Omega is an amazing number. We know it has a digit in its binary expansion that is 0 or 1, yet it is impossible to formulate why. It is impossible to come up with a train of thought that explains it. There is no explanation that can be written down on a piece of paper.<p>So we are left with the weird conclusion:<p>1. It has the value it has for no reason.<p>2. It has the value it has for a reason that is impossible to formulate.