= 27d567bc2d48d9f40e9ccc20ea370b15)
JoshuaZ comments on A Limited But Better Than Nothing Way To Assign Probabilities to Statements of Logic, Arithmetic, etc. - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d){kind=logo}
Comments (16)
It may be relevant to look at how mathematicians use heuristics to actually make conjectures that seem plausible. The heuristic for there being infinitely many Mersenne primes seems to be of a flavor very similar to what you are doing here.
Unsurprisingly, Terry Tao has an excellent post about this sort of thing.
It's interesting that he talks about "structure", and how the heuristics work best when there's the least structure. I guess he'd describe what I'm doing as including limited structure?
He's also brought attention to a problem with my proposal. I didn't think you could ever end up certain of a falsehood. But in a probabilistic model of numbers, he proved that there are infinitely many solutions to x^3 + y^3 = z^3. A robot with that probabilistic model would be certain that Fermat's Last Theorem is false.
Well, maybe it would. I wish I had the time today to learn to analyze this whole idea more precisely, instead of just conjecturing left and right!