The Status of the Infinite

A friend of mine who is a philosopher of mathematics says that the biggest debates his field is having is on the status of the infinite. Here are three introductory problems -- not by far the whole thing, but an introduction to the thing.

4 comments:

james said...

Geometry gets a little funny in spacetime when you try to build in Heisenberg uncertainty.

Grim said...

Well, that's another thing that philosophers debate: whether Heisenberg's ideas are really permanent problems, or whether it is in principle possible to overcome them.

james said...

It looks built in. If you could evade it, there'd be some consequences that appear not to be true. I can't reproduce the details--have to go look them up again.

Ymar Sakar said...

The popular counter to Heisenberg is to talk about the macro level being different from the micro or quantum level. So it doesn't matter if Heisenberg's laws/rules apply to electrons or quantum states. The macro state is immune, supposedly.

However, I would think the difference between atomic and macro scale, is due to human ignorance and the inability to understand what's really going on at the core of matter, substance, and energy. Which the quantum model, the standard model, may shed a lot of light on.