‘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
…□□□□□□□□□□□□□□□■□……..
…□□□□□□□□□□□□□□□□……..
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…□□□□□□□□□□□□□□□□■□□□□……..
…□□□□□□□□□□□□□□□□□■□□□□□□□□□………..
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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

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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.
Z
…□□□□□□□□□□□□□□□□□■□……..
…□□□□□□□□□□□□□□□□□……..
…□□□□□□□□□□□□□□□■□□……..
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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