Greg Buchholz in the site's comments linked to Gregory Chaitin's "How real are real numbers?"[1] and asks, > Isn't it a little bit crazy to talk about computat

Greg Buchholz in the site's comments linked to Gregory Chaitin's "How real are real numbers?"[1] and asks, > Isn't it a little bit crazy to talk about computations on real numbers, when most of them are uncomputable/unnameable? [1] https://arxiv.org/pdf/math/0411418.pdf https://arxiv.org/pdf/math/0411418.pdf > Experimental physicists know how difficult accurate measurements are. No physical quantity has ever been measured with more than 15 or so digits of accuracy. Mathematicians, however, freely fantasize with infinite-precision real numbers. Nevertheless within pure math the notion of a real number is extremely problematic. We’ll compare and contrast two parallel historical episodes: > 1. the diagonal and probabilistic proofs that reals are uncountable, and > 2. the diagonal and probabilistic proofs that there are uncomputable reals. > Both case histories open chasms beneath the feet of mathematicians.