Talk:Mathematical coincidence

Conway's climb to a prime

The prime factorization of 13532385396179 is equal to 13×53²×3853×96179 which uses the same digits and ordering as the number itself. I don't know if this is considered a coincidence or not. — Preceding unsigned comment added by 71.179.19.89 (talk) 23:03, 14 December 2017 (UTC)

Indeed; added to the Decimal coincidences section. Renerpho (talk) 15:27, 15 April 2024 (UTC)

Nonce word suggestion

I am here to propose that 'decimaleasemeta' be used, eventually, as synonymous and eventually clearer than what is meant by 'mathematical coincidences' collectively here. It is difficult to come up with a mathematical coincidence that is known to toddlers, for example, before the expression '2.718281828' -- the 10-digit calculator's unhidden value of exp(1) -- is seen. I have no use in mind; this would be new. It just forms an abbrevatory single word out of 'decimal e's meta', 'meta' not really being a proper word generally other than in informal ways.

Nanocentury

(I'm putting this in a new section because the comment I'm replying to is years old and my reply will be a leaf in the forest if posted inline.)

>$\pi$ seconds is a nanocentury (ie $10^{-7}$ years); correct to within about 0.5%

>* Yes, or 3, or 3.1, or... basically, nothing special about pi here.

You conveniently forget to mention that although a nanocentury is 1.004π s, it's 1.018·3.1 s and 1.052·3 s.

Insofar as it's a coincidence there is in some sense nothing special about π here, but that's basically just an argument for deleting this entire article. But if you compare it to π, it's remarkable how much closer it is than compared to even 3.1 and that's kind of the point of a coincidence. So I don't understand why it was removed.

Another coincidence?

987654321 / 123456789 ≈ 8.0000000729 ≈ 8 180.244.139.139 (talk) 16:12, 10 March 2024 (UTC)

That could be done in any non-tiny base and follows from how bases work so it's not a coincidence. In base 10: 123456789×8 = 123456789×(10-1-1) = 1234567890 - 123456789 - 123456789 = 1111111101 - 123456789 = 987654312. PrimeHunter (talk) 22:52, 10 March 2024 (UTC)

Coincidence about 7^q = 10^p

Quote from article: << $\,7^{510}\approx 10^{431}$. This is equivalent to ${\log 7}\approx {\frac {431}{510}}$ >>

What is the significance of this fact? Of course you can approximate $\lg 7$ by infinitely many rational numbers p/q which will lead to approximations $7^{q}\sim 10^{p}$. Any pair of non-zero non-unit natural numbers (and not only) have the same approximate equialities. One can agree that $2^{10}\sim 10^{3}$ is interesting because exponents are small and precision is quite impressive, but 510 and 431 are large enough to be interesting. — Preceding unsigned comment added by 46.39.51.110 (talk) 11:37, 13 April 2024 (UTC)

The same question for << $6^{9}=10077696$, which is close to $10^{7}=10000000$. Also, $6^{9}-10(6^{5})=9999936$, which is even closer to $10^{7}=10000000$ >>and << $\,7^{6}=117649\approx {\frac {10^{7}}{85}}=117647.0588$ >>.

Removed, per the above, and because no citations were given that would demonstrate how this was notable. Renerpho (talk) 15:13, 15 April 2024 (UTC)

Earth solar orbit

(See section "Planet Earth", added recently about pi*10^7 ) Again, there is no significance in that, no specific of pi there, just about "3" or "3.15", etc. See also discussions above in the current talk page (sections "Not-Coincidences Removed" and "nanocentury"). Please, remove it. 46.39.51.121 (talk) 14:24, 24 April 2024 (UTC)

Fine structure constant

@Renerpho: Which are the "good sources" that call the near equality of alpha to 1/137 a coincidence? Dondervogel 2 (talk) 12:30, 9 October 2024 (UTC)

@Dondervogel 2: Most importantly in relation to the work of Arthur Eddington, who believed in an exact value of 1/137.

Eddington had long argued that it must be 1/136, but eventually switched to 1/(136+1) when experimental evidence began to disagree with his earlier theory. To quote Helge Kragh's Magic Number: A Partial History of the Fine-Structure Constant, which gives a good overview of the history of the fine-structure constant (p.413): For the rest of his life, Eddington stuck to the integer 137 which he claimed to have "obtained by pure deduction, employing only hypotheses already accepted as fundamental in wave mechanics." In his subsequent work he deduced the number in somewhat different ways, but we need not be concerned with these. As late as 1944, in his very last publication, he quoted the experimental value $\alpha ^{-1}=137.009$ and concluded that the small discrepancy was a problem for the experiment rather than the theory.

Shortly after Eddington's death, Edmund Whittaker's wrote in Theory of the Constants of Nature, p.144: In the first paper, which appeared in December 1928, he [Eddington] asserted that the fine-structure constant [...] must be the reciprocal of a whole number, which was determined in a second paper (Feb. 1930) to be 137.

Eddington's "pure deduction" turned out to be false, of course, based on nothing but numerology. He had been misled by his belief that this number must be an integer to look for all kinds of reasons to justify that idea, where in fact it was just coincidental (his calculations arrived at 136 and 137 just by chance). To quote Kragh again: Eddington's reasoning was based on a peculiar mixture of mathematics and epistemology that made (and makes) it difficult to understand his theory.

See also Eddington number, as well as Arthur Eddington#Fundamental theory and the Eddington number. This probably wouldn't have mattered much if it hadn't come from such a famous physicist. Renerpho (talk) 15:52, 9 October 2024 (UTC)

You are contradicting yourself because Eddington clearly believed it was not a coincidence, so I repeat the question: Which reliable source can be cited to support the argument that the proximity of 1/alpha to an integer is a coincidence? Dondervogel 2 (talk) 16:04, 9 October 2024 (UTC)

Eddington clearly believed it was not a coincidence -- Yes, but by the time he switched from 136 to 137, he was pretty much alone with his belief that this was more than a coincidence. The monicker "Arthur Adding-one" was not a compliment! Renerpho (talk) 16:22, 9 October 2024 (UTC)

So how do I know others believed it is a coincidence? I'm still waiting for an RS to support this claim. Dondervogel 2 (talk) 16:30, 9 October 2024 (UTC)

I already provided two such sources. What else do you need? If you want one that uses the word "coincidence", I can't offer that. If you want sources that call Eddington's ideas misled, baseless, and numerology (which is generally assumed to be based on mathematical coincidences), there are plenty. I gave two. Renerpho (talk) 16:31, 9 October 2024 (UTC)

@Dondervogel 2: This article (from OMNI Magazine, 1988) may serve as a third: [1] Renerpho (talk) 16:34, 9 October 2024 (UTC)

I never mentioned Eddington. You did. His theories are but a distraction from my question.

If there are no reliable sources supporting your claim that the proximity to 137 is a coincidence (irrespective of what Eddington did or did not claim), then the claim is an unsupported one and does not belong in an article about mathematical coincidence.

The article you link describes countless attempts to explain why it is NOT a coincidence. Sure, they are failed attempts. And so what? There were also countless failed attempts at proving Fermat's last theorem. Those failed attempts did not make magically make the theorem untrue, nor did they stop Andrew Wiles from believing the theorem was true.

I do not plan to contribute further until others have weighed in. Dondervogel 2 (talk) 17:09, 9 October 2024 (UTC)

I never mentioned Eddington -- Of course you did. In your reply to my original comment.

Eddington's "theory" is central to the question, so complaining that I continue to refer to him is an odd choice. Have you read the article by Kragh?

Here is a reference that explicitly calls it coincidental (prominently featuring Eddington's theory, of course): [2] Renerpho (talk) 21:22, 9 October 2024 (UTC)

The "Feynman point" and WP:Original research

@Quack5quack: Thanks for your edit about the "Feynman point". You are correct that Six nines in pi calls the attribution to Feynman into question. There is one problem with the reference for that article though: The reference is this blog by Wikipedia user DavidWBrooks; compare the discussion at Talk:Six nines in pi#Did he do it? that preceded that blog entry. To quote the blog:

But there’s a problem: As was discovered by several Wikipedia editors, Feynman probably didn’t say it. These editors, including me, stumbled across the issue while improving the Wikipedia article titled “Feynman point.” [...] Turns out that Wikipedia can generate new knowledge, not just disseminate existing knowledge. Pretty cool!

That's some impressive research, but right now it is also a textbook example of WP:Original research. Or has this information since been covered by a reliable source, so we can replace the reference? Renerpho (talk) 18:55, 4 January 2025 (UTC)

I wrote about it in a published article in a daily newspaper, not just a blog post - the blog is owned by the paper, and this is a reprint of the column - and that's usually accepted as a "reliable source" - DavidWBrooks (talk) 00:28, 6 January 2025 (UTC)

I've made the requisite change to that article per your note. If nobody can cite the exact lecture or paper where Feynman claimed knowledge of it, it really should be called a misattribution or a ghost attribution. As Abraham Lincoln said, anyone can make up anything on the internet without proper citations. -- Quack5quack (talk) 19:46, 4 January 2025 (UTC)

@Quack5quack: The attribution to Arndt & Haenel (2001) is strange, considering that Eric Weisstein's MathWorld called it the Feynman Point by May 1999;[3] compare Weisstein's CRC concise encyclopedia of mathematics published that same year.[4] The March 1998 edition of Concise Encyclopedia of Mathematics already does so as well.[5] That's the earliest mention of it that I can find with a quick search of the Internet Archive. Whether or not the attribution is a mistake, we cannot blame it on Arndt and Haenel's 2001 book (as the 2016 blog post doesn't do so)! We probably shouldn't blame it on Weisstein either. I still think that the blog post is original research, and is not fit as a reference on Wikipedia. And neither is the rest of the talk page discussion that is currently used (if only implicitly). Renerpho (talk) 00:34, 5 January 2025 (UTC)

Although it's interesting that Weisstein (1999) cites a 1998 book by Arndt and Haenel...[6] That edition is not available online, but the 2013 edition of that book mentions the Feynman point three times.[7] Renerpho (talk) 00:50, 5 January 2025 (UTC)

@DavidWBrooks and XOR'easter: About the blog vs. WP:OR thing, that may be okay, although I'm not feeling good about the author of a reliable source also being the Wikipedia editor they are writing about. It's just a bit hard to untangle. How do we take a WP:NPOV if the source is so close to Wikipedia itself?

There have been a few edits to Six nines in pi over the past few days (with Quack5quack's edit largely being reverted), which is why I am tagging XOR'easter. And I'm still not sure if citing Arndt and Haenel's 2001 book is a good idea, given that we can find citations from the late 1990s that may or may not lead back to the first edition of that book (depending largely on the exact timing of Weisstein's publication vs. theirs). See my previous comments.

To speculate a bit: Assuming that the claim originates with Arndt and Haenel (which we don't know for sure), I think it was Weisstein's inclusion in MathWorld that popularized it. Renerpho (talk) 03:13, 8 January 2025 (UTC)

To clarify, I have no problem with doing research into this kind of stuff on-wiki. I've done this myself.[8][9] In my opinion, this only becomes a problem when we use talk page discussions as sources, by proxy of a secondary source -- like a newspaper article by a Wikipedia editor who writes about themselves. Citogenesis happens so easily! Renerpho (talk) 03:29, 8 January 2025 (UTC)

I agree that the newspaper item being cited as a source was written by the wikipedia editor doing some of the editing (that's me) looks weird, at the very least. Certainly feels OR-ish. But I contacted Gleick, who responded, and published the result in a creditable public source where it could be seen and, if necessary, refuted. That's the sort of work that is done all the time by sources that we cite. So I think it's legit, even if a bit self-referential! - DavidWBrooks (talk) 14:41, 8 January 2025 (UTC)

The point of citing Arndt and Haenel isn't to say that they originated the claim. It's to substantiate that the claim has been made. I removed the MathWorld citation because MathWorld is sloppy, particularly on matters of terminology (see previous discussions about them).

I don't see a problem with citing the Brooks column as a source in this context. It's a mildly unusual situation, but so what? The problem with citogenesis is if somebody makes up a claim in a Wikipedia article, that story gets repeated elsewhere, and those repetitions are then used to cycle the claim back with a spurious respectability. This isn't that. XOR'easter (talk) 04:11, 8 January 2025 (UTC)