Comment by cousin_it

11 years ago

Yeah, that might avoid paradox at the cost of requiring a specific kind of judge. But then I think you need to fully specify the judge's reasoning, and that's a very difficult problem, it might be even AI-complete. I don't know of any computer program that would be able to judge the descriptions of current winning entries.

Maybe this quote from the googology wiki will set you on a more productive track:

Googologists generally avoid many of the common responses such as "infinity," "anything you can come up with plus 1," "the largest number that can be named in ten words," "the largest number imaginable," "a zillion," "a hundred billion trillion million googolplex" or other indefinite, infinite, ill-defined, or inelegant responses. Rather googologists are interested in defining definite numbers using efficient and far reaching structural schemes, and don't attempt to forestall the unending quest for larger numbers, but rather encourage it. So perhaps a more accurate description of the challenge is: "What is the largest number you can come up with using the simplest tools?"