Archives for posts with tag: Lee Smolin

Events rather than things

The West has, from the Greeks onwards, been ‘object-based’ as opposed to ‘event-based’ at any rate with regard to natural philosophy. The only prominent Western thinker to have seriously supposed that matter, and thus by implication the entire physical universe, was inherently unstable and might conceivably disappear into thin air, i.e. revert to the nothingness from which it came, was Descartes. But, being a believer ─ a deist at any rate ─ like practically everyone else of his time, Descartes was able to bring God into the picture  to save not just appearances but (physical) reality itself. Descartes would have had a much larger audience in India than in Europe and Stcherbatsky states that a remark of Bergson’s summarizing Descartes’ theory, once translated into Sanskrit, “sounds just like a quotation from a Sanscrit text” (Note 1).
But the resounding success of the Newtonian paradigm firmly based on the concepts of matter, force and motion silenced such mystical sounding speculations. It is only in the 20th century that we find natural philosophers, or ‘scientists’ as they now consider themselves, talking about ‘events’ as such at all. Einstein’s theory of Special Relativity (SR) concern ‘events’ ─ “occurrences that every observer would agree took place such as an explosion” as the author of a textbook on Relativity defines them ─ rather than things and a good deal of SR is taken up with the (ultimately insoluble) problem of ordering events so as to plot the operational range of causality. Bertrand Russell remarks :“From all this [‘all this’ being a discussion of Relativity] it seems to follow that events, 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. (…) Thus ‘matter’ is not part of the ultimate material of the world, but merely a convenient way of collecting events into bundles.” (Note 2)
But Russell  does not follow up this particular line of thought mainly because of his misguided belief that mathematics was essentially an extension of logic. A sceptic and a rebel with respect to so many leading dogmas of his time, Russell was not the main to question the dogma of continuity which is so deeply embedded in Western mathematics.

As for Einstein, his basic philosophic position is not easy to determine but seems to have been, at least during his middle period, that ‘fields’ were the primary reality. Ultimately everything was part of a single ‘Unified Field’ which was continuous, and ‘matter’ was merely “that portion of the field which is particularly intense“. This is, of course, incompatible with the basic assumption of Ultimate Event Theory, namely that reality is made up of discrete bundles of ultimate events. However, these ‘observables’ can be viewed as disturbances of an underlying, invisible, all-pervading substratum which is continuous, somewhat in the manner that ripples or foam are discrete disturbances of a fluid that is continuous (or at any rate appears so to us). So there is, conceivably, an underlying ‘continuous’ entity after all (as David Bohm for one believed) but such an entity, source and origin of All That Is is not directly observable and thus does not properly speaking fall within the remit of science.

Space-time ultimates
Whitrow, in one of his numerous books on time, advances the idea of a minimal unit of time, the chronon, and suggests a plausible value based on the diameter of an elementary particle divided by c the speed of light. This was the first time I came across the idea in a Western writer. Whitrow also has some useful comments to make on the illogicality of calculus which always treats time and motion as continuous variables but, like Russell, he does not pursue this line of thought.
More recently, in his very remarkable book, A New Kind of Science, Stephen Wolfram writes:
The only thing that ultimately makes sense is to measure space and time taking each connection in the casual network to correspond to an identical elementary distance in space and elementary distance in time. One may guess that this elementary distance is around 10 (exp -35) meters , and that the elementary time interval is around 10 (exp -43) seconds.”    (p. 520)
        He draws the conclusion :
“Whatever these values are, a crucial point is that their ratio must be a fixed speed, and we can identify this with the speed of light. So this means that in a sense every connection in a causal network can be viewed as representing the propagation of an effect at the speed of light.”
        This certainly is a crucial point but I would prefer to see this fixed space-to-time ratio as simply defining the operation of causality, i.e. it is a speed barrier which no effect propagated from one ultimate event to another can exceed, or even attain (Note 2).
More recently still, Lee Smolin writes:
“If space and time consist of events, and the events are discrete entities that  can be counted, then space and time themselves are not continuous. If this is true, one cannot divide time indefinitely. Eventually we shall come to the elementary events, ones which cannot be further divided and are thus the simplest possible things that can happen. Just as matter is composed of atoms,  which can be counted, the history of the universe is constructed from a huge  number of elementary events” Lee Smolin, Three Roads to Quantum  Gravity p. 41-2  Phoenix Paperback Edition.
      However, Lee Smolin  writes in another place:
“A causal universe is not a series of stills following on, one after the other. [Why not?] There is time, but there is not really any notion of a moment of time. There are only process (sic.) that follow one another by causal necessity.”  (Ib. p. 55)


Lee Smolin thus, seemingly, pins his faith on ‘processes’ rather than ‘ultimate events’, whereas, for me, a process is simply a tightly connected chain of  events : in UET, it is the constituent ultimate events that are fundamental, not  the ensemble.
Also, Lee Smolin, reverting to a conception of Leibnitz, dispenses with the independent existence of what I call the Locality :“There is no meaning to space that is independent of the relationships among  real things in the world. Space is not a stage which might  be empty or full [Why not?], onto which things come and go. Space is nothing apart from the things that exist; it is only an aspect of the relationships that hold  between things.” Ib.  p. 18
I don’t see this. Rather, if anything at all happens (and seemingly ‘something’ does), then it must happen somewhere and this ‘somewhere‘ must seemingly already in some sense exist, even pre-exist, otherwise nothing could happen because there would be nowhere where it could happen. Smolin even goes so far as to attack the very idea of Space-Time possessing a ‘structure’ and declares, quite incorrectly as far as I can make out, that this never was Einstein’s conception. From my point of view, reducing Space-Time to ‘relations’ is throwing out the baby and keeping the bathwater. What Smolin views as the fictitious entity, ’empty space’, I see as the underlying reality while ‘relationships among real things in the world‘ are not even a secondary reality : in my book, they are still farther down the actuality scale, coming well after the ‘real things’ Smolin refers to (i.e. ultimate events).

Causal Set Theory
Causal Set Theory, a contemporary version (or extension?) of General Relativity that is, in this country, chiefly promoted by Professor Fay Dowker, is  the most appealing of contemporary cosmological theories because it maintains that ‘Space-Time’ is fundamentally discrete ─ “This reasoning [concerning the physics of Black Holes] leads us to the conclusion that every region of spacetime (and not only the horizon of a black hole) should be fundamentally discrete”. The quotation comes from Causal Set Theory as a Discrete Model for Classical Spacetime by F. Soss Rodriguez of Imperial College, London. This very professional article is available free on the Internet, or was when I downloaded it. It is not, however, for the general reader since it requires extensive knowledge of topology, logical theory and the mathematics of GR. Much more approachable is Introduction to causal sets: an alternative view of spacetime structure by David D. Reid, also available on the Internet.

A Contemporary Theory of Events?
Although Causal Set Theory is committed to discreteness, it is not essentially a theory of events and their interactions. On the other hand, A Formal Ontological Theory Based on Timeless Events by Gustavo E. Romero from the Instituto Argentino de Radioastronomia of Buenos Aires really is a genuine event-based physical theory, the first that I have come across from a contemporary thinker.
Although the author says at the beginning “I assume as background knowledge the predicate calculus, set theory, semantics, and real analysis”, the text is just about approachable by the general reader, at least in parts. The author covers much of the ground that I have laboriously been exploring since I first conceived of Ultimate Event Theory after reading Stcherbatsky’s great book, Buddhist Logic. Romero specifically mentions Buddhist thinkers as the leading promoters of the ‘event-based’ paradigm, admirably summarizing their position as
The whole world [for them] is an inter-dependent storm of events that, here and there, cluster giving the illusion of stability and delivering the illusion of being”.
Although the confident use of symbolic logic gives this paper a style and concision that I can at present only envy, there is a danger that the crucial philosophic issues ─ and by implication, physical issues as well ─ are not sufficiently highlighted. My main disagreement as far as I can see is as follows. The author quite rightly distinguishes between the Universe, U, which is “the composition of all things” and the World, W, which is “the composition of all actual events and processes”. Also, he writes, quite properly, Events do not change, they simply are”.
        However, he goes on to declare, “The totality of events is changeless, otherwise there would be an event not included in the totality, which is absurd”. But this is not in the least absurd! Unless, of course, one believes, as I suspect Romero does, that, as I put it, “Everything that can have occurrence already has occurrence”. This is indeed the view of Barbour, the author of The End of Time, and many others and is implicit in the Block Universe version of General Relativity (which is the current orthodox theory of Space/Time inasmuch as there is one). That Romero adheres to this view is shown by his defining the World as “the composition of all actual events and processes” ─ the weasel word being ‘actual’. Hopefully, not all possible events are also actual; for if they were/are there is “nothing new under the sun” and as far as I am concerned there would be no point in living.

Einstein and Time

Einstein, towards the end of his life, did indeed come to believe that ‘past, present and future’ were “a stubbornly persistent illusion“as he put it and he was serious enough about this to mention it in a latter of soi-disant sympathy to the widow of one of Einstein’s longest friends, Besso, on the event of the latter’s death. Nonetheless, there is evidence that Einstein was much troubled by the implications.
Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something essentially different from the past and future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation” (Note 3)
It is ironic that the Western thinker who first placed events rather than things under the spotlight, namely Einstein, was also the man who dealt a devastating, possibly lethal, body blow to the renascent event-paradigm. For Einstein initiated a re-examination of the concept of simultaneity and his ponderings ended up by establishing that the term has little or no meaning on a universal scale. That there are events that are not unambiguously ‘ordered in time’ ─ the so-called ‘space-like’ events of SR ─ led on eventually (sic) to the idea that “everything is simultaneous”, for that is what the Block Universe theory implies. For there is ‘no before and after’, only a sickly ‘eternal present’. Such a conception is, just possibly, ‘correct’ physically speaking but is utterly unacceptable psychologically: it would make nonsense of all our social institutions (especially laws) and inherited ways of thinking. It is far worse than the ancients’ blind belief in fate, for the latter only implied that certain events were predestined and unalterable, not that all of them were.
S.H.  4/12/19

Note 1. More specifically, Stcherbatsky quotes Bergson (Creative Evolution p. 23-24) as writing, “the world of the mathematician deals with a world that dies and is reborn at every instant, the world which Descartes was thinking of when he spoke of continuous creation”. Stcherbatsky comments, “This idea is quite Buddhistic and…put into Sanscrit… sounds like a quotation from an Indian text” (Buddhist Logic, footnote p. 109).
Quite why Bergson should have thought  that the mathematician’s world was instantaneous is unclear; certainly the world of Euclidian geometry is not in the least ephemeral, on the contrary it views shapes sub specie aeternitatis which is why Plato endorsed it so emphatically. Bergson was perhaps thinking of differential equations which model physical changes over increasingly smaller intervals of time, but, even here, continuity rather than discontinuity is the name of the game.

Note 2. It is traditional, but by no means obligatory, to identify the actual speed of light with this ‘maximum transmission speed‘ for all physical or informational processes. Quite possibly, light, likewise other speedy particles such as neutrinos, approach but do not actually reach this speed, which allows us to attribute to them a small mass. Today, the consensus seems to be that the neutrino does possess a small mass. To my mind, nothing material can have strictly zero mass: this is a contradiction in terms. A strictly massless particle is certainly impossible in Newtonian physics since it would have absolutely no capacity to resist any attempt to change its state of rest or constant rectilinear motion ─ it would be the ultimate puff-ball.

Note 3.  From Carnap, Intellectual Autobiography  (quoted Smolin).  “Moreover,” Smolin adds, “Einstein was not satisfied by Carnap’s reply and repeated that “such scientific descriptions cannot possibly satisfy our human needs; that there is something about the Now which is just outside the realm of science” ”       Smolin, Time Reborn p. 91-2





A completely axiomatic theory purports to make no appeal to experience whatsoever though one doubts whether any such expositions are quite as ‘pure’ as their authors claim. Even Hilbert’s 20th century formalist version of Euclid, his Grundlagen der Geometrie, has been found wanting in this respect ─ “A 2003 effort by Meikle and Fleuriot to formalize the Grundlagen with a computer found that some of Hilbert’s proofs appear to rely on diagrams and geometric intuition” (Wikipedia).

What exactly is the axiomatic method anyway? It seems to have been invented by the Greeks and in essence it is simply a scheme that divides a subject into :
(1) that part which has to be taken for granted in order to get started at all ─ in Euclid the Axioms, Definitions and Postulates (Note 1); and
(2) that part which is derived by valid chains of reasoning from the first, namely the Theorems ─ Heath calls them ‘Propositions’.
A strictly deductive, axiomatic presentation of a scientific subject made perfect sense in the days when Western scientists believed that an all-powerful God had made the entire universe with the aid of a handful of mathematical formulae but one wonders whether it is really appropriate today when biology has become the leading science. Evolution proceeds via random mutation plus ruthless selection and human societies and/or individuals often seem to owe more to happenstance and experience than reasoning and logic. Few, if any, important discoveries in mathematics have been strictly deductive: I doubt if anyone ever sat down of an evening with the Axioms of von Neumann Set Theory in order to deduce something interesting and original, and certainly no one ever learned mathematics that way (except possibly a robot). For all that, the structural simplicity and elegance of the axiomatic method remains extremely appealing and is one of the reasons why Euclid’s Elements and Newton’s Principia are among the half dozen best-selling books of all time ─ though few people read them today.
Apart from the axioms which are an integral part of a science or branch of mathematics, there exist also certain methodological principles (or prejudices) which, properly speaking, don’t belong to the subject, but nonetheless determine the general approach and overshadow the whole work. These principles should, ideally, be stated at the outset though they rarely are.

There are two principles that I find I have used implicitly or explicitly throughout my attempts to kick-start Ultimate Event Theory. The first is Occam’s Razor, or the Principle of Parsimony, which in practice means preferring the simplest and most succinct explanation ‘other things being equal’. According to Russell, Occam, a mediaeval logician, never actually wrote that “Entities are not to be multiplied without necessity” (as he is usually quoted as stating), but he did write “It is pointless to do with more what can be done with less” which comes to much the same thing. The Principle of Parsimony is uncontroversial and very little needs to be said about it except that it is a principle that is, as it were, imposed on us by necessity rather than being in any way ‘self-evident’. We do not really have any right to assume that Nature always chooses the simplest solution: indeed it sometimes looks as if Nature enjoys complication just for the sake of it. Aristotle’s Physics is a good deal simpler than Newton’s and the latter’s much easier to visualize than Einstein’s: but the evidence so far seems to favour the more complicated theory.
The second most important principle that I employ may be called the Principle of Parmenides, since he first stated it in its most extreme form,
       “If there were no limits, there would be nothing”.
In the context of Ultimate Event Theory this often becomes:
        “If there were no limits, nothing would exist, except (possibly) the Locality itself”
and the slightly different “If there were no limits, nothing would persist”.

      This may sound unexceptional but what I deduce from this principle is highly controversial, namely the necessity to expel the notion of actual infinity from science altogether, and likewise in mathematics (Note 2). The ‘infinite’ is by definition ‘limitless’ and so falls under the ban of this very sensible principle. Infinity has no basis in our sense experience since no one, with the exception of certain mystics, has ever claimed to have ‘known’ the infinite. And mystical experience, though perfectly valid and apparently extremely enjoyable, obviously requires careful assessment before it can be introduced into a theory, scientific or otherwise. In the majority of cases, it is clear that what mystics (think they) experience is not at all what mathematicians mean by the sign ∞ but is rather an alleged reality which is ‘non-finite’ in the sense that any form of measurement would be totally inappropriate and irrelevant. (It is closer to what Bohm calls the Implicate Order as opposed to the Explicate Order ─ unhappy names for a  very useful dichotomy). In present-day science, ‘infinity’ simply functions as a sort of deus ex machina (Note 3) to get one out of a tight spot, and even then only temporarily. As far as I know, there is not a scrap of evidence to suggest that any known process or observable entity actually is either ‘infinitely large‘ or ‘infinitely small’. All energy exchanges are subject to quantum restrictions (i.e. come in finite packages) and all sorts of entities which were once regarded as ‘infinitely small’ such as atoms and molecules can now actually be ‘seen’, if only via an electron tunnelling microscope. Even the universe we live in, which for Newton and everyone else alive in his time, was ‘infinite’ in size, is sometimes thought today to have a finite current extent and is certainly thought to have a specific age (around 13.8 billion years). All that is left as a final bastion of the infinity delusion is space and time and even here one or two noted contemporary physicists (e.g. Lee Smolin and Fay Dowker) dare to suggest that the fabric of Space-Time may be ‘grainy’. But enough on this subject which, in my case,  tends to become obsessive.
What can an axiomatic theory be expected to do? One thing it cannot be expected to do is to give specific quantitative results. Newton showed that the law of gravitation had to be  an inverse square distance law but it was some time before a value could be attributed to the indispensable gravitational constant, G. And Eddington quite properly  said that we could conclude simply by reasoning that in any physical universe there would have to be an upper bound for the speed of a particle or the  transmission of information, but that we would not be able to deduce by reasoning alone the actual value of this upper bound (namely c ≈ 108 metres/second).
It is also legitimate, even in a broadly axiomatic presentation, to appeal to common experience from time to time, provided one does not abuse this facility. For example, de Sitter’s solution of Einstein’s field equations could not possibly apply to the universe we (think we) live in, since his solution required that such a ‘universe’ would be entirely empty of matter ─ which we believe not to be the case.
One would, however, require a broadly axiomatic theory to lead, by reasoning alone, to some results which, as it happens, we know to be correct, and also, if possible, to make certain other predictions that no rival theory had made. And a  theory which embodies a very different ‘take’ on life and the world might still prove worthwhile stating even if it is destined to be promptly discarded: it might prepare the ground for other, more mature,  theories by pointing in a certain  unexpected direction. Predictive power is not the only goal and raison d’etre of a scientific theory : the old Ptolemaic astronomy was for a long time perfectly satisfactory as a predictive system and, according to Koestler, Copernicus’s original heliocentric system was no simpler. As a piece of kinematics, the Ptolemaic Earth-centred system was adequate and, with the addition of more epicycles could probably ‘give the right answer’ even today. However, Copernicus’s revolution paved the way for Galileo’s and Newton’s dynamical world-view in which the movements of planets were viewed in terms of applied forces and so proved far more fruitful.
It is also worth saying that a different world-view from the current established one may remain more satisfactory with respect to certain specific areas, while being utterly inadequate for other purposes. If one is completely honest, one would, I think, have to admit that the now completely discredited magical animistic world-view has a certain cogency and persuasiveness when applied to aberrant human behaviour:   this is why we still talk meaningfully of charm, charisma, inspiration, luck, jinxes, fascination, fate ─ concepts that belong firmly to another era.
Finally, the world-views of other cultures and societies are not just historical curiosities : people in these societies had different priorities and may well have noticed, and subsequently sought to explain, things that modern man is unaware of. Ultimate Event Theory has its roots in the world-views of societies long dead and gone: in particular the world-view of certain Hinayana Buddhist monks in Northern India during the first few centuries of our era, and that of certain Native Amerindian tribes like the Hopi as reflected in the
structure of their languages (according to the Whorf-Sapir theory).

                                                                                                                                SH  26/09/19

Notes :
Note 1  The status of the fourth and last Euclidian subsection, the Definitions, is not entirely clear: they were supposed to be ‘informative’ only in the manner of an entry in a dictionary and “to have no existential import”. On the other hand, Russell concedes that “definitions are often nothing more than disguised axioms”.

Note 2 This is in line with Poincare’s categorical statement, “There is, and can be, no actual infinity”. Gauss, often considered the greatest mathematician of all time, said something similar.

Note 3 A deus ex machine was , in Greek tragedy, a supernatural being who was lowered onto the stage by a sort of crane and whose purpose was to ‘save’ the hero or heroine when no one else could.
Larry Constantine, in an insightful letter to the New Scientist (13 Aug 2011 p. 30), wrote : “Accounting for our universe by postulating infinite parallel universes or explaining the Big Bang as the collision of “branes” are not accounts at all, but merely ignorance swept under a cosmic rug — a rug which itself demands explanation but is in turn buried under still more rugs.”