**Cosmogony 101 (Version A)**

Suppose you are a supernatural being or a student taking a laboratory course in Cosmogony 101 at some faraway university and you have decided to create a universe that consists of moving things.

(1) You must first create space and time, since motion consists of being located somewhere in space at some time and somewhere else in space at other times.

(2) Both space and time must be metric spaces, so that you can speak of distances between parts of space and distances between parts of time and divide one by the other and compute speeds for your moving objects.

(3) A metric space is a set the elements of which are "points" in the case of space and "instants" in the case of time and in either case have a size of zero and have no parts.

(4) Your moving objects, in order to occupy space, must occupy either single points of space or sets containing many points (two or more, maybe infinitely many, maybe more than merely infinitely many). In the latter case, however, they have parts, and, in particular, they have smallest and indivisible parts that occupy single points. Thus your moving objects must either be particles, objects that occupy exactly one point of space at each instant of time at which they exist, or else sets of many such particles (two or more). Thus when you get around to making your moving objects, all you will make will be moving particles. Whatever other moving objects there are will be sets of particles.

(5) Now suppose that your particles move at different speeds. There will then be no way to say what the speed of any one of them is. Since you cannot see space and can see only the particles, the best that you will be able to do will be to say that this particle has a relative speed of such-and-such with respect to that particle, but there will be no definite and non-arbitrary way to break this relative motion down into so much motion of particle A and so much motion of particle B. The notion that any one particle even has any such property as a speed that is just its own speed would, however, under such circumstances, be incoherent, as, then, would the notion that the speed of one particle is different from the speed of some other particle. The hypothesis that the particles have different speeds thus implies its own senselessness and cannot be true. The alternative is that all the particles have the same speed.

(6) Suppose now that the speed of all particles varies with the passage of time. Again there would be no way to say what this speed is. There would be no way to distinguish between a process that happened at a constant rate and one that did not. There would be no way to distinguish between a clock that ticked off time at a constant rate and one that did not. But without a clock that ticks at a rate that is guaranteed to be constant, the notion of time needed for computing a speed is lacking and again there is no sense in saying that the particles have one speed rather than some other speed. The notion that there is some quantity which is *the* speed of the particles is, under such circumstances, incoherent, and with it the notion that this speed varies. The hypothesis that the particles have a variable speed thus implies its own senselessness and cannot be true. The alternative is that the speed of the particles is constant.

(7) Thus you must create nothing but particles and these must all have the same constant speed. Otherwise, your notion of a universe of moving objects is incoherent.

(8) It is clear now that the particles must be particles not only in the sense of being appropriately small (occupying one point at a time), but also in the sense of being separated each from any other by empty space, for a geometrically solid object has no freedom to move in such a way that each point-occupying part of it moves at the same constant speed (other than that the entire object move at that speed, in a constant direction, forever – but there are no such objects).

(9) There must be no more than countably many particles, for more than that many could get together to form an impossible geometrically solid object. On the other hand, since the universe is infinitely large (assuming that space is Euclidean), there must be infinitely many particles, since fewer would either clump together in a finite region of space or disperse until there were no combinations of them. Since there are dispersive as well as aggregative processes going on, we can assume that any region of space of finite volume contains only finitely many particles (possibly none if the region is sufficiently small).

(10) The velocity of a finite set of particles is **v** = (**v**1 + ... + **v**n)/n, or perhaps **v** = (m1**v**1 + ... + mn**v**n)/(m1 + ... + mn), where n is the number of particles, the** v**i are their velocities and the mi are their masses. Since vectors partially cancel each other when they add unless they are parallel, this velocity can have any magnitude from and including 0 up to and including c, though it has the speed c only in case each of the added vectors is parallel to each of the others, and this speed can change as the directions in which the constituent particles move change.

This explains why we live in a world that consists of some very small things that move all at the constant speed c, while all large things move at variable speeds that are less than c, and maybe zero.