zlacker

>>tromp+(OP)
The problem, as stated, provably has no answer. Assume such a number exists. Call it n. Now define a new 64-bit numbering scheme such that each number x is interpreted as n+x. n+x > n, which invalidates the hypothesis. There needs to be more constraints for this to be interesting. Like largest number representable where the representation is closed under addition and multiplication, or something like that.

>>4death+ay6
> There needs to be more constraints for this to be interesting.

Scott Aaronson's quote in the article provides this constraint:

> Precisely because the Turing machine model is so ancient and fixed, whatever emergent behavior we find in the Busy Beaver game, there can be no suspicion that we “cheated” by changing the model until we got the results we wanted.

Your "each number x is interpreted as n+x" is a clear example of the cheating that makes for an uninteresting scheme.