The Rise and Fall of Atomism

So-called ‘primitive’ soceties by and large split the world into two, what I call the Manifest (what we see, hear &c.) and the Unmanifest (what we don’t but in some way seem to be aware of). For the ‘primitives’ everything originates in the Unmanifest, especially the really drastic and inexplicable changes like earthquakes, storms, floods, but also more everyday but nonetheless mysterious occurrences like giving birth, changing food by heating it, growing up, dying. The Unmanifest is much more important than the Manifest and the shaman, or his various successors, the ‘sage’, ‘prophet’, ‘initiate’, and so forth,  claims to have special knowledge because he or she has ready access to the Unmanifest which normal people do not. Ultimately, a single principle or ‘force’ drives everything, what has been variously termed in different cultures mana, wakanda, ch’i ….  Mana is ‘what makes things go’, in particular what makes them more, or less, successful. If the cheetah can run faster than all other animals, it is because the cheetah has more mana and the same goes for the racing car; it is because he has more mana that a warrior wins a contest, because a young woman has more mana than her rivals that a young girl  has more suitors, and so on. Charm and charisma are watered down modern versions of mana.
Our civilization is founded on that of Ancient Greece (much  more so than on ancient Palestine). The Greeks, the ones we take notice of at any rate, seem to have been the first people to have disregarded the Unmanifest entirely and to have considered that supernatural beings, whether they existed or not, were not required if one wanted to understand the universe and its physical processes. Democritus of Abdera, whose works have unfortunately been lost,  kicked off a vast movement which has ultimately led to the building of the Hadron Particle Collider, with his amazing statement, reductionist if ever there was one, Nothing exists except atoms and void.
Atoms and void, however, proved to be not quite enough to describe the universe : Democritus’s whirling atoms and the solids they composed when they settles themselves were seemingly subject to certain  ‘laws’ or ‘natural principles’ such as the Law of the Lever or the Principle of Flotation, both clearly stated by the brilliant Archimedes.  A new symbolic language, that of higher mathematics, was needed to talk about such things since the “Book of Nature is written in the language of mathematics” as Kepler, a Renaissance successor and admirer of the Greeks,  put it. Geometry stipulated the basic shapes and forms to which the groups of atoms were confined when they settled down — and so successfully that, since the invention of the high definition microscope, ‘Platonic solids’ and other fantastical shapes studied by the Greeks can actually be seen embodied in the arrangement of molecules in rock crystals and in the fossils of minute creatures known as radiolarians.
To all this Newton added the important notion of Force and gave it a precise meaning, namely the capacity to alter a body’s state of rest or unaccelerated straight line motion, either by way of contact (pushes and pulls) or, more mysteriously, by  ‘attraction’ which could operate at a distance through a vacuum. Nothing succeeds like success and by the middle of the nineteenth century Laplace had famously declared that he had “no need of that hypothesis”  — the existence of God — to explain the movements of heavenly bodies and Helmholtz had declared that “all physical problems were reducible to mechanical problems” and thus, in principle, solvable by applying Newton’s Laws. As to everything else, not only spirituality but even human thoughts and emotions, the implication was (and Hobbes and La Mettrie even spelled this out categorically) that such matters were also ultimately reducible to “matter and motion” and that it was only a matter of time before everything would be completely explained.
The twentieth century has at once affirmed and destroyed the atomic hypothesis. Affirmed it because molecules and atoms have been shown to exist and can even be ‘seen’ on an electron microscope. They are, moreover, undoubtedly involved in most, possibly all, physical processes including mental processes. However, atoms have turned out not to be indestructible or even indivisible as the early scientists supposed.  Atomism and materialism have, by a curious circular route, led us back to a place not so very far from our original point of departure since the new scientific buzzword, ‘energy’, has disquieting similarities to mana.  No one has ever seen or touched ‘Energy‘ any more that they have ever seen or touched mana. And, strictly speaking, Energy signifies in physics ‘Potential Work’, i.e. Work which could be done but is not actually being done, where Work has the precise meaning, Force × distance moved in the direction of the applied force. (We are nonetheless constantly assured in popular and not so popular books that “at bottom the universe is radiant energy” whatever that means.)
The present era thus exhibits the contradictory tendencies of being on the one hand militantly secular and ‘materialistic’ both in the acquisitive and the philosophic senses of the word, while the basis of all this development, good old solid ‘matter’ composed of  “hard, massy particles” (Newton)  and “extended bodies” (Descartes) has all but evaporated. When he wished to refute the idealist philosopher, Bishop Berkeley, Samuel Johnson famously kicked a stone, but it would seem that Bishop Berkeley has had the last laugh.

A New Starting Point?

Since the wheel of thought concerning the physical universe has, in a sense, more or less turned full circle, a few brave souls have wondered whether, after all, ‘atoms’ and ‘extended bodies’ were not the best starting point, and one might do better starting with something else. What? On the fringes of science and philosophy, there was for a while a certain resurgence of ‘animism’ in the form of Bergson’s élan vital (‘Life-force’) , Dreisch’s ‘entelechy’ and similar concepts. The problem with such theories is not that they are implausible — on the contrary they have strong intuitive appeal — but that they seem to be scientifically and technologically sterile, since it is not clear how such notions can be represented symbolically by mathematical (or other) symbols and tested in laboratory conditions.
Einstein pinned his faith on ‘fields’ and went so far as to state that “matter is merely a region where the field is particularly intense”. However, his attempt to unify physics was unsuccessful : unsuccessful for the layman because the ‘field’ is an elusive concept at best, and unsuccessful for the physicist because Einstein never did succeed in unifying mathematically the four basic physical forces, gravity, electro-magnetism and the strong and weak nuclear force.
More recently, there have been several attempts to present and attempt to elucidate the universe in terms of ‘information’, even to view it as a vast computer (though one wonders quite how literally we are supposed to take this). As far as I am concerned the weakness of such an approach is that it is so crudely anthropomorphic, projecting onto the universe the current human fascination with computing : one hopes that the universe or whatever is behind it has better things to do than simply pile up and sift information like the Super Brains of Olaf Stapledon’s remarkable fantasy Last and First Men.

The Event

During the Sixties and Seventies, at any rate within the booming counter-culture, there was, for a while, the feeling that the West had somehow ‘got it wrong’ and was leading everyone towards disaster with its obsessive emphasis on material things. The principal doctrine of the hippie movement was that experiences were more important than possessions — and the more outlandish the experiences the better.  Zen-style ‘Enlightenment’ seemed more to the point than the Eighteenth century movement of the same name which had spearheaded Europe into the secular, industrial era. A few physicists, such as Fritjof Capra, argued that although classical physics was very materialistic, modern physics “wasn’t like that” and had strong similarities with the key ideas of eastern mysticism. However, though initially attracted, on further examination I found modern physics with wave/particle duality, quantum entanglement and uncertainty everywhere rather too weird, and what followed after, String Theory, completely unintelligible and for that matter devoid of the slightest confirmation  so far.
Moving towards middle age, I realized with increasing alarm, given the highly technological era I had the misfortune to be born into,  that I had entirely forgotten all the elementary mathematics I had reluctantly learned at school and set about remedying this.  I had no trouble with geometry and (whole) Number Theory, the Greek sciences, but found Calculus a major stumbling block, not because it was difficult as such but because its principles and procedures were so completely unreasonable. D’Alembert is supposed to have said to a student who expressed some misgivings about manipulating infinitesimals, “Allez à l’avant; la foi vous viendra” (“Keep going, conviction will follow”), but in my case it never did. Typically, the acceleration (change of velocity) of a moving body is computed by supposing the velocity of the body to be constant in the neighbourhood of a particular moment in time, then reducing this interval as much as possible. And the velocity of the same body is computed by supposing its position to be fixed (stationary) during a particular small interval of time and then reducing this interval likewise. In effect, ‘classical’ Calculus had its cake and eating it too —  something we all like doing if we can get away with it — by setting (δx) at non-zero and zero simultaneously in the same equation. ‘Modern’, i.e. post mid nineteenth-century Calculus, solved the problem by the ingenious concept of a ‘limit’, the key idea in the whole of Analysis. Mathematically, it is irrelevant whether or not a particular function actually attains  a given limit (assuming it exists) just so long as it approaches it more and more closely. (For more specific details see a future post on my other website www.originsofmathematics.com). But what anyone with an enquiring mind wants to know is whether in reality the moving arrow actually attains its goal or the closing door actually slams shut (to use two examples mentioned by Zeno). As a matter of fact in neither case do they attain their objectives according to Calculus, modern or classical,  since, except in the most trivial case of a constant function, ‘taking the derivative’ involves throwing away non-zero terms on the Right Hand Side which we have no right to get rid of. In any case, as Zeno of Elea pointed out over two thousand years ago, if the body is in motion it is not at a specific point, and if  situated exactly at a specific point, is not in motion. I don’t see how one can quarrel with the logic of that, Calculus or no Calculus.
This whole issue can, however, be easily resolved by the very natural supposition (natural to me at any rate) that intervals of time cannot be indefinitely diminished and that motion consists of a succession of stills in much the same way as a film we see in the cinema gives the illusion of movement. Calculus only works, inasmuch as it does work, if the increment in the independent variable is ‘very small’ compared to the level we are interested in, and the more careful textbooks warn the student against relying on Calculus in cases where the minimum size of the independent variable is actually known — for example  in molecular thermo-dynamics where it cannot be smaller than that of a single molecule.
All this will be examined in detail later but suffice it to say that I was suddenly convinced that ‘time’ was not continuous, as it is always assumed to be in mathematics — indeed I had always felt it to be a succession of moments —  and that there was indeed a minimal possible ‘interval of time’ and which, moreover, was absolute and not dependent on the position or motion of an observer. I was heartened when, subsequently, I read that nearly two thousand years ago, certain Indian thinkers had advanced the same supposition and even, in one or two cases, apparently attempted to give an estimate of the size of such an ‘atom of time’. More recently, Whitrow, Stefan Wolfram and one or two others, have given estimates as will be examined in due course. The essential was that I suddenly had the barebones of a physical schema : ‘reality’ was composed of  events, not of objects, and these events were decomposable into ‘ultimate events’ which had a fixed spatial and temporal extension. Ultimate Event Theory was born, though it has taken me some twenty-five years to pluck up the courage to put the theory into the public domain, so enormous is the paradigm shift involved in these few innocuous sounding assumptions.    S.H. (Tuesday 28 June 2011)

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