Timeline for A hat puzzle question—how to prove the standard solution is optimal?
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6 at 14:34 | comment | added | Joel David Hamkins | Perhaps it was the Hardin Taylor article, which is Math Monthly, and it also has hat puzzles in it. | |
| Aug 6 at 14:30 | comment | added | Andrea Ferretti | Maybe I remember it wrong. It was something I read by randomly browsing in the library some 15 years ago or so. The proof stuck, but the reference has evaporated from my brain. I am not 100% certain it was Notices, and I cannot locate it anymore, so I suggest you go on anyway. Sorry I cannot be more helpful | |
| Aug 5 at 14:54 | comment | added | Joel David Hamkins | @AndreaFerretti By the way, if you could give me a reference to that Notices article, I would be very grateful, since I had a plan to write a Mathematical Shorts column for the Notices giving a brief account of this very theorem, but if it has already appeared in the Notices I shall write on something else. But I can't find anything yet in Notices. | |
| Aug 5 at 13:51 | comment | added | Joel David Hamkins | @AndreaFerretti This is the theorem of Hardin and Taylor, available at Christopher S. Hardin and Alan D. Taylor. A peculiar connection between the axiom of choice and predicting the future. Amer. Math. Monthly, 115(2):91–96, 2008. I am also writing about this theorem in my book---I call it the nearly perfect prediction theorem---and I have another summary article planned on it. And yes, I agree, it is a wonderfully surprising result, my favorite kind of theorem, where the proof is elegantly simple and yet the result totally surprising. | |
| Aug 5 at 13:33 | comment | added | Andrea Ferretti | I don't have the article reference anymore, but if you are interested I remember the (very simple) proof | |
| Aug 5 at 13:32 | comment | added | Andrea Ferretti | ...agree on an interval $]-\infty, t[$ for some $t > s$. The theorem is then that there exists an oracle such that, whatever is the actual history of the unverse, it predict the future at $s$ for all $s \notin B$, where $B$ is a denumerable set of bad times | |
| Aug 5 at 13:30 | comment | added | Andrea Ferretti | Namely, assume the history of the universe is a function $\mathbb{R} \to S$, where $S$ is the set of states and the input variable is time. An oracle is a function $o$ that gives you, for each partial history $g_s \colon ]-\infty, s[ \to S$, a continuation to a function $g = o(g_s) \colon \mathbb{R} \to S$ that agrees with $g_s$ on the common domain. Then when you know the actual history of the universe, call it $h$, you can get the oracle $o(h_s)$, where $h_s$ is the restriction of $h$ to $]-\infty, s[$. We say that the oracle predicts the future at $s$ if $o(h_s)$ and $h$ agree on (segue) | |
| Aug 5 at 13:23 | comment | added | Andrea Ferretti | @JoelDavidHamkins I remember reading a very nice essay on hat puzzles on AMS Notices - unfortunately I cannot locate it anymore. But it ended with a nice problem that shows that - under certain assumptions - it is possible to predict the future | |
| Aug 4 at 16:06 | answer | added | Alex van den Brandhof | timeline score: 4 | |
| Aug 1 at 8:45 | comment | added | Wolfgang | Fascinating question... When I saw the title, I thought first it is about a tiling (can be a.k.a. puzzle) by the hat monotile :) | |
| Jul 31 at 14:33 | answer | added | Andrea Ferretti | timeline score: 2 | |
| Jul 27 at 13:09 | answer | added | Emil Jeřábek | timeline score: 2 | |
| Jul 25 at 8:01 | comment | added | user21820 | @bof: You could always ignore my.. err.. son... | |
| Jul 24 at 17:14 | answer | added | Steven Landsburg | timeline score: 7 | |
| Jul 24 at 13:30 | vote | accept | Joel David Hamkins | ||
| Jul 24 at 7:02 | history | became hot network question | |||
| Jul 24 at 4:22 | comment | added | Gerry Myerson | @bof, the system does allow us to flag comments for moderator attention. | |
| Jul 24 at 3:51 | comment | added | bof | @GerryMyerson There are times when I wish the system allowed us to downvote comments. | |
| Jul 24 at 2:28 | comment | added | Gerry Myerson | It doesn't say that the three people are men, but, if they are, we can call this the Man-hat-tan puzzle. | |
| Jul 24 at 0:18 | comment | added | RobPratt | puzzling.stackexchange.com/questions/tagged/hat-guessing | |
| Jul 24 at 0:15 | answer | added | Steven Landsburg | timeline score: 12 | |
| Jul 23 at 23:15 | answer | added | Lucenaposition | timeline score: 13 | |
| Jul 23 at 23:09 | answer | added | RavenclawPrefect | timeline score: 21 | |
| Jul 23 at 23:08 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 64 characters in body
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| Jul 23 at 22:58 | history | asked | Joel David Hamkins | CC BY-SA 4.0 |