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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
272 points bdr | 1 comments | 28 Jun 25 16:53 UTC | HN request time: 0.345s | source
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seeknotfind ◴[28 Jun 25 17:25 UTC] No.44406443[source]▶
> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand.

I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual comparison.

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1. Straw ◴[28 Jun 25 17:37 UTC] No.44406571[source]▶
Yes, that's right, dividing by that ratio essentially barely affects the number in a sense that 'adjacent' numbers in that notation give a much bigger change.

10↑↑10,000,000 / (sand grains per universe) is vastly larger than, say, 10↑↑9,999,999

So on system we're using to write these numbers, there's really no better way to write (very big)/ (only universally big) than by writing exactly that, and then in the notation for very big, it pretty much rounds to just (very big).