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Comment by andrewflnr | Hacker News Reader

Crap, you're right. Wait, I mean, of course I meant volume when I said "size".

But I think you can seriously make the argument that not only is "largest number" an empirical question, but the answer depends on your units. I'm not sure that's more absurd than the stuff in TFA.

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You aren't trolling, but it is trivial to come up with larger numbers that are, in a sense, just as practical. Memory suggests that if the universe has a finite size then there is a finite amount of information that can be stored in it. "The states of data that could be stored in the observable universe interpreted as a hard dive" is a much, much larger quantity than size of the universe in Plank Lengths.

However, what if we want to theorise about what, if anything, sits outside the observable universe? You seem to be suggesting that it will always be finite, which is optimistic to say the least. Just because we can't observe something doesn't mean that it isn't real, and that we won't get utility out of modeling it. Infinity might be out there.

The value of BB(v), where BB is the Busy Beaver function, and v is the volume of the observable universe in planck length cubes, ought to suffice.

I hope you didn’t want a number you could actually figure out....

Can't we keep on applying the BB function i.e BB(BB(BB(...(BB(v)))) given that every application of BB still results in a finite number?

yes, but "can" is rather optimistic.

The largest number I saw written out is the number of symmetries in the monster group, spelled out on wikipedia (iirc).

Yes, and you can generalize this to BBN(v, N), which means N applications of BB to v. If we replace N with v, it becomes a single parameter BBN(v). Then we can apply this thing to itself, and so on. So, with any finite storage space, we can represent an arbitrarily large number in this fashion. Thus, finite storage does not set an upper bound on the number that can be represented.

I'm actually going to say that's not a real number until you actually build that busy beaver. For one thing, the Bekenstein Bound is doing to come into play.

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