zlacker

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+(OP)
Posits formerly unums, these are amazing. The best solution I've seen. Look up John Gustafson. This article doesn't mention him or posits. They can expand with inaccuracy but retain precision. Or sacrifice precision for accuracy. Making the best use of the bits depending on the application.

>>4death+(OP)
> 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.

>>tromp+U31
That doesn’t provide a constraint. The quote you mentioned is about why to model computation as a Turing machine vs. some other model, not about how to “find the largest number representable in 64-bits”, which doesn't have an answer.

>>4death+bq1
I believe tromp implies a constraint of “existed before we started answering the question”.

>>4death+bq1
I gave an answer for the largest number known to be representable in 64 bits with a scheme that is clearly not cheating.

>>tromp+vD1
Define “cheating”.