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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 2 comments | 28 Jun 25 16:53 UTC | HN request time: 0.432s | source
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charcircuit ◴[28 Jun 25 18:58 UTC] 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. unsnap_biceps ◴[28 Jun 25 19:05 UTC] No.44407263[source]▶
I'm confused about this example, isn't the count of grains of sand equal to the count of observable universes so it'd be a single grain of sand per universe?
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2. heftig ◴[28 Jun 25 19:33 UTC] No.44407484[source]▶
The "about" does a lot of heavy lifting in this example. Dividing 10,000,000_10 by the number of grains that fit into one universe doesn't change it much. The 10,000,000 would get smaller somewhere in the deep depths of the decimal fraction.