You are Not Even Wrong, in this instance. Math is not a simulation of the real world; to take a simple example, both Euclidean and hyperbolic geometry are self

You are Not Even Wrong, in this instance. Math is not a simulation of the real world; to take a simple example, both Euclidean and hyperbolic geometry are self-consistent and useful, and yet clearly different. So "the rock solid foundation" of math is not the real world, but rather sets of self-consistent axioms. The halting problem is not an attempt to predict the future with math; it's a description of a property of algorithms which is inherently non-computable. You cannot, in the general case, prove whether an algorithm halts or not. So as to your the question of whether the "randomness" comes from trying to predict the future...the answer is not yes, nor is it no. The question is not sensible. The article was very poorly written though, so I'm not surprised it causes confusion. If you are interested in actually learning about Omega, I recommend http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html which is an amazing introduction to all these ideas.