Chris Liss on Nostr: I was aware of different levels of infinity, say the higher level of the reals and ...

I was aware of different levels of infinity, say the higher level of the reals and the higher level still of the sets that can be made with reals. But in my Claude chat I got some insight as to WHY real numbers can’t map with the naturals the way rationals do, and it got pretty deep.

The real numbers we use like pi and e are the exceptions in that you can generate them with relatively compressed information, kind of like rationals. But reals are uncompressible like reality itself. In fact the rationals are literally rational — figments of the reasoning mind, only a map, so to speak, whereas reals are the territory itself.

When you think about it, there is no circle in nature, no 3, no cutting something in half. They are all abstractions. But reals are reality in its actual detail. Rationals are finitely describable, reals are not except for the few exceptions like pi and e. Otherwise you cannot describe a real with a finite amount of information. Just like you can’t describe or map reality faithfully with a finite map. Which leads to Godel and Wittgenstein.