Comment by im3w1l
11 years ago
Yeah, I agree that it becomes less well defined. The problem with Berry's paradox is that it refers to itself. I circumvented paradox, by only refering to shorter descriptions of the number, than the description I gave. If that strategy works really depends on what the judge thinks though. Assuming he accepts refering to his own potential judgements of shorter sequences but not longer or equally long, the solution would work and the rules would be paradox free.
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?"
http://googology.wikia.com/wiki/Googology#History