Dialogue 1

Eager: Teacher, why do you think that we can't know much about space and time? It is clear that space and time are continuous and infinite, isn't it?

Wise: Not right. The problem is motion. It's not easy to combine any concept of space-time with motion we see in the world. You can choose by yourself. Suppose, time and space are continuous. And suppose that an object which is moving now was at rest at some time earlier. Then, we cannot find a moment when the motion starts.

Eager: Let me see… For every moment when the object is moving we can find an earlier moment when it doesn't, then divide this interval into two, then again into two, and finally arrive at the earlier moment when the object is still moving. And we can do that for any particular time when the object moves!

Wise: Right. Suppose that time is discreet while space is continuous. Then, the faster runner can never reach the slower one. Indeed, he should first cover the initial distance between them. At this time the slower runner will also cover some distance, which should be covered by the faster runner and so on. Thus, we obtain an infinite number of space intervals (of infinitely diminishing lengths) covered by the faster runner before he gets the slower one. An infinite number of finite time durations means infinite time - the faster never reaches the slower.

Eager: I think I know what happens when time and space are both discreet. Then, at any particular time at a given point of space any object is at rest, which means that it would not change its position later. We have no motion at all! The last alternative is continuous time and discreet space. What is the problem there?

Wise: If time is continuous and space is discreet then motion can not be continuous (continuous motion requires disappearance of a moving object everywhere except the knots of space). For jump-like motion we can use the same arguments as for the case of discreet space and time.

Eager: Should we think that there is no motion in the world?

Wise: We discuss this later. 