Timeline for What is the most "informative" Yes/No math question you know?
Current License: CC BY-SA 4.0
7 events
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| May 6, 2022 at 3:52 | comment | added | Timothy Chow | This is a clever idea. However, it is just barely conceivable that the aliens could prove that 1 and 2 are equivalent, that 3 and 4 are equivalent, etc., and therefore proving that the answer to the question is YES, without giving away how to prove or disprove any individual statement. (Though even in this case, we would presumably learn a lot of valuable math.) | |
| May 5, 2022 at 7:24 | comment | added | Jukka Kohonen | @Emil, good point. Mitigating that risk in a systematic fashion would be an interesting task of metamathematics, careful wording ("Is it provable in XXX" vs. "Is it true that..."), and probabilistic reasoning (assessing the probabilities, risks and utilities associated with each proposed subquestion). If we really care about getting the most out of that single question (and if we believe we are going to get the answer as promised), we would better set up a multi-year, well-funded project to design the question. Besides mathematicians, we might need xenolinguists and xenolawyers in the project! | |
| May 4, 2022 at 15:35 | comment | added | Ville Salo | I see you wrote "very likely", and covered this possibility. | |
| May 4, 2022 at 15:34 | comment | added | Ville Salo | @EmilJerabek Could be that e.g. P=NP and the Riemann hypothesis are both independent, but are actually equivalent. | |
| May 4, 2022 at 14:31 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| May 4, 2022 at 13:43 | comment | added | Emil Jeřábek | You run a considerable risk that at least one of these 100 questions is independent of ZFC, in which case very likely the whole XOR is independent, and the answer will give you no proof whatsoever. | |
| May 4, 2022 at 11:39 | history | answered | Jukka Kohonen | CC BY-SA 4.0 |