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Sure. There is definitely a googolth digit of pi. Computing what the digit is, however, is not necessary to prove that such a digit exists.
by viscountchocula 3y ago
Sure. There is definitely a googolth digit of pi. Computing what the digit is, however, is not necessary to prove that such a digit exists.
- raincole 3y agoIt's a quite bad analogy because the googolth digit of pi is completely constructive. (You don't need to calculate it, but it is constructive) P = NP proof could be not constructive.
- archgoon 3y ago[dead]
- paulddraper 3y agoProving the Nth digit of pi exists is not (necessarily) constructive. Though to make it an actual proof and not a truism you might say "when writing pi in the shortest decimal representation, there is a millionth digit". Proving pi is irrational would suffice, without actually calculating the first million digits.
- xhkkffbf 3y agoNote: finding arbitrary digits of pi doesn't require finding the preceding digits. It's kind of freaky. https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...
- wddkcs 3y agoMy intuition was that if a proof for P = NP exists, it would be incomparable to the kind of Pi example you provide- Pi is defined as an irrational ratio, so the existence of whether x digit of Pi exists. It would instead be like saying, 'the x digit of P is 7, and here is a proof that is not a straight calculation'. The idea of a proof which can demonstrate knowledge of X digit of Pi, without verification, doesn't click for me.