Focussing on the largest text still intact to reach us from the Atomists - Lucretius' De Rerum Natura - Serres mobilises everything we know about the related scientific work of the time (Archemides, Epicurus et al) in order to demand a complete reappraisal of the legacy. Crucial to his reconception of the Atomists' thought is a recognition that their model of atomic matter is essentially a fluid one - they are describing the actions of turbulence, which impacts our understanding of the recent disciplines of chaos and complexity. It explains the continuing presence of Lucretius in the work of such scientific giants as Nobel Laureates Schroedinger and Prigogine.
This book is truly a landmark in the study of ancient physics and has been enormously influential on work in the area, amongst other things stimulating a more general rebirth of philosophical interest in the ancients.
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FIRST MODEL: DECLINATION IN A FLUID MILIEU
Everyone knows that atomist physics is an ancient doctrine but a contemporary discovery. It is a matter of science, the science of Perrin, Bohr or Heisenberg, whereas the ancient doctrine is only 'philosophy' or even poetry. Like history in general, that of the sciences has a prehistory. Just as there is no mathematics before the Greek miracle of Thales and Pythagoras, so there is no physics before the blessed classical age, before what has, roughly since Kant and the Enlightenment, been called the Galilean revolution. During this prehistory, 'philosophy' slumbered. We recognise, I believe, ideologies, religious or otherwise, by their use of the calendar as a dramatic device: before or after the birth of Christ, before or after the foundation of Rome or the first year of the Republic, before or after the establishment of the positivist catechism, before or after the Galilean revolution. Nothing will ever again be as it was. Here is the age of metaphysics; there is the age of positivism.
From Cicero to Marx and beyond, down to our own time, the declination of atoms has been treated as a weakness of the atomist theory. The clinamen is an absurdity. A logical absurdity, since it is introduced without justification, the cause of itself before being the cause of all things; a geometrical absurdity, in that the definition that Lucretius gives is incomprehensible and confused; a mechanical absurdity, since it is contrary to the principle of inertia and would result in perpetual motion; a physical absurdity in general, since it cannot be shown experimentally. No one has ever seen a heavy body swerve suddenly from its path as it falls. Therefore, it is not a matter of science. And so the clinamen finds a haven in subjectivity, moving from the world to the soul, from physics to metaphysics, from the theory of inert bodies in free fall to the theory of the free movements of living beings. It is the last secret of the decision of the subject, its inclination. Lucretius's text itself points in this direction, speaking soon enough of the will as torn from destiny and of horses that hurl themselves from their open stalls. Modern materialists dislike this rupture in determinism and regard it as the idealism of a free subject. The whole discussion of indeterminism will later reproduce the classical debate on the subject of the clinamen in the domain of the sciences.
On the other hand, the absurdity of such a principle is another proof, and a decisive one this time, of the prehistoric status of Greco-Roman physics. This was not a science of the world but an impure mixture of metaphysics, political philosophy and musings on individual freedom, projected onto the things themselves. Hence the crude critical outcome: there was no atomist physics in Antiquity. What is more, no applied sciences in general and the clinamen on which it is based is just an immaterial property of the subject. We must read Lucretius's De rerum natura as humanists or philologians and not as a treatise on physics.
Let us go back to Book 2, where declination is introduced. It is characterised primarily by two phrases. Paulum and tantum quod momen mutatum dicere possis: atoms, in free fall in space, deviate from their straight trajectory 'a little ... just so much as you might call a change of motion' (2: 219–20). Their deviation is as small as can be, and the alteration in their movement is as small as description allows. Lucretius repeats and redefines this deviation a little further on: nec plus quam minimum, 'not more than the least possible' (2: 244). Classical editions note a rhetorical device in these lines. The thing is so absurd and so far from our experience that the physicist minimises it, as if to hide it. Now, anyone who has ever read any Latin texts on mathematics, and more specifically on differential calculus, will recognise 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 produced at once 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.
On the subject of fluxions, let us examine the atomic cataract in which this infinitely small angular deviation is produced. In the preceding lines, Lucretius shows that the movement of bodies cannot take place from low to high, and the examples he cites are instructive. To explain the movement of fire, he uses liquid models: the flow of blood, the red gush which spurts, the fluidity of water, umor aquae (2: 197). In the same way, just prior to the passage on the clinamen, he shows us the lightning path obliquely crossing the rainfall, nunc hinc, nunc illinc (2: 214), now on this side, now on that. And the same rain is there again in the definition of declination, imbris uti guttae (2: 222), like the drops of rain. There we have it.
The absurdity of all this to critique, and perhaps the whole question, arises from what has always been considered the original fall of atoms in the global framework of a mechanics of solids. All the more so since the emergence of the inaugural Galilean moment in this discipline. For us, mechanics is first and foremost that of solids. It is clear-cut. The mechanics of fluids is or has been only a special case, which the most important texts, that of Lagrange, for example, only take up in the final pages and as an afterthought. But now we must reverse the perspective. Modern science is born, or has its renaissance, in the works of Torricelli, Benedetti, da Vinci, those of the Accademia del Cimento, which concern fluids as much if not more than solids. The Latin world is as one on this subject: Vitruvius expressly devotes a book in his treatise on architecture, the eighth, to the flow of water, and Frontinus writes an entire book on the aqueducts of Rome. A century before Lucretius, the works of Archimedes had raised hydrostatics to a state of perfection equal if not superior to that of ordinary statics. And both in his own time and before him the works and achievements of the Greek hydraulic engineers were remarkable.
If it is absurd that a small solid mass might at some moment deviate from the orbit of its fall, let us see whether the same is true where the primary atomic cataract is like a stream, like a flux, like the flow of a liquid. Lucretius says elsewhere that physics is about masses, fluids and heat. And since for him everything flows, nothing is truly of an invincible solidity, except for atoms.
In the primary cataract, atoms are not touching. When encounters and connections occur, bodies are characterised according to their resistance. The hardest, like diamond, stone, iron or bronze, owe their solidity to the fact that their atoms are tangled, branching, knotted into a tightly packed fabric. As we move towards the fluids and gases, the atoms are rounder and smoother rather than hooked, of course, but in particular they are less tangled among themselves. We could even say that, when the fabric is completely unravelled, we are in the presence of a very subtle flow, in any case one that is not globally solid.
So there is flow; we will call it a laminar flow. This means that however small the laminae cut from the flow may be, the movement of each is strictly parallel to the movement of others. This model is faithful to the description in De rerum natura. These lamellae are its elements; they are solids but the cataract is fluid. Now a laminar flow is ideal and in effect theoretical. In the real world it is very rare that all the local flows remain parallel. They always become more or less turbulent. The question to be raised, which we ask here, is the following: How do vortices form? How does turbulence appear in a laminar flow? Parallel flow is taken initially as a simple model. Perhaps originary, I do not know, but in any case much less complicated or tangled than a swirling flow. Now the question we raise and which we are in the process of resolving, by way of many experiments and localised theories, is exactly Lucretius's question. I will formulate it again: if the fall of atoms is an ideal laminar cataract, what are the conditions under which it enters into concrete experience, that of vortical flow?
Now this vortex, tourbillon – [TEXT NOT REPRODUCIBLE IN ASCII], dine, [TEXT NOT REPRODUCIBLE IN ASCII] dinos – is nothing but 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 of rotation and translation given by the flow and the fall, the laminar cascade. Question: how does rotation appear? Answer: the clinamen is the smallest imaginable condition for the original formation of turbulence. In the De Finibus, Cicero wrote that atomorum turbulenta concursio, that is, atoms meet in and by turbulence.
Let us return to the text: just as the oblique flight of the lightning bolt cuts across the parallel lines of rain nunc hinc, nunc illinc, here and there, so declination appears in laminar flow as the minimum angle in the inception of turbulence, incerto tempore, incertisque locis (at times quite uncertain and uncertain places, 2: 218–19). A fresh argument with which traditional science may accuse Lucretius of ignorance and imprecision. This has nothing to do with science, since the incident is uncertain in time, uncertain in place, and in each case undetermined. The argument says nothing about the model or the description, but a great deal about its own ideal of science. For it to carry weight, knowledge should have nothing to say about chance distributions. What Lucretius says, however, remains true, that is, faithful to the phenomenon: turbulence appears stochastically in laminar flow. Why? I do not know why. How? By chance, with respect to space and time. And, once again, what is the clinamen? It is the minimum angle for the formation of a vortex, appearing by chance in a laminar flow.
The only line of Lucretius that everyone knows by heart is the very famous Suave mari magno (2: 1), generally translated as a rhapsody to selfish serenity. It opens Book 2, where declination is introduced. Now, our cultural memory only retains the first part. The passage continues, turbantibus aequors ventis. Here are vortices in a fluid medium, water and wind, presented as a heading, at the beginning of the world. A repetition of the Democritean diné.
A first model may already be constructed. A working hypothesis and experimental protocol. To understand the atomist undertaking and not consider it absurd and archaic, we must give up the general framework of solid mechanics. It is that of our modern world, its distinctive technology and its speculation. Perhaps the Mediterranean world needed water more than tools; perhaps it was more preoccupied with rain, storms and rivers. It built reservoirs and aqueducts. Hydraulics were important to it. What is hard to understand here is not the local occurrence of declination, but its inscription in another mechanics, another science than that of fluids. For Lucretian, physics is entirely immersed in it.
Who can fail to see that a flow does not remain parallel for long, who can fail to see that a laminar flow is merely ideal and theoretical? Turbulence soon appears. In relation to theory, the appearance of concrete experience is contemporaneous with that of vortices. Declination is their beginning. Nothing here is absurd. Everything is exact, precise and even necessary.
We must therefore outline a sheaf of parallels. Then at some point in the flow or cataract, mark a small angle and, from this, a spiral. In this movement, the atoms, separate until now, will meet: atomorum turbulenta concursio. But the text is still more precise: it refers to mathematics, to a differential calculation, to the ideal of a great number, to a whole corpus implicit in the model. We need then to look for a man, the one who wrote and conceived this corpus.
The work of physics begins. Here is the protocol. Here are the experiments, the complete models, the awaited mathematisation and the countless applications.
ANALYSIS OF THE HYDRAULIC MODEL
A history of the angle. When the classics try to describe will, freedom or uncertainty, they often appeal to the image of a pendulum or balance. The infinitesimal angle of the beam, the smallest change in the balance of the pans – here is decision, determination, sometimes anguish, unrest. This is not declination, says Leibniz, it is inclination. These simple machines are models. And poor models, because they are static. The theory behind them at the time was of equilibrium, their machines were stators – statues – and their psychology, a mechanics or rather, the image of a statics. You forget about geometry and you think you are talking about the subject, but in fact you are only talking about machines. This forgetting will last a long time, long enough at least so that by the beginning of the nineteenth century the angle in the atom is nothing but the freedom of the subject. Reality grows faint, a dream of the soul. We must therefore go back to the Greeks.
Their classical method is the measurement of segments. Hence, their sections or their polytomies. Their primary figure, the triangle, is in fact a trilateral: primary in the possible construction of figures on a plane, and thus primary in the world, as we see in the Timaeus. We have to wait a considerable time for the measurement of angles to be added to the measurement of other elements, sides or other things, that is, for the formulation of trigonometry. The angle remains a shape, a corner, like a quality, and it resists efforts at quantification. Its trisection remains, 17 for example, a very difficult problem. It is acute, pointed, obtuse and noticeable. It is less easily abstracted than a length or a segment, by which I mean less easily related to number. Perhaps more so to movement; this is why with a view to measurement figures must be superposed, and so transported. It is precisely because they are angled.
Now the first possible angle that may be constructed or perceived, the smallest that may be formed, so that nothing can be inserted between the two lines which open, is that which lies between a curve and its tangent. In the language of geometry, it may be called nec plus quam minimum or in the language of mechanics paulum, tantum quod momen mutatum dicere possos (2: 219–20). In other words, the angle appears at the same time as curvature. Between two straight lines or two line segments, this minimal angle makes no sense. When calculating with shapes or rectilinear solids in general we only need 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, and it is reasonable to suppose, as do Heiberg and Tannéry, that the theory of irrational numbers served him as a springboard towards atomism. In each case, it is a question of divisibility and indivisibility. In each case, the last division recedes beyond our reach. This is not all: we know, from a reference in Plutarch and by a section of Archimedes's Method, that Democritus provided solutions for the volume of a cone or a cylinder, 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. This presupposes a differential division, and so once again an atomist interpretation. Democritus is the Pythagoras of things, of the irrational and of the differentiable. It is inevitable that the first integrator should take things to be formed of a crowd of subliminal atoms. Not yet of an infinite 'sum' of infinitely small things, but of a very great number of subdivided things. In this way, one crosses the threshold of perception at the same time as that of operation.
Excerpted from "The Birth of Physics"
Copyright © 1977 Les Editions de Minuit.
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