Re:How the Square Root of 2 Became a Number
by hifromwork on Saturday June 22, 2024 @08:30AM
(#40758633)
>I'd like to understand - Can you explain this? It seems like it would be easy to have a Turing machines that uses the other two Turing machines, adding one digit at a time until it finds a difference.
I assume it runs into problems when you try to check if 2 > 2.
Re:How the Square Root of 2 Became a Number
by xscott on Saturday June 22, 2024 @10:27AM
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It's very funny how that's a really good example and made it click instantly. Thank you.
Re:How the Square Root of 2 Became a Number
by tshaddox on Saturday June 22, 2024 @03:40PM
(#40761578)
> Heh, but how many digits can you actually provide? Not too many. So have you really thought of the number in any meaningful sense when you barely know any of its digits?
I’ve never thought through very many digits of pi either. Or even 1/3 for that matter!
I'd like to understand - Can you explain this? It seems like it would be easy to have a Turing machines that uses the other two Turing machines, adding one digit at a time until it finds a difference.
> I mean, I've thought of noncomputable reals like Chaitin constants.
Heh, but how many digits can you actually provide? Not too many. So have you really thought of the number in any meaningful sense when you barely know any of its digits?
Also interesting that computer languages themselves are countable, so while it's hard to specify the digits algorithmically for the Chaitin constant of any computer language, you already know that the set of ALL Chaitin constants are countable.