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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 1 comments | 28 Jun 25 16:53 UTC | HN request time: 0s | source
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Scarblac ◴[28 Jun 25 17:29 UTC] No.44406478[source]▶
It boggles my mind that a number (an uncomputable number, granted) like BB(748) can be "independent of ZFC". It feels like a category error or something.
replies(12): >>44406574 #>>44406590 #>>44407165 #>>44407378 #>>44407396 #>>44407448 #>>44407506 #>>44407549 #>>44408495 #>>44409048 #>>44410736 #>>44413092 #
Straw ◴[28 Jun 25 17:39 UTC] No.44406590[source]▶
The category error is in thinking that BB(748) is in fact, a number. It's merely a mathematical concept.
replies(7): >>44406641 #>>44406756 #>>44406982 #>>44407096 #>>44407244 #>>44407342 #>>44428546 #
dtech ◴[28 Jun 25 18:31 UTC] No.44406982[source]▶
It's as much a number as 12
replies(1): >>44407039 #
lupire ◴[28 Jun 25 18:39 UTC] No.44407039[source]▶
Only if you believe that a number you can't count is a number. You can believe that, but it's a leap.
replies(1): >>44407274 #
falcor84 ◴[28 Jun 25 19:06 UTC] No.44407274[source]▶
Couldn't you make the same argument for sqrt(2), or better yet for zero [0]?

[0] https://en.wikipedia.org/wiki/Zero:_The_Biography_of_a_Dange...

replies(2): >>44407319 #>>44428624 #
1. Straw ◴[30 Jun 25 22:29 UTC] No.44428624[source]▶
sqrt(2), and pretty much everything else you can think if, is computable- there's a program that can output rational numbers arbitrarily close.

BB(n) is not.