Also, keep in mind that it's not just a result about programming / halting problem. It has implications for the foundations of mathematics. For example, if y

Also, keep in mind that it's not just a result about programming / halting problem. It has implications for the foundations of mathematics. For example, if you formalize math such that you can measure the bit-length of theorems about numbers, you'll find that in the limit, to have a theory of all true theorems up to length N-bits, you'll need O(N) bits of axioms. (I'm probably not saying that in the best possible way: again, I'm no technician in these matters.)