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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 1 comments | | HN request time: 0.992s | source
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charcircuit ◴[] No.44407196[source]
>imagine you had 10,000,000_10 grains of sand. Then you could … well, uh … you could fill about 10,000,000_10 copies of the observable universe with that sand. I hope that helps people visualize it!

People can't visualize numbers that big. There's more ways to express numbers than just counting them. For example a single grain of sand has infinite states it can be in (there are an infinite amount of real numbers), so you could say a single grain of sand could represent BB(6). Combinations can grow exponentially, so that may be something useful to try and express it.

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1. Xcelerate ◴[] No.44407250[source]
At some point big numbers become much more about the consistency strength of formal systems than “large quantities”.

I.e., how well can a system fake being inconsistent before that fact it discovered? An inconsistent system faking consistency via BB(3) will be “found out” much quicker than a system faking consistency via BB(6). (What I mean by faking consistency is claiming that all programs that run longer than BB(n) steps for some n never halt.)