I can't believe I never actually gave final rankings for this challenge. Strap in, we'll go in ascending orderhttps://twitter.com/qntm/status/1165724680206061568 …
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Old joke from the Look Around You episode on "Maths"https://twitter.com/qntm/status/1165726300805505024 …
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This is the only submitted number whose position I'm genuinely uncertain of. Kruskal's weak tree function is extremely fast-growing, but tree(3) is relatively small, with lower bounds in the quadrillions range. Placement here is tentativehttps://twitter.com/heyandy889/status/1165749618044493824 …
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This isn't well-defined, but in most scenarios your mum is at least contained within the observable universe, so this is bounded above by about a googolhttps://twitter.com/raspofabs/status/1165781895734530051 …
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I'm not 100% certain what the leading exclamation mark here is for, but ignoring that, there are 277 nines, so that's 10^(10^277 - 1), slightly more than a googolplexhttps://twitter.com/Cameron__Devine/status/1165850650279739392 …
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In Knuth's arrow notation this is "99↑↑89"... except that "base 9^999" means we read "99" as 9 * 9^999 + 9 in decimal, and "89" as 8 * 9^999 + 9 in decimal. So that's a little less than (10↑1000)↑↑↑2. Three arrows. Sizeable...https://twitter.com/NatanMelzer/status/1166376298559758336 …
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If by "And so on" we assume that the nines continue for the remainder of the Tweet, that's 276 nines. That's still three arrows, but a MUCH larger exponenthttps://twitter.com/waynejwerner/status/1165837725410504704 …
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haha Knuth up-arrows go brrrhttps://twitter.com/halcanary/status/1165734655292837890 …
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Nobody specifically entered Graham's number, but this is slightly bigger than that, and easily outclasses any expression using a small, writeable number of up-arrowshttps://twitter.com/tef_ebooks/status/1165725289705607169 …
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This is a pretty large number. Kruskal's much faster-growing TREE function is such that TREE(3) obliterates Graham's number in terms of scale. This, however, is TREE^41(420)https://twitter.com/LostSnowdrift/status/1166096988904906752 …
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I could be dead wrong about this but I'm fairly sure Kruskal's TREE function is computable with much less than a ~120 state Turing Machinehttps://twitter.com/ijks_w/status/1165727070305038337 …
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This value is smaller than, but probably in the vicinity of, BB(9999) in terms of scale, therefore far surpassing BB(120) abovehttps://twitter.com/linyks/status/1165748190890483712 …
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The Radó maximum shift function is closely related to BB in terms of growth rate but this is the first entry to start using such functions recursively instead of just passing in basic literal numbers. Excellent callhttps://twitter.com/mcallisterjp/status/1166353418002284545 …
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Not 100% certain that this is the winner but it looks suspiciously similar in construction to Rayo's number, which won a large number duel at MIT. Well donehttps://twitter.com/MaskedTorah/status/1167006809296531456 …
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Now to take a big sip of coffee and assume I made no errors whatsoever
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End of conversation
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