User blog comment:Sbiis Saibian/Googology101 - Part I/@comment-1605058-20141023055529/@comment-5982810-20141023151016

I KNEW you were going to bring that up. Let me just ask you this: Why are you so bad an intuiting the more precise meaning of informal language. Obviously I'm not speaking about "naming numbers" purely on principle. My article makes it clear that there is a distinction to be made between what can be done in principle and in practice, and that as googologist's we are not just theoretist's but practioners. "To name" means, informally, that the description is small enough that we can actually describe it in practice. It's not important how this is defined precisely. We can know exactly what the cut off point is, but for any cut off point you would arbitrarily use, say no more than 10^80 bits for example, we can formalize this informal statement and say, if we find a sufficiently large number that takes less than 10^80 bits to define, then there is at least one number smaller that takes more than that to describe. This is because the maximum number of information to describe any integer in decimal is about log(n), using decimal notation. So if we find a way to describe a number better than log(n), like a googolplex with 10^10^100 (9 characters as oppose to the googol+1 characters it would take in decimal), we can be more or less assured that there exists a number less which takes more than 9 characters to describe.

Was that really unclear?