3 ms·
But is the theory that such work can continue forever?
by kridsdale3 2y ago
But is the theory that such work can continue forever?
- wizzwizz4 2y agoThere's a point at which it becomes impossible: the nth Busy Beaver number is independent of ZF, for n≤745 (ref: https://wiki.bbchallenge.org/wiki/Cryptids https://wiki.bbchallenge.org/wiki/Cryptids). So no, such work cannot continue forever. We don't know whether such work can continue up to that point. The only way to find that out is to explore the relevant mathematics, and see if we find something fundamentally irreducible. There's no long-term pattern to the proofs, despite the presence of short-term patterns. (In this sense, the hunt for Busy Beavers is computationally irreducible – but there are still easier and harder ways of approaching the hunt.)