A SUMMARY ON THE DIVISIBILTY OF MOTION AND REST

                        A SUMMARY ON THE DIVISIBILTY OF MOTION AND REST

Magnitude and motion are correlative, so that if magnitude is composed of indivisibles, so must motion, which traverses it. And if this is impossible for magnitude, then it is also impossible for motion. To illustrate this, take a magnitude (or road) that consists of points A, B and C. When the mobile reaches B point it must either be in motion or have completed its motion. If it is still in motion, then B must be divisible; otherwise the motion would be complete at that point and the sum of the motion from A to C would not be divisible motions but discrete moments [like frames in a video]. Then, if motion consists of discrete moments, it would follow that something has completed a motion without having been in motion. Also it would follow that at each point on the route the mobile would be at rest, while it was supposed to be in motion. Also the segments of motion corresponding to each of the points on the route would also be rests, and thus the whole motion would be composed of non-motions.

Because time corresponds to magnitude, if magnitude could be infinite, such as a line without beginning or end point, so would time be (since any finite time at a finite velocity will only traverse a finite magnitude). And if magnitude is infinitely divisible, so is time. The argument can validly be reversed: If time is infinite in length, so must magnitude be (because any motion, however slow will eventually traverse a finite magnitude); and if time is infinitely divisible, so must magnitude be. From this we have another argument why no continuous magnitude or part thereof is indivisible. This can be shown inductively by positing two mobiles of different velocities. When the faster one crosses the first supposedly indivisible part, the slower one will have crossed only part way, proving that the supposedly indivisible segment is divisible.

The term "now" is often used for a period, like "today", but "now" is precisely indivisible and present in every time. It is the limit between the past and the future, and as such must be one. The now terminating the past and beginning the future cannot be two contiguous "nows", because otherwise time would be composed of an aggregate of indivisible "nows", which is impossible, since it is continuous. Nor can there be an interval between the two "nows", because that would be a period of time or at least another "now"; in either case the "now" would be divisible. Were the "now" to be divisible it would have to include some of the past or the future; in that case some of the future would be in the past and some of the past in the future. Therefore the "now" which terminates the past and begins the future must be one "now". All motion occurs in time and must be intermediate between two extremes, with part of the mobile towards one extreme and part of it towards the other. This is obvious of the three species of motion, but, even though generation and corruption are substantial changes and instantaneous, they are preceded by alteration of a subject. Some alteration, like electricity in a wire, seems instantaneous, but precise measurements can show that it too takes place in time.

Motion is divided according to the motion of the parts of the mobile, since both time and the mobile is continuous and divisible. Thus the entire motion belongs to the entire mobile, just as the parts of it belong to the parts of the mobile. Motion is also divided according to time, since there is less motion in less time. There are five things related to motion which are similarly divided: (1) time, (2) motion, (3) the very act of being moved, (4) the mobile which is being moved, and (5) the species of motion, i.e. the place, quality or quantity. The divisibility of the mobile is the basis of the divisibility of all the others.

First, it is clear that 'coming to rest' is part of motion, and this takes place in time. just as we have seen that no part of motion can be said to be first, so no part of coming to rest can be said to be first. Since rest itself is continuous in time, it can have no first part because each part is divisible. Something is at rest if throughout a definite period of time(from one "now" to another) it is one and same state, for example in one place. Therefore nothing can be at rest and at motion at the same time with respect to the same kind of motion.