**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.

*Copyright © 1995-1997 ANG. All rights reserved.*