowing,” if we retain Benveniste's suggestion concerning the morphology of the word as composed of rhein (flow) + –thmos (manner or way of).

As a matter of fact, a list of Democritus' works preserved by Diogenes Laërtius (3^rd cent. AD) showed that Democritus wrote a book entitled Περὶ τῶν διαφερόντων ῥυσμῶν – Perì tôn diapherόntôn rhusmôn – Of the Different Rhythms (of Atoms), which was consistent with the use of rhuthmόs as shape, but that he also wrote another book entitled Περὶ ἀμειψιρυσμιῶν – Perì ameipsirusmiôn – Of Changes of (Atomic) Rhythms, which implied, since the atoms could not change shape, that rhuthmόs was used as changing form of the compounds they constituted. Hence the Greek grammarian Hesychius of Alexandria (5^th or 6^th cent. AD) noted in his Lexicon: “Ameipsirusmeîn (Democritus) : [concerning] the compound, to change [rhythm] or form.” (p. 110, my trans.) In this particular case, Jean-Paul Dumont noticed,

the term ῥυθμός [rhuthmόs] can hardly designate, as Diels and Liddell and Scott claim, the form or figure (σχῆμά [skhêmá]), notably because the atoms cannot change form, as it was supposed by the following title. In this last text, the figure is not that of the atoms, but that of the compound. (Dumont, 1991, p. 885, my trans.)

To tell the truth, there are few philological evidence that rhuthmόs was used to designate the changing shapes of the atomic compounds—another one was yet given by Theophrastus (ca. 371-ca. 287 BC), the successor of Aristotle as head master of the Peripatetic School (see Michon, 2018b)—but such kind of use was quite likely for theoretical reasons too. Since all atomistic doctrines considered that the countless bodies populating the universe were undergoing constant changes concerning their matter as well as their form, the essentially changeable nature of their atomistic compounds must have triggered the elaboration of a new concept of form.

According to Simplicius of Cilicia (ca. 490-ca. 560 AD), who probably quoted directly from Aristotle's lost monograph On Democritus, in Democritus' physics the atomic compounds took shape by the gathering of clusters of “resembling” atoms, “for by nature like is moved by like, and things of the same kind move toward one another, and each of the shapes produces a different condition when arranged in a different combination.” (Simplicius, Commentary on Aristotle's Physics, 28.4-26) As already mentioned above, in another treaty, he also explained that

in the unlimited void the atoms, separated from each other and differing in size, position, and order, move in a vacuum and, after meeting each other, collide with one another, bounce in the direction in which chance launches them, while the others agglutinate according to the congruence of figures, magnitudes, positions and orders, and remain together to complete in this way the generation of compounds. (Simplicius, Commentary on Aristotle's On the Heavens 242.15, my trans.)

The agglutination of these resembling atoms was brought about through their “weaving together” that “Abderites, such as Democritus, called ‘interlocking.'” Then they hold together “up to the time when some stronger force reaches their environment and shakes them and scatters them apart.” (Simplicius, Commentary on Aristotle's On the Heavens, 303a7, and 295.1-22, trans. I. Mueller – trans. J. Barnes)

Therefore we can readily agree with Pierre Sauvanet's conclusion.

Leucippus and Democritus provide to rhythm its very first conceptual meaning as “rhythm” of atoms. But it is clear that we must not mean by this their fall, their deviation, in short, their movement, but their design, their structure, in a word, their schema, and even more precisely not the schema of the atoms themselves but that of their compounds. Rhythm is the form taken by atoms in ephemeral conjunction. The rhythm of atomists is the instantaneous schema of the underlying structure of the world, through the incessant combination of atoms of matter. (Sauvanet, 1999, pp. 43-44, my trans.)

In the pre-Platonic atomistic world forms did exist, individualized entities did last for a certain period of time, but they were essentially changeable, transitory, fluent. Accordingly rhuthmós was probably a key concept in this worldview. Direct evidence favorable to this hypothesis was scarce but acceptable; but there was plenty of indirect evidence which made it more than plausible. In any case, contrary to Serres' claim, it was not a whirl nor a vortex. Such concepts seemed to be posterior by at least a century.

As far as we know, Leucippus and Democritus did not use the term rhuthmós to name the primordial dînos, nor the term dînos to refer to the generation processes of the bodies populating. Except for the larger cosmic bodies, like the moon, the sun and the earth, those were brought about by stochastic encounters, bouncing and agglutination of atoms. However, there were sufficient evidence to legitimately think that rhuthmós was then used to refer to the impermanent yet consistent forms of the atomic compounds that had formed through these processes—an maybe to the specific manner of these very processes.

Rhuthmic Mathematics

This lack of interest and understanding for Benveniste's work was quite unfortunate. It severed Serres from an important resource that could have helped him to address the issues he was otherwise so luminously discussing.

Nevertheless, his reflection remains enlightening, rhythmologically speaking. As a matter of fact, although he could not see clearly the real relationship between the first Atomists and their followers, he uncovered two important aspects of Greek science that before his research were, if not entirely ignored, at least largely underestimated: the genuine power of the ancient mathematics to develop infinitesimal calculus and the central significance of the hydraulic model for physics. Since both innovations allowed to overcome some limitations of former arithmetic and geometry and get beyond those of physics due to the primacy of statics and Pythagorean mathematics, both have produced the conditions for a significant transformation of the notion of rhuthmos into that of dinos.

According to Serres, the Greeks opened, much before it has been commonly admitted, the path that would lead to the infinitesimal calculus. In the 5^th century BC, some thinkers, Democritus (ca. 460-ca. 370 BC) and maybe others, already realized that it was possible “to construct or perceive the first possible angle, or the smallest that may be formed, so that nothing can be inserted between the two lines which open,” by considering a curve and its tangent. This subtle idea resulted in a bunch of revolutionary discoveries that fecundated Greek mathematics up to Archimedes (287-212 BC), that were eventually to be lost but that we can reconstruct from some sufficiently convincing pieces of evidence.

If we are calculating with shapes or rectilinear solids we only need, in general, ordinary mathematics. If, on the contrary, we square or cube curved elements, we must at least switch to a differential proto-calculus. And thus to Democritus. He left two lost books on irrational lines and solids [...] we know, from a reference in Plutarch and by a section of Archimedes' Method, that Democritus provided solutions for the volume of a cone or a cylinder, or for that of their sections, and doubtless more generally for that of a solid of revolution. Heiberg and Philippson think, correctly, that he achieved this by integration. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 10, same idea p. 101)

This “integral pre-method,” which for the first time “raised the question of the infinitesimal” (p. 101), was called “exhaustion.” It was a well-known calculus method that was usually attributed to Archimedes but for which, Serres claimed, we actually should credit Democritus as well. Serres presented its general features for two and three dimensions problems, while emphasizing its dynamic aspect.

Let us return to exhaustion. Imagine a square inscribed in a circle. It does not fill it, by any means. It leaves empty places, like hollows outside the fullness of its angles. It leaves empty places. An imprint inscribed in the circle, and that does not describe it faithfully. Let us increase the number of sides, this operation absorbs the voids and fills their emptiness. The imprint little by little, begins to take up the outline, by closer and closer approximation. As the number increases, the two schema tend towards the same shape. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 102)

If he [Democritus] knew how to integrate the volume of a conic section, or of a cone from that of a cylinder and in relation to that of the pyramid, it is no doubt because, before the great Syracusean [Archimedes], he had conceived the idea of exhaustion: to fill a curve with a polygonal outline, a circle with a square turned myriagon, a cone with a pyramid that has an increasing number of faces. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 102)

Then Serres convincingly emphasized the philosophical consequences of this new “pre-method.” This proto-integral-calculus and the theory of irrational numbers that accompanied it had probably been the mathematical basis for Democritus' atomistic ontology and therefore, I shall add, of his theory of form.

It is reasonable to suppose, as do Heiberg and Tannéry, that the theory of irrational numbers served him as a springboard to atomic interpretation. In both cases, it is a question of divisibility and indivisibility. In both cases, the last division recedes beyond our reach. [...] This [the volume of a solid of revolution] presupposes a differential division, and so once again an atomist interpretation. [...] It is inevitable that the first integrator should take things to be formed of a crowd of subliminal atoms. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 10)

He even credited Democritus for having anticipated Lucretius' concepts of clinamen and simulacra.

Through his approach to irrational numbers and introduction of the infinitesimal, Democritus the mathematician produces the conditions of atomism, its instruments and its objects alike; through the question of the minimum angle in contact with the circle and the sphere, he brings out declination, tangency and contingency; through the volume of solids and the pre-method of integration, he makes the theory of simulacra quantifiable and plausible. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 103)

The second major contribution Serres was referring to is that of Archimedes of Syracuse (287-212 BC). We do not know if Democritus was already capable to address, based on his lost works on differential calculus, the complex mathematical problems raised by fluid mechanics or hydraulics that ensued from his atomic ontology. But, Serres argued, we have strong evidence that Archimedes produced all necessary concepts to that end and therefore was, maybe for the first time, able to fully mathematize the Democritean atomic model (Serres, 2000, p. 11-12).

To mathematize the model successfully, I therefore need: 1. A mathematical or arithmetic theory of element. 2. A geometrical theory of tangent. 3. A geometry of forms of revolution. 4. A theory of spirals. 5. An infinitesimal calculus. 6. A mechanics of equilibrium. 7. A hydrostatics. Now, as if miraculously, this list of requisites corresponds exactly to a very well-known catalogue of works [those of Archimedes]. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 12)

Archimedes provided during the 3^rd century BC a theory of numerical increase with his Sand-Reckoner, a theory of spirals already integrating tangents and differential calculus with the book On Spirals, a theory of deviation and a theory of equilibrium with On Plane Equilibriums, a theory of forms of revolution with the two treatises On Conoids and Spheroids, and On the Sphere and Cylinder, and a theory of hydrostatics with his essay On Floating Bodies.

Nothing is missing, now, for the mathematization of the model. It is furnished with a geometry, with a theory of numeration and numbers, with an analysis of series and large populations, with an axiom of the infinite, with a metrics and a refined description of the forms of revolution (in general conic), of spirals or vortices, of the agitated profile of the flow, with a statics and a hydrostatics of the declining angle. And its disciplines, taken together, are not disparate: they are focused, like the model itself, on a global theory of deviation. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, pp. 23-24)

To conclude his comments on this matter, Serres underlined both the novelty of Archimedes' thought, compared to the more famous Plato and Euclid, and consequently of his own views concerning the history of the mathematization of physics.

Archimedes is the Euclid of the Epicurean world. [...] Everything is there, nothing is lacking, the inventory is complete. Atom-grains in the infinite void, the minimal of differential angle of the vortex produced, and the deviation from equilibrium in the fluid medium. [...] It begins with Democritus, and the edifice is completed, crowned, by Archimedes. A mathematical physics, close to the world and proven, in fact existed among the Greeks, who were not supposed to have one. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, pp. 24-25)

One could add that this mathematization of Democritean physics entailed also, most probably, the mathematization of one of the atomist concepts in which we are most interested: that of rhuthmós as an “impermanent form” or possibly a “way of flowing.” Let us see how we can, thanks to Serres' contribution, give credit to this conjecture.

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Michel Serres and the Rhuthmoi of the Flow – Part 2

Pascal Michon — 2019-12-04T09:00:00Z

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Rhuthmic ontology

Having set up the larger scientific frame, Serres introduced Lucretius' ontology. He did not pay attention to the atoms themselves but it is worth noticing that Lucretius described them as endowed with various size, weight, and “shape” (figura) which was an accurate translation of the Democritean rhuthmós. (De rerum natura, 2.748-482)

Serres started from Book 2 where the concept of clinamen – declination was introduced as “depellere paulum, tantum quod momen mutatum dicere possis” (2.219-220): atoms, in free fall in space, deviated, drove away, from their straight trajectory “a little, just so much that you can call it a change of movement.” Their deviation was as small as possible, and the alteration in their movement was as small as description allowed. Serres claimed that this definition of the clinamen was exactly what posterior mathematicians in the 17^th century called “differential” or “fluxion.”

Anyone who has ever read any Latin texts on mathematics, and more specifically on differential calculus will recognize here two canonic definitions of the potential infinitely small and the actual infinitely small. This is not an anachronism; the relationship of atomism to the first attempts at infinitesimal calculus is well known. From the outset, Democritus seems to have simultaneously produced a mathematical method of exhaustion and the physical hypothesis of indivisibles. We can see here one of the earliest formulations of what will be called a differential. The clinamen is thus a differential, and properly, a fluxion. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 4)

The vortex – dinê/dînos in Greek – turbo in Latin – was, Serres claimed, the primitive form of the “construction of things,” of “nature in general,” “according to Epicurus and Democritus.”

Now this vortex [tourbillon], δίνη – dinê / δῖνος – dînos, is none other than the primitive form of the construction of things, of nature in general, according to Epicurus and Democritus. The world is first of all this open movement, composed of rotation and translation. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 6, same idea p. 50, 91)

And this idea was to be taken up and elaborated further by posterior atomists, ancient as well as modern.

For Lucretius, as for us, the universe is a global vortex of local vortices. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 127)

As we saw above, this attribution to Democritus was a questionable claim, but it did not matter here. The question was: how does rotation appear in the laminar cascade constituted by the fall and flow of atoms? Lucretius' stunning answer was: by the clinamen, which was the Latin name he gave to the unpredictable swerve of atoms.

When atoms move straight down through the void by their own weight, they deflect a bit in space at a quite uncertain time and in uncertain places, just enough that you could say that their motion has changed. But if they were not in the habit of swerving, they would all fall straight down through the depths of the void, like drops of rain, and no collision would occur, nor would any blow be produced among the atoms. In that case, nature would never have produced anything. (De rerum natura, 2.216-224, trans. Brad Inwood)

Serres underlined the basic ontological assumption that supported this statement. The agglutination of atoms by which natural things came to be—and, I shall add, took their impermanent shape or rhuthmós—was the result of a turbo which was itself triggered by a clinamen in the constant atomic cataract which constituted the metaphysical dynamic background of the world as it appeared to us.

The clinamen is the smallest imaginable condition for the original formation of turbulence. In the De finibus, Cicero wrote that atomorum turbulenta concursio. Atoms meet in and by turbulence. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 6)

As many other specialists, Serres noticed that this concept presupposed a critique of straight determinism. Declination appeared in the laminar flow of atoms “incerto tempore, incertisque locis” – “at an indefinite time and place,” (2. 218-219) i.e. by chance.

What Lucretius says, however, remains true—that is, faithful to the phenomenon: turbulence appears stochastically in laminar flow. Why? I don't know. How? By chance, with respect to space and time. And, once again, what is the clinamen? It is the minimum angle of formation of a vortex, appearing by chance in a laminar flow. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 6)

Then Serres emphasized the difference in Latin between turbo – “a round form in movement like a spinning top, a turning cone or vortical spiral,” and turba – “a large population, confusion and tumult.” But from a rhythmic perspective, this difference was clearly reminiscent of an older, now well-known, Greek opposition between something intrinsically mobile but “no longer disorder,” which precisely was called rhuthmós, and “the mad dancing of Bacchic festivals,” that was commonly considered as arruthmía.

The first designates a multitude, a large population, confusion and tumult. It is disorder: the Greek τύρβη – túrbê, is also used of the mad dancing in Bacchic festivals. But the second is a round form in movement like a spinning top, a turning cone or vortical spiral. This is no longer disorder, even if the whirl is of wind, of water or of storms. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 28)

The process of generation, duration, and corruption of things was thus entirely determined by the change from turba into turbo and vice versa, and could be accounted for by what he called “a general theory of turbulence” (p. 81).

The world in its globality may be modeled by vortices. The origin of things and the beginning of order consist simply in the narrow space between turba and turbo, an incalculable population tossed by storms, by unrest, in vortical movement. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 28)

The genesis of a thing started stochastically with a clinamen – deviation and developed through a turbo – vortex. Once a minimal angle or deviation occurred in the atomic fall, the atoms started, by their interactions and the new deviations they provoked in the flow, to organize themselves into a vortex.

The clinamen is indeed the smallest deviation and the optimal slope. Here is the descent, the thalweg, the creode [neologistic porte manteau coined by C.H. Waddington meaning “necessary path”]. It is the optimized road to constitution. A track opened trough which the flow is swallowed up, a funnel for atoms towards conjunctive existence. Here is the bed of the river: designed, calculated, set down, as the condition of genesis. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 33, my expl.)

Serres insisted on the fact that this process was “statistically of extreme rarity” and, because it only occurred “by chance,” it had been rejected by classical physics, which sought to enforce the concept of universal law.

Yes, it holds by a miracle. And by a miracle I mean the case statistically of extreme rarity. [...] Hence the scandal of declination in the eyes of classical and modern physicists: it interrupts the universality of the laws. It opens the closed system. It places the physical law under the rule of exception. Under the protective roof of its solid angle. And yet, that is the way it is. Lucretius is right. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 77)

Each vortex grew more or less rapidly, stabilized, lasted for a certain amount of time, then regressed and faded away.

The stochastically distributed exception in the cataract, under the differential cones of declination, where the flow inclines, returns in [a waterspout/a rush] [revient en trombe], diversifies, develops locally [se noue localement] and constructs an aggregation that is temporarily stable because unstable. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 78, my mod.)

Surprisingly, Serres did not use at first the term rhuthmós although it was clearly a process generating rhuthmoi, in the pre-Platonic sense. A turbo was characteristically an impermanent form. But some pages below, clearly alluding to the pre-Socratic terminology without yet citing his source, I mean Benveniste, he finally proposed the term “rhythm” as the most adequate term to name the basic ontological phenomenon of vortex.

A word is needed to express the simple elements: a word like rhème. When the vortex constitutes it in form, it is called rhythm. [...] Everywhere there are models of the most general theory, that of floods and paths, of elementary rhèmes, capable of intertwining, here and there, into syrrhèmes, connective rhythms. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 89)

At the end of his essay, Serres claimed as his own the discovery that the pre-Platonic “rhuthmos” was actually a “vortex in the flow,” a form “adopted by atoms in conjunction in the first dinos.”

Direct physical experience, simple practice, reveal the rhuthmos in the rhein, or the vortex in the flow, or the reversible in the irreversible. Rhythm is a form, yes, it is the form adopted by atoms in conjunction in the first dinos. In the beginning is the cataract, the waterfall: here is the reversibility to this irreversibility: thus rhuthmos. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 154 )

We have already seen that rhuthmós was not used, contrary to Serres' claim, by Democritus to designate the first dînos nor any other smaller dînos, although it was, with great probability, used for atomic compounds, i.e. any generated thing. Therefore, it was no marvel that posterior atomists like maybe Epicurus—of which we have very few texts—and with more likelihood Lucretius have used their own concept of turbo at least partly in the pre-Platonic sense of rhuthmós.

I should now add that Benveniste, contrary to what Serres bluntly asserted, clearly anticipated this ulterior use. I'll recall here some elements deduced from his analysis.

1. A pre-Platonic rhuthmós was not a “Form,” an “Idea,” an εἶδος – eîdos, but a shape “as it presents itself to the eyes” of the observer. Far from being outer-worldly, it belonged to the phenomenal world. 2. It was not fixed, immobile, and eternal; it had a life of its own. 3. It did not “designate the fulfillment of [the] notion [of shape] but the particular modality of its fulfillment.” And Benveniste concluded: 4. That was the reason why it was “appropriate for the pattern of a fluid element” and commonly denoted an “improvised, temporary, changeable form.”

There was not a single word in that four-part description that did not apply to Lucretius' turbo. A turbo was not an eîdos but an observable shape; it was not fixed, immobile and eternal and had a life of its own; since it was constantly moving yet having a certain consistency, it did not designate that peculiar shape as something fulfilled but the particular modality of its fulfillment; last but not least, it was particularly appropriate for the pattern of a fluid element.

However, we see that there was a slight difference between the older concept of rhuthmós and the one that we may induce from Lucretius' concept of turbo, probably the same as between the proto-infinitesimal calculus developed in the 5^th century and the more elaborated mathematics of the 3^rd up to the 1^st century. Whereas the former was an impermanent and changeable form, observed at a certain moment of time, which was very loosely defined and had still a certain duration, the latter was now intrinsically moving and changing. It was a form that was constantly in-forming, per-forming and de-forming itself. Therefore this undetermined moment of observation was now reduced to a minimum, i.e. to the infinitesimal moving time-length or “limit” between two segments of time.

It was as if—to recall Benveniste—the meaning of rhuthmós would not any longer be determined by its older uses (as impermanent shape) but only by its morphology (as sheer mode of fulfillment), getting thus closer maybe to the core of the ancient atomist doctrine. Since this moment of suspense was entirely overcome, the last link with the Platonic paradigm was definitively severed. Rhuthmós might now be taken as a pure way of flowing, a mode of fulfilling a process (generation, existence, decay, disappearance) or an action (dancing, playing music, performing, reading poetry). But this did not mean a break or an unbridgeable gap with the ancient atomist tradition. Lucretius' turbo was clearly a direct heir of Democritus' rhuthmós.

In other words, Serres was right when he claimed that the Lucretian turbo was tightly related to the pre-Platonic rhuthmós. It undoubtedly appeared as a refined version of this concept. But he was clearly wrong and even dishonest when he claimed that Benveniste did not anticipate this ulterior use and appropriated his discovery without citing him.

Rhuthmic Individuation Theory

Let us stick though to the positive part of Serres' contribution which allowed to elaborate further the meaning of this conceptual kinship. We will see below, when we deal with Lucretius' theory of knowledge, that in Book 4 Lucretius famously opposed any skeptic stand by deploying a self-refutation argument. Our senses never lied, only our interpretations of their data. To deny that we have access to knowledge through the senses—its only possible entry route—was a philosophical stance that disqualified its own adherents by depriving them of any possible grounds for its assertion (4.469–522).

But Serres' reading of this passage emphasized a different aspect of Lucretius' argument which staged a building built on inaccurate and deviating lines that represented reason if “the senses from which it arises are false.” Serres summarized verse 4.513 to 4.522 as follows.

Take a building. To begin with, if the measuring-stick is false and the square inaccurate thanks to a deviation from right angles (in the plural, of course, and not only for the particular case of the verticals), if the level (of a plum-line or water level) is off one way or the other (either by the angle of the line or a deviation of the bubble), then by virtue of this defect and this inclination everything will be built leaning, askew, sloping to the front, pushed backwards, discordant; the building already seems to want to collapse, it collapses, betrayed by errors in the initial judgment. And so it is that reasoning is necessarily false and irregular when the senses [sens] from which it arises are false. End of quote. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 44)

According to Serres, apart from his argument against skepticism, this example was chosen by Lucretius to suggest that any human artifact and more generally any natural being are naturally “in danger of collapse” the constant and unpredictable swerve of atoms.

Every concrete Latin term that reproduces the deviation from equilibrium, the angle of asymmetry, or the inclined slope, around the κανών – canôn, the canonical, the rule of the Epicurean mason, is here brought together all at once. [...] The earth shakes and the house falls. All conjunctive tissue is sapped by the void. Nothing is full but the heart of the atom, that is to say the atom. And only the void is immortal, like particles. Death is this return to particular clouds, the crumbling into dust and for dust. [...] So if these buildings, which is to say all of nature, are in danger of collapse, it is simply because they were, at the manifold dawn of times, erected, built, on a deviation of equilibrium. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 44-45)

But the metaphor bore yet another meaning that came to light by contrast with Vitruvius' architectural concept of eurhythmy (see Michon, 2018a, chap. 6). As a matter of fact, in the very next line Serres reversed Lucretius' argument to show that, although the clinamen was always destroying existing beings, buildings do stand up, living beings do live, things do have shapes, at least for a certain period of time that depends on the magnitude of the “original declination.”

Their duration even increases as the angle grows smaller. [...] Consequently, the model is compatible with the canon. Nothing crumbles except by pronation and supination, by original deviation. [...] The canon, far from suppressing declination, requires it, and requires that it be small and original. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 45)

Everything was born from a vortex but any vortex depended for its ephemeral existence both on its rotation and an infinitesimal angle that sustains it. Buildings do stand stiff not because they are symmetrical, well balanced and built according perfect verticals—“eurhythmic” in a Vitruvian sense—but because they integrate tiny angles and are dynamic centers or kinds of cone where myriads of fluxes reach for a time equilibrium.

Now underground rivers erode the earth, hurricanes tear off the roof. The wall threatens to give way, it leans, it is going to fall. No, the flow, reversed, soon straightens it and pushes it back. By the unevenly starred wind rose, it slowly describes a very small solid angle. [...] This small differential cone saves the building from collapse. It marks the bordered, limited space, in which such an aggregation is temporarily removed from the universal legislation. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 75)

To hold on in equilibrium needed a tiny disequilibrium. Any regular or symmetrical figure rested on infinitesimal irregularity or dissymmetry.

Why does it hold? Simply because it does not hold completely. Every case will be a minimum degree [out of plumb] [il faut un minimum de faux aplomb]. There has to be a minimally open solid angle. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 77, my mod.)

According to Serres, atomists, especially Lucretius, did bridge, with this peculiar concept of equilibrium by disequilibrium, the divide between Heraclitus and Parmenides, flow and form, without depending for individuation on Plato's solution by “participation to ideal Forms.”

Physics, at this time, seemed to have to chose between the mobility of Heraclitus and the base of Parmenides. At least Plato formulated the problem this way. And resolved it otherwise. The atomists founded, and for all time, the science of things themselves, in the absence of dynamics, by saying yes to both sides: everything flows, there is a canôn. By a rigorous statics of movement. By a canonics of fluency. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 45)

Infinitesimal declination thus provided the generative concept that allowed to bridge and synthesize rest and movement.

Declination is a tremendous physical and mechanical discovery. It breaks with the common antithesis of rest and movement, of Parmenides and Heraclitus, much more completely than Plato did. [...] Through declination, it is movement that is stable, in the path of its flow, in its general direction and its passage point by point. It is what ensures the most profound and exact invariance, although tradition down to the present day has seen only paradoxes there. For it is the condition of a great synthesis between statics and dynamics. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 129)

But one could add that Lucretius' synthesis was also at odds with Aristotle's “hylomorphic” solution. Whereas Aristotle claimed that any being was the result of the action of a form that allowed, essentially by providing an end, the potential of a certain amount of matter to actualize itself through its in-formation, Lucretius strongly denied the existence of such forms. Forms did appear by themselves through stochastic gatherings of atoms in vortices. (4.823-857)

Serres emphasized that Lucretius' infinitesimal theory of becoming and individuation was much closer to the truth—and to current modern physics—than the gross dialectic of being and non-being that developed in the West up to Hegel.

Two hundred years of philosophy have accustomed us to different arrangement. It seems clear to us that movement is produced by being and non-being, as though by thesis and antithesis. Now, moving has nothing to do with being or nothingness; the idea reflects a crucial confusion between mechanics and something else. Or rather, it is the admission that everything is projected onto kinematics. Ontology conceals itself behind the theory of movement. This is an outdated thesis: all of physics reduces to mechanics. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 60).

Lucretius' way to insert a principle of movement and change into the being itself did not resort to such massive principle as the Hegelian negation. It consisted only in an infinitesimal angle that deviated the atomistic flow and created the turbulences that we observe in nature and history.

We may even think, since there was for Lucretius no distance between thought and reality, that the logic that supported reasoning as much as nature was itself a turbulent or rhuthmic dialectic in which classical logic based on syllogism and law of excluded middle was not replaced by a Hegelian dialectic articulating, through time, being and non-being, affirmation and negation, truth and error, but a whirling play between matter and void, arguments curling back upon themselves from some tiny original deviation and truth winding around error.

Serres then recapitulated Lucretius' theory of individuation. By clearly specifying the concepts of clinamen and turbo, he gave a better comprehension of that of rhuthmós as well—or maybe I should write now: that of rhuthmos because it transferred it into our world. Something quite significant for our rhythmology was introduced here for the first time: the possibility of a physics which would not be based on Plato-style concepts of repetition, periodic movement, oscillation, briefly on metrics, but on fluxes, declinations and vortices, i.e. on rhuthmoi.

Let us return to the cataract. It rains down universally, everywhere and all the time. Declination is the minimum solid angle that introduces a change in the general movement. [...] An instant later, turbulence forms a pocket in the three-dimensional flow. A local pocket where the flows, adrift, go back upon themselves. In this place of singularity, these flows change their direction, their force, their volume. And this exchange can be, by chance and temporarily, homeorrhetic. The world as we know it, for example, is such a pocket. [...] This pocket, this seed, this island, this turbulence, holds a certain time before disintegration, before being carried away by the cataract, the current of atoms that wear it out and break it. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 76-77)

Rhuthmic Physics and Space-Time Theory

Serres identified in Lucretius' physics two kinds of original chaos, two kinds, so to speak, of turba: the “streaming-chaos” and the “cloud-chaos.” At first, he argued, the processes ordering these two different kinds seemed comparable; they both resulted from a dînos – vortex.

Lucretius describes two forms of chaos: the streaming-chaos, the laminar flow of elements, a parallel flow in the void, drawn out like fibered space; the cloud-chaos, a disorganized fluctuating, Brownian mass of dissimilarities and oppositions. [...] [but] the solution is unchanged, the original figure and movement remain the same, it is the Democritean dinos. The vortex is thus the pre-order of things, their nature, in the sense of nativity. Order upon disorder, whatever the disorder may be; the vortex arises by a fluxion in the first hypothesis, which is that of chaos-flow, and by fluctuation in the second, which is that of fluctuating chaos. There are indeed no stabilities except in a universe in which everything flows, unstable. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 31)

But on second thought, he felt that those two views on chaos eventually led to two very different traditions in physics: a classical tradition ending in positivism; a repressed tradition—which I proposed to call “baroque” by analogy with other sciences and arts in the same period (Michon, 2015a)—which bravely addressed the problems of “chaotic multiplicity” and “order by fluctuation” and anticipated “our problems.”

Yes, the solution is the same; yet, it is not the same, neither for epistemology nor for the history that will follow. The first of these hypotheses opens a classical knowledge, in which disorder is minimized: it is the path which leads from Archimedes to Pascal and Newton, mechanics and hydraulics, and an infinitesimal calculus, the science of fluxions. Here, coherence is preserved between the local and the global. During the course of this history, which goes up to Laplace, and up to a dominant positivism, the second hypothesis is dormant. Today, it is reawakening, out of some of Leibniz' dreams and from the other side of Laplace, where chaotic multiplicity slept. Order by fluctuation has become our problem, and our world has become that in which the local and the global no longer harmonize. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 31)

I won't discuss here this claim because it would need more than a few lines and take us too far from our current argument. But it certainly was an important suggestion that we will have to remember. Let us focus on Lucretius' physics. Serres distinguished three layers in its construction. The first was “local and original” and started with a clinamen which triggered a vortex.

The first model is local and original. It simply simulates the look of a fluid. Atoms cascade in a laminar flow down an infinite channel without banks. The void is a generalized hollow body. Inclination, then, imposes itself, the precursor of turbulence. It is produced, as experience shows, in an aleatory manner, at indefinite times and places. Every nascent object is initially a vortex, as indeed is the world. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 50)

The second was “global” and accounted for the “duration” of the things that had been generated in this way—despite their essential dynamism and impermanence.

The second model is global. It takes the whole path into account. To the inclination, defined as minimal, there necessarily corresponds a maximal descent. The law of formation, the law of the duration of things and of the world. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 50)

The third, which was a theory of the “natura naturata,” i.e. a physics of the world as it is, was proposed by Serres to synthesize the first two, which accounted for the “natura naturans,” i.e. for the metaphysical dynamism that makes the world and the things appear, become and disappear (p. 51).

By insisting on this “third model,” Serres wanted to show that Lucretius' was quite close to our most recent model of nature as complex and open system of systems. Lucretius did not content himself with the model of the atomic cascade, the clinamen and the vortex; he contemplated a much larger and more powerful model of the world as “vortex of vortices, interlacings or networks of waves.”

Let us now construct the third model. Every object, naturally, emerges like Aphrodite from a flux of elements. By the above-mentioned models. Born from this and, as soon as it is born, complex, twined, twisting its long thick hair, it begins to transmit, in floods and in all directions, a star of flow: its wear and its time. It radiates various waves: heat, odors, sounds, simulacra, subtle atoms. In the same way or inversely, it receives the flow emitted around it, from the vicinity and the edges of the open universe alike. [...] At birth the singular cascade is transformed: no longer here and there, in and for some local object, but integrally and for its global flow, in a multiplicity of rivers, streaming by all paths, transverse, diagonal, intersected, complex. The summation of the dispersed inclinations in space and time in the cataract produces, in the maximal descent, a complex weave of flows that begin from the unified nappe. The world is a vortex of vortices, interlacings or networks of waves. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 50)

Nature was thus seen as a complex system whose elements never stopped moving and changing. It was, so to speak, fluent but not entirely liquid. It was composed of crisscross intertwined fluxes which generated things and living beings that lasted a certain amount of time before disappearing again. All vortices were in relation with one another. All rhythms were interacting with each other.

If nature, that is to say an ensemble of linked things, not an incoherent or chaotic ensemble of objects, but a communicating ensemble that functions as outlined, is to exist, it is absolutely necessary that these vortices [tourbillons] be in relation one to another. It is necessary that, in a certain manner, they be chained together or lead to each other. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 94)

Since Lucretius used the theory of the four elements and established between them a cycle of transformation, he seemed to support the view of a global equilibrium. Nature seemed thus “an equilibrium in the midst of the fluencies” and a “fluency through equilibrium.” Adsidue quoniam fluere omnia constat – In constant flux do all things stream (5.280). Contrary to what Barthes believed, the “homeostasis” was balanced by a “homeorrhesis.”

In general, nature seeks an equilibrium in the midst of the fluencies, and seeks fluency through equilibrium. We would say today that there are fluctuations, homeostasis [tendency towards a relatively stable equilibrium between interdependent elements, especially as maintained by physiological processes], then homeorrhesis [steady flow, term introduced in the 1940s by Waddington]. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 56, my clarif.)

But this re-use of the four-elements physics cycles should not be over-interpreted. The concept of “system” which was presupposed by Lucretius was actually different from the Stoics' because it did not entail any “hierarchy” or “tight order.”

Invariance is global. Physics describes a system, but not one that is hierarchic, deductive, or tightly ordered [monté serré], as in the series of the Stoics: it is a set [il est ensembliste – like in modern mathematics], its general equilibrium a balance sheet that takes account of the stochastic. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 58, my expl.)

It was also different from the most common concept that had been popularized in some disciplines in the 20^th century—according to a kind of late Platonic worldview—as closed mechanic system in perfect equilibrium. Here, at least two reasons made perfect equilibrium impossible. There were always new clinamen that stochastically introduced disorganization as well as new constructions and orders. Moreover, there was always entropy, loss of energy that provoked change, wear, decay and death. After a certain amount of time, each local vortex as our world's global vortex itself faded away.

Nature, that is to say birth, that is to say death, is the line inclined by the angle that produces a global vortex, which the wear of time brings back to the straight. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 58)

This was the reason why the circulation of fluxes in nature never occurred as “perfect circles” and rather followed spiral and vortex patterns.

If these circulations are perfect circles, then the movement finds its equilibrium, the world is immortal, it proceeds to eternity. This is the stroke of genius in atomist physics: there is no circle, there are only vortices. No exact rounding off, no pure circumference, [only] spirals that shift, that erode. The circle winds down in a conical helix. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 58, my clarif.)

This conclusion explained why Serres glimpsed in Lucretius a theory of time that was clearly at odds with Plato's. In the Timaeus, the latter considered time as “an image of Eternity moving according to number” and with Aristotle who, in his Physics, defined time as “number of motion in respect of ‘before' and ‘after'.” Given the crucial role played by the turbo in Lucretius' ontology and physics, time itself might be defined, Serres suggested, as “the fluctuation of turbulences.”

Turbulence is the functional figure of constitution and formation, everything happens as if it integrated declination. This is the dinê of Democritus. It then becomes the global figure of transformation in general, as the clinamen was its minimal or local operator. Things, and so nature, are formed by atomic conjunction in and through this very vortex; but, what is more, they exist and continue in and through it; finally, they destroy themselves, come apart, as if it were dwindling to nothing. Time is the fluctuation of turbulences, which make time, maintain it in their implications, set it going and finally allow it to disappear. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 91)

One basic assumption of the Platonic/Aristotelian paradigm, which tended to equate rhythm with meter (in the sense of measure and number), was then replaced by a much more supple conception of time. The latter was not any more considered as a completely regular and numbered course reflecting eternity or only measuring movement, but already as a turbulent flow providing accelerations, decelerations and returns, generations, stabilizations, mutations and disappearances. Time was “implicated” in the various ways of flowing, the rhuthmoi. It was itself rhuthmic.

Another feature of the Lucretian theory of time—as the most recent theories, as a matter of fact—was that the latter was “irreversible,” whereas modern Newtonian time was, at least theoretically, “reversible.”

Newtonian time, reversible, is the mark of resistance to the irrevocable. It is absent from this physics, and this is why our forefathers could not imagine for a single moment that there might exist a Lucretian physics. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 125)

According to Serres, who was aware of contemporary research on “irreversibility”—Ilya Prigogine won the Nobel Prize in 1977, the very same year The Birth of Physics was published—Lucretian time was thus closer to a “Bergsonian thermodynamic time.”

Pardon me, but the clock that Lucretius sets right in the middle of nature cannot tell Newtonian time; because it [elle – the clock] is the whole of things, between their birth and their collapse, it records a Begsonian, that is to say a thermodynamic, time. An irreversible, irrevocable time, pointing like the endless flow of atoms, flowing, rushing, crashing towards fall and death. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 125)

Parallel to this new conception of time, Lucretius developed, Serres argued, a new conception of space whose originality we better understand if we compare it with that common in 17^th century science. Classical physics simplistically opposed, Serres remarked, “space” as an abstract and empty room and “figures” as limited and “metred and masterable” entities furnishing this empty and neutral space. Lucretius' physics instead considered form as “simplex” and space as “rich in complexities.” In other words, exactly as time, space was not homogeneous nor uniformly measurable. Space was not metric. It was also clearly rhuthmic.

Form, here, is a simplex; space is rich in complexities, it is divided, it bifurcates, it is filled with knots and confluences, it is the conjunctive web of the topology and of the ars combinatoria, it is the tattered strips of the ars coniectandi, of the event, of circumstance. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 51)

The metrical space, exactly as the Platonic rhythm when it was applied to space—for instance in Vitruvius—depended on an “algebra of proportions.” From Euclid to Descartes, this was the same concept of space. Euclidean geometry was consistent with metrics and opposed to rhuthmics.

The Cartesian figure refers back to Euclid's geometry, it is a metrics, dominated by algebra of proportions. [Measurable, mastered] [métrisable, maîtrisée]. The master and possessor of nature metricates his space. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 51, my mod.)

Even if it still lacked the concept of force and any consistent dynamics, the ancient atomist physics thus suggested a combine rhuthmic conception of time and space—what Serres prudently called a “vectorial space”—which anticipated them both by more than two thousand years.

Atomist physics is based much more upon a vectorial space than on a metric space. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 62)

As far as we are concerned, thanks to Serres' analysis, Lucretius' physics appeared clearly as an expression of a rhythmological or better yet, rhuthmological perspective and, at the same time, it enriched it with new concepts such as intertwined fluxes, interacting rhuthmoi and open systems as well as new fluent concepts of time and space.

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Michel Serres and the Rhuthmoi of the Flow – Part 3

Pascal Michon — 2019-12-04T08:30:00Z

Sommaire

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Rhuthmic Perception Theory

At the juncture point between ontology and knowledge was the soul. According to Lucretius, the soul consisted of two parts: the animus, located in the chest, which commanded intellectual operations and will, and the anima which was spread throughout the body, received perceptions and transmitted in turn the impulses of the command center. The soul in both aspects could be shown to be corporeal (3.94-416). To make it short, anthropology could be reduced to physics and the human beings to turbines.

In Book 3 and again at the beginning of Book 6, Lucretius compared the body with a vessel which contained the soul as it would a finer fluid. But, Serres noticed, this metaphor did not bring us away from the flowing nature of things. This vessel leaked while being necessary to the concentration of the soul. Body and soul were necessarily co-existing.

So the vessel is porous, the basin crazes. It is, very precisely, an open system. Very superior, in its complexity, to an automaton in an interior medium. By the channels that it has left free the animated fluid flows and escapes. Effusion: it leaves; diffusion: it spreads. It loses its concentration, it spills everywhere, it takes up the volume available to it. From the locally open to the globally open. Everywhere and at random, the soul returns to the world and to chaos. It is therefore mortal, by a physicalist death, aleatory diffusion; it cannot exist without the body, that basin which ensures its concentration, at least for a while. It would spill if it were not constrained. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 69)

Body and soul, if we may call them so, constituted a unitary complex that was “stable for a time” and “postpone[d], for a little while, the end anticipated by the law of dissolution” because it consisted in an “open system” which was “ the seat of an exchange of flows.”

But the vessel itself is a flow, although thicker and more complex. [...] The vessel and its fluid leak. But they are stable for a time. They can postpone, for a little while, the end anticipated by the law of dissolution. [...] This is his stroke of genius: the body, an open system, is the place or the seat of an exchange of flows; they enter, they leave. But these flows are, unitarily food and drink, Eros or perception, and intellectual information. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 69)

As one may know, Lucretius believed that among the various fluxes that penetrated the body-soul, one was particularly important since it allowed knowledge of the world: the one composed of the simulacra that were emitted by the multitude of things composing our environment. These simulacra were atom-thin and lightning-fast “images,” that streamed from the surfaces of solid objects (or sometimes form spontaneously in mid air) and entered the eyes or mind to cause vision, visualization and dreams. In this theory of knowledge, Serres emphasized principally four aspects.

1. The simulacra streamed in all directions like “a spray of chreodes” as “an optimal form of the volume occupied by an object” from the “sur-face” of the “body” (summo de corpore).

There is a flux given off by things. By things taken as limiting cases [de manière extrémale – as limits in mathematical sense]: summo de corpore (surface of the body), used eight times in forty lines (IV, 40 ff.). The surface is the summit, it is an upper face. I said a moment ago an ultrastructure. The simulacrum detaches itself as the optimal form of the volume occupied by an object, as a sur-face [super-ficie]. [...] In the vicinity of its banks, the object is no more than a spray of chreodes. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, pp. 39-40, my expl.)

2. They streamed the same way the atoms did in the primordial cascade.

If the model of perception is materialist, if the simulacra are formed of atoms and if their flow is governed by the general laws of propagation, then one model is reducible to the other. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 42)

3. Contrary to skeptics' claim, they conveyed the exact shape of the object, provided they did not unexpectedly swerve, “here [was] the formation of turbulence,” or naturally encountered obstacles or other flows of atoms.

This river never ceases to flow. Here is the formation of turbulence: liquidissima caeli tempestas, perquam subito fit turbida foede – ... just when the climate of the skies is clearest, it turns most suddenly dark and foul. (4. 168) (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 42)

4. We were ourselves both constantly emitting fluxes and immerged in “a space of communication” which was crossed by “fluxes of fragrance, of voices flying in the wind, of heat and cold, spume and bitterness” and “dense with waves.”

Everything flows, objects are springs. Fluunt, fluviis, undis aequoris, fluenter, fluendi. Waves and fluxes of fragrance, of voices flying in the wind, of heat and cold, spume and bitterness. The perceptual space is dense with waves. All things are transmitters [émettrices], without interruption and in every direction; our senses ceaselessly receive. We are plunged into the space of communication. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 49)

Thus perception is an encounter, a collision or an obstacle, one of many intersections on the way. The perspective subject is an object of the world, plunged into the objective fluencies. Receiver, in its place, transmitter form every point of view. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 49)

This theory of perception and the larger theory of knowledge that it supported, which has been so many times mocked and ridiculed, were actually, Serres argued, closely related with the progresses made in mathematics thanks to Democritus and Archimedes. Coming back to the method of exhaustion presented above, he concentrated on the shrinking serrated space between the curve, the circle or the solid of revolution one tried to measure and the “broken polygonal path” with its “infinite increase in angles” that topped the “square turned myriagon” or “the pyramid that has an increasing number of faces” (p. 102). This extremely thin and irregular space was, according to him, the real as much as the intellectual source of the simulacra which were conceptualized in the poet-philosopher's mind and generated in reality from this infinitesimal space.

Now this operation [of exhaustion], strictly speaking, both has and does not have an end. In the vicinity of the smallest, we must decide. It is the passage to the limit. The curve precisely envelops this broken polygonal path. The surface is a boundary. It is an infinitely thin garment, cast upon this complex conjunction. A replication, as it were, though more of an application. Now observe the fluctuating muddle that separates and unifies the border and the conjunction, the limit surface and the infinite increase in angles. Literally and without metaphor, this space is fluent. It is the mobile deviation of a fine fidelity. Here, quite simply, is the genealogy of the simulacra, of these motile idols emanating from the surfaces, of the limit of the εἶδος – eîdos. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 102)

Serres compared Lucretius' theory of perception to Leibniz's theory of small perceptions and found it much more precise because it took account both of “the shape at the limit frontiers of atomic constitution” and of “the fluctuations of the phenomenon.”

It is an anologon, on the same model, of the Leibnizian theory of small perceptions. Even richer, it would seem, more complete and better constructed, since it takes account through its borders of the appearance of the shape at the limit frontiers of atomic constitution, and of the fluctuations of the phenomenon. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 103)

Although it certainly shed a new light on the theory of simulacra, this suggestion has triggered discussions among specialists. But, as far as we are concerned, it illuminated a question that we crossed already many times: the Atomist particular theory of form which supported the definition of the Democritean concept of rhuthmós—and Plato's and Aristotle's critiques against it. Through the streams of simulacra, which faithfully transmitted “bit by bit,” in a finer sense than that of computer science, all points constituting the constantly changing envelop of an object, that from was finely transposed into the sense of view. The rhuthmós was transmitted as the integral sum of the simulacra.

The flying wraps are the fluctuating edges, and the surfaces [are] limits. Summo de corpore. The simulacra peel away from things as when addressed via infinitesimals. [They are as numerous as you like.] Each object becomes the source of an infinity of envelops. [...] Every form is enveloped by an infinity of adherences, sliding infinitely from the virtual to the actual. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 103, my mod.)

In other words, Lucretius provided a theory of perception that was perfectly adequate with the rhuthmic aspect of atomist ontology. What the simulacra conveyed was the invisibly changing and impermanent shape of the things. The simulacra conveyed eurhythmically—in the sense of Xenophon (see Michon, 2018a)—the shape of any observed thing: because of their infinitesimal nature, they most perfectly fit the upper surface of the body, the exact limit of the atomic cluster, the ultimate envelop of the thing, exactly as the eurhythmic armor fitted well the warrior's body. Lucretius' theory of knowledge, which was naturally larger than his theory of perception, was based on an eurhythmic transfer of information.

Rhuthmic Theory of Forms

Similarly as Barthes' discussion on idiorrhythmy, Serres' meditation on Lucretius provided the elements of a most convincing critique of the Platonic metrical paradigm and, if I may say so, a powerful rhuthmical theoretical alternative.

As for physics, Serres noticed, Plato did not draw out enough information from observation. For instance, when in the Republic he reflected on the spinning top (436d sq.), he completely failed to notice the very peculiar nature of this toy. He did not realize that such a simple artifact could open entirely new paths to physics particularly by tightly coupling rest and movement (p. 29).

But Plato's main problem was maybe more theoretical than empirical because he did not lack spirit of observation. Plato's very speculation, Serres argued, has been limited principally by the primacy he granted to geometry upon theory of number and, in the latter, to rational upon irrational numbers. In contrast, Lucretius' physics obviously benefited from the elaboration by Democritus, maybe, and Archimedes, more surely, both of a new geometry and a new arithmetic (p. 29).

With Democritus and Archimedes, the Pythagorean mathematical paradigm that irrigated Plato's thought and resulted in Euclid's Elements, was subtly challenged. A “local mathematics, or, as it will be called, a differential geometry” opposed a “global mathematics.”

In the three cases listed, the indivisible [tangent and atom], declination [clinamen] and contours [with the theory of knowledge through perfectly fitting simulacra], we are concerned with a local mathematics, or, as it will be called, a differential geometry, an ultra-precise analysis of proximity, which in every place repeats the question: what happens as close as possible to the singularities? They are all different from the recognized Greek tradition, the one leading straight from Thales or Pythagoras to Plato. Strictly, they are also contrary to each other. Democritus takes for his subjects what for Platonists is an accident, and what for Pythagoreans was a disaster. They may be contrasted as a local and a global mathematics, as a science of idols and a science of ideas. [...] To the eyes of a Platonist the mathematics in question is false; for an Epicurean that of the Timaeus or of the dominant tradition is false. By true or false I mean these values with regard to the chosen system. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 103, my mod.)

One of the main stakes of this mathematical divide was the concept of form and consequently that of rhythm: its Platonic definition as heavenly, eternal, abstract and “global-mathematical,” i.e. “rational” entity (as much as its Aristotelian more empirical version) versus an earthly, ephemeral, concrete and “local-mathematical,” i.e. “differential” one. Whereas the former was based on the concept of “Idea” and reached directly (or indirectly through observation) by the intellect, the latter mobilized that of “idol” or simulacra and was first to be observed through the senses then elaborated by the mind. In other words, Archimedes and maybe Democritus provided the necessary mathematical and physical devices to give plain meaning to Democritus' particular concept of form, i.e. rhuthmós. They allowed for the first time a genuine rhuthmic epistemology.

The ideal forms of geometry are not transparent, invariable and empty, they are dense and compact, full almost to saturation, of a complex tissue, and covered, around the edges, with invisible veils which yet allow them to be seen, infinitesimal limits that nonetheless are there. Differential robes that glide over the shapes. [...] Hence the two opposing theories of knowledge: idols and ideas. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 103-104 – Serres' italics)

Ontologically speaking, there were no perfect, permanent, eternal and fixed Forms. These, mostly circle, triangle, rational numbers and proportions, were to be replaced by an Archimedean paradigm of helix, vortices, irrational numbers and infinitesimal calculus.

The Pythagorean or Platonic circle becomes the Archimedean helix. In other words, nature is not endowed with perpetual motion. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 58)

Physically speaking, “forms” were constantly in “nascent state,” they never stopped appearing, changing and melting. Forms produced new forms which produced in turn another generation of forms.

What is nature, if not the aggregate of objects, these forms that are in a nascent state and which transform this form? Thus the open circulation of the flow in general, the indefinitely broken cycle of spirals. Pseudo-solid volumes in which implication is undone, whose resistance melts. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 92)

Form produces forms, the productive agent and the product each causing the other. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 106)

Epistemologically, “forms” were not Platonic “ideal Forms, seen as empty and transparent” of which human beings met only deficient replicas and which could be known, strictly speaking, only through speculation.

The mathematics of the Epicureans, emerging with Democritus and given canonical form by Archimedes, is a science of images [idoles]: neuter producing infinite multiplicities of form. Auto-productive forms. The thing was inevitable given the realism of the compact and the dense, a prelude to physics; it opposes point by point the realism of ideal Forms [idéalités], seen as empty and transparent. Either the lucid subject and the luminous object, or the subject-object compact through and through. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 106)

They were not either Aristotelian forms that would be reached through observation but that would be productive and final entities driving the process of actualization of matter until completion. They were only occurring shapes, observed in reality or dream, and recognized by the transmission of the infinite number of infinitesimal points that compose the envelope of things.

But how can we explain this physical process [of production of forms], in its turn? With mathematics. With Democritus, who revealed the atomic constitution of shapes, and the infinite process of formation of their edges. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 106, my mod.)

According to Serres, this new physics triggered no less than “a paradigm shift” in physics, that became “more physicalist, less mathematicised (since it lacks a probabilistic organon) than Platonic knowledge, more phenomenal, less metrical,” according to a “fluid model.”

We would say that what we have here is paradigm shift. Science remains science and laws remains laws, what changes is the global contract. The general design of what the learned agree to call physics. [...] Epicurus, Lucretius changed the paradigm. [...] The new knowledge is aware of stochastic phenomena: incerto tempore incertisque locis does not signify the nullity of place and time, and thereby a passage to the soul outside the world of sensible qualities, but simply aleatory scattering [2.263]. It is informed, since Democritus by infinitesimal questions. It is inspired by hydrodynamic models and looks towards the formation of living systems. It is more physicalist, less mathematicised (since it lacks a probabilistic organon) than Platonic knowledge, more phenomenal, less metrical. But, above all, Athens is by the sea. The elective model is fluid. It is no longer crystal, or the five polyhedral solids, the body of the Timaeus, it is flow. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 112)

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Michel Serres and the Rhuthmoi of the Flow – Part 4

Pascal Michon — 2019-12-04T08:00:00Z

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On Some Limitations of the Atomist Physical Paradigm

In order to remain as objective as possible, I would like to finish this discussion with a few comments concerning some limitations of Lucrecius' as well as Serres' atomist physical perspectives. Actually both lacked consistent and adequate poetics and theory of language, and this is maybe the main reason why Serres did not understand the significance of Benveniste's 1951 philological contribution concerning the notion of rhuthmos, which had been probably the very first step towards the rhuthmic linguistics of discourse that he had eventually developed and presented in his two famous collections of essays in 1966 and 1974 (see Michon, 2010a).

Lucretius, due maybe to his legitimate distrusts towards some aspects of Aristotle's biology and physics—especially his equating of formal and final cause—did not pay any attention to his Rhetoric and Poetics. Instead, he indulged in a vague Epicurean imaginative reconstruction of the origin of poetry in the idyllic time of aboriginal men. His extreme naturalistic strategy, which had wonderful critical virtue regarding Platonism and mainstream Aristotelism, was quite limited when it came to accounting for language and poetry.

Men, he claimed, did invent language to express their “needs,” just as children do when they “point with fingers” at things and animals when they cry to express their “fear or pain” or when “they burst with joy” (Book 5, 1028-1061). Music appeared as imitation of the “liquid notes of birds” and the “whistlings of the wind athrough the hollows of the reeds.” (Book 5, 1379-1383) And poetry in turn was born from the music played and danced by shepherds “lounging with friends in the soft grass beside a river of water, underneath a big tree's branches.” (Book 5, 1392-1398)

This was all that was to be found, in the whole poem, on language and poetry. But this regrettable lack was also imperiling Serres' approach. Around the middle of his study, he asked an excellent and inescapable question: “Why is this text on physics a poem, why did Lucretius, writing it in Latin for the first time, write in verse?” (p. 135) But his answer was not at the level one could expect after reading such a wonderful essay which contributed so much to the recovery of the ancient rhuthmic physics. Serres was not that far from his hero. He confused poetry and music, rhythm and music. Even worse, whereas Lucretius was writing poetry and concretely elaborating poetic rhythms, Serres was a committed Aristoxenian without knowing it (on Aristoxenus see Michon, 2018a). He remained on the wrong side of Aristotle, whose Poetics he strangely disregarded and replaced by a physical and informational theory of noise to answer his own question.

How does this music [Lucretius' poem] emerge from the chaos-noise of the background, and how does the rhythm emerge from the pitcher's flow without return? (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, p. 135-136)

Since he did not have the theoretical means to address this issue, Serres tried to apply physics to an object that was much too complex to be accounted for by a theory of vortices emerging from the “background noise.” Such an explanation could possibly account for the formation of articulated sounds but what about phonemes in their differences? What about words in their idiomatic variations? What about texts? What about poems? The few answers he provided to these questions were quite limited, to say the least.

Language, according to him “emerge[d] from noise” by “declination, by drift” (p. 135). Poetry was limited to verse or parallel lines; rhythm was close to metrics; meaning arose from an absence of meaning by “something like a rotation” (p. 146).

Lucretius' poem was “written in a vortex,” it was “a vortex,” as any other natural production. It “turn[ed] back on itself without meeting itself [Il se boucle sans se boucler]” (p. 139).

These descriptions were so vague that they could even be true. But what made a poem different from a simple rock or an animal? How was it specifically organized? How did it flow? Why, for instance, the choice by Lucretius of a Greek genre, the didactic poem? Why the hexameter? How was the story told? How did it sound? How did it affect the reader or listener? What made it still interesting, moving, valuable to us? All these simple questions, that Aristotle addressed so carefully in his Poetics (for a thorough analysis, see Michon, 2018a), remained without answer in Serres' essay. Although he uncovered in Lucretius' poem a physics that had been forgotten for centuries, an essential part of it disappeared, probably because it did not fit in a simplistic physical approach. Lucretius' writing, poetry, prosody, poetic rhuthmos, and the poetic transsubject that animated it, all these aspects that fascinated Aristotle seemed irrelevant to the modern philosopher of science.

I think that these limitations concerning language and poetry were partly responsible, since the concept of subject—I do not say subjectivity or Self—depends on that of language, for the lack of convincing ethics too (for the concepts of “subject” and “transsubject” that I borrow from Meschonnic see Michon 2010a). It is quite difficult indeed to elaborate a convincing ethics based on human beings who are not only treated as rocks and rats but also as mute and deaf. Something was utterly lacking in this rhythmic physics: the bright side of Aristotle that was however brilliantly heralded by Meschonnic during the same period (see chapter below).

In Serres' account, Lucretius' ethics might be reduced to a naturalistic ethics, which ended up being utterly individualistic and merely consisted in a mystical retreat from the turbulences of society. The telos, as Barthes put it, was to identify with the world as it remained still underneath the conflicts and disasters of history and “rejoin material being [...] where no ripple has yet troubled the surface of the waters.”

The soul is knotted like the world. And like the world, it is unstable, deviating from equilibrium. Physics, psychology, give an account of these scattered knots where disturbances form. [...] Ataraxy returns to the initial turbulence, before any disturbance in the straight line of the flow. The wise man is the fundamental world. He rejoins material being, this ground of being itself where no ripple has yet troubled the surface of the waters. (The Birth of Physics, 1977, trans. Jack Hawkes, 2000, , p. 127)

But this did not account for the obvious fact that Lucretius was part of intellectual and artistic circles and painfully aware of the violence of the Roman society during the dreadful times of the end of the Republic. Neither for that other fact that Epicureans explicitly rejected the Stoic ideal of the wise man, living in complete autarchy, needing nobody's company, and preferred the paradisiacal image of a pleasure shared by a circle of friends gathered together in a garden. Actually, as many other philosophers, Serres confused what a poet said explicitly, the enunciated, l'énoncé—his proclaimed naturalistic worldview—and his way of saying it, the enunciation, l'énonciation —his poetry, his particular use of language, his specific rhuthmos, and the transsubject he launched thanks to it through time towards us. Lucretius did write for his friend Memmius and for us. Hence Serres did not wonder if the rhuthmos of the poem itself could not imply another ethics, a socially and politically oriented ethics that would contaminate from within Lucretius' naturalistic discourse.

With Serres' essay on Ancient atomism, we have reached another edge of the French rhythmic constellation of the 1970s and 1980s.

1. Whereas Lefebvre, Foucault and Barthes had mostly explored the ethical and political potential of the rhythmic perspective, and left aside, except in a few cases, its ontological, physical, and epistemological aspects, Serres focused on the latter and developed them into a comprehensive worldview, while inversely neglecting social and historical issues. In short, he provided a remarkable physical counterpart to his predecessors' social critiques, that could have help them to improve their theoretical sharpness and consistency, had they paid attention to it, just as he could have himself complemented his physics with their social reflections, if he had taken them into account. But as in any other constellations, although those stars appeared from afar to be close to each other, they were not acting together and had actually very few intellectual relationships.

2. However, something that was still missing from the first reflections on rhythm had now clearly emerged—at least in retrospect. Just as Barthes in his course on idiorrhythmy the very same year 1977, and in patent contrast to Lefebvre and Foucault, Serres firmly endorsed the opposition between the pre-Platonic concept of rhuthmos and the Platonic concepts of rhythm. For him, there was a clear opposition between two scientific paradigms: a “metrical” and a “fluid” one that we may call rhuthmical. The latter was the key towards a more innovative kind of thought, whereas the former could only recast any critical and imaginative scientific attempt into the deterministic dominant order.

3. Although Serres, unlike Barthes, did not acknowledge his debt, he actually brilliantly prolonged Benveniste's seminal study. Emulating Barthes' elaboration of a renovated ethical and political theory from the concept of rhuthmos, Serres engaged in a comparable reworking of physics from that of turbo. In Lucretius' poem, the term turbo meant, exactly as rhuthmós as a matter of fact, an impermanent form appearing and lasting for a certain period of time in a flow, observable by human beings. It fully complied with Benveniste's definition. But it had also some new features that made it more precise than its predecessor and that are worth summarizing here.

3.1 First, it was coupled with another concept, the clinamen – the inclination or turning aside, i.e. an infinitesimal angle appearing by chance in a flow, which explained the turbo's generation as well as its vanishing. The clinamen was a necessary conceptual extension that provided to the rhuthmós-turbo an ontological basis consistent with the new mathematical knowledge on minimal angle between a curve and its tangent.

3.2 The new mathematics made it also possible to overcome the ingenuous simplism of the older definition of rhuthmós based on an observation at a “certain moment of time” that was not very clearly specified. Thanks to the possibility to think of a mobile infinitesimal limit between time-lengths, it was now possible to present a rigorous account of the concepts of “way of flowing” or “mode of fulfilling a process or an action,” “appearance” and “disappearance.”

3.3 Lucretius provided a philosophical basis for the development and duration of things which did not call neither upon Plato's nor Aristotle's theory of individuation. Things appeared through stochastic gatherings of atoms in vortices and they lasted for a certain amount of time, due to an original tiny disequilibrium that made their temporary equilibrium possible.

3.4 Lucretius' physics provided a larger frame that extended the concept of turbo to nature as a whole. The latter was a turbo of turbines, a vortex of vortices, a network of interlacing and turbulent fluxes. It therefore powerfully opposed the Stoic model of a hierarchical and ordered system and anticipated our present idea of a complex system. Better yet, since it took into account the notion of decay, loss of energy, it anticipated the most recent concepts of open system and irreversibility. In nature, the circulation of fluxes never occurred as perfect circles and rather followed spiral and vortex patterns.

3.5 Time was not conceived any more as “an image of Eternity moving according to number” (Plato) nor as “number of motion in respect of ‘before' and ‘after'” (Aristotle). It was not considered as completely regular and homogeneous. It looked like a turbulent and rhuthmic flow providing accelerations, decelerations and returns, generations, stabilizations, mutations and disappearances.

3.6 Space was not either an abstract, empty and neutral room furnished with figures which could be perfectly measured and mastered. As time, it was not considered as homogeneous and metric (in the modern sense of metric system). It was endowed too with a certain turbulent quality that made it rhuthmic.

3.7 Anthropology was also thought of according to the physics of turbines. Body and soul, the latter with its two parts animus and anima, made up just one single vortex of vortices plunged into the larger dynamic system of nature. They constituted an open system, a seat of an exchange of flows that remained stable for a time.

3.8 This conception of the human being as mere element of nature supported a theory of perception which, Serres argued, was largely based on the new Archimedean mathematics. Indeed, the concept of flow of simulacra was not only coherent with the atomist worldview, it was also consistent with the differential calculus of the shapes that, so to speak, enveloped the things. This theory of perception gave a quite powerful account of a transfer of information whose infinitesimal bits most perfectly fitted the complicated surfaces of things.

3.9 This novel theory of perception was associated with a new theory of form. Forms were inner-worldly entities that appeared by chance and that could be best described through physical examination and mathematical calculus. Since they were impermanent yet observable, they were properly rhuthmoi. But since their perception depended on the flows of simulacra that perfectly fitted the things which sent them towards us, this transmission could also be characterized as eurhythmical—in Xenophon's sense (see Michon, 2018a).

In short, through his innovative study of Democritus' poem, Serres demonstrated the remarkable, yet entirely forgotten, extension of the Ancient rhuthmic thought that had covered no less than mathematics, ontology, individuation theory, physics and space-time theory, perception theory and theory of forms, at least until the 1^st century BC. It also allowed him to draw some possible lines between this forgotten Ancient thought and the most Modern theories of chaos and complexity that were emerging at the time.

Naturally this remarkable achievement had also some limitations that should not be deemed as marginal. Let us summarize them here briefly.

1. These limitations pertained first to Lucretius' as much as Serres' ways to treat language and poetry. Since the former disregarded Aristotle's contribution to rhetoric and poetics, and the latter ignored the posterior traditions that stemmed out of it, particularly in his time in the works of Benveniste and Meschonnic, language and poetry were unaccounted for, or only through myths. Language miraculously hatched from animal cries or natural sounds—sounds of the wind “athrough the hollows of the reeds” for Lucretius or plain noise for Serres—while poetry idyllically developed in aboriginal shepherd groups resting under trees on some river banks or, less romantically if not less mysteriously, as vortices of word. In both ancient and modern physics, nothing accounted for the fact that human beings speak and even turn, sometimes, speech into art.

2. Another problem, which was closely related to the previous one, concerned the ethics resulting from the physicists' naturalistic premises. As Barthes as a matter of fact, Serres agreed with the weak suggestions made by Lucretius who advocated small communities of friends enjoying leaving together and developing artistic activities. His concepts of society and State were even less elaborated than those of Barthes. He too was faithful to the anarchist and aesthetic spirit of 1968. It was difficult anyhow to imagine how such an ethics based on retreat—that is, somehow, on an inconsistent condemnation of the rhuthmic nature of things—could oppose the overwhelming rhythmic ethics and politics set up by Plato on authoritarian basis and circulated by his countless followers. It would be closer, actually, to some features of the original Aristotelian ethics and politics (see Michon, 2018a), but the paradoxical lack of poetics impeded any rapprochement.

3. Last problem: Serres did not realize that writing or composing poetry in a certain manner, with a certain rhuthmós, was in itself an ethical stand. It generated a transsubject that transformed in the first place the poet than the reader or the member of the audience (Michon, 2010a). As a poet, Lucretius knew that practically but he never mentioned it and made no comment on this particular dimension of poetry in which aesthetics and ethics merge.

Unlike Diderot, Goethe, or even Nietzsche, who had in the past succeeded in joining their materialist views of nature with a non-reductive view of humanity based on an independent theory of language and art (Michon, 2018b), Serres was unable to associate them within a common frame. To put it in a nutshell, Lucretius' physics—and by the same token Serres' philosophy—was a wonderful piece of rhuthmic thought that shed a bright light on numerous ontological and physical issues, but, because it lacked a theory of language and a poetics, it also lacked a credible anthropology, indulged in a simplistic naturalism and, consequently, only proposed very poor ethics and politics.

Next chapter

L'espace et le temps. Approches en philosophie, mathématiques et physique – Préface

Christophe Bouriau et al. — 2014-10-03T16:18:32Z

C. Bouriau et al., « Préface » dans L'espace et le temps. Approches en philosophie, mathématiques et physique, Paris, Kimé, 2011, 254 p. Paru dans la revue Philosophia Scientiæ n° 3/ 2011 (15-3), p. 9-16. Également accessible ici. Nous remercions Christophe Bouriau de nous avoir donné l'autorisation de reproduire ce texte sur RHUTHMOS.

Ce volume fait suite à un colloque qui s'est tenu les 25 et 26 mars 2010 à la faculté des Sciences et Techniques de l'université Henri Poincaré de Nancy. L'objectif était de faire se rencontrer philosophes, historiens des sciences, physiciens et mathématiciens autour de la question de la nature de l'espace et du temps.

Cette question connaît indéniablement un important regain d'intérêt dans la communauté scientifique. Y répondre est devenu, pour de nombreux physiciens, primordial dans la construction d'une théorie quantique de la gravitation, dernier

échelon, pense-t-on, avant d'accéder à une théorie unifiée de la nature inerte. Le questionnement dépasse largement le processus d'investigation normal du physicien théoricien. La capacité des équations à nous révéler ce qu'elles savent de l'espace-temps semble s'être maintenant épuisée et l'heure est revenue pour le physicien de se tourner vers le philosophe. On se plaît à imaginer Einstein dans une situation analogue il y a un peu plus d'un siècle. Conscient des limitations de la physique classique héritée de Newton, il comprend qu'il doit revenir sur les concepts les plus fondamentaux sur lesquels se fonde la théorie. Sa réflexion l'amène à une nouvelle définition du concept de simultanéité. Dans l'article fameux de 1905, Einstein présente brillamment sa nouvelle théorie relativiste comme une conséquence logique de cette nouvelle définition. On se plaît donc à rêver, qu'un siècle plus tard, une nouvelle redéfinition des concepts d'espace et de temps permettra de donner une nouvelle impulsion à la recherche en physique.

L'espace et le temps n'ont pourtant joué pendant longtemps qu'un rôle secondaire en physique. Réminiscences du monde supra-lunaire immuable d'Aristote, espace et temps sont absolus dans la physique newtonienne. Simple contenants pour la matière, ils ne tiennent qu'un second rôle de spectateurs. L'espace est traditionnellement présenté comme le théâtre dans lequel se jouent les événements physiques. L'enchaînement de ces événements se fera avec la même régularité pour tous les observateurs, indépendamment de leur position et de leur vitesse. La grande fécondité de la physique newtonienne tient au fait qu'espace et temps ont gagné au cours du XVII^e siècle une structure mathématique. La position spatiale est maintenant quantifiée par les coordonnées cartésiennes. À l'axe temporel viennent s'ajouter trois axes spatiaux, même si la direction du premier par rapport aux trois autres est relative puisque dépendante de l'observateur. La mécanique livre la connaissance de la trajectoire qui lie les coordonnées spatiales des points matériels avec le temps. Déjà une relativité galiléenne met en relation la perception de l'espace par différents observateurs. Les coordonnées cartésiennes mesurées par chacun d'entre eux sont reliées par des transformations galiléennes faisant explicitement intervenir le temps. Disjoints, espace et temps n'en sont donc pas moins indissociables en mécanique newtonienne.

Le bel édifice théorique résiste vaillamment à l'épreuve du temps. À la fin du XVIII^e siècle, aucun phénomène physique ne semble désormais hors d'atteinte de l'approche newtonienne. La conception sous-jacente d'espace et de temps apparaît incontournable pour les physiciens mais aussi pour les philosophes. Kant confère à l'espace et au temps le statut particulier de données intuitives a priori de l'entendement humain. Non seulement la nature, mais aussi notre manière de l'appréhender, sont construites autour de l'espace et du temps tels que les décrit Newton. Les nouveaux champs d'investigation de la physique au cours de la première moitié du XIX^e siècle ne viennent pas troubler cette situation idyllique. L'émergence de la thermodynamique montre néanmoins qu'une théorie physique efficace peut présenter une structure différente de la mécanique newtonienne. En outre, en introduisant une asymétrie entre les deux sens possibles d'écoulement du temps, le second principe semble recéler une explication physique possible à l'écoulement du temps qui viendrait compléter la conception newtonienne.

La découverte des géométries non-euclidiennes vient obscurcir un tableau trop parfaitement dressé. On presse la philosophie kantienne de justifier le rôle particulier qu'elle attribue à l'espace et au temps. La description newtonienne est examinée en détail. On s'interroge, comme le fait en particulier Henri Poincaré, sur la pertinence d'une géométrie plutôt qu'une autre pour décrire les phénomènes physiques. La théorie de l'électromagnétisme proposée par Maxwell vient troubler un peu plus encore les certitudes des newtoniens. L'interaction électromagnétique ne se propage plus à distance et de manière instantanée mais est transportée par des champs. Contrairement à la physique newtonienne, la nouvelle théorie n'est pas invariante sous les transformations de Galilée mais sous celles de Lorentz. Une révolution balaie le petit monde de la physique théorique. Newton s'efface devant Einstein. Espace et temps sont désormais totalement indissociables et jouent un rôle actif dans la transmission de l'interaction gravitationnelle. C'est parce que toute masse courbe localement l'espace-temps et que cette courbure peut se propager au sein du tissu spatio-temporel qu'une accélération est ressentie à distance.

L'onde de choc provoquée par la révolution einsteinienne n'a pas encore dépassé le cercle des experts qu'une nouvelle secousse se profile déjà à l'horizon. Une nouvelle physique s'impose aux chercheurs s'intéressant aux phénomènes à l'échelle atomique. On y découvre un monde étrange qui a bien peu à voir avec le monde macroscopique. L'électron, qu'on imaginait bien volontiers comme une particule ponctuelle, semble se diluer dans l'espace et, à la manière d'une onde, interfère avec les autres électrons et avec lui-même. Pire encore, la nature ne consent pas à révéler simultanément sa position et sa vitesse. La physique est maintenant à l'étroit dans l'espace-temps d'Einstein. La douce courbure provoquée par la distribution de la matière laisse place à une intense agitation à l'échelle de Planck. La relativité générale se révèle inadaptée à la quantification : les fluctuations quantiques déstabilisent l'édifice théorique. Comme au début du XX^e siècle, la nécessité d'une nouvelle approche fait son chemin parmi les physiciens. Les pistes sont nombreuses : théorie des cordes, géométrie non-commutative, théorie des boucles quantiques. Chacune met en avant une nouvelle conception de l'espace-temps.

Le présent volume souhaite faire partager les réflexions de divers spécialistes, physiciens, mathématiciens, philosophes, historiens des sciences, touchant les représentations de l'espace et du temps du XVIII^e au XX^e siècle, qui toutes abordent de manière plus ou moins directe le problème général suivant : l'espace et le temps sont-ils de simples idéalités conventionnelles, de simples instruments théoriques modifiables selon leur champ d'application, ou bien dénotent-ils quelque chose dans la réalité ? Leur nature respective s'impose-t-elle à notre pensée ou bien sommes-nous libres de les concevoir et définir comme nous le voulons, pourvu que ces conceptions et définitions soient théoriquement fécondes ?

L'article d'Olivier Bruneau montre l'importance de Newton pour Colin Maclaurin, qui à l'aide notamment de concepts considérés aujourd'hui comme fictionnels, ceux du temps et de l'espace absolus newtoniens, parvient à traiter efficacement la question de la figure de la Terre. Certes, l'espace et le temps absolus ne sont pas des fictions pour Newton ; il semble en revanche que pour Maclaurin, l'important réside davantage dans la valeur opératoire de ces notions plutôt que dans leur éventuelle réalité ontique. Il est intéressant d'observer ici qu'une approche fictionnaliste de l'espace et du temps, où l'on se contente de raisonner « comme si » ces notions dénotaient quelque chose dans la réalité, permet néanmoins un traitement correct des phénomènes. Il reviendra à Hans Vaihinger, auteur de la fameuse Philosophie du comme si (1911) et attentif lecteur de Newton, de manifester la fécondité d'une telle conception des outils scientifiques : ce n'est pas parce qu'une notion est dépourvue de corrélat réel qu'elle doit être rejetée, car elle peut être utile, voire indispensable au traitement correct de la réalité.

Dans une optique également idéaliste et conventionnaliste, Louis Allix se propose à travers diverses expériences de pensée de montrer qu'en faisant varier certaines propositions générales touchant les traits caractéristiques de l'espace, du temps, et de la causalité, il deviendrait possible de résoudre à nouveaux frais des énigmes classiques telles que la flèche de Zénon, Achille et la tortue ou le bateau de Thésée. L'article a ainsi le mérite de montrer que la manière dont nous posons certains problèmes théoriques et concevons leur solution dépend de certaines décisions, le plus souvent implicites, concernant la nature de l'espace et du temps. Il pose aussi la question très intéressante de savoir si ces variations contre-intuitives infligées aux représentations communes de l'espace et du temps ne pourraient pas malgré tout être compatibles avec certaines expériences de la réalité. De manière plus générale, l'article soulève la question de notre liberté par rapport aux concepts d'espace et de temps : sommes-nous libres de les définir comme nous le voulons, en nous fondant sur le seul critère de la fécondité théorique ? Jusqu'où cette liberté peut-elle s'étendre ?

Steven Bland, dans une perspective similaire, s'intéresse au conventionnalisme de Poincaré sous l'angle de la « révisionabilité » des théories face à l'expérience scientifique. Il démontre notamment que la doctrine poincaréienne échappe à la critique classique fondée sur certaines formes de holisme, grâce à sa profonde maîtrise de la nature fondamentale des connaissances scientifiques. Conventionnalisme et faillibilisme, touchant la manière de concevoir l'espace et le temps, sont ici clairement articulés l'un à l'autre.

Jean Eisenstaedt insiste pour sa part sur le caractère laborieux et collectif des récentes découvertes scientifiques concernant l'espace-temps. On sait bien que les faits historiques présentés en quelques lignes dans les manuels scolaires masquent généralement la formidable activité intellectuelle qui a permis une découverte ou l'élucidation d'un problème. La relativité générale n'échappe pas à cette règle. Ainsi, l'intuition géniale d'Einstein ne doit pas faire oublier que la compréhension fine de la relativité générale a nécessité durant plusieurs décennies les efforts de quelques-uns des plus grands physiciens. Jean Eisenstaedt nous relate comment l'existence d'une singularité dans la solution de Schwarzchild, décrivant notamment l'espace-temps au voisinage d'un trou noir, a pu être source de confusion. Il faudra attendre l'analyse du problème faite par Robertson puis les travaux de Kruskal en 1960 pour qu'enfin émerge un consensus au sein de la communauté des relativistes.

Dans un même esprit de recherche collective, Bernard Guy nous propose un programme de recherche destiné à reprendre un certain nombre de questions fondamentales de la physique contemporaine, afin de dégager des pistes permettant de revoir les concepts d'espace et de temps dans les sciences humaines et dans la vie quotidienne. Il se fonde pour cela sur une discussion de ces concepts, non en termes de substance, mais en termes relationnels : il convient en effet de rechercher dans toute relation un aspect spatial et un aspect temporel, afin de surmonter les difficultés conceptuelles ou logiques qui surviennent dans une perspective qui consiste à séparer trop arbitrairement la notion d'espace et celle de temps.

Jean-Yves Heurtebise, de son côté, s'attache à critiquer aussi bien une conception idéaliste du temps comme forme de notre représentation (thèse kantienne) qu'une conception instrumentaliste ou conventionnaliste réduisant le temps à un simple outil théorique efficace mais dépourvu de réalité (conception duhémienne par exemple). Il s'attache à montrer que la thèse selon laquelle le temps serait une qualité première ou une propriété de la Nature soulève en réalité moins de difficulté que la thèse idéaliste, pourtant beaucoup plus répandue, qui repose selon lui sur des présupposés méthodologiquement critiquables, et se heurte à certaines contradictions. L'article défend au final une conception du temps qui n'est ni strictement réaliste, ni strictement idéaliste, mais qui présente la temporalité comme « un intermédiaire entre une réalité ontologique et une représentation subjective ».

Prenant également ses distances à l'égard de la conception idéaliste, Christian Maes souligne qu'en balayant la conception d'un espace-temps a priori, la relativité générale a ouvert la voie à une réflexion nouvelle sur sa nature. Il est désormais légitime de s'interroger : pourquoi trois dimensions spatiales et une temporelle ? Quelle topologie pour l'espace-temps ? Pourquoi le temps ne s'écoule-t-il que dans une seule direction ? On se prend à rêver que les réponses à ces questions pourraient être données par une théorie unifiant dans un même formalisme les constituants les plus élémentaires de la matière avec l'espace et le temps. Il ne resterait alors plus aux physiciens qu'à patiemment déchiffrer la signification profonde de la théorie pour y découvrir l'explication à tous les phénomènes physiques, quelle que soit l'échelle de longueur à laquelle ils se produisent. Christian Maes s'inscrit dans la lignée de théoriciens plus proches de disciplines considérées moins fondamentales, comme la physique de la matière condensée, qui rejettent ce point de vue et affirment l'existence de phénomènes macroscopiques émergents, dominants mais pourtant très largement imprévisibles à partir des seules théories microscopiques. En se fondant sur l'observation que l'irréversibilité n'apparaît que dans la thermodynamique, il explique comment le sens d'écoulement du temps pourrait être une propriété émergente de l'espace-temps et non une propriété fondamentale. Il se fait également l'écho de la proposition fracassante de l'inexistence à l'échelle microscopique de la gravitation, qui serait un effet purement entropique et donc elle aussi un phénomène émergent.

Le terme d'émergence est également au cœur de l'article de Sharon Ford. Alors que les physiciens se contentent de la description des relations entre particules élémentaires, l'auteur nous invite à une réflexion sur leur nature propre. À partir d'entités immuables, puissances pures, émergeront les différentes particules du modèle standard, bosons médiateurs des interactions ou fermions. Ces entités fondamentales sont les trajectoires lumineuses, les géodésiques, du modèle Light-like Network Account développé par Sharon Ford. Comme dans les théories des cordes, des dimensions supplémentaires d'espace-temps, ouvertes ou compactifiées, permettent d'engendrer chacune des différentes particules et rendent inutile tout recours à différentes familles de particules. La masse émerge de la topologie des trajectoires. Finalement, l'identification des bosons de jauge avec le champ de puissance achève de construire le monde à partir du seul mouvement spatio-temporel d'un unique champ en puissance.

Alexis de Saint-Ours, pour sa part, montre que le concept de temps intègre diverses composantes notionnelles (changement, évolution, flux, présent, passé, futur, irréversibilité, simultanéité, causalité, etc.) qui ne s'agrègent pas toutes pour former un concept univoque du temps. Suivant le cadre théorique où elles s'inscrivent, ces composantes se conjuguent selon des modalités différentes, pour former tel ou tel concept du temps. L'article montre ainsi qu'il serait plus pertinent de parler de « figures » du temps plutôt que du temps au singulier. Il identifie cependant un trait commun à ces différentes figures du temps : c'est à chaque fois le changement qui permet de mesurer le temps, de sorte que la célèbre proposition d'Aristote, selon laquelle le temps est la mesure du changement, mériterait peut-être d'être inversée.

Gunnar Declerck, quant à lui, pose directement la question de la nature de l'espace : qu'est-ce que l'espace ? Pourquoi y a-t-il de l'espace plutôt que rien ? Il plaide pour une tentative d'explication de l'espace qui — contrairement à celle des sciences de la Nature qui néglige l'espace phénoménal du sujet — prenne en compte l'espace que nous construisons dans la perception, de manière à nous rendre intelligible le monde des possibles dont nous disposons. C'est à une genèse de l'espace que l'article nous invite, dans une perspective à la fois empiriste et constructionniste.

Pendulum Waves

2012-12-01T07:00:00Z

What it shows : Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning ! Aliasing and quantum revival can also be shown.

How it works : The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations. When all 15 pendulums are started together, they quickly fall out of sync—their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

Setting it up : The pendulum waves are best viewed from above or down the length of the apparatus. Video projection is a must for a large lecture hall audience. You can play the video below to see the apparatus in action. One instance of interest to note is at 30 seconds (halfway through the cycle), when half of the pendulums are at one amplitude maximum and the other half are at the opposite amplitude maximum.

Comments : Our apparatus was built from a design published by Richard Ber [1] at the University of Maryland. He claims their version is copied from one at Moscow State University. D^r. Jiri Drabek at Palacky University in the Czech Republic has informed us that it was originally designed and constructed by Ernst Mach, professor of mathematics in Praha and Vienna around the year 1867. The demonstration is used in the Czech Republic under the name Machuv vinostroj—the « Wavemachine of Mach. » The apparatus we have was designed and built by Nils Sorensen.

James Flaten and Kevin Parendo [2] have mathematically modeled the collective motions of the pendula with a continuous function. The function does not cycle in time and they show that the various patterns arise from aliasing of this function—the patterns are a manifestation of spatial aliasing (as opposed to temporal). Indeed, if you've ever used a digital scope to observe a sinusoidal signal, you have probably seen some of these patterns on the screen when the time scale was not set appropriately.

Here at Harvard, Prof Eric Heller has suggested that the demonstration could be used to simulate quantum revival. So here you have quantum revival versus classical periodicity !

Ce texte et la vidéo qui l'accompagne sont tirés de « Harvard Natural Sciences Lecture Demonstrations » en ligne ici. Ils nous ont été obligeamment signalés par Jean-Paul Vignal.

[1] Am J Phys 59(2), 186-187 (1991).

[2] Am J Phys 69(7), 778-782 (2001).

Self-organized criticality

Per Bak, Chao Tang et Kurt Wiesenfeld — 2011-06-25T20:04:15Z

Cet article, qui a fait date dans la théorie des systèmes dynamiques, a paru originellement dans Physical Review Letters, en juillet 1987.