First kind: FALL Opposite PHYSICS ATOMISATION: Second kind . 1 qUlva ence Op osite Equivalence Exception deviation from
equilibrium First kind: CLINAMEN MECHANICS AGGREGATION: Second Kind: PHYSICS
The universal law of rhe rush to equilibrium is double. lfit is the fall of heavy bodies, it is mechanics, if it is automation, it is physics. The fall is the mechanical equivalent of atomisation, and it is more simple. It says, in pure movement, what dissemination says in matter. Now, if something exists, this is because aggregation takes place, physically speaking, by and in matter. There is an exception to the general rule of irreversible atomisation. Hence its mechanical equivalent, simpler in pure move ment: the clinamen, as a local deviation from equilibrium.
describes the beam is identically the starry circuit of the flow. Solid angle, or cone, that is turbo in Latin.
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. Or, quite precisely, the smallest turbulence. In the light of the constructible models and the phenomena experienced during the meteora, things become clear. An instant and a minimum deviation are enough. 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. Fragile and protected by the round roof of minimal declination. Stable-unstable through homeorrhesis.
Experiences
This pocket, this seed, this island, this turbulence, holds for a certain time before disintegration, before being carried away by the cataract, the current of atoms that wear it out and break it. They preserve themselves by their differential deviation from every static law. This appears a paradox and yet is not: this temporary stability is only possible at the price of a small discrepancy in relation to the law of universal stability. For every static law is in fact either a law of falling, the first type, or a law of disintegration, the second type. Why does this hold? Simply because it does not hold completely. Every case will be a minimum degree out of true. There has to be a minimally open solid angle. Yes, it holds by a miracle. And by a miracle I mean the case statistically of extreme rarity. And Lucretius says just this: incerto tempore, incertisque locis, by chance, here and there, amid the universal cataract, by a stochastic dispersal, these deviations happen, these micro-turbulences or minimal cones occur from out of these islands or pockets. Bolts of lightning in the clouds, waterspouts. At the heart of some of these singularities, the flows equilibrate, the sea does not rise, the Nile regulates its floods and its falls, the compass card is roughly symmetrical. And so, it holds. Homeorrhesis, homeostasis, miracles at the heart of the general torrent, extremely rare local cases. To be wholly precise: exceptions to the static law. But, once again, exceptions as close as possible to the common root of the ordinary law, by this differential deviation. 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 laws under the rule of exception. Under the protective roof of its solid angle. And yet, that is the way it is. Lucretius is right.
He accomplished the revolution being carried through by the sciences of today and which philosophy continues to neglect. If the fall is universal, if its law, both kinds, can never suffer any exception, then every construction becomes impossible: there will be no world, there can be no physics. Correlatively, there will be neither discourse nor sense. And this indeed is the case, at least for closed systems. Now it happens, and no one can do anything about it, that at least something exists some of the time. This pebble, as it rolls along the thalweg, this house built with my hands, the smooth body of this woman, and this world under the sun. Our science has said, without really knowing it, that all this must not be. It is impossible. Reason delivered up to the death instinct and tending towards chaos. And every discourse is impossible. Yet, you speak and I understand. Thus there are open systems. Thus there are exceptions to the rule. Thus there is a nature. By this I mean that in the
sheet-water of the cataract, an aleatory scattering of turbulences and singularities are in the process of being born, at indefinite places, at improbable times. In the vicinity of birth, in generalised death. In this sense, at once rigorous and statistical, without nature there could be no physics. Without nature, that is to say, birth, the open, the exception, the miracle, the deviation. Science is no longer within order; order is equilibrium, death, and chaos. It is entirely within the extraordinary. Science is, throughout, the organon of the miracle, and the miraculous discourse. Science no longer partakes of the general, but of the ultra rare. Discourse is not ordinary, sense and sign are exceptional. And the minimal condition of this displacement, of which I have said elsewhere that the Copernican revolution was by comparison but a child's game, you will call declination. The principle of reason defines two reasons. Closed reason, equilibrium and chaos, cataract, indeed maintains that there is nothing. And shows it. If there is something, it is a nature. The rare formation of pockets, of islands, of waterspouts and seeds. The ultra-rare and aleatory birth, by the little deviation within a vicinity: that which is ready to be born, what is going to be born or to appear, in the open proximity of the differential inchoation. So the term of nature, in its very grammatical formation, makes declination inevitable. In the cataract of the meaningless, in which the atom-letters rush towards their fall, here is the birth of meaning. Discourse is a deviation from equilibrium as this or that state of things. As exceptional, as rare, as declined. It too, breaks the flow, the flow of things themselves. Atomist physics is a critique of closed reasoning. No. Not a critique. It is an architectonics of the opening in false perpendicularity founded on the irrepressible flight of the stable. Not a critique, but a clinic. The stable flees, and only the unstable can hold. The clinamen. This is how it is. And it is only this way as long as it turns. Lucretius is among us, he speaks
the same language as we do, his feet on the same earth.
As a consequence, things, phenomena, the world in its entirety, are all models for theory, and wrought by these two laws of nature. The law of death, universal, flowing in waves towards equilibrium, infinitely, and the stochastically distributed exception in the cataract, under the differential cones of declination, where the flow inclines, returns in a waterspout, diversifies, develops locally and constructs an aggregation that is temporarily stable because unstable. From which the vessels, the family of vessels, basins opened by declination itself, ceaselessly inclined, or in rupture of equilibrium, holding by a miracle and threatening to fall, whole sections crumbling into the cascade of the great flood if they
Experiences
pass the limit of rupture, but retaining their organisation for a time under the leaning roof where the beams bend. The framework delineates the declining world.
When we compare two or more manuscripts that have probably been subjected to successive recopies and we find that one of them has a passage or section that is more obscure than the equivalent sections of the other manuscripts, the rule expects us to choose the more obscure. In all likelihood it is the authentic or original text. The copyist, in fact, faced with a difficulty of understanding, steps back and can translate clearly. Clearly for him. For the easiest thing is interference, the simplest is the transmitter. A rule which is known by the name lectio difficilior,
choice ·of the most difficult reading. Just as if the series of copies ran towards maximum entropy. Now, analysis may apply the same rule as epigraphy. The interpreter, too, helps texts along.
Up until now, I have adopted the lectior difficillima on the atomism of the ancients. Here, the obscure section, the incomprehensible passage, or better, the paradoxical fact, is the introduction, the existence, the appearance of the clinamen. Translations softened the difficulty for rhetorical purposes. I have shown that it concerned an infinitesimal language, thereby explaining the recourse to Democritus, who instituted differential calculus on the basis of geometry and statics. A solution that illuminates the mathematical organon of presentation, but which leaves dark the thing itself. Which remains incomprehensible so long as history lacks a physics of open systems, and has not made the deviation from equilibrium possible. Which remains the more difficult before the revolutionary reversal which makes the clinamen the exception and the law, and makes knowledge of nature the science of the rare and not the general. The deviation from equilibrium as an ultra-rare exception to the universal laws of fall and dispersion is the only principle possible for the temporaty constitution of bodies, hurled into the irreversible cataract of the second law of thermodynamics. Only contemporary science allows us to see the darkness of the fact directly and to explain why interpretation always recoils before this most difficult reading.
Now this is even more difficult than it seems. I will explain. Everyone seems to agree that there was no physics, I mean mathe matical physics, before the end of the Renaissance. This thesis is debatable. In fact, there was none, at least before Euler and his theory of vibrating strings, at best before Fourier, with his analytic theory of heat. Before these two moments, there was only mechanics and geometry. Optics, in Gauss' approximation, is only geometry, the treatment of
heavy bodies is only mechanics. Then the emergence of physics occurs, in effect, in an interval around what we call the Industrial Revolution.
And so the new contribution of the classical age is precisely dynamics. For Galileo, Leibniz, the Bernoullis, right up until Lagrange. And so this means, roughly speaking, that the Ancients had nothing but a statics; and, beyond the language of the mathematician, a theory of equilibrium and of rest. And their limit is Archimedes, once again.
These historical references, simple and clear to all, make the difficulty plain. I have shown up to now that the whole question discussed by Lucretius was that of equilibrium. Bodies, aggregate or elementary, rush towards rest, either by the movement of falling, or by the scattering of their constituents. They fall and break, and it is all the same, just a question of statics; the reading returns, and it is the easiest. It is compatible with everything we know about the history of the sciences. Here is equilibrium, here is the deviation from equilibrium. But let us compare all this to Archimedes' treatise on Floating Bodies. I do not think I have yet shown the extraordinary dissymetry of the two works. From proposition VIII of the Book I and until the end, almost all of the theorems address the angle of inclination of a solid submerged with respect to its axis of symmetry. Most of the geometric proofs in Archimedes tend to show that a floating body left to find equilibrium in fluid reestablishes its axis and effaces the angle of inclination. In other words, Archimedes' hydrostatics removes an angle that Lucretius, on the contrary, introduces.
Allow me to return, for the moment, to Book VI, on the Meteora. It seems there is no rest here. A general theory of the flow. Thus a dyna mics? No, nonetheless; for I have shown that in the end everything con tinually returns to equilibirium, by the general process of homeorrhesis.
Hence I return to statics, and the most difficult reading is still the easiest. The homeorrhetic equilibrium is compatible with the general readings of the history of sciences.
Let us go into detail. Examine, for example, the explanation of thunder and lightning. They are produced, as we know, by the friction between clouds. And the clouds themselves are carried by the winds, on the pathways of the winds. Nothing, here, which has to do with rest or equilibrium, quite the reverse. There are the waves, sunt etiam fluctus per nubila.9 Fluctus is not only the flow or the flood, it is also agitation, disorder. But we know this well enough, those of us who speak of fluctu ation. Then, going up the series: wave, fluctuation, friction, lightning, ripping. But the hurricane sometimes surges in a cloud, hollows it out
Experiences
and causes it to explode. Line 126 says of this process: turbine versanti. I assume that the flow of the wind was a translation, that in the encounter with the cloud its movement changes. Which leads to an interesting observation: there are flows, but fluctuations; there are floods, but turbulence. The book on the Meteora is the book of turbulence. The examples just cited are only aerial. Here is the waterspout: versabundus enim turbo descendit.IO A liquid column in movement running straight on the waters. Here is the fiery summit of Etna: ut Aetnae expirent ignes interdum turbine tanto. II The fires exhaled by the broken crater in enormous spirals. As we have seen, the process is the same in earth quakes, in which the wind vortices in the cavities of the earth, opens an abyss and destroys cities. Turbulence at a stroke is trans-elementary: earth, air, fire, water. But, in book five, it affects the world, the move ment of the heavens, after Democritus: quanto quaeque magin sint terram sidera propter, tanto posse minus com caeli turbine ferri. 12 The more
closely the stars neighbour the earth, the less quickly they can be carried off in the circular vortex of the sky. So also with the moon: jlaccidiore etenim quanto iam turbine fertur inferior quam sol, etc.I) As it carries off the moon, this vortex is more languid in its given place below the sun . . . As for its form, at least what appears accidental, the waterspout, eruption, thunder, lightning, becomes the law of the movements of the universe. Whereupon we again find a correlation between the exception and the rule. Here, perhaps, is an opening to the words of Heraclitus, according to which lightning governs the universe. These are words on which Heidegger and his school have pronounced so many grandiose sublimities, and yet they simply mean that we never steer a vessel except by the angle of inclination given to the rudder, around which the streams of water leave their turbulence; then the lightning flashes and crashes like a perceptible clinamen, around which the winds and the clouds form their vortices.I4
The final outcome, the general theory of flow does not lead uniquely towards homeorrhesis. It also leads to a general theory of turbulence, general because trans-elementary, and generalised to the movements of the heavens. General finally because it traverses chance accidents and law-governed orders. Turbo, thus, is an important word. Quite close to
turba, the crowd, disorder, number and great number, the throng, chaos and agitation, we have already seen and discussed this. Quite close to
disturbare, destruction, bursting. But finally meaning a change in move ment. Now, since the elements, in statics, are in free fall in the void, all parallel to each other, is the turbo the result of the momen mutatum?
Things now become wonderfully simple. Take some flow, of water, wind or fire, of matter or of atoms. Ideally, without any constraint, each of its waves moves in parallel with all the others. We say of this flow that is laminar. Everything happens �s if each separable lamella in the flow acts without regard for any other. Hence there is only one question: how, in this flow, does turbulence happen? Or: how does a laminar flow become turbulent?
From hereon I am released from any recourse to contemporary knowledge that is cutting edge, as they say. To aid my understanding I have at my disposal a classical science, a science old as Archimedes and the Greek hydraulicists: fluid mechanics. Let me say this: Lucretian physics is modelled on a mechanics of flows. This is our experience. Fluid flows in hollow bodies: clouds, rainstorms and waterspouts, seas and volcanoes (the sky and the earth receive from the infinite in sufficient quantity all the elements that can suddenly make the shaking earth quake, hurl devastating turbulence through the sea and the lands,
rapidus percurrere turbo,'5 make the fire of Etna overflow and to kindle the sky), the Nile and rivers in flood, lakes, baths, menorrhea, water from wells and fountains, finally the lodestone. All bodies sink and everything flows: perpetuo fluere (VI, 922) nec mora necrequies interdatur ulla fluendi (VI, 933), without truce or rest, and all bodies are hollow
(VI, 936). Then the clouds reappear, bearers of germs and death, to destroy every living thing (perteurbarunt, VI, I097). Perturbatus enim totus trepidabant (VI, 1280): return to disorder. The exception, the law, the return to chaos. Everything flows, turbulence appears, temporarily retains a form, then comes undone or spreads. Physics is entirely projected on the current events of hydraulics in general. The physics of Lucretius is a hydraulics.
This remains true to descriptions of experience. From lightning to the lodestone, and from perception to the wearing away of things. Is this true for theory? Let us examine Book II. It begins with the famous line:
suave, mari magno turbantibus aequora ventis, which is now suddenly stripped of its psychologism. How, in open sea, in the greatest hollow, without the various flows suffering any constraint from the shores, does the general turbulence of air or water appear. Thus a treatise on the mechanics of fluids. And the first line has the status of a title. The reading is thereby made easier. Yet no. For the problem raised, that of turbulence, is no longer a static question, it is a dynamic question. Not of hydrostatics, but hydrodynamics. And this is incompatible with the state of sciences in Antiquity. We fall, once again, upon a lectio
Protocol
difficilior. It seems obvious, but it is impossible. Inversely, homeorrhesis was not obvious, but it was possible. It was an equilibrium. Rhesis, here,