"Why should I believe in a real number if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it? And each of these things ha

"Why should I believe in a real number if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it? And each of these things happens with probability one! The real line from 0 to 1 looks more and more like a Swiss cheese, more and more like a stunningly black high-mountain sky studded with pin-pricks of light." ...see chapter 5 of Meta Math! by Gregory Chaitin: https://arxiv.org/pdf/math/0404335.pdf https://arxiv.org/pdf/math/0404335.pdf