Comment by yarg
3 years ago
It all depends on what values you're willing to leave unrepresentable.
(Bearing in mind that the set of operations that you can accurately support in your number system also depends on the set of representable values.)
If you don't really care you can go arbitrarily high.
Very true, but in all fairness the proposed solution of using Turing machines is pretty reasonable. I think the title is a play on Scott Aaronson's "largest number" game.
Sure, but where do you stop?
I think a more interesting question is "what's the largest number usefully representable in 64 bits?".
My thinking is that the article isn't really investigating the largest number you can share in 64 bits- as you say, it's sort of meaningless. Instead, like the biggest number game, it's a lead in to talk about some neat topics in theoretical computer science
Yeah, just define a 1-bit type of the values {0, MAX}, for some very large number MAX. And now we‘ve represented a very large number with a 1-bit value!
It's trivial in the extreme cases, but similar logic was used to implement the floating points - it compromised on the accuracy of results, but gave us a number system that's useful across a range of scales.
If we could find some set of staggeringly large values, perhaps even infinite, with some useful set of operations that could be performed on them (and mapping back to the set) then we can come up with ridiculous answers that aren't necessarily useless.