The Rise and Fall of Atomism

So-called ‘primitive’ societies by and large split the world into two, what one might call the Manifest (what we see, hear &c.) and the Unmanifest (what we don’t perceive directly but intuit or are subliminally aware of). For the ‘primitives’ everything originates in the Unmanifest, especially drastic and inexplicable changes like earthquakes, sudden storms, avalanches and so on,  but also more everyday but nonetheless mysterious occurrences like giving birth, changing a substance by heating it (i.e. cooking), growing up, aging, dying. The Unmanifest is understandably considered to be much more important than the Manifest — since the latter originates in the first but not vice-versa — and so the shaman, or his various successors, the ‘sage’, ‘prophet’, ‘initiate’ &c. claims to have special knowledge because he or she has ready access to the Unmanifest which normal people do not.  The shaman and more recently the priest is, or claims to be, an intermediary between the two realms, a sort of spiritual marriage broker. Ultimately, a single principle or ‘hidden force’ drives everything, what has been variously termed in different cultures mana, wakanda, ch’i ….  Ch’i is ‘what makes things go’ as Chuang-tzu puts it, in particular what makes things 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; a warrior wins a contest of strength because he has more mana, a young woman has more suitors because of mana and so on.
Charm and charisma are watered down modern versions of mana and, like mana, are felt to originate in the beyond, in the non here and now, in the Unmanifest. This ancient dualistic scheme is far from dead and is likely to re-appear in the most unexpected places despite the endless tut-tutting of rationalists and sceptics; as a belief system it is both plausible and comprehensible, even conceivably contains a kernel of truth. As William James put it, “The darker, blinder strata of character are the only places in the world in which we catch real fact in the making”.
Our own Western civilization, however,  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 physical universe: basic natural processes properly understood sufficed (Note 1). 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 settled themselves down were seemingly subject to certain  ‘laws’ or ‘general principles’ such as the Law of the Lever or the Principle of Flotation, both clearly stated in quantitative form by Archimedes.  But a new symbolic language, that of higher mathematics, was required to talk about such things since the “Book of Nature is written in the language of mathematics” as Kepler, a Renaissance successor and great admirer of the Greeks,  put it. Geometry stipulated the basic shapes and forms to which the groups of atoms were confined when they combined together to form regular solids — and so successfully that, since the invention of the high definition microscope, ‘Platonic solids’ and other fantastical shapes studied by the Greek geometers can actually be ‘seen’ today 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 constant straight line motion, either by way of contact (pushes and pulls) or, more mysteriously, by  ‘gravitational 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 while Helmholtz declared that “all physical problems are reducible to mechanical problems” and thus, in principle, solvable by applying Newton’s Laws. Why stop there? The dreadful implication, spelled out by maverick thinkers such as Hobbes and La Mettrie,  was that human thoughts and emotions, maybe life itself,  were also ultimately reducible to “matter and motion” and that it was only a question of time before everything would be completely explained scientifically.
The twentieth century has at once affirmed and destroyed the atomic hypothesis. Affirmed it because molecules and atoms, at one time considered by most physicists simply as useful fictions, can actually be ‘seen’ (i.e. mapped precisely) with an electron tunnelling microscope and substances ‘one atom thick’ like graphene are actually being manufactured, or soon will be. However, atoms have turned out not to be indestructible or even indivisible as Newton and the  early scientists supposed.  Atomism and materialism have, by a curious circuitous route, led us back to a place not so very far from our original point of departure since the 20th century 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 in physics is ‘Potential Work’, i.e. Work which could be done but is not actually being done  while ‘Work’ in physics has the precise meaning, Force × distance moved in the direction of the applied force.  Energy is not something actual at all, certainly not something perceptible by the senses or their extensions, it is “strictly speaking a definition rather than a physical entity, merely being the first integral of the equations of motion” (Heading, Mathematical Methods in Science and Engineering p. 546). It is questionable whether statements in popular science books such as “the universe is essentially radiant energy” have any real meaning — taken literally they imply that the universe is ‘pure potentiality’ which it clearly isn’t.
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 foundations of this entire Tower of Babel, 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 the Bishop  has had the last laugh.

A New Starting Point?

Since the wheel of thought concerning the physical universe has more or less turned full circle, a few brave 20th century souls have wondered whether, after all, ‘atoms‘ and ‘extended bodies’ were not the best starting point, and that one might do better starting with something else. What though? There was in the early 20th century a resurgence of ‘animism’ on the fringes of science and philosophy,  witness 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. In particular, it is not clear how such notions can be represented symbolically by mathematical (or other) symbols, let alone tested in laboratory conditions.
Einstein, for his part, 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 via a ‘Unified Field’ 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 combining mathematically the four basic physical forces, gravity, electro-magnetism and the strong and weak nuclear forces.
More recently, there have been one or two valiant attempts to present and attempt to elucidate the universe in terms of ‘information’, even to view the extent of viewing it as a vast computer or cellular automaton (Chris Langton, Stephen Wolfram et al.). But such attempts may well one day appear just as crudely anthropomorphic as Boyle’s vision of the universe as a sort glorified town clock. Apart from that one hopes that the universe, or whatever is behind it, has better things to do than simply pile up endless stacks of data like the odious Super Brains of Olaf Stapledon’s prescient SF fantasy The Last and First Men whose only ’emotion’ is curiosity.

The Event

During the Sixties and Seventies, at any rate within the booming counter-culture, there was a feeling that the West had somehow ‘got it wrong’ and was leading everyone towards disaster with its obsessive emphasis on material goods and material explanations. The principal doctrine of the hippie movement, inasmuch as it had one, was that “Experiences are more important than possessions” — and the more outlandish the experiences the better.  Zen-style ‘Enlightenment’ suddenly seemed much more appealing than the Eighteenth century movement of the same name which spearheaded Europe into the secular, industrial era . A few physicists, such as Fritjof Capra, argued that, although classical physics was admittedly very materialistic in the bad sense, modern physics “wasn’t like that” and had strong similarities with the key ideas of eastern mysticism. However, though initially attracted, I found modern physics (wave/particle duality, quantum entanglement, Block Universe, &c. &c.) a shade too weird, and what followed soon after, String Theory, completely opaque to all but a small band of elite advanced mathematicians .
But the trouble didn’t start in the 20th century. Newtonian mechanics was clearly a good deal more sensible but Calculus, when I started learning mathematics towards middle age, proved to be a major stumbling block, not so much because it was difficult to learn as because its basic 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 during a certain ‘short’ interval in time; we then reduce this interval ‘to the limit’ and, hey presto! we have the derivative appearing like the rabbit out of the magician’s hat. But if the particle is always accelerating its speed is never constant, and if the particle is always moving, it is never at a fixed location. The concept of ‘instantaneous velocity’ is mere gobbledeegook as Bishop Berkeley pointed out to Newton centuries ago. In effect, ‘classical’ Calculus has its cake and eats it too — something we all like doing if we can get away with it — since it merrily sets δx to non-zero and zero simultaneously on opposite sides of 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 speaking, it turns out to be irrelevant whether or not a particular function actually attains  a given limit (assuming it exists) just so long as it approaches closer than any desired finite quantity . But what anyone with an enquiring mind wants to know is whether in reality the moving arrow actually attains its goal or whether the closing door ever actually slams shut (to use two examples mentioned by Zeno of Elea). 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, however puny, we have no right to get rid of just because they are inconvenient. 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, it is not in motion. 
     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 of measurement 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 dn cannot be smaller than that of a single molecule.
In any case, on reflection, I realized that I had always felt ‘time’ to be discontinuous, and life to be made up of a succession of discrete moments. This implies — taking things to the limit —  that there must be a minimal  ‘interval of time’ which, moreover, is absolute and does not depend on the position or motion of an imaginary observer. I was thus heartened when, in my vasual reading, I learned that nearly two thousand years ago, certain Indian Buddhist thinkers had advanced the same supposition and even apparently attempted to give an estimate of the size of such an ‘atom of time’ that they referred to as a ksana. More recently, Whitrow, Stefan Wolfram and one or two others, have given estimates of the size of a chronon  based on the Planck limit — but it is not the actual size that is important as the necessary existence of such a limiting value (Note 2).
Moreover, taking seriously the Sixties mantra that “experiences are more important than things” I wondered whether one could, and should, apply this to the physical world and take as a starting point not the ‘fundamental thing’, the atom, but the fundamental event, the ultimate event, one that could not be further decomposed. The resulting general theory would be not so much physics as Eventrics, a theory of events which naturally separates out into the study of the equivalent of the microscopic and macroscopic realms in physics. Ultimate Event Theory, as the name suggests, deals with the supposed ultimate constituents of physical (and mental) reality – what Hinayana Buddhists referred to as dharma(s) — while large-scale Eventrics deals with ‘historical events’ which are massive bundles of ultimate events and which have their own ‘laws’.
        The essential as far as I was concerned was that I suddenly had the barebones of a physical schema : ‘reality’ was composed of  events, not of objects (Note 3), or “The world is the totality of events and not of things” to adapt Wittgenstein’s aphorism.  Ultimate Event Theory was born, though it has taken me decades to pluck up the courage to put such an intuitively reasonable theory into the public domain, so enormous is the paradigm shift involved in these few innocuous sounding assumptions.       S.H. (3/11/ 2019)

Note 1 There exists, however, an extremely scholarly (but nonetheless very readable) book, The Greeks and the Irrational by E.R. Dodds, which traces the history of an ‘irrational’ counter-current in Greek civilisation from Homer to Hellenistic times. The author, a professor of Greek and a one time President of the Psychical Research Society, asked himself the question, “Were the Greeks in fact quite so blind to the importance of non-rational factors in man’s experience and behaviour as is commonly assumed both by their apologists and by their critics?” The book in question is the result of his erudite ponderings on the issue.

Note 2 Caldirola suggests 6.97 × 10−24 seconds for the minimal temporal interval, the chronon ─ what I refer to by the Sanscrit term ksana. Other estimates exist such as 5.39 ×10–44  seconds. Causal Set Theory and some other contemporary relativistic theories assume minimal values for spatial and temporal intervals, though I did not know this at the time (sic).

Note 3 Bertrand Russell, of all people, clearly anticipated the approach taken in UET, but made not the slightest attempt to lay out the conceptual foundations of the subject.  “Common sense thinks of the physical world as composed of ‘things’ which persist through a certain period of time and move in space. Philosophy and physics developed the notion of ‘thing’ into that of ‘material substance’, and thought of material substance as consisting of particles, each very small, and each persisting throughout all time. Einstein substituted events for particles; each event had to each other a relation called ‘interval’, which could be analyzed in various ways into a time-element and a space-element. (…) From all this it seems to follow that events, and not particles, must be the ‘stuff’ of physics. What has been thought of as a particle will have to be thought of as a series of events. (…) ‘Matter’ is not part of the ultimate material of the world, but merely a convenient way of collecting events into bundles.”  Russell, History of Western Philosophy p. 786 (Counterpoint, 1979

 

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