# 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:** 7
**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, 9:29am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/121 "2020-11-06T09:29:59Z")
> [@DPRK](#): > > the mingling of binary and decimal notation being extra stupid. Even worse: remember 1.44 “megabyte” floppy discs? They stored 1,474,560 bytes, which is 1440\*1024. Which means that their definition of “megabyte” was 210·103, mixing binary and decimal in _the same unit_. ---
**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 6, 2020, 1:42pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/122 "2020-11-06T13:42:43Z")
ETA: should have read the thread up to now before responding to this post from last night. Welcome to the department of redundancy department. > [@Sigene](#): > > 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. The point (heh) is NOT that there’s a spot on the map that represents where you are. As you say, that’s trivial. The point is there’s a spot on the map that represents where _something_ is, and that point on the map is sitting exactly on top of the actual real _something_. It may be hard to figure out which specific place is that something, but there provably is such a place. - Move the map at random. The _something_ may change. But there will still be a something on the map that’s exactly on top of the same _something_ on the ground. - Crumple the map at random. The _something_ may change. But there will still be a something on the map that’s exactly on top of the same _something_ something on the ground. - Fold the map up neatly just like it came from the store. The _something_ may change. But there will still be a something on the map that’s exactly on top of the same _something_ something on the ground. - Lay the map out flat, but upside down so the printing is face down. The _something_ may change. But there will still be a something on the map that’s exactly on top of the same _something_ something on the ground. Bottom line: As long as the map isn’t torn, there’s guaranteed to be someplace where the map is perfectly aligned with the reality underneath it. That’s rather unexpected to the naïve observer. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [November 7, 2020, 1:58am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/123 "2020-11-07T01:58:04Z")
I am indeed naive and I don’t get it. How large must the map be? I cannot prove that there is no alignment so why must I assume there is? Alignment along what axis? Even a topo map is only accurate to ~6 feet so I cannot accurately locate my table on the map. Clearly I am missing the point. ---
**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 7, 2020, 2:26am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/124 "2020-11-07T02:26:55Z")
It’s not about a real physical map (although it will still work within the degree of error). With a perfect map, the theorem holds true down to the smallest measurement possible. It’s about math, not mapping. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [November 7, 2020, 2:33am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/125 "2020-11-07T02:33:47Z")
Thanks, I assumed it’s something like that. But then what if my map is only one atom? Or a single electron? ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [November 7, 2020, 2:37am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/126 "2020-11-07T02:37:16Z")
Integer squares are rare in the triangular number series. ---
**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 7, 2020, 9:34am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/127 "2020-11-07T09:34:56Z")
> [@Dr.Strangelove](#): > > Even worse: remember 1.44 “megabyte” floppy discs? They stored 1,474,560 bytes, which is 1440\*1024. Which means that their definition of “megabyte” was 210·103, mixing binary and decimal in _the same unit_ . I thought I was going to argue this as I thought they contained 1.44 \* 1024 \*1024 (which would at least be consistent at the surface level), but you’re right; the storage capacity is 1.44 \* 1024 \* 1000 ugh. They should really have been labelled 1.40625 MB ---
**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 7, 2020, 9:39am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/128 "2020-11-07T09:39:20Z")
> [@Mangetout](#): > > They should really have been labelled 1.40625 MB Or 1.44 kibikilobytes. ---
**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 7, 2020, 9:57am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/129 "2020-11-07T09:57:55Z")
> [@Crane](#): > > But then what if my map is only one atom? Or a single electron? Doesn’t matter how small you get; it’s a mathematical statement that doesn’t depend on the granularity of the real world. However, by picking an _electron_ you get into some tricky territory. The map must at least have non-zero size: you can’t compress everything into a single point. But as best anyone can tell, the electron _does_ have a zero size. No one thinks this is actually the case since it causes problems with infinities, but on the other hand we don’t have a theory of nature that works at that level. Pick a proton instead. They have non-zero size. The map can be the size of a proton, or a billionth of that, or smaller. Just not zero. ---
**Author:** ![sbright33](https://avatars.discourse-cdn.com/v4/letter/s/8e8cbc/32.png) [@sbright33](https://boards.straightdope.com/u/sbright33)\ **Post date:** [November 7, 2020, 2:32pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/130 "2020-11-07T14:32:01Z")
Someone above said there are no odd looking numeric strangeness… ---
**Author:** ![sbright33](https://avatars.discourse-cdn.com/v4/letter/s/8e8cbc/32.png) [@sbright33](https://boards.straightdope.com/u/sbright33)\ **Post date:** [November 7, 2020, 3:39pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/131 "2020-11-07T15:39:22Z")
You guys are good at math please give me some ideas. > [@Election results today](https://boards.straightdope.com/t/election-results-today/924977): > > Can someone please help me with specific numbers or ideas why the election may not be called today? Has a presidential election ever been called on a weekend? During a popular football game? Do any of these issues matter at all? Clearly it can’t be JUST math. PA in particular. The 0.5 comes into play to avoid a recount. Seems that the remaining votes must be less than what is needed to go back below 0.5 with some finite margin of certainty? Opinion, math, facts, history please. I promise not to look for strange patterns in the answer… ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [November 7, 2020, 5:00pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/132 "2020-11-07T17:00:20Z")
Forgive my density but the significance completely escapes me. Why a map image? Why not torn? Why does placing the map in an area it represents have any significance? There needs to be more there there. ---
**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 7, 2020, 5:21pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/133 "2020-11-07T17:21:32Z")
In reverse order … For the correspondence to occur there has to be a chance. If I place a map of Los Angeles on a dinner table in Chicago, there’s no possibility that any point printed on the map will align with any real point underneath the map on the table. But if I place a map of Chicago, or of Illinois, or of the USA on that same table in Chicago there _will_ be an aligning = “corresponding” point. Not may be; _will_ be. Tearing the map in any way breaks the continuity upon which the result depends. It’s conceptually similar to the idea that certain elements of calculus fail if they’re applied to a non-continuous or non-smooth function across the discontinuity / non-smoothness. Not sure what you mean by “map image”. The map, be it real paper, something displayed on a screen, or just a mathematical model, has to have some degree of specificity to be said to exist at all. Once it exists, even conceptually, and has a position in real space that meets the criteria of the theorem, it _will_ have a corresponding point. As an example of this idea, imagine I take a photo of that Chicago dinner table (or whole dining room including the table) and print that out. Then set that paper entirely on the table. Bingo: we have a map, and therefore we _will_ have a correspondence at some point. The math has (of course) been generalized way past paper maps on kitchen tables to discussing all sorts of other correspondences between mathematical things, where the term “map” describes operators that convert from one such thing to another. Whether any of that would make sense to you (any you) depends on how much mathematical background you have. I don’t know how much math background you @Crane specifically have, and in any case I’m getting out near the edge of my own math qualifications, so I’ll stop here before I say something wrong / stupid. ---
**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 7, 2020, 10:12pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/134 "2020-11-07T22:12:08Z")
Lemme give this a try, but as I begin to write this I don’t know how long-winded this will be… hang tight. The map correspondence thing has a simpler variant in just one dimension instead of two dimensions, and this is the version that I first heard. It took me all of about 5 seconds to see, intuitively, why it must be true. Imagine this, and maybe even try to draw it on paper: Draw a horizontal straight line segment several inches long from a point A to a point B. Put tick marks at regular intervals along the line and number them, so you have some scale of measure marked on your line segment. Now imagine this carefully before you draw it: Picture drawing another line segment, identically marked, above your first line segment. But instead, lay a piece of string there (still marked with the same scale and numbers as the original segment), then fold and tangle that string any way you want, and set that above your original line segment. Two requirements you must follow for this to work: Your piece of folded tangled string must lie entirely above your straight line segment – it cannot stick out to the left or right at either end. And your piece of string must be continuous – that is, all in one piece and not broken anywhere. Now, every point of your string lies directly above some point of the line segment. But mostly, the numbered points of the string don’t lie above their like-numbered points of the line. But the theorem under discussion guarantees that somewhere along that tangled piece of string there must be at least one point that lies directly above it’s like-numbered point on the line. Now think about that for a while and see if you can figure out why it must be true. The same theorem applies to a two-dimensional region as well, and that is where “maps” come in. If you have a map of some finite bounded region (like your hometown) laid out on the table, and you put a crumpled-up copy of an identical map on top of it, then somewhere on the crumpled-up copy there will be some point that lies directly above its counterpart point on the flat map. But the crumpled-up map must lie entirely above the flat map (not sticking out on any side), and both maps must be “continuous”, that is, have no rips or holes in them. (I’m pretty sure it doesn’t matter if the two maps are drawn at the same scale or different scales.) ---
**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 8, 2020, 11:52am UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/135 "2020-11-08T11:52:53Z")
> [@Dr.Strangelove](#): > > Or 1.44 kibikilobytes. We’re lucky, in a way, that kibi/mebi/tebi supplanted the use of kilo/mega/tera for the power of two approximates, and that we didn’t have to keep using the wrong term for those, as well as accepting some new, also wrong set of terms for the powers of ten versions. It so easily could have gone that (wrong) way, given the established nature of the terms. ---
**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 8, 2020, 12:10pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/136 "2020-11-08T12:10:43Z")
Or not: > **[Kilobyte](https://xkcd.com/394/)** > > I would take 'kibibyte' more seriously if it didn't sound so much like 'Kibbles N Bits'. ---
**Author:** ![sbright33](https://avatars.discourse-cdn.com/v4/letter/s/8e8cbc/32.png) [@sbright33](https://boards.straightdope.com/u/sbright33)\ **Post date:** [November 8, 2020, 3:08pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/137 "2020-11-08T15:08:53Z")
Related topic > **[Joe Biden's votes violate Benford's Law (Mathematics)](https://gnews.org/articles/180194)** > > Joe Biden's election data violate the Benford's law used to check if a set of numbers are natural or fabricated. This is another proof of voter fraud by the Democrat Party. It can be used to identify which states and counties had fraud. Make a list of counties a candidate won. Another where he wouldn’t have in 2016. If a county is on all 3 lists, then investigate further. SIMPLE and cost effective. Great example of strange numeric coincidences? ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 8, 2020, 3:51pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/138 "2020-11-08T15:51:24Z")
> [@sbright33](#): > > Great example of strange numeric coincidences? When it was first discovered, [Benford’s Law](https://en.wikipedia.org/wiki/Benford%27s_law) might well have been considered a “strange numerical coincidence”; but there are legitimate mathematical reasons behind it. As for the claim that Biden’s votes violate 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 8, 2020, 3:52pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/139 "2020-11-08T15:52:09Z")
> [@sbright33](#): > > Make a list of counties a candidate won. > Another where he wouldn’t have in 2016. > If a county is on all 3 lists, then investigate further. You left a few things out there. Like the three lists. I only count two. And “would” is a prediction. Which means even if honestly derived it might be wrong. Care to try writing that again? Carefully this time using complete sentences to express complete ideas?. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [November 8, 2020, 3:53pm UTC](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478/140 "2020-11-08T15:53:13Z")
LSL/Senegoid, Thanks for the effort guys! But, it sounds like the rules are that if I have a data set ‘a’ and I overlay it with a data set ‘b’ so that some points coincide then some points are coincident. That much would fall even within my math acumen. [Previous page](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478.md?page=6) [Next page](https://boards.straightdope.com/t/strange-numeric-coincidences-that-should-occur-only-rarely/924478.md?page=8)