Timeline for Game of Chess and axiomatic systems [closed]
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2013 at 15:09 | vote | accept | ARi | ||
| Jun 12, 2013 at 14:31 | history | closed |
Andrés E. Caicedo Steven Landsburg Noah Schweber Andreas Blass Noah Stein |
not a real question | |
| Jun 12, 2013 at 14:03 | comment | added | The User | “If formalised mathematics were as simple as chess, once we would have described the formal language we have choosen, we would not have to do more than writing our proofs down in this language, like the author of a treatise on chess which is written in his notation for matches … together with some commentaries—if necessary.” | |
| Jun 12, 2013 at 13:22 | history | edited | ARi | CC BY-SA 3.0 |
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| Jun 12, 2013 at 13:21 | comment | added | The User | It might be off-topic, but this reminds me of a nice description/comparison by Bourbaki: « Si la mathématique formalisée était aussi simple que le jeu d’échecs, une fois décrit le langage formalisé que nous avons choisi, il n’y aurait plus qu’à rédiger nos démonstrations dans ce langage, comme l’auteur d’un traité d’échecs écrit dans sa notation les parties qu’il se propose d’enseigner, en les accompagnant au besoin de commentaires. » | |
| Jun 12, 2013 at 12:58 | answer | added | Joel David Hamkins | timeline score: 3 | |
| Jun 12, 2013 at 12:49 | comment | added | Noah Schweber | Looking at your other questions as well, I think you should put in more effort to make precise what you are asking for. I have no idea what an answer to this question, for example, would consist of. | |
| Jun 12, 2013 at 10:38 | history | edited | ARi | CC BY-SA 3.0 |
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| Jun 12, 2013 at 7:43 | history | edited | ARi | CC BY-SA 3.0 |
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| Jun 12, 2013 at 7:39 | comment | added | dfeuer | That "given our computational resources" bit makes it much trickier to view this as an axiomatic system, because proofs aren't entirely compositional. Knowing that a proof of $p$ exists and that a proof of $q$ exists does not necessarily imply that a proof of $p \land q$ exists—the latter proof may be too long to be valid. | |
| Jun 12, 2013 at 6:56 | comment | added | Waldemar | Not really an answer but a comment to the statement “Assuming that the game has not/cannot be solved given our compute resources”. Let’s look at the calculations showing how difficult it is to solve chess by brute-force. Chess game tree complexity = 10^123 ; Bremermann's Limit = 1.36 × 10^50 bits per second per kilogram ; Mass of the Universe = 10^53 kg ; Age of the universe = 4.354 × 10^17 seconds ; No. of chess games analyzed by the universe turned into the best computer possible < 10^121 | |
| Jun 12, 2013 at 6:02 | comment | added | Gerry Myerson | What does it mean for something to be "homologous" to an axiomatic system? | |
| Jun 12, 2013 at 5:16 | answer | added | Steven Landsburg | timeline score: 6 | |
| Jun 12, 2013 at 4:57 | history | asked | ARi | CC BY-SA 3.0 |