Bill S.
Infinity and spacetime are kind of like apples and oranges.
Spacetime is a physical idea but infinity is more of a
descriptive idea. In concept there is no reason why spacetime cannot be infinite. It may or may not be, I'll leave that up
to the physicists who are studying the lifetime of the universe.
If spacetime is infinite it just means that the length, breadth,
width, and age of the universe are beyond measurement, even in
concept. If the universe is infinite that doesn't keep us from
moving around in spacetime.
No body claims that you can reach infinity in any way. In fact
that is one of the things about infinity. Whatever type of
infinity you are looking at, the integers, the number of points
on a line, etc, the class is infinite, but the members of the
class, such as 1 or 1,000,395,0001 are are not. But you can't
write down a number that I can't write down a larger one. So
that makes the class of integers infinite. It doesn't keep
me from doing simple arithmetic. So I can do mathematics on
spacetime even if it turns out to be infinite.
And then of course there is a mathematics that applies to
infinities. I have been give just the barest look at
the classification of infinities. I don't think I want to
even start actually trying to learn about it.
Bill Gill
