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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 6 comments | 28 Jun 25 16:53 UTC | HN request time: 0s | source | bottom
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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.
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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.
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1. dtech ◴[28 Jun 25 18:31 UTC] No.44406982[source]▶
It's as much a number as 12
replies(1): >>44407039 #
2. 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.
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3. 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...

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4. Dylan16807 ◴[28 Jun 25 19:11 UTC] No.44407319{3}[source]▶
For sqrt(2) I can tell you the order of magnitude and output as many digits as you want. I think that's plenty specific for this use case.

For zero I can not only do that, I can also count to it if you let me count both up and down, which seems like a very simple ask.

replies(1): >>44408632 #
5. falcor84 ◴[28 Jun 25 22:17 UTC] No.44408632{4}[source]▶
But that's the thing - each generation struggles with whether some new thing is a number. We're typically very inclusive, accepting imaginary numbers and even weirder things like surreal numbers, which we definitely can't count.

But as someone in this generation, I see a good argument for rejecting the big busy beaver numbers, which are provably outside of the realm of calculating with all the resources of our universe's runtime, from being fully accepted as numbers, any more than the first uninteresting number [0].

[0] https://en.wikipedia.org/wiki/Interesting_number_paradox

6. Straw ◴[30 Jun 25 22:29 UTC] No.44428624{3}[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.