Archives for category: Hinayana

 Although, in modern physics,  many elementary particles are extremely short-lived, others such as protons are virtually immortal. But either way, a particle, while it does exist, is assumed to be continuously existing. And solid objects such as we see all around us like rocks and hills, are also assumed to be ‘continuously existing’ even though they may undergo gradual changes in internal composition. Since solid objects and even elementary particles don’t appear, disappear and re-appear, they don’t have a ‘re-appearance rate ’ ─ they’re always there when they are there, so to speak.
However, in UET the ‘natural’ tendency is for everything to flash in and out of existence and virtually all  ultimate events disappear for ever after a single appearance leaving a trace that would, at best, show up as a sort of faint background ‘noise’ or ‘flicker of existence’. All apparently solid objects are, according to the UET paradigm, conglomerates of repeating ultimate events that are bonded together ‘laterally’, i.e. within  the same ksana, and also ‘vertically’, i.e. from one ksana to the next (since otherwise they would not show up again ever). A few ultimate events, those that have acquired persistence ─ we shall not for the moment ask how and why they acquire this property ─ are able to bring about, i.e. cause, their own re-appearance : in such a case we have an event-chain which is, by definition,  a causally bonded sequence of ultimate events.
But how often do the constituent events of an event-chain re-appear?  Taking the simplest case of an event-chain composed of a single repeating ultimate event, are we to suppose that this event repeats at every single ksana (‘moment’ if you like)? There is on the face of it no particular reason why this should be so and many reasons why this would seem to be very unlikely.    

The Principle of Spatio-Temporal Continuity 

Newtonian physics, likewise 18th and 19th century rationalism generally, assumes what I have referred to elsewhere as the Postulate of Spatio-temporal Continuity. This postulate or principle, though rarely explicitly  stated in philosophic or scientific works,  is actually one of the most important of the ideas associated with the Enlightenment and thus with the entire subsequent intellectual development of Western society. In its simplest form, the principle says that an event occurring here, at a particular spot in Space-Time (to use the current term), cannot have an effect there, at a spot some distance away without having effects at all (or at least most?/ some?) intermediate spots. The original event sets up a chain reaction and a frequent image used is that of a whole row of upright dominoes falling over one by one once the first has been pushed over. This is essentially how Newtonian physics views the action of a force on a body or system of bodies, whether the force in question is a contact force (push/pull) or a force acting at a distance like gravity.
As we envisage things today, a blow affects a solid object by making the intermolecular distances of the surface atoms contract a little and they pass on this effect to neighbouring molecules which in turn affect nearby objects they are in contact with or exert an increased pressure on the atmosphere,  and so on. Moreover, although this aspect of the question is glossed over in Newtonian (and even modern) physics, each transmission of the original impulse  ‘takes time’ : the re-action is never instantaneous (except possibly in the case of gravity) but comes ‘a moment later’, more precisely at least one ksana later. This whole issue will be discussed in more detail later, but, within the context of the present discussion, the point to bear in mind is that,  according to Newtonian physics and rationalistic thought generally, there can be no leap-frogging with space and time. Indeed, it was because of the Principle of Spatio-temporal Continuity that most European scientists rejected out of hand Newton’s theory of universal attraction since, as Newton admitted, there seemed to be no way that a solid body such as  the Earth could affect another solid body such as the Moon thousands  of kilometres with nothing in between except ‘empty space’.   Even as late as the mid 19th century, Maxwell valiantly attempted to give a mechanical explanation of his own theory of electro-magnetism, and he did this essentially because of the widespread rock-hard belief in the principle of spatio-temporal continuity.
The principle, innocuous  though it may sound, has also had  extremely important social and political implications since, amongst other things, it led to the repeal of laws against witchcraft in the ‘advanced’ countries ─ the new Legislative Assembly in France shortly after the revolution specifically abolished all penalties for ‘imaginary’ crimes and that included witchcraft. Why was witchcraft considered to be an ‘imaginary crime’? Essentially because it  offended against the Principle of Spatio-Temporal Continuity. The French revolutionaries who drew the statue of Reason through the streets of Paris and made Her their goddess, considered it impossible to cause someone’s death miles away simply by thinking ill of them or saying Abracadabra. Whether the accused ‘confessed’ to having brought about someone’s death in this way, or even sincerely believed it, was irrelevant : no one had the power to disobey the Principle of Spatio-Temporal Continuity.
The Principle got somewhat muddied  when science had to deal with electro-magnetism ─ Does an impulse travel through all possible intermediary positions in an electro-magnetic field? ─ but it was still very much in force in 1905 when Einstein formulated the Theory of Special Relativity. For Einstein deduced from his basic assumptions that one could not ‘send a message’ faster than the speed of light and that, in consequence,  this limited the speed of propagation of causality. If I am too far away from someone else I simply cannot cause this person’s death at that particular time and that is that. The Principle ran into trouble, of course,  with the advent of Quantum Mechanics but it remains deeply entrenched in our way of thinking about the world which is why alibis are so important in law, to take but one example. And it is precisely because Quantum Mechanics appears to violate the principle that QM is so worrisome and the chief reason why some of the scientists who helped to develop the theory such as Einstein himself, and even Schrodinger, were never happy with  it. As Einstein put it, Quantum Mechanics involved “spooky action at a distance” ─ exactly the same objection that the Cartesians had made to Newton.
So, do I propose to take the principle over into UET? The short answer is, no. If I did take over the principle, it would mean that, in every bona fide event-chain, an ultimate event would make an appearance at every single ‘moment’ (ksana), and I could see in advance that there were serious problems ahead if I assumed this : certain regions of the Locality would soon get hopelessly clogged up with colliding event-chains. Also, if all the possible positions in all ‘normal’ event-sequences were occupied, there would be little point in having a theory of events at all, since, to all intents and purposes, all event-chains would behave as if they were solid objects and one might as well just stick to normal physics. One of the main  reasons for elaborating a theory of events in the first place was my deep-rooted conviction ─ intuition if you like ─ that physical reality is discontinuous and that there are gaps between ksanas ─ or at least that there could be gaps given certain conditions. In the theory I eventually roughed out, or am in the process of roughing out, both spatio-temporal continuity and infinity are absent and will remain prohibited.
But how does all this square with my deduction (from UET hypotheses) that the maximum propagation rate of causality is a single grid-position per ksana, s0/t0, where s0 is the spatial dimension of an event capsule ‘at rest’ and t0 the ‘rest’ temporal dimension? In UET, what replaces the ‘object-based’ image of a tiny nucleus inside an atom, is the vision of a tiny kernel of fixed extent where every ultimate event occurs embedded in a relatively enormous four-dimensional event capsule. Any causal influence emanates from the kernel and, if it is to ‘recreate’ the original ultimate event a ksana later, it must traverse at least half the ‘length’ (spatial dimesion) of one capsule plus half of the next one, i.e. ½ s0 + ½ s0 = 1 s0 where s0 is the spatial dimension of an event-capsule ‘at rest’ (its normal state). For if the causal influence did not ‘get that far’, it would not be able to bring anything about at all, would be like a messenger who could not reach a destination receding faster than he could run flat out. The runner’s ‘message’, in this case the recreation of a clone of the original ultimate event, would never get delivered and nothing would ever come about at all.
This problem does not occur in normal physics since objects are not conceived as requiring a causal force to stop them disappearing, and, on top of that, ‘space/time’ is assumed to be continuous and infinitely divisible. In UET there are minimal spatial and temporal units (that of the the grid-space and the ksana) and ‘time’ in the UET sense of an endless succession of ksanas, stops for no man or god, not even physicists who are born, live and die successively like everything else. I believe that succession, like causality, is built into the very fabric of physical reality and though there is no such thing as continuous motion, there is and always will be change since, even if nothing else is happening, one ksana is being replaced by another, different, one ─ “the moving finger writes, and, having writ, moves on” (Rubaiyat of Omar Khayyam). Heraclitus said that “No man ever steps into the same river twice”, but a more extreme follower of his disagreed, saying that it was impossible to step into the same river once, which is the Hinayana  Buddhist view. For ‘time’ is not a river that flows at a steady rate (as Newton envisaged it) but a succession of ‘moments’ threaded like beads on an invisible  chain and with minute gaps between the beads.

Limit to unitary re-appearance rate

So, returning to my repeating ultimate event, could the ‘re-creation rate’ of an ultimate event be  greater than the minimal rate of 1 s0/t0 ? Could it, for example, be  2, 3 or 5 spacesper ksana? No. For if and when the ultimate event re-appeared, say  5 ksanas later, the original causal impulse would have covered a distance of 5 s0   ( s0 being the spatial dimension of each capsule) and would have taken 5 ksanas to do  this. Consequently the space/time displacement rate would be the same (but not in this case the individual distances). I note this rate as c* in ‘absolute units’, the UET equivalent of c, since it denotes an upper limit to the propagation of the causal influence (Note 1). For the very continuing existence of anything depends on causality : each ‘object’ that does persist in isolation does so because it is perpetually re-creating itself (Note 2).

But note that it is only the unitary rate, the distance/time ratio taken over a single ksana,  that cannot be less (or more) than one grid-space per ksana or 1 s0/t0 : any fractional (but not irrational) re-appearance rate is perfectly conceivable provided it is spread out over several ksanas. A re-appearance rate of m/n s0/t0  simply means that the ultimate event in question re-appears in an equivalent spatial position on the Locality m times every n ksanas where m/n ≤ 1. And there are all sorts of different ways in which this rate be achieved. For example, a re-appearance rate of 3/5 s0/t0 could be a repeating pattern such as

Reappearance rates 1
















and one pattern could change over into the other either randomly or, alternatively, according to a particular rule.
As one increases the difference between the numerator and the denominator, there are obviously going to be many more possible variations : all this could easily be worked out mathematically using combinatorial analysis. But note that it is the distribution of ™the black and white at matters since, once a re-appearance rhythm has begun, there is no real difference between a ‘vertical’ rate of 0™˜™˜●0● and ˜™˜™™˜™˜™˜™˜●0™˜™˜●0 ™˜™™˜™˜ ˜™˜™ ─ it all depends on where you start counting. Patterns with the same repetition rate only count as different if this difference is recognizable no matter where you start examining the sequence.
Why does all this matter? Because, each time there is a blank line, this means that the ultimate event in question does not make an appearance at all during this ksana, and, if we are dealing with large denominators, this could mean very large gaps indeed in an event chain. Suppose, for example, an event-chain had a re-appearance rate of 4/786. There would only be four appearances (black dots) in a period of 786 ksanas, and there would inevitably be very large blank sections of the Locality when the ultimate event made no appearance.

Lower Limit of re-creation rate 

Since, by definition, everything in UET is finite, there must be a maximum number of possible consecutive gaps  or non-reappearances. For example, if we set the limit at, say, 20 blank lines, or 200, this would mean that, each time this blank period was observed, we could conclude that the event-chain had terminated. This is the UET equivalent  of the Principle of Spatio-Temporal Continuity and effectively excludes phenomena such as an ultimate event in an event-chain making its re-appearance a century later than its first appearance. This limit would have to be estimated on the  basis of experiments since I do not see how a specific value can be derived from theoretical considerations alone. It is tempting to estimate that this value would involve c* or a multiple of c* but this is only a wild guess ─ Nature does not always favour elegance and simplicity.
Such a rule would limit how ‘stretched out’ an event-chain can be temporally and, in reality , there may not after all be a hard and fast general rule  : the maximal extent of the gap could decline exponentially or in accordance with some other function. That is, an abnormally long gap followed by the re-appearance of an event, would decrease the possible upper limit slightly in much the same way as chance associations increase the likelihood of an event-chain forming in the first place. If, say, there was an original limit of a  gap of 20 ksanas, whenever the re-appearance rate had a gap of 19, the limit would be reduced to 19 and so on.
It is important to be clear that we are not talking about the phenomenon of ‘time dilation’ which concerns only the interval between one ksana and the next according to a particular viewpoint. Here, we simply have an event-chain where an ultimate event is repeating at the same spot on the spatial part of the Locality : it is ‘at rest’ and not displacing itself laterally at all. The consequences for other viewpoints would have to be investigated.

Re-appearance Rate as an intrinsic property of an event-chain  

Since Galileo, and subsequently Einstein, it has become customary in physics to distinguish, not between rest and motion, but rather between unaccelerated motion and  accelerated motion. And the category of ‘unaccelerated motion’ includes all possible constant straight-line speeds including zero (rest). It seems, then,  that there is no true distinction to be made between ‘rest’ and motion just so long as the latter is motion in a straight line at a constant displacement rate. This ‘relativisation’ of  motion in effect means that an ‘inertial system’ or a particle at rest within an inertial system does not really have a specific velocity at all, since any estimated velocity is as ‘true’ as any other. So, seemingly, ‘velocity’ is not a property of a single body but only of a system of at least two bodies. This is, in a sense, rather odd) since there can be no doubt that a ‘change of velocity’, an acceleration, really is a feature of a single body (or is it?).
Consider a spaceship which is either completely alone in the universe or sufficiently remote from all massive bodies that it can be considered in isolation. What is its speed? It has none since there is no reference system or body to which its speed can be referred. It is, then, at rest ─ or this is what we must assume if there are no internal signs of acceleration such as plates falling around or rattling doors and so on. If the spaceship is propelling itself forward (or in some direction we call ‘forward’) intermittently by jet propulsion the acceleration will be note by the voyagers inside the ship supposing there are some. Suppose there is no further discharge of chemicals for a while. Is the spaceship now moving at a different and greater velocity than before? Not really. One could I suppose refer the vessel’s new state of motion to the centre of mass of the ejected chemicals but this seems rather artificial especially as they are going to be dispersed. No matter how many times this happens, the ship will not be gaining speed, or so it would appear. On the other hand, the changes in velocity, or accelerations are undoubtedly real since their effects can be observed within the reference frame.
So what to conclude? One could say that ‘acceleration’ has ‘higher reality status’ than simple velocity since it does not depend on a reference point outside the system. ‘Velocity’ is a ‘reality of second order’ whereas acceleration is a ‘reality of first order’. But once again there is a difference between normal physics and UET physics in this respect. Although the distinction between unaccelerated and accelerated motion is taken over into UET (re-baptised ‘regular’ and ‘irregular’ motion), there is in Ultimate Event Theory, but not in contemporary physics, a kind of ‘velocity’ that has nothing to do with any other body whatsoever, namely the event-chain’s re-appearance rate.
When one has spent some time studying Relativity one ends up wondering whether after all “everything is relative” and quite a lot of physicists and philosophers seems to actually believe something not far from this : the universe is evaporating away as we look it and leaving nothing but a trail of unintelligible mathematical formulae. In Quantum Mechanics (as Heisenberg envisaged it anyway) the properties of a particular ‘body’ involve the properties of all the other bodies in the universe, so that there remain very few, if any, intrinsic properties that a body or system can possess. However, in UET, there is a reality safety net. For there are at least two  things that are not relative, since they pertain to the event-chain or event-conglomerate itself whether it is alone in the universe or embedded in a dense network of intersecting event-chains we view as matter. These two things are (1) occurrence and (2) rate of occurrence and both of them are straight numbers, or ratios of integers.
An ultimate event either has occurrence or it does not : there is no such thing as the ‘demi-occurrence’ of an event (though there might be such a thing as a potential event). Every macro event is (by the preliminary postulates of UET) made up of a finite number of ultimate events and every trajectory of every event-conglomerate has an event number associated with it. But this is not all. Every event-chain ─ or at any rate normal or ‘well-behaved’ event-chain ─ has a ‘re-appearance rate’. This ‘re-appearance rate’ may well change considerably during the life span of a particular event-chain, either randomly or following a particular rule, and, more significantly, the ‘re-appearance rates’ of event-conglomerates (particles, solid bodies and so on) can, and almost certainly do, differ considerably from each other. One ‘particle’ might have a re-appearance rate of 4, (i.e. re-appear every fourth ksana) another with the same displacement rate  with respect to the first a rate of 167 and so on. And this would have great implications for collisions between event-chains and event-conglomerates.

Re-appearance rates and collisions 

What happens during a collision? One or more solid bodies are disputing the occupation of territory that lies on their  trajectories. If the two objects miss each other, even narrowly, there is no problem : the objects occupy ‘free’ territory. In UET event conglomerates have two kinds of ‘velocity’, firstly their intrinsic re-appearance rates which may differ considerably, and, secondly, their displacement rate relative to each other. Every event-chain may be considered to be ‘at rest’ with respect to itself, indeed it is hard to see how it could be anything at all if this were not the case. But the relative speed of even unaccelerated event-chains will not usually be zero and is perfectly real since it has observable and often dramatic consequences.
Now, in normal physics, space, time and existence itself is regarded as continuous, so two objects will collide if their trajectories intersect and they will miss each other if their trajectories do not intersect. All this is absolutely clearcut, at least in principle. However, in UET there are two quite different ways in which ‘particles’ (small event conglomerates) can miss each other.
First of all, there is the case when both objects (repeating event-conglomerates) have a 1/1 re-appearance rate, i.e. there is an ultimate event at every ksana in both cases. If object B is both dense and occupies a relatively large region of the Locality at each re-appearance, and the relative speed is low, the chances are that the two objects will collide. For, suppose a relative displacement rate of 2 spaces to the right (or left)  at each ksana and take B to be stationary and A, marked in red, displacing itself two spaces at every ksana.

Reappearance rates 2

Clearly, there is going to be trouble at the  very next ksana.
However, since space/time and existence and everything else (except possibly the Event Locality) is not continuous in UET, if the relative speed of the two objects were a good deal greater, say 7 spaces per 7 ksanas (a rate of 7/7)  the red event-chain might manage to just miss the black object.

This could not happen in a system that assumes the Principle of Spatio-Temporal Continuity : in UET there is  leap-frogging with space and time if you like. For the red event-chain has missed out certain positions on the Locality which, in principle could have been occupied.

But this is not all. A collision could also have been avoided if the red chain had possessed a different re-appearance rate even though it remained a ‘slow’ chain compared to the  black one. For consider a 7/7 re-appearance rate i.e. one appearance every seven ksanas and a displacement rate of two spaces per ksana relative to the black conglomerate taken as being stationary. This would work out to an effective rate of 14 spaces to the right at each appearance ─ more than enough to miss the black event-conglomerate.

Moreover, if we have a repeating event-conglomerate that is very compact, i.e. occupies very few neighbouring grid-spaces at each appearance (at the limit just one), and is also extremely rapid compared to the much larger conglomerates it is likely to come across, this ‘event-particle’ will miss almost everything all the time. In UET it is much more of a problem how a small and ‘rapid’ event-particle can ever collide with anything at all (and thus be perceived) than for a particle to apparently disappear into thin air. When I first came to this rather improbable conclusion I was somewhat startled. But I did not know at the time that neutrinos, which are thought to have a very small mass and to travel nearly at the speed of light, are by far the commonest particles in the universe and, even though millions are passing through my fingers as I write this sentence, they are incredibly difficult to detect because they interact with ordinary ‘matter’ so rarely (Note 3). This, of course, is exactly what I would expect ─ though, on the other hand, it is a mystery why it is so easy to intercept photons and other particles. It is possible that the question of re-appearance rates has something to do with this : clearly neutrinos are not only extremely compact, have very high speed compared to most material objects, but also have an abnormally high re-appearance rate, near to the maximum.
RELATIVITY   Reappeaance Rates Diagram         In the adjacent diagram we have the same angle sin θ = v/c but progressively more extended reappearance rates 1/1; 2/2; 3/3; and so on. The total area taken over n ksanas will be the same but the behaviour of the event-chains will be very different.
I suspect that the question of different re-appearance rates has vast importance in all branches of physics. For it could well be that it is a similarity of re-appearance rates ─ a sort of ‘event resonance’ ─ that draws disparate event chains together and indeed is instrumental in the formation of the very earliest event-chains to emerge from the initial randomness that preceded the Big Bang or similar macro events.
Also, one suspects that collisions of event conglomerates  disturb not only the spread and compactness of the constituent events-chains, likewise their ‘momentums’, but also and more significantly their re-appearance rates. All this is, of course, highly speculative but so was atomic theory prior to the 20th century event though atomism as a physical theory and cultural paradigm goes back to the 4th century BC at least.        SH  29/11/13



Note 1  Compared to the usual 3 × 108 metres/second the unitary  value of s/t0 seems absurdly small. But one must understand that s/t0 is a ratio and that we are dealing with very small units of distance and time. We only perceive large multiples of these units and it is important to bear in mind that s0is a maximum while t0 is a minimum. The actual kernel, where each ultimate event has occurrence, turns out to be s0/c* =  su so in ‘ultimate units’ the upper limit is c* su/t0.  It is nonetheless a surprising and somewhat inexplicable physiological fact that we, as human beings, have a pretty good sense of distance but an incredibly crude sense of time. It is only necessary to pass images at a rate of about eight per second for the brain to interpret the successive in images as a continuum and the film industry is based on this circumstance. Physicists, however, gaily talk of all sorts of important changes happening millionths or billionths of a second and in an ordinary digital watch the quartz crystal is vibrating thousands of times a second (293,000 I believe).


Note 2  Only Descartes amongst Western thinkers realized there was a problem here and ascribed the power of apparent self-perpetuation to the repeated intervention of God; today, in a secular world, we perforce ascribe it to ‘ natural forces’.

In effect, in UET, everything is pushed one stage back. For Newton and Galileo the  ‘natural’ state of objects was to continue existing in constant straight line motion whereas in UET the ‘natural’ state of ultimate events is to disappear for ever. If anything does persist, this shows there is a force at work. The Buddhists call this all-powerful causal force ‘karma but unfortunately they were only interested in the moral,  as opposed to physical, implications of karmic force otherwise we would probably have had a modern theory of physics centuries earlier than we actually did.

Note 3  “Neutrinos are the commonest particles of all. There are even more of them flying around the cosmos than there are photons (…) About 400 billion neutrinos from the Sun pass through each one of us every second.”  Frank Close, Particle Physics A Very Short Introduction (OUP) p. 41-2 


General Laws :  I suspect that there are no absolutely general ‘laws of Nature’, no timeless laws such as those given by a mathematical formula : such a formula at best only indicates norms or physical constraints. Of all so-called laws, however, the most general and the most solidly established are arithmetic (not physical) laws, rules based on the properties of the natural numbers. To this extent Pythagoras was in the right.

Platonic Forms  Plato was also essentially right in proclaiming the need for ‘ideal’ forms : patterns which are not themselves physical but which dictate the shape and behaviour of physical things. But he was wrong to see these patterns as geometrical, and thus both static and timeless (the two terms are equivalent). With one or two exceptions contemporary science has done away with Platonic Forms though it still puts mathematics in the supreme position.
In practice, I do not see how one can avoid bringing in a secondary ‘ideal’ domain which has a powerful effect on actual behaviour. In Ultimate Event Theory, associations of events and event-chains, once they have attained a critical point, bring into existence ‘event schemas’ which from then on dictate the behaviour of similar collections of events. From this point onwards they are ‘laws’ to all intents and purposes but there was a time when they did not exist and there will perhaps be a future time when they will cease to be operative.
Random GenerationTake the well-known example of interference patterns produced by photons or electrons on a blank screen. It is possible to fire off these ‘particles’ one at a time so that the pattern takes shape point by point, or pixel by pixel if you like. At first the dots are distributed randomly and in different experiments the pattern builds up differently. But the final pattern, i.e., distribution of dots, is identical ─ or as nearly identical as experiment allows. This makes no kind of sense in terms of traditional physics with its assumption of strict causality. The occurrence of a particular event, a dot in a particular place, has no effect whatsoever (as far as we can tell) on the position of the next dot. So the order of events is not fixed even though the final pattern is completely determinate. So what dictates which event comes next? ‘Chance’ it would seem. But nonetheless the eventual configuration is absolutely fixed. This only makes sense if the final configuration follows an ‘event schema’ which does, in some sense, ‘exist’ though it has no place in the physical universe. This is a thoroughly Platonic conception. O

 Ultimate Reality   Relatively persistent patterns on an  underlying invisible ‘substance’ ─ that is all there is in the last resort. Hinduism was quite right to see all this as an essentially purposeless, i.e. gratuitous, display ─ the dance of Shiva. Far from being disheartening, this perspective is inspiring. It is at the opposite extreme both to the goal-directed ethos of traditional Christianity ─ the goal being to ‘save’ your soul ─ and to the drearily functional universe of contemporary biology where everything is perpetually seeking a fleeting  physical advantage over competitors.
What, then, is the difference between the organic and the inorganic?  Both are persistent, the inorganic more so than the organic. Without a basic ‘something’, nothing visible or tactile could or does exist. Without persistence there would be no recognizable patterns, merely noise, random flashes of light emerging from the darkness and subsiding into darkness after existing for a moment only. ‘Matter’ is an illusion, a mental construct : patterns of light (radiation) emerging and disappearing, that is all there is.

Dominance  The ‘universe’ must be maintained by some sort of force, otherwise it would collapse into nothingness at any moment. For Descartes this force came from God, Schopenhauer views it as something inherent in Nature, as what he calls ‘Will’ and which he views as being entirely negative, indeed monstrous. This ‘force’ is what I term dominance, the constraining effect one event or event-chain has on another (including on itself), and without it everything would slow down and very soon disappear without leaving a trace. Take away Schopenhauer’s Will, the force of karma, and this is what would happen ─ and in the Buddhist world schema will eventually happen. For Buddhism, the natural state of everything is rest, inaction, and the universe came about because of some unexplained disturbance of the initial state of rest, indeed is this disturbance. Subsequently, it is as if the ‘universe’ were frantically trying to get back to its original state of complete rest but  by its ceaseless striving is precisely making this goal more and more unattainable.

Disappearance  In both traditional and contemporary physics, it is impossible for an object to simply disappear without leaving a trace. The dogma of the conservation of mass/energy says that nothing ever really disappears, merely changes its form. However, according to Ultimate Event Theory, ultimate events are appearing and disappearing all the time and they need no ‘energy’ to do this. Certain of these ultimate events produced at random eventually coalesce into repeating event-chains we perceive as solids or liquids because they acquire ‘persistence’ or self-dominance, but it is conceivable that they can, in certain exceptional circumstances, lose this property and in such a case they will simply stop reappearing.
Are there any genuine cases where objects have completely disappeared in this way? The only evidence for them would seem to be anecdotal : one hears of certain Hindu magic-men who are able to make small objects disappear and appear in a different place but it is, of course, difficult to judge to distinguish genuine magic from the stage variety. And any such alleged cases rarely if ever get investigated by scientists since the latter are terrified of being accused of credulity or worse. Professor Taylor who investigated Uri Geller was told by colleagues that no reputable scientists would do such a thing. Clearly, if one is not allowed to investigate a phenomenon it has no chance of ever being verified which is what the rationalist/scientific lobby desire.
Contemporary science and rationalist thinking implicitly assumes that ‘real’ entities, while they actually exist, exist continuously ─ in fact the previous statement would be regarded as so obvious as to be hardly worth stating. But in UET nothing exists for more than an instant (ksana) and entities that seem to exist for a ‘long time’ are in reality composed of repeating ultimate events strongly bonded together. If reality is ‘gapped’, as UET affirms, all so-called objects alternately appear and disappear (though so rapidly that we do not notice the change) so  there is much less of a problem involved in making something disappear. Instead of actually destroying the object in some way (and in the destructive process transferring the object’s mass into different mass or pure energy) it would simply be sufficient to prevent an event cluster reappearing which is not quite so hard to imagine. In UET, an apparent object reappears regularly because  it possesses ‘self-dominance’; if it could be made to lose this property, it would not reappear, i.e. would disappear, and it would not necessarily leave any trace. Moreover, to make something disappear in this manner. it would not be necessary to use any kind of physical force, high temperature, pressure and so on. To say that the theoretical possibility is there is not, of course, the same thing as saying that a supposed occurrence actually takes place : that is a matter of experiment and observation. In my unfinished SF novel The Web of Aoullnnia devotees of a  mystical sect called the Yther are not only convinced that the entire universe is going to disappear into the nothingness from which it emerged, but  believe that they should hasten this progressive movement which they call Aoullnnia-yther where yther means ‘ebbing’, ‘withdrawal’, hence the name of the sect. Although contemporary Buddhists do not usually put it quite so starkly, essentially the aim of Buddhism is to return the entire universe to an entirely quiescent state “from which it never will arise again”.

On the other hand, deliberately bringing something into existence from nothing is just as inconceivable in Ultimate Event Theory as in contemporary physics, maybe more so.                  SH  22/5/13


It is said that certain Gnostic sects which flourished in North Africa during the first few centuries of our era not only encouraged but actually required candidates to give a written or verbal account of how they thought the universe began (Note 1). It would be interesting to know what these people came up with and, most likely, amongst a great deal of chaff there were occasional anticipations of current scientific theories. It is mistaken to imagine that great ideas go hand in hand with experimentation and mathematical implementation : on the contrary, important ideas often predate true discovery by centuries or even millennia. Democritus’ atomic theory (VIth century BC) could not possibly have been ‘proved’ prior to modern times and he certainly could not possibly have put it in quantum or even Newtonian mathematical form. Similarly, one or two brave people put forward the germ theory of disease while the ‘miasmic’ theory was still orthodoxy ─ and were usually dismissed as cranks.
As a body of beliefs, ‘science’ is currently entering a period of consolidation comparable to that experienced by the early Church after its final victory over paganism. Materialism has decisively vanquished idealism and religion is no longer a force to be reckoned with, at least in the West. Along with increasing potency and accuracy goes a certain narrowing of focus and a growing intolerance : science is now a university phenomenon with all that this implies and no .longer a ‘pastime of leisured persons’. To some extent, this tendency towards orthodoxy is inevitable, even beneficial : as someone said it doesn’t matter too much if a poet departs from  the prescribed form of a sonnet, but it may matter a great deal if a bridge builder uses the wrong equations. Nonetheless, there are warning signs : ‘scientific correctness’ has replaced not only free enquiry but the very idea of scientific validity. Professional scientists worry, not so much about whether their results are flawed or their theories tentative, as to whether they are going to get in trouble with the establishment, and offending the latter can have grave career and financial consequences.

        It is true that free, indeed often extremely erratic  speculation, is still allowed  in certain areas, especially cosmology and particle physics. But it is subject to certain serious constraints. Firstly, it is only permitted to persons who already hold more than one degree and who are able to couch their theories in such abstruse mathematics that journals find it difficult to find anyone to peer review the work. Is not this how it should be? Maybe not. Certainly, you are likely to need some knowledge of a subject before cobbling together a theory but there is such a thing as knowing too much. Once someone has been through the mill and spent years doing things in the prescribed manner, it is well nigh impossible to break out of the mental mould ─ and this is most likely the reason why really new ideas in science come from people in their twenties (Einstein, Heisenberg, Dirac, Gamow et al. et al.), not because of any miraculous effect of youth as such.

        So. Where’s all this leading?  I didn’t do science at university or even at school which puts me in many respects at an enormous disadvantage, but this has certain good aspects as well. I have no vested interest in orthodoxy and only accept something because I am convinced that it really is true, or is at least the best theory going for the time being. Almost all current would be innovators in science, however maverick they may appear at first sight, take on  board certain key doctrines of modern science such as the conservation of energy or the laws of thermo-dynamics. But one might as well  be killed for a sheep as a lamb and I have finally decided to take the plunge and, instead of trying to fit my ideas into an existing official framework, to swim out into the open sea, starting as far back as possible and  assuming only what seems to be essential. I originally envisaged ‘Ultimate Event Theory’ as a sort of ‘new science’  but now realize that what I really have been trying to do is give birth to a new ‘paradigm’ ─ a ‘paradigm’ being a systematic way of viewing the world or reality. Should this paradigm ever come to fruition, it will engender new sciences and new technologies, but the first step is to start thinking within a different framework and draw conclusions. In other words, one is obliged to start with theory ─ not experiment or mathematics though certainly I hope eventually experiments will give support to the key concepts and that a new symbolic system will be forthcoming (Note 2).

       Four Paradigms

 To date there have been basically four ways of viewing the world, three all-englobing ‘paradigms’ : (1) The Animistic paradigm; (2) the Mechanistic paradigm; and (3) the Information Paradigm and (4) the Event Paradigm.
According to (1) the universe is full of life, replete with ‘beings’ in many respects like ourselves inasmuch as ‘they’ have emotions and wills and cause things deliberately to happen. This conception goes far beyond mere belief in a pantheon of gods and goddesses : as Thales is supposed to have said, if a lodestone draws a piece of iron it is exercising ‘will’ and “All things are full of gods”. This world-view lasted a very long time and, even though it is largely discredited today, it still has plenty of life  left in it which is why we still speak of ‘charm’, ’charisma’, ‘fate’, and so on and why, despite two centuries of rationalistic propaganda, most of the population still believes in ‘jinxes’ and in ‘spirits’ (as I myself do at least part of the time).
The countless deities and “thrones, principalities and powers” against whom Saint Paul warns the budding Christian eventually gave way to a single all-powerful Creator God who made the world by a deliberate act of will. In its crudest form, Mechanism views the universe as a vast and complicated piece of clockwork  entirely controlled by physical and mathematical laws, some of which we already know. No living things of any sort here unless we make an exception for humanity and, even if we do make such an exception, it is hard to see how free will can enter the picture. Modern science has dispensed with the  Creator retained the mechanistic vision somewhat updated by quantum uncertainty and other exotic side effects.
The invention of the computer and its resounding success sometimes seems to be ushering in a new paradigm: the universe is an enormous integrated circuit endowed with intelligence of a sort and we are the humble bits. Seductive though this vision is in certain respects, it is not without serious dangers for the faithful since it looks disturbingly like a sort of reversion to the most ancient paradigm of all, the animistic one ─ the universe is alive and capable of creating itself and everything else out of itself.
The paradigm that I am working with harks back to certain Indian Buddhist thinkers of the early centuries AD though I originally discovered it for myself when I knew nothing about Buddhism and Taoism. No Creator God, no matter or mind as such, only evanescent point-like entities (‘dharmas’, ‘ultimate events’) forming relatively persistent patterns on a featureless backdrop which will eventually be returned to the original emptiness (‘sunyata’) from which the “thousand things” emerged.

Broad schema of Eventrics 

Following my own instincts and the larger cosmology of Taoism and other mystical belief systems, I divide reality into two broad categories, what I call the Manifest and the Unmanifest, each of which is further divided into two, the Non-Occurrent and the Occurent. If one feels more comfortable with a symbolic notation, we can speak of K0  and K1 with further regions K00 and K01, K10 and K11.  Of the Unmanifest Non-Occurrent, K00, little need or can be said. It is the ultimate origin of everything, the original Tao, Ain Soph (‘the Boundless’) of Jewish mysticism, the Emptiness of nirvana, the vacuum of certain contemporary physical theories (perhaps).

To be continued)

Note 1  As soon as Christianity, or a particular version of it, became the official religion of the declining Roman Empire, all such cosmological speculation was actively discouraged and penalized.

Pagoda I want to start by expressing my gratitude to MeetUp in general and the London Futurists in particular for enabling this event to take place at all, the first time ever that my ideas have been aired in a public place. I intended to conclude the meeting with an expression of my debt to MeetUp,  the Futurists and founder/organiser David Wood, but unfortunately this slipped my mind as the meeting broke up fairly rapidly after a full hour in the cold. (A summary of my talk will be given in a subsequent post.)
The meeting at the Pagoda on Sunday was, as far as I am concerned, well attended — I did not expect or desire  crowds. All those present seem to have had serious intent and to judge by the thoughtful comments made in the discussion afterwards (drastically curtailed because of the cold) they grasped the main drift of my argument. Some missed the meeting because of the weather or did not find us because we were hidden behind a wall on the south side of the Pagoda.

Two persons have already said they would like to have heard the talk and wondered whether there could be a repeat. However, I feel that my ideas are rather far from the framework and general ethos of the London Futurists — though naturally if asked I would be glad to repeat the talk indoors somewhere at a later date. Instead, I plan to have a monthly series of talks/discussions on various issues arising from ‘Ultimate Event Theory’, the scientific and philosophical system I am currently developing. The place will remain the Peace Pagoda, Battersea Park, South facing wall, at 2 p.m. on a date to be announced, probably the last Sunday of each month — watch this site in January. If no one comes at all, the session won’t be wasted since I will be periodically renewing my contact with the ideas of the Buddha via the beautiful edifice in Battersea Park.

What follows is ‘matters arising’ from the talk:

Three stages

It is said that every new scientific idea goes through three stages : Firstly, they say it is not true, secondly, they say it is not important and, thirdly, they credit the wrong person.
Although I am to my knowledge the first person to have taken the world-view of Hinayana Buddhism seriously as a physical theory (as opposed to a religious or metaphysical doctrine), it is entirely appropriate that the first time Ultimate Event Theory was presented verbally to the public the venue was the Peace Pagoda (built by practising Buddhist craftsmen) since the theory I am developing, “Ultimate Event Theory”, can be traced back to the founder of one of the five great world religions, Buddhism.
Our science stems from the Greeks, in particular the atomist Democritus of Abdera  whose works have unfortunately been lost. He is credited with the amazing statement — reductionist if ever there was one —  “Nothing exists except atoms and void“. These atoms Democritus (and Newton) believed to be indestructile and eternal. Although we now know that some atoms decay, the statement is not so far out : around us are protons and neutrinos that have existed since the Big Bang nearly 15 billion years ago (or very soon afterwards). And as for the void, it is healthier and more vibrant than ever, since it is seething with quantum activity (Note 1).
Dharma    But around the same time when Democritus decided that the ultimate elements of existence were eternal atoms, Gautama Buddha in India reached exactly the opposite conclusion, namely that the dharma (‘elements’) were evanescent and that everything (except nirvana) ‘lasted for a moment only’.  A Buddhist credo summarised the teaching of the Buddha thus: “The Great Recluse identified the elements of existence (dharma), their causal interconnection (karma) and their ultimate extinction (nirvana)” (Stcherbatsky, The Central Conception of Buddhism).
I must emphasize that the theory I am developing, Ultimate Event Theory, is a physical theory (though it has ramifications far beyond physics) and does not presuppose any religious belief, still less is it an underhand way of ‘preaching Buddhism’ or any other form of religion. The Buddha himself founded no Church and spent the latter part of his long life wandering around India giving talks in the open air to anyone who cared to listen. My original interest in Buddhist theory was ‘scientific/philosophical’ rather than ‘spiritual’.  It seemed to me that Gautama Buddha had, through the practice of meditation, intuited certain basic features of physical and mental reality, and concluded correctly that matter, mind, soul, personality and so on are all ‘secondary’ not primary entities — in today’s parlance they are ’emergent’ entities. He also saw, or rather felt, that ‘existence’ was not continuous but that everything (incuding the physical universe) is, as it were, being destroyed and recreated at every instant (the Theory of Instantaneous Being). I do not personally, however, conclude that the personality, consciousness, free will and so on are ‘illusory’ as the Buddhist tradition seems to have inferred, merely not primary, not basic.  At bottom we are seemingly all made up of elementary particles and forces between these particles but at a deeper level still I believe that everything is composed of momentary ‘ultimate events’ flashing into existence and then disappearing for ever. As far as I am concerned the buck stops here : beyond the dharma lies only the Absolute, the ground of all being, and this, though it can perhaps be glimpsed by mystics, is wholly outside the domain of science, rational thought and mathematics. “The Tao that can be named (or measured)  is not the original Tao”.      SH  5 December 2012

Note 1  For the claim that Space/Time is “grainy” see Is Space Digital by Michael Moyer, Scientific American Feb. 2012, also  “How big is a grain of space-time?”  by Anil Ananthaswamy (New Scientist 9 July 2011)


Genesis of Ultimate Event Theory :  My life could be divided into two periods, the first ending one morning in the late seventies when I came across a curious book with the bizarre title Buddhist Logic in Balham Public Library, Battersea, London.  In this book for the first time I came across the idea that had always seemed to me intuitively to be true, that reality and existence were not continuous but discontinuous and, moreover, punctured by gaps — as the German philosopher Heidegger put it  “Being is shot through with nothingness”. A whole school of thinkers, those of the latter Hinayana, took this statement as so obvious it was hardly worth arguing about (though they did produce arguments to persuade their opponents, hence the title of the book).
This well-written tome of Stcherbatsky, not himself a practising Buddhist, thus introduced me to the ideas of certain Hinayana thinkers during the first few centuries of the modern era (Dignaga, Vasubandhu et al.)  I saw at once how ‘modern’ their views were and how, with a certain ingenuity, one could perhaps transform their ‘metaphysics’ into a physical theory very diffferent from what is taught today in schools. These deep and subtle thinkers, in every way the equal of the Greeks, had no interest in developing a physical theory for its own sake since their concern was with personal ‘enlightenment’ rather than the elucidation of the physical world.  Had they and their followers wished it, quite conceivably the world-wide scientific revolution would have taken place, not in the then backward West, but in India. But maybe the time was has now come for the insights of these men to take root some 1,800 years later on the other side of the world and to eventually become the basis of a new science and a new technology. Matter is getting thinner and thinner in contemporary physics so why not drop it entirely and stop viewing the world as the interaction of atoms or elementary particles ? According to Buddhism the ‘natural’ tendency of everything is not to last for ever (like Newton’s atoms) but to disappear and the relative persistence of certain rare event-chains is to be ascribed to a causal binding force, sort of physical equivalent of karma. There is no Space/Time continuum, only a connected discontinuum which is full of gaps. The universe itself will come to an end and everything will return to the absolute quiescence3 of nirvana — though some later Buddhist thinkers, like some conteomporary cosmologists, envisage a never-ending cycle of emergence/extinction/emergence……

Recommended Reading  Those interested in Buddhism as a ‘way of life’ are recommended to start (and also perhaps finish) with Conze, A Short History of Buddhism. This book really is short (132 small size pages) and so good that I seriously doubt whether anyone really needs to read any other book on the subject (unless they want to follow up a particular aspect of the theory) : the writing is clear, concise, comprehensive, pungent. If I were allowed to take only twenty books on a desert island, this would be one of them.
The Russian scholar Stcherbatsky whose books had such a big effect on me has written three seminal works covering the three main aspects of (Hinayana) Buddhism. The Central Conception of Buddhism concerns what I call ‘ultimate events’ (dharma),  Buddhist Logic deals in the main with causality (karma) and The Buddhist Conception of Nirvana with nirvana as one might expect.  Although it is the second book, Buddhist Logic (Volume 1 only), that influenced me, most interested readers would probably find it forbidding in aspect and would be advised to read the Central Conception of Buddhism first (100 pages only) , and not to bother at all with The Buddhist Conception of Nirvana which I found quite poor.


To all whom it might concern:   I am speaking to the London Futurists (plus anyone else who cares to come along) on “Does Infinity Exist?” at the Peace Pagoda, Battersea Park, London  2 p.m. Saturday 8th December

This incidentally will be the first time that I will be talking about Ultimate Event Theory in public (and it is only last year that I started putting posts up about it). (It has taken me all of thirty-five years to reach this point of no return.) It seems that the Pagoda is entirely the right location for such a discussion though it was not deliberately chosen by me, indeed not chosen at all. I had originally aimed to hold the meeting (the first I have ever called on such a subject) indoors somewhere in a venue in central London but could find nowhere available for this date chosen entirely at random. Then a few Sundays ago, my partner, the painter Jane Maitland, suddenly said “Why don’t we visit Battersea Park today?”, something we never do — the last time I was there was at least eight years ago. We passed by the Pagoda but didn’t go into it. That night it suddenly came to me that the best place to meet up was the Pagoda. Why the best place? Because the origins of Ultimate Event Theory go back all of two thousand and five hundred years to the ponderings of an Indian ascetic about the nature of the physical world and the misery of human existence.

‘Speed’ is not a primary concept in the Système Internationale d’Unités  : it is defined by means of two quantities that are primary, the unit of length, the metre,  and the unit of time, the second. ‘Speed’ is the ratio distance/time and its unit is metres/second.
It is, I think, possible to disbelieve in the reality of motion but not to disbelieve in the reality of distance and time, at least in some sense.
The difficulty with the concept of motion and the associated notions of speed and velocity, is that we have somehow to combine place (exact position) and change of place for  if there is no change in a body’s position, it is motionless. The concepts of ‘exact position’ and movement are in fact irreconcilable (Note 1)  : at the end of the day we have to decide which of the two we consider to be more fundamental. For this reason there are really only two consistent theories of motion, the continuous process theory and the cinematographic theory.
The former can be traced at least as far back as Heraclitus, the Ionian philosopher for whom “all things were a-flowing” and who likened the universe to “a never ending fire rhythmically rising and falling”. Barrow, Newton’s mathematics teacher, was also a proponent of the theory and some contemporary physicists, notably Lee Smolin, seem to belong to this camp.
Bergson goes so far as to seriousoly assert that, when a ‘moving object’ is in motion, it does not occupy any precise location whatsoever (and he is not thinking of Quantum Wave Theory which did not yet exist). He writes,
“… supposons que la flèche puisse jamais être en un point de son trajet. Oui, si la flèche, qui est en mouvement, coincidait jamais avec une position, qui est de l’immobilité. Mais la flèche n’est jamais a aucun point de son trajet”.
(“Suppose that the arrow actually could be at a particular point along its trajectory. This is possible if the arrow, which is on the move, ever were to coincide with a particular position, i.e. with an immobility. But the arrow never is at any point on its trajectory”.)
So how does he explain the apparent fact that, if we arrest a ‘moving’ object we always find it at a particular point ? His answer is that  in such a case we ‘cut’ the trajectory and it falls, as it were, into two parts. But this is like the corpse compared to the living thing ― c’est justement cette continuité indivisible de changement qui constitue la durée vraie” (“It is precisely the indivisible continuity of change that constitutes true durastion”) .

The cinematographic theory of movement finds its clearest expression in certain Indian thinkers of the first few centuries AD —:
“Movement is like a row of lamps sending flashes one after the other and thus producing the illusion of a moving light. Motion consists in a series of immobilities. (…) ‘Momentary things,’ says Kamalasila, ‘cannot displace themselves, ‘because they bdisappear at that very place at which they have appeared’.” Stcherbatsky, Buddhist Logic vol. I pp.98-99

For almost as long as I can remember, I have always had a strong sense that ‘everything is discontinuous’, that there are always breaks, interludes, gaps. By this I do not just mean breaks between lives, generations, peoples and so on but that there are perceptible gaps between one moment and the next. Now, western science, partly  because of the overwhelming influence of Newton and the Infinitesimal Calculus he invented, has definitely leaned strongly towards the process theory of motion, as is obvious from the colossal importance of the notion of continuityin the mathematical sciences.
But the development of physical science requires both the notion of ‘continuous movement’ and precise positioning. Traditional calculus is, at the end of the day, a highly ingenious, brilliantly successful but hopelessly incoherent procedure as Bishop Berkeley pointed out in Newton’s own time. Essentially Calculus has its cake and eats it too since it represents projectiles in continuous motion that yet occupy precise positions at every interval, however brief (Note 2).
In Ultimate Event Theory exact position is paramount and continuous motion goes  by the board. Each ultimate event is indivisible,  ‘all of a piece’, and so, in this rather trivial sense, we can say that every ultimate event is ‘continuous’ while it lasts (but it does not last long). Also, K0 , the underlying substratum or event Locality may be considered to be ‘continuous’ in a rather special sense, but this need not bother us anyway since K0 is not amenable to direct observation and does not interact with the events that constitute the world we experience. With these two exceptions, “Everything is discontinuous”. This applies to ‘matter’, ‘mind’, ‘life’, movement, anything you like to think of.    Furthermore, in the UET model, ultimate events have occurrence in or on three-dimensional grid-points on the Locality, but these grid-points are not pressed right up against one another (as in certain other  models such as that of Lee Smolin). No, there are (by hypothesis) real, and in principle measurable, breaks between one grid-position and the next and consequently between one ultimate event and its neighbours if there are any, or between each of its its consecutive reappearances.
Furthermore, in the UET model, ultimate events have occurrence in (or on) three-dimensional grid-points on the Locality, but these grid-points are not pressed right up against one another as they are in certain other discontinuous physical  models (Note 3). In Ultimate Event Theory there are real, and, in principle, measurable gaps breaks between one grid-position and the next and consequently between one ultimate event and its neighbours if there are any, or between each of its consecutive reappearances.
What we call a ‘body’ or ‘particle’ is a (nearly) identically repeating event cluster which, in the simplest case, consists of a single endlessly repeating ultimate event. The trajectory of the repeating event as it ‘moves’ (appears/reappears) from one three-dimensional frame to the next may be presented in the normal way as a line — but it is a broken, not a continuous line.
It is a matter of common experience that certain ‘objects’ (persisting event-clusters) change their position relative to other repeating event-clusters.  For illustrative purposes, we consider three event-chains composed of single events that repeat identically at every ksana (roughly ‘instant’). One of these three event-chains, the black one Z is considered to be ‘regular’ in its reappearances, i.e. to occupy the equivalent grid-point at each ksana. Its trajectory or eventway will be represented by a column on black squares where each row is a one-dimensional representation of what in reality is a three-dimensional region of the Locality. The red and green event-chains, X  and  Y  are displaced to the right laterally by one and three grid-positions relative to at each ksana (Note 4).

         X   Y                              Z

        In normal parlance, Y is a ‘faster’ event-chain (relative to Z) than X and its speed relative to Z is three grid-positions (I shall henceforth say ‘places’) per ksana . The speed of  X  relative to Z is one place/ksana. (It is to be remarked that Y reappears on the other side of  Z without ‘colliding’ with it).
Of course, this is a simplified picture : in reality event-chains will be more spread out, i.e. will consist of many more than a single element per ksana; also,  there is no reason a priori why they should be made up of events that reappear during every ksana. But the point is that ‘velocity’ in Ultimate Event Theory is a straight numerical ratio (number of grid-positions)/(number of  ksana)  relative to a regular repeating event-chain whose trajectory is considered to be vertical.  Note that Y reappears on the other side of  Z without ‘colliding’ with it.      S.H.  27/7/12


Note 1 :     “A particle may have a position or it may have velocity but it cannot in any exact sense be said to have both” (Eddingon).

Note 2 :  Barrow, Newton’s geometry teacher, wrote, “To every instant of time, I say, there corresponds some degree of velocity, which the moving body is considered to possess at that instant”. Newton gave mathematical body to this notion in his ‘Theory of Fluxions’, his version of what came to be known as the Infinitesimal Calculus.

Note 3      According the Principle of Relativity, there is no absolute direction for a straight event-line, and any one of a family of straight lines can be considered to be vertical. Other things being equal, we consider ourselves to be at rest if we do not experience any jolts or other disturbances and thus our ‘movement’ with that of Z, a vertical line.  However, if we were ‘moving’, i.e. appearing and reappearing at regular intervals, alongside or within (straight) event-chains or  Y, we would quite legitimately consider ourselves to be at rest and would expect our event-lines to be represented as vertical.
The point is that in classical physics up to and including Special Relativity the important distinction is not between rest and constant straitght-line motion but between accelerated and unaccelerated motion, and both rest and constant straight-line motion count as unaccelerated motion. This capital distinction was first made by Galileo and incorporated into Newton’s Principia. 
The distinction between ‘absolute’ rest and constant straight-line motion thus became a purely academic question of no practical consequence. However. by the end of the nineteenth century, certain physicists argued that it should be possible after all to distinguish between ‘absolute rest’ and constant straight-line motion by an optical experiment, essentially because the supposed background ether ought to offer a resistance to the passage of light and this resistance ought to vary at different times of the year because of the Earth’s orbit. The Michelsen-Morley experiment failed to detect any discrepancies and Einstein subsequently introduced as an Axiominto his Theory of Special Relativity the total equivalence of all inertial systems with respect to the laws of physics. He later came to wonder whether there really was such a thing as a true inertial system and this led to the generalisation of the Relativity principle to take in any kind of motion whatsoever, inertial systems being simply a limiting case.
What I conclude from all this is that (in my terms) the Locality does not interact physically with the events that have occurrence in and on it; however, it seems that there are certain privileged pathways into which event-chains tend to fall. I currently envisage ultimate events, not as completely separate entities, but as disturbances of the substratum, K , disturbances that will, one day, disappear without a trace. The Hinayana Buddhist schema is of an original ‘something’ existing in a state of complete quiescence (nirvana) that has, for reasons unknown, become disturbed (samsara) but which will eventually subside into quiescence once again. The time has come to turn this philosophic schema into a precise physical theory with its own form of mathematics, or rather symbolic system, and my aim is to contribute to this development as much as is possible. Others will take things much, much further but the initial impulse has at least been given.

Note 4  Of course, this is a simplified picture : in reality event-chains will be more spread out, i.e. will consist of many more than a single element per ksana; also,  there is no reason a priori why they should be made up of events that reappear during every ksana.

S.H.  22/7/12