Timeline for Why does the bitxor function appear in Nim?
Current License: CC BY-SA 3.0
30 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jun 27, 2015 at 3:07 | history | edited | Halbort |
edited tags
|
|
| Jun 25, 2015 at 2:43 | comment | added | Timothy Chow | @MarkS. Of course what you say is correct, but what I was trying to counteract was the notion that Nim is just some arbitrary game with idiosyncratic rules coming out of nowhere, and that we can't expect any kind of deep explanation of the behavior of such an ad hoc structure, any more than we can expect any deep mathematics to emerge from studying the baseball rule book. | |
| Jun 24, 2015 at 13:20 | comment | added | Mark S. | @Timothy Chow, This may not be exactly what you meant to imply, but certainly Nim isn't the only closed class of impartial game positions with representatives of every class: "take one token from a heap and split the remainder into exactly three smaller heaps" is one example, but there are non-heap games, too. As an aside, impartial games can be combined in a fair number of ways you might consider natural (say, 3-10), but the others wouldn't go with the rules of standard heap games like Nim nicely. | |
| Jun 24, 2015 at 0:40 | comment | added | Timothy Chow | @PerAlexandersson : Nim is far less ad hoc than you might think at first glance; arguably, it's canonical in some sense. In Winning Ways they cook up lots of other games, but as long as they're impartial two-person games where the last player to move wins, they all reduce to Nim. XOR arises because of the definition of the sum of two games, as Douglas Zare has explained. If you change the way you combine two games then you can indeed get other operations, but there aren't that many natural ways to combine two games. | |
| Jun 23, 2015 at 18:39 | vote | accept | Halbort | ||
| Jun 23, 2015 at 16:39 | vote | accept | Halbort | ||
| Jun 23, 2015 at 18:39 | |||||
| Jun 23, 2015 at 16:39 | vote | accept | Halbort | ||
| Jun 23, 2015 at 16:39 | |||||
| Jun 23, 2015 at 16:26 | comment | added | Halbort | Why was my question downvoted? What problem should I address? | |
| Jun 23, 2015 at 16:14 | review | Close votes | |||
| Jun 24, 2015 at 8:14 | |||||
| Jun 23, 2015 at 15:32 | vote | accept | Halbort | ||
| Jun 23, 2015 at 16:39 | |||||
| Jun 23, 2015 at 15:31 | vote | accept | Halbort | ||
| Jun 23, 2015 at 15:31 | |||||
| Jun 23, 2015 at 15:30 | vote | accept | Halbort | ||
| Jun 23, 2015 at 15:31 | |||||
| Jun 23, 2015 at 15:29 | answer | added | Theo Johnson-Freyd | timeline score: 3 | |
| Jun 23, 2015 at 15:17 | history | edited | Halbort | CC BY-SA 3.0 |
deleted 7 characters in body
|
| Jun 23, 2015 at 14:35 | comment | added | Mark S. | You may also be interested in math.stackexchange.com/q/1178163/26369 and/or math.stackexchange.com/q/416042/26369 | |
| Jun 23, 2015 at 13:46 | comment | added | Halbort | There are many binary functions that have similar degrees of minimalism. What specific properties of the xor allow it to be the solution to Nim. | |
| Jun 23, 2015 at 13:44 | history | edited | Halbort | CC BY-SA 3.0 |
added 261 characters in body
|
| Jun 23, 2015 at 13:44 | comment | added | Johannes Hahn | What about the obvious answer "xor is natural and minimalist" doesn't satisfy you? You should make more precise what you are asking here. | |
| Jun 23, 2015 at 11:40 | vote | accept | Halbort | ||
| Jun 23, 2015 at 15:30 | |||||
| Jun 23, 2015 at 6:35 | answer | added | Douglas Zare | timeline score: 11 | |
| Jun 23, 2015 at 5:30 | answer | added | Will Sawin | timeline score: 14 | |
| Jun 23, 2015 at 4:34 | history | edited | Halbort |
edited tags
|
|
| Jun 23, 2015 at 3:44 | history | edited | Halbort | CC BY-SA 3.0 |
added 87 characters in body
|
| Jun 23, 2015 at 3:12 | comment | added | Halbort | I see your point Per Alexandersson. However, to find such games, very contrived rules would need to be devised. What qualities then of the xor yield such a natural and minimalist game such as Nim? | |
| Jun 23, 2015 at 3:09 | comment | added | Per Alexandersson | Is it the right question? I mean, cant we cook up games where say primes or some exotic operator appears also? Nim perhaps just happens to be the right game for xor. But I would be happy to see a different answer. | |
| Jun 23, 2015 at 2:58 | review | Close votes | |||
| Jun 23, 2015 at 13:49 | |||||
| Jun 23, 2015 at 2:55 | history | edited | Halbort | CC BY-SA 3.0 |
added 17 characters in body
|
| Jun 23, 2015 at 2:33 | review | First posts | |||
| Jun 23, 2015 at 3:11 | |||||
| Jun 23, 2015 at 2:33 | history | asked | Halbort | CC BY-SA 3.0 |