“In the last analysis it is the ultimate picture which an age forms of the nature of its world that is its most fundamental possession”
Burtt, The Metaphysical Foundations of Modern Science
Today, since the cultural environment is so violently anti-metaphysical, it has become fashionable for physical theories to be almost entirely mathematical. Not so long ago, people we now refer to as scientists regarded themselves as ‘natural philosophers’ which is why Newton’s great work is entitled Philosophiae Naturalis Principia Mathematica. When developing a radically new ‘world-view’, the ‘reality-schema’ must come first and the mathematics second, since new symbolic systems may well be required to flesh out the new vision ─ in Newton’s case Calculus (though he makes very sparing use of it in the Principia).
Newton set out his philosophic assumptions very clearly at the beginning, in particular his belief in ‘absolute positioning’ and ‘absolute time’ ─ “All things are placed in time as to order of succession; and in space as to order of situation” (Scholium to Definition VIII). And, as it happened, the decisive break with the Newtonian world-view did not come about because of any new mathematics, nor even primarily because of new data, but simply because Einstein denied what everyone had so far taken for granted, namely that “all things are placed in time as to order of succession” ─ in Special Relativity ‘space-like separated’ pairs of events do not have an unambiguous temporal ordering. The case of QM is more nuanced since the mathematics did come first but it was the apparent violation of causal process that made the theory so revolutionary (and which incidentally outraged Einstein).
The trouble with the current emphasis on mathematics is that, from an ‘eventric’ point of view, the tail is wagging the dog. What is real is what actually happens, not what is supposed to happen.
Moreover, mathematics is very far from being so free from metaphysical and ‘intuitive’ assumptions as is generally assumed. Arithmetic and number theory go right back to Pythagoras who seems to have believed that, at bottom, everything could be explained in terms of whole number relations, hence the watchword “All is Number” (where number meant ‘ratio between positive integers’). And this ancient paradigm received unexpected support from the 20th century discovery that chemistry depends on whole number ratios between the elements (Note 1).
The rival theory of continuous quantity goes back to Plato who, essentially for philosophic reasons, skewed higher mathematics decisively towards the geometrical which is why even those parts of Euclid that deal with (Whole) Number Theory (Books VII ─ X) present numbers as continuous line segments rather than as arrays of dots. And Newton invented his Fluxions (what is now known as the calculus) because he believed reality was ‘continuous, ─ “I consider mathematical Quantities in this place not as consisting of very small parts but as described by a continued Motion…..These Geneses really exist, really take place in the Nature of Things” (Newton, De Quadratura).
The hold of the continuous, as opposed to the discrete, over mathematicians and physicists alike has been extraordinarily strong and held up the eventual triumph of the atomic hypothesis. Planck, the man who introduced ‘quanta’ into physics, wrote “Despite the great success that the atomic theory has so far involved, ultimately it will have to be abandoned in favour of the assumption of continuous matter”.
Even contemporary branches of mathematics are far from being so ‘abstract’ as their authors claim, witness the excessive importance of the misleading image of the ‘Number Line’ and the general prejudice in favour of the continuous. Only logic is ‘reality-schema free’ and even here, there are systems of ‘deviant logic’ that attempt to make sense of the quantum world. The wholesale mathematisation of physics has itself been given philosophic support by authors such as Tegmark who claim that “at bottom reality is mathematical, not physical”.
All this to say that I make no apology for presenting a broad-brushed reality-schema or ‘world-view’ before attempting to develop a symbolic model and make predictions. It seems we need some sort of general ‘metaphysical’ schema if only as a form of intellectual housekeeping, and it is much better to lay one’s cards on the table from the very beginning (as Newton does).
So, what is the schema of Eventrics and Ultimate Event Theory? The fundamental notion is of the ultimate event (an event that cannot be further decomposed). I believe there are such things as events and that they are (at least for the purposes of this theory) more fundamental than ‘things’. I also claim that events must ‘have occurrence’ somewhere ─ hence the need for an Event Locality which either precedes all events or is brought into existence as and when events ‘have occurrence’. Secondly, since most of the events that I and other humans are familiar with seem to be caused by other, usually preceding, events, I feel that this datum needs to be introduced into the theory at the very start. There is thus, by hypothesis, a Casual Force operating on and between (most) events. This force I term Dominance in order to emphasize its usually one-sided operation, and perhaps also to be able to extend the sense a little (Note 2).
I have thus already found it necessary in a theory of events to introduce two entities that are not events, namely the Locality and Dominance. Nonetheless, they are very closely tied up with the production of events, since without the first nothing at all could happen (as I see it), and, without the second, all events would be disconnected from each other and reality would be a permanent vast blooming confusion which, reputedly, it is for the new-born infant.
Are all events caused by other events? This is the deterministic view which was for a long time favoured by the scientific community. The 19th century cosmologist Laplace went so far as to claim that if the positions and momenta of all bodies at the present moment were known, the entire future evolution of the universe could be deduced using only Newton’s laws. But, as we know, Quantum Mechanics and the Uncertainty Principle has put paid to such naïve assumptions; the notion of a strictly random event has now become entirely respectable. It can be loosely defined as “an event without causal predecessors” or, in the jargon of UET, “an event that has no passive relation of dominance to any other event that has occurrence on the Locality”. Because of QM and other considerations, I thus found it essential from the very outset to leave some room for ‘undominated’ or ‘random’ events in the general schema. (Not only that, I shall argue that, at one time, random events greatly outnumbered ordinary caused events.)
This naturally leads on to the question of origins and whether we need any. Most ‘origin-schemas’ require the prior existence either of ‘beings of another order’ (Brahman, God, Allah, Norse gods &c.) or of states that are barely conceivable to us mere mortals (Nirvana, the original Tao, the Quantum Vacuum &c.). All such beings/states/entities are other, fundamentally different from the world we (think we) know and the beings within it.
A few ‘origin-schemas’ envisage the universe as remaining basically the same at all times, or at most evolving from something not fundamentally different from the world we now (think we) inhabit. The Stoic cosmology of Eternal Recurrence, Fred Hoyle’s Steady State and perhaps the Hawking-Hartle ‘No Boundary’ theory fall into this class. For the partisans of these schemas, the present universe is ‘self-explanatory’ and self-sufficient, requiring nothing outside itself for its existence or explication (Note 3).
For a long time modern science did indeed adhere to the ‘self-explanatory’ point of view, but current physical orthodoxy is a strange mixture of ‘other-‘ and ‘no-other’ origin-schemas. After dismissing for decades the question of “What was there before the Big Bang?” as meaningless, most current cosmological theories involve pre Big Bang uni- or multi-verses very different from our own but still ‘obeying the laws of physics’ which, though distilled uniquely from observations of this world, have somehow become timeless and transcendent, in effect replacing the role of God Himself.
Partly for rational and partly for non-rational, i.e. temperamental, reasons I subscribe firmly to the first class of ‘origin theories’. I do not believe the physical universe is ‘self-explanatory’ notwithstanding the amazing success of the natural sciences, and it is significant that present cosmological theorists have themselves found it necessary to push back into uncharted and inaccessible territory in their search for ultimate origins. The quasi-universality of religious belief throughout history, which, pared down to its essentials, means belief in a Beyond (Note 4) is today explained away as an ingrained habit of wishful thinking, useful perhaps when times are bad but which humanity will eventually outgrow. However, I don’t find this explanation entirely convincing. There is perhaps more to it than that; this feeling that there is a reality beyond the physical sounds more like a faint but strangely persistent memory that the world of matter and its enforcers have never been able to completely obliterate. (This was precisely the view of the Gnostics.)
Be that as it may, I do assume an ultimate origin for events, a source which is definitely not itself composed of events and is largely independent even of the Locality. This source ejects events randomly from itself, as it were, or events keep ‘leaking out’ of it to change the metaphor. The source is familiar to anyone who is conversant with mysticism, it is the Brahman of Hinduism, the original Tao of Lao Tse, Ain Soph, the Boundless, of the Kabbalah, and what Bohm calls the ‘Explicate Order’. It is unfashionable today to think in terms of ‘potentiality’ and contrast it with ‘actuality’, but it could be said that this source is “nothing in actuality but everything in potentiality”. Ain Soph is, as Bohm emphasizes, immeasurable in the strong sense ─ measurement is completely irrelevant to it. Since science and mathematics deal only with the measurable and the formal, Ain Soph does not fall within their remit ─ but equally well one can maintain, as all mystics do, that such a thing/place/entity is beyond our comprehension (but perhaps not entirely beyond our apprehension).
What, however, above all one must not do is to mix the measurable and the immeasurable ─ which is exactly what Cantor did, to the great detriment of modern mathematics. Inasmuch as the Unknowable can be known, science and mathematics are definitely not suitable means: ritual, ecstatic dance or directed meditation are traditionally regarded as more suitable ─ and part of their purpose is precisely to quieten or sideline the rational faculty which is, in this context, a hindrance rather than a help.
Ain Soph, or whatever one wants to call the source, should not have any role to play in a physical or mathematical theory except, at most to function as the ultimate origin of uncaused events. We can, in practice, forgot about it. This means, however, that ‘infinity’, ‘eternity’ and suchlike (pseudo)concepts should have no place in science or in mathematics since they belong entirely to the immeasurable (Note 5).
‘Reality’ thus splits up into two ‘regions’, which I name the Unmanifest and the Manifest. The former is the ultimate source of all events but does not itself consist of events, whilst the latter is ‘manifest’ (to us or other conscious beings) precisely because it is composed of events that we can observe.
These two regions themselves divide into two giving the schema:
(1) The Unmanifest Non-Occurrent
(2) The Unmanifest Pre-Ocurrent
(3) The Manifest Occurrent
(4) The Manifest Post-Occurrent.
Why do we need (2.) and (4.)?
We need (2) largely because of Quantum Mechanics ─ more precisely because of the ‘orthodox’ Copenhagen interpretation of QM. This interpretation in effect splits the physical world into two layers, one of which is described by the wave function in its ‘independent state’ while the other arises when a human intervention causes the wave function to ‘collapse’ — an interesting metaphor. In the former (pure) state, whatever ‘goes on’ (and something apparently does) lacks entirely the specificity and discreteness of an ultimate event. We are, for example, invited to believe that a ‘photon’ (or rather a photo-wavicle) has no specific location prior to an intervention on our part ─ rather misleadingly termed a ‘measurement’. There is thus a layer of reality, and ‘physical reality’ at that, which does not consist of events but which seemingly does in some sense exist, and is all around and even in us. There is thus the need for an intermediary level between the remoteness of the true Unmanifest and the immediacy of the world of actual events we are familiar with (Note 6).
What of (4.), the Manifest Post-Occurrent ? It would seem that there are ‘entities’ of some sort which are not observable, not composed of bona fide observable events, but which are nonetheless capable of giving rise to observable phenomena. I am thinking of such things as archetypes, myths, belief systems, generalized abstractions such as Nation, State, Humanity, perhaps even the self, Dawkins’s memes and so on. Logic and rational discourse tend to dismiss such things as pseudo-entities: there is the well-known anecdote of the tourist being shown around the Oxford colleges and asking where the university is. But the ‘university’ does have a reality of a sort, something in between the clearcut reality of a blow to the head and the unreality of a meaningless squiggle.
Moreover, it is in (4.) that I place such things as mathematical and physical theories. As far as I am concerned it is not the Oxford tourist but people like Tegmark (and Plato) who are guilty of a ‘category mistake’: in my terms, they situate mathematics in (1.), the Unmanifest Non-Occurrent, rather than in (4.) the Manifest Post-Occurrent. (1.) is a wholly transcendent level of reality, while (4.) is a manufactured realm which, though giving an appearance of solidity, would not exist, and would never have existed, if there had never been any human mathematicians (or other conscious beings). The Platonic view of mathematics, though tempting, is, I believe, a delusion: mathematics was made by man(kind) and was, originally at any rate, an extrapolation from human sense-impressions, though admittedly it is a very successful one. SH 20/12/19
Note 1. See the chapter on the ‘New Pythagoreanism’ in Shanks’s excellent book, Number Theory, or, for a more accessible treatment, in Valens’s The Number of Things.
Note 2 Dominance is roughly the equivalent of the Buddhist/Hindu concept of karma ─ but applied to all categories of events, not just morally significant ones.
Note 3. Newton granted a small role to God in the evolution of the universe, for example stopping heavenly bodies converging together, but Leibnitz argued that it was blasphemous to suppose any such intervention was needed since this implied that the Creator had not been a good enough designer in the first place. “No need for miracles” became a principal tenet of the Enlightenment though most thinkers found it necessary to introduce a Prime Mover to ‘get the ball rolling’, so to speak. Even this shadowy deus ex cathedra faded away into nothingness by the time of Laplace who famously informed Napoleon, “I had no need of that hypothesis” ─ the hypothesis in question being the existence of God.
Note 4 The Koran, for example, addresses itself specifically to “those who believe in the unseen” (Koran sutra 2 ‘The Heifer’ v. 3).
Note 5. This is precisely the point made by Lao Tse in the very first line of the Tao Te Ching which may be translated, “The Tao that can be named is not the original Tao”. Lao Tse was writing at a time when language, not mathematics or physics, was the most advanced intellectual achievement, and, were he alive today would doubtless have written “The Tao that can be mathematized is not the original Tao”.
Note 6. QM is, incidentally, not the only system that posits an intermediary realm between the Limitless and the Limited. Hinayana Buddhism has a curious theory about ‘events’ passing through various stages of progressive ‘realization’ before becoming actual ─ most Indian author for some reason cite 17.
Dharma 