# Strange numeric coincidences that should occur only rarely **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [November 1, 2020, 11:22am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478 "2020-11-01T11:22:36Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 5, 2020, 1:14pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/101 "2020-11-05T13:14:54Z")
There are many versions of topological fixed-point theoremata. I think what you are talking about here is that if you start with (something homeomorphic to) a non-empty, compact, convex subset of a Euclidean space, and map it continuously to itself, then there will be a fixed point. If the map is not continuous, or the domain is not compact or has holes in it then the argument will not work. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [November 5, 2020, 1:42pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/102 "2020-11-05T13:42:09Z")
> [@Mangetout](#): > > If the map is 1:1 scale and you lay it over the mapped area (so every point corresponds), then slide it 1cm to the west, no point will correspond. > I think for the theorem to be guaranteed to work, the map has to be placed so it is fully contained within the boundaries of the mapped area (which will almost invariably mean it must be at a smaller scale than 1:1) That’s pretty much what I said, a map of the US placed on the US. However I also believe that it works if the map is within the boundaries as well. The way I was exposed to the theorem was take a 10 x 10 grid with the numbers 1 to 100 on it, crumble it up and drop it on a copy of the grid. You are guarantied one number will be on top of itself. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 5, 2020, 1:44pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/103 "2020-11-05T13:44:30Z")
Here’s a really bizarre one for computing pi: [![](https://img.youtube.com/vi/HEfHFsfGXjs/maxresdefault.jpg "The most unexpected answer to a counting puzzle") ](https://www.youtube.com/watch?v=HEfHFsfGXjs) And here’s why it works: [![](https://img.youtube.com/vi/jsYwFizhncE/maxresdefault.jpg "Why do colliding blocks compute pi?") ](https://www.youtube.com/watch?v=jsYwFizhncE) ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [November 5, 2020, 2:10pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/104 "2020-11-05T14:10:24Z")
That was fascinating, thank you. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [November 5, 2020, 2:16pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/105 "2020-11-05T14:16:15Z")
> [@Senegoid](#): > > (I’m not sure if there is any requirement that the maps be at the same scale.) I’d say that by crumpling the map, but then treating it as a flat object in terms of its position above the un-crumpled map, you are effectively changing the scale of the map you are crumpling (not in any sort of consistent way, but you’re shrinking it) ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [November 5, 2020, 2:35pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/106 "2020-11-05T14:35:26Z")
> [@Mangetout](#): > > I’d say that by crumpling the map, but then treating it as a flat object in terms of its position above the un-crumpled map, you are effectively changing the scale of the map you are crumpling (not in any sort of consistent way, but you’re shrinking it) Exactly. The scaling has no need to be consistent. Just don’t tear the crumpled map even a smidgen. All this is, stretching a point, little more than the 2D topologically sophisticated version of the **[Intermediate Value Theorem](https://en.wikipedia.org/wiki/Intermediate_value_theorem)**: > Given a continuous real-valued function on a domain containing [x1 … x2] … > if y1 = f(x1) and y2 = f(x2) and (wlog) y1 \< y2 > then for every y1 \< y_n_ \< y2 there exists some x_n_ such that y_n_ = f(x_n_) Or in plain English: If you start at 2 and end at 5, you have to have gone through 4 (and 3, and 4.785, and …) to get there, no matter how much you zigged and zagged along the way., ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 5, 2020, 2:36pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/107 "2020-11-05T14:36:37Z")
“Crumpling” sounds continuous. Whether the surface remain flat or smooth is not relevant. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 5, 2020, 4:52pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/108 "2020-11-05T16:52:19Z")
Another application of the fixed point theorem is that at any instant there is at least one on earth that has no wind. The “You can’t comb the hair on billiard ball” theorem. If you could, you could find a fixed point free mapping of the sphere to itself by moving each point one cm in the direction the wind is pointing. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [November 5, 2020, 5:26pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/109 "2020-11-05T17:26:20Z")
Another variation: At any moment, there must exist two points on the earth’s surface that are at the same temperature. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 5, 2020, 6:22pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/110 "2020-11-05T18:22:29Z")
Merely saying it like that sounds pretty weak; applying the Borsuk–Ulam theorem to the surface of the Earth proves the “coincidence” that at any given moment there are two _antipodal_ points with the same temperature _and_ barometric pressure, for example. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 5, 2020, 9:13pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/111 "2020-11-05T21:13:18Z")
Which was my reply when Mangetout said the same thing. And of note, the Hairy Ball Theorem only applies to spheres of even dimension. It’s easy to find a “combing” for a one-dimensional sphere (that is to say, a circle), and it’s not too hard to do it for a three-dimensional one, either (i.e., one embedded in four-dimensional space). ---
**Author:** ![Sigene](https://avatars.discourse-cdn.com/v4/letter/s/df788c/32.png) [@Sigene](https://boards.straightdope.com/u/Sigene)\ **Post date:** [November 5, 2020, 10:36pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/112 "2020-11-05T22:36:47Z")
I don’t know what this means. WHat corresponding point on your table? My table doesn’t have a map on it I think I need more of an explanation what you mean. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [November 5, 2020, 10:54pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/113 "2020-11-05T22:54:40Z")
Get a paper map of your town. Put it on your kitchen table. Somewhere on that map is the area that represents your lot. Within that area on the map is a spot on the map (probably a very small one) that presents your kitchen table in your kitchen in your house on your lot in your town. Somewhere within all the molecules of that spot on the map representing your kitchen table, there’s at least one molecule where the map molecule is sitting exactly on top of the exact table molecule it represents. ---
**Author:** ![Sigene](https://avatars.discourse-cdn.com/v4/letter/s/df788c/32.png) [@Sigene](https://boards.straightdope.com/u/Sigene)\ **Post date:** [November 6, 2020, 3:35am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/114 "2020-11-06T03:35:04Z")
thanks…but that seems pretty much standard. Any map of an area I’m in will have a representation of where I’m at. I mean, thats the primary point of maps, isn’t it. Take any map of an area you are in, of any size and orientation. There is a point on that map that corresponds to exactly where you are standing. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 6, 2020, 4:14am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/115 "2020-11-06T04:14:04Z")
> [@Sigene](#): > > There is a point on that map that corresponds to exactly where you are standing. “Where you’re standing” isn’t a point, though; it’s a blob. The theorem says more than that: there is a _zero-size_ point on the map that corresponds to the same point on the landscape that it is above. And it doesn’t matter how crinkled or distorted the map is (as long as you don’t tear it). That said, your basic intuition is correct. Assuming the map isn’t too distorted, and the scales are similar to real maps, you can find the point with a kind of divide-and-conquer approach, starting with where you’re standing. From there, your infinitely detailed map will picture a blade of grass exactly on top of the real one it corresponds to, and a cell in that blade of grass corresponding to the real one, and so on all the way down. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [November 6, 2020, 5:04am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/116 "2020-11-06T05:04:37Z")
> [@Mangetout](#): > > At any given time, there is always at least one place on the surface of the Earth that is the same temperature as the the antipode of that place. There must be some other condition for this to be true like the temperature vary continuously. Otherwise set temperature at 20 for every point in the Northern hemisphere and on the equator from 0W \<= longitude \< 180W and at 10 for every point in the Southern hemisphere and the equator from 0E \< longitude \<= 180 E ---
**Author:** ![Sigene](https://avatars.discourse-cdn.com/v4/letter/s/df788c/32.png) [@Sigene](https://boards.straightdope.com/u/Sigene)\ **Post date:** [November 6, 2020, 5:16am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/117 "2020-11-06T05:16:01Z")
Holy SHIT!!! ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 6, 2020, 5:28am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/118 "2020-11-06T05:28:31Z")
If you aren’t impressed, you can just not say anything. The map is just an example; the generalized theorem covers many more situations (as noted). ---
**Author:** ![Moris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/moris/32/2846_2.png) [@Moris](https://boards.straightdope.com/u/Moris)\ **Post date:** [November 6, 2020, 7:22am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/119 "2020-11-06T07:22:25Z")
53 EDO is pretty amazing when it comes to numerical coincidences, if you’re into music theory. > **[53 equal temperament](https://en.wikipedia.org/wiki/53_equal_temperament?wprov=sfla1)** > > Pages for logged out editors learn more > > In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios). Play (help·info) Each step represents a frequency ratio of 2.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{bo... ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 6, 2020, 9:23am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/120 "2020-11-06T09:23:40Z")
In that vein, there is the coincidence that 210 ≈ 103 , which to this day confuses people buying storage drives, especially when the free space is listed by the operating system using BSD-style abbreviations like “1.1T”, the mingling of binary and decimal notation being extra stupid. [Previous page](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478.md?page=5) [Next page](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478.md?page=7)