Talk:Six nines in pi

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This article has been mentioned by a media organization: David Brooks (12 January 2016). "Wikipedia turns 15 on Friday (citation needed)". Granite geek. Retrieved 12 January 2016. With this in hand, the name of the Wikipedia article has since been changed to "Six nines in pi," and Hofstadter's column has been referenced.

The page does not properly display at page resolutions under about 1000px of width. This is because the image is floating to the right, and the full digits of pi do not wrap next to it. Thus, the image covers up the digits. Anyone who can fix this, please do. --TechnoGuyRob 22:13, 25 November 2006 (UTC)[reply]

The problem also occurs on high resolutions with a large font size. I've factored the number of digits, and thus used blocks of 13 digits (using a table) so that the browser will automatically display as many blocks as it can on each line. It needs to be checked on MS Internet Explorer, which I don't have.   — Lee J Haywood 22:47, 25 November 2006 (UTC)[reply]

Thanks, Lee. In Firefox, it messed up the last row for me with the spacing, so I added in a hack: I put white-colored zero's after the 9s. This isn't necessarily problematic, but definitely not desired, so anyone who knows a way that preserves both wrapping and spacing, please change the page accordingly. --TechnoGuyRob 00:57, 26 November 2006 (UTC)[reply]

Not everybody use graphical browsers and white backgrounds, and the zeros are confusing for those who can see them. I changed them to the actual digits of pi that come after the Feynman point. Henning Makholm 01:15, 26 November 2006 (UTC)[reply]

Is there a reasoning underlying blocks of 13 digits? Or might it as well be 5, 10 or 20? Should it be reformatted?Proborc (talk) 09:47, 11 March 2009 (UTC)[reply]

There's no reason to reformat now; it looks fine. 13 digits is somewhat arbitrary (as 5, 10, or 20 would be), but I'll say it was a smart choice: 767=13×59, so using a block of 13 means the 99999 occurs at the end of a block. :) Shreevatsa (talk) 09:53, 11 March 2009 (UTC)[reply]

The phrase 'consecutive numbers' is used consistently when what is meant is 'repeated numbers' or 'consecutive occurrences of the same number'. Isn't there some better way to put this?

Agreed. Changed to "identical" Sir Isaac Lime (talk) 14:04, 1 July 2009 (UTC)[reply]

Sir Isaac, "consecutive" does not mean increasing like 1,2,3,4; it means digits that occur in adjacent positions. And simply saying "identical" digits does not make much sense — the "1" in the first decimal place is identical to the "1" in the third decimal place, but that is not what we care about in the article. Your edits have just made several sentences meaningless instead of confusing; I'll revert it for now and see what to do... probably "consecutive identical digits" is what we unfortunately need to use. Shreevatsa (talk) 14:30, 1 July 2009 (UTC)[reply]

Do you mean randomly chosen natural number? An irrational number isn't guaranteed to have an equal chance of any particular digit sequence to occur -- it merely cannot be stated as the ratio of two whole numbers. While it's not proven or known if pi itself is a natural number, it seems that if you are going to make a probabilistic analysis of it you should just go ahead and assume it is. Otherwise, how will you what the expected values are? —Preceding unsigned comment added by 65.215.26.189 (talk) 14:50, 25 September 2008 (UTC)[reply]

Oh actually I meant to say normal, not natural. —Preceding unsigned comment added by 65.215.26.189 (talk) 20:57, 21 October 2008 (UTC)[reply]

Since the set of numbers which are not normal has zero measure, I guess that with any "decent" probability distribution it is almost sure that you'd get a normal number. -- Army1987 – Deeds, not words. 13:47, 22 December 2008 (UTC)[reply]

The article calls these 9's an "intriguing coincidence" and states its probability of occurring at .08%. This is misleading, since it doesn't consider that Feynman would have noticed six 4's or six 7's, or for that matter seven 2's or five 6's. Once you add up all the probablilities of finding a series of repeated numbers somewhere near the beginning, it's hardly a coincidence at all.66.183.132.33 (talk) 06:21, 7 November 2009 (UTC)[reply]

I understand your point, but what the article actually says is "the probability of six 9s occurring this early in the decimal representation is only 0.08%" (emphasis added). This is a sourced quote, and to qualify it with our own observations would be contrary to Wikipedia's policy on original research. Even considering that other repeats are possible, though, the Feynman point is still remarkable for how early it occurs – note, for example, that there are no runs of five or even four consecutive identical digits before the Feynman point. Adrian J. Hunter^{(talk•contribs)} 07:37, 7 November 2009 (UTC)[reply]

The chance of "141592" occurring early is small too, but happens right off the bat. Bubba73 ^{You talkin' to me?} 02:49, 9 November 2012 (UTC)[reply]

I think this is ridiculous, but User:CBM insists on this: WP:CITE says "[...] editors should not change an article with a distinctive citation format to another without gaining consensus." Therefore I am asking everyone to signal here, if he/she does not want to see <references /> replaced by {{reflist}}. If no one complains until Feb. 28, I'll replace it. --bender235 (talk) 23:02, 7 February 2010 (UTC)[reply]

I think you are confused about the purpose of the language in WP:CITE. The point of that part of WP:CITE is, like WP:ENGVAR, to avoid this sort of discussion by simply deferring to the established style. As long as {{reflist}} changes the size of text, I feel it is inappropriate to use. Other people are free to start articles that do use {{reflist}}, and I respect that by not removing it. On the other hand, articles that are started with foornotes but without {{reflist}} deserve equal respect. The guideline explicitly says that the first established style is the one that should be respected. — Carl (CBM · talk) 23:09, 7 February 2010 (UTC)[reply]

Carl, you need to realize that just because someone started an article doesn't mean the citation style the author chooses is set in stone. Wikipedia as a whole continuously progresses, new templates are developed, existing templates get new features, etc.

The one basic principle of Wikipedia is that no one owns an article. And because of that, no one should be put in the position to determine the design/layout of an article from now to all eternity. That would be absurd. --bender235 (talk) 03:44, 8 February 2010 (UTC)[reply]

The point of things like ENGVAR is that everyone has their own preferences, and so articles would spend lots of time bouncing between different styles without a guideline to just leave them as they are. It is true that nobody owns the content of an article, but for issues such as whether to use "color" or "colour" and which citation style to use, our practice is that the first significant contributor gets to decide. — Carl (CBM · talk) 12:13, 8 February 2010 (UTC)[reply]

(Since I was asked to reply here.) As far as I can tell, the only significant difference, if any, is in the size of text, and there seems to be no good reason to change (or discuss) this. Shreevatsa (talk) 23:46, 7 February 2010 (UTC)[reply]

(Also asked to reply here.) <references/> was added in November 2006 ([1]) when {{reflist}} was only one month old and was presumably not yet well-known. As Bender235 noted on Carl's talk page, new referencing templates can introduce improved functionality to Wikipedia. But by Carl's interpretation of WP:CITEHOW, a new template would not be incorporated into existing articles without discussion in every article's talk page, stymying progress. This is surely not the intention of WP:CITEHOW. I've always assumed WP:CITEHOW was to discourage editors from wasting time and frustrating other contributors by changing the entire citation style, eg from <ref> style to Author (date) style. I don't think contributors are expected to obtain consensus before making such a trivial change as Bender235 has made. Adrian J. Hunter^{(talk•contribs)} 10:45, 8 February 2010 (UTC)[reply]

If nobody objects, then (somewhat trivially) nobody objects. But when someone does object to a change in style, WP:CITEHOW has clear advice: "where there is disagreement, the style used by the first editor to use one should be respected." I can explain why I object to the small font size: I think it trivializes the role of references, and reinforces the viewpoint that references are just a sort of decoration that is hung on the article to make it look better. If we actually expect people to read and use the references, we should keep the font size the same as the surrounding text.

Of course this is a stylistic argument, and I don't expect everyone to agree with me. The point of the "first major contributor" rule is that there will never be agreement on these sorts of minor issues (because of the bike shed effect) and so we need some arbitrary rule to make the decision. The rule that we have arrived at is to use whatever styler was established first. — Carl (CBM · talk) 12:13, 8 February 2010 (UTC)[reply]

Ok. You make a very reasonable point, one that I hadn't thought of. I'd been under the impression you objected to the change per se, without preferring one style over the other. I guess we should all leave the article as it is then, lest we find ourselves forever immortalised for others' amusement. Adrian J. Hunter^{(talk•contribs)} 13:51, 8 February 2010 (UTC)[reply]

It really makes no sense to me why the creator of an article, although he should know (per WP:OWN) "that others will edit it" and may even delete all of the initial content, still has the "power" to determine the article's style for all eternity. Those "minor issues" like templates and overall appearance are part of what will be edited by someone, sooner or later. As WP:OWN states: "You cannot stop everyone in the world from editing "your" stuff, once you have posted it to Wikipedia. As each edit page clearly states: If you do not want your writing to be edited, used, and redistributed at will, then do not submit it here." --bender235 (talk) 14:28, 8 February 2010 (UTC)[reply]

That is referring to content, rather than style. The reason that ENGVAR and CITEHOW are the way they are is to give an arbitrary but simple rule to resolve style discussions, so that people can spend more time thinking about the content and less time thinking about stylistic matters. — Carl (CBM · talk) 14:37, 8 February 2010 (UTC)[reply]

But style discussions should not be suppressed. The Wikipedia:Manual of Style has been modified numerously over the past years, and will be modified in the future. That rule of thumb "leave the original style if there's no consensus" does not mean that the style can't be changed if there is consensus. --bender235 (talk) 15:01, 8 February 2010 (UTC)[reply]

Indeed. But WP:CITE is clear that there is not consensus about how to style citations. That's why WP:CITE has two different passages about how the originally-chosen citation style should be maintained. — Carl (CBM · talk) 16:24, 8 February 2010 (UTC)[reply]

Bender235, I think the idea is that style discussions ought to be consolidated at a relevant project page, such as WT:CITE or WT:MOS. If a consensus were to emerge that one particular style was outright superior to another, then editors would be justified in replacing the deprecated style with the superior style in any article, and each article's first significant contributor would have no special power. But Carl has demonstrated that, in the case of <references/> vs {{reflist}}, no such consensus presently exists. That being the case, there's no point having separate debates about the merits of each style on the talk pages of thousands of individual articles. Instead, we go with the first significant contributor as an arbitrary but simple way of resolving the choice of style, freeing our time to focus on content. Adrian J. Hunter^{(talk•contribs)} 04:28, 9 February 2010 (UTC)[reply]

WP:CITE explicitely says that there is no recommened standard for all of Wikipedia. Yet for a single article, the editor(s) can decide to change the citation style. And we do right here? Does anybody oppose using {{Reflist}} for any reason other than poiting out that Wikipedia as a whole has no recommended standard as of now? --bender235 (talk) 13:06, 9 February 2010 (UTC)[reply]

Carl/CBM has already opposed using reflist, so his opposition means there is no consensus to change. In the hope of terminating this trivial discussion, I also hereby oppose the change: I like the bigger font. I hope this makes it clear that there is no consensus to change, and no reason to prolong this discussion. Shreevatsa (talk) 13:41, 9 February 2010 (UTC)[reply]

Okay. End of discussion. --bender235 (talk) 13:51, 9 February 2010 (UTC)[reply]

Sorry to be late to the party; also opposing. There's enough to do on Wikipedia that we don't need such squabbles. htom (talk) 21:28, 15 February 2010 (UTC)[reply]

I understand Feynman was joking. However, did he actually follow through and learn the sequence? This could be a fun/interesting addition to the article. --62.107.127.132 (talk) 17:41, 10 June 2010 (UTC)[reply]

Did Feynman ever say that? The Penguin Dictionary of Curious and Interesting Numbers only confirms that there are six nines at the Feynman point, not that Feynman recognized them. The only references to Feynman are the Pi – Unleashed book by Arndt and Haenel (2001), which gives no reference to a text or lecture by Feynman, and the Mathworld link, which also does not confirm Feynman’s involvement in this observation. Lending the weight of Feynman’s name to this observation blatantly aggrandized the notion of this piece, raising it to notability which it would not have without that label.

— Rgdboer (talk) 21:53, 29 November 2015 (UTC)[reply]

Ooooh - interesting point. The "Pi-Unleashed" reference is one sentence on page 3 and is, as you state, unreferenced. [2] - DavidWBrooks (talk) 01:24, 30 November 2015 (UTC)[reply]

Well its an internet meme now with one fellow on Utube reciting the sequence for pi to the Feynman point and numerous bloggers taking inspiration for this well-labeled point. One article mentions Surely You're Joking, Mr. Feynman, but no page reference. Wikipedia is cited as a source frequently. This article came to my attention as I was looking for articles containing "Feynman mathematics" since some antipathy is notable in his book QED. The narrative of suggested rationality plays into his fame as a gamester, but why would he want to suggest pi rational ? — Rgdboer (talk) 02:17, 30 November 2015 (UTC)[reply]

I can't find it in "Surely You're Joking" - it's not in the index and I don't recall it. He liked to prank people, and suggesting in a subtle way that pi is rational would probably appeal to him. On the other hand, he has risen to the level of fame where lots of things are attributed to him - physics' version of Mark Twain or Shakespeare or Yogi Berra. - DavidWBrooks (talk) 12:14, 30 November 2015 (UTC)[reply]

His autobiography No Ordinary Genius says on page 30 that from an early age he identified pi with the ratio of the circumference to the diameter of a circle rather than its decimal representation. The James Gleick biography must still be checked, but so far no trace of an authentic quote. — Rgdboer (talk) 20:38, 30 November 2015 (UTC)[reply]

Gleich's biography is 438 pages of text and 27 of bibliography. There is no mention of pi in the index. Any help in finding a source would be appreciated. — Rgdboer (talk) 01:52, 17 December 2015 (UTC)[reply]

I sent Gleick an email, asking if he knew anything about it. We'll see if he (a) can read all his fan email, and (b) responds. - DavidWBrooks (talk) 02:33, 17 December 2015 (UTC)[reply]

Gleick wrote back the next morning - impressive. He says he doesn't recall ever hearing of the Feynman point or of any such comment by Feynman. Of course, absence of evidence is not evidence of absence but this is still pretty telling from a guy who delved into Feyman's life so deeply.

He doesn't want the email cut-and-pasted, and personal correspondence isn't legitimate sourcing on wikipedia, so I'm not quite sure what to do with this in the article. Any thoughts? - DavidWBrooks (talk) 15:06, 17 December 2015 (UTC)[reply]

We could mention that there are no clear connections of the Feynman point to Feynman, and that it is not mentioned in Feynman (auto-)biographies. It would be interesting to find out who coined the name. —Kusma (t·c) 15:18, 17 December 2015 (UTC)[reply]

I have vague-ified the intro a bit, to reflect this uncertainty. I've also emailed Springer, which published "Pi Unleashed", to see if I can contact the authors and find out their source, since their book seems to be the main source of the claim. The plot thickens! - DavidWBrooks (talk) 20:24, 17 December 2015 (UTC)[reply]

I did a little bit of digging on Usenet. This reminded me of where I first read about the idea. In Metamagical Themas, Douglas R. Hofstadter claims that he tried to do this as a kid (full text here). I am now willing to believe that there is no connection of the "Feynman point" to Feynman at all, and that it should be called "Hofstadter point". Maybe your further research can clear this up -- or you could ask Hofstadter what he thinks about Feynman's name being associated with this idea. —Kusma (t·c) 09:26, 18 December 2015 (UTC)[reply]

Well done - what a memory! I have emailed Hofstadter to see what he thinks. - DavidWBrooks (talk) 00:28, 19 December 2015 (UTC)[reply]

What Hofstadter wrote for his May 1982 column in Scientific American was:

I myself learned 380 digits of pi when I was a crazy high school kid. Later I met several other people who had outdone me. All of us had forgotten most of the digits, but we all remembered the first 100 solidly, and so we would occasionally recite them in unison – a rather esoteric pleasure.

There is no mention of the six nines. — Rgdboer (talk) 03:03, 3 January 2016 (UTC)[reply]

There is in the book edition, see the link I posted, the book itself, or this book review. —Kusma (t·c) 06:59, 3 January 2016 (UTC)[reply]

No response from Hofstadter to my email yet. - DavidWBrooks (talk) 14:50, 3 January 2016 (UTC)[reply]

Yes, so we have Hofstadter (1985) and Ardnt & Haenel (2001) taking note of the six nines. Perhaps a Move to Six nines in pi is in order, then see if it survives a WP:AfD. — Rgdboer (talk) 23:33, 3 January 2016 (UTC)[reply]

I am boldly implementing this excellent suggestion. —Kusma (t·c) 14:59, 4 January 2016 (UTC)[reply]

I have no problem with your bold rename, but for consistency you should also re-word those parts of the article that use the term "Feynman point" or "Feynman's point" (I count at least 5 occurences), as well as the sentence in the lead that starts "It has been named after physicist Richard Feynman ...". Gandalf61 (talk) 15:17, 4 January 2016 (UTC)[reply]

Well, it has been named after Feynman, in a way. But I have tried to tone down the Feynman connection further. —Kusma (t·c) 15:26, 4 January 2016 (UTC)[reply]

Good move. The Feynman quote itself could in principle stay as long as there are RS, but the named after part is not appropriate after the move. If that would be established, no move would have been needed. Gap9551 (talk) 15:29, 4 January 2016 (UTC)[reply]

Agreed - I don't think saying "It is commonly called "Feynman point"" in the article is consistent with the rename. If "Feynman point" is indeed the common name for this concept - even if we think that name is incorrect - then the article should not have been renamed. Wikipedia:Article titles says "In discussing the appropriate title of an article, remember that the choice of title is not dependent on whether a name is "right" in a moral or political sense". Gandalf61 (talk) 15:37, 4 January 2016 (UTC)[reply]

If you can improve the wording, by all means do so. —Kusma (t·c) 15:44, 4 January 2016 (UTC)[reply]

I changed 'commonly' to 'sometimes' which I think can be more easily defended, but I'm open to alternatives too. Gap9551 (talk) 15:51, 4 January 2016 (UTC)[reply]

(unindent) Dear fellow editors - thank you for improving my newspaper column this week. [3] - DavidWBrooks (talk) 13:18, 12 January 2016 (UTC)[reply]

Note that tau (also known as 2pi), the real circle constant, has a feynman point of 7 consecutive 9s!

http://tauday.com/tau_digits — Preceding unsigned comment added by 84.19.220.235 (talk) 13:36, 5 July 2011 (UTC)[reply]

I have removed the section on Tau. Tau is sensationalist hokey by a few on the fringe of the mathematical community, lacks wide acceptance, and as such content about it (other than content about how it is a fringe phenomenon in the mathematical community) is uncyclopedic. See the above comment 'the real circle constant' for further evidence as to the nuttery of these Tau-folk. 69.166.22.210 (talk) 02:50, 13 August 2011 (UTC)[reply]

Whatever -- it isn't pseudo-science in the ordinary sense, since it's defined as simply the constant value 2π which (just as claimed) appears in numerous trigonometric relations and other mathematical formulas. The real question is whether it appears in reliable sources... AnonMoos (talk) 06:18, 13 August 2011 (UTC)[reply]

It is still an interesting fact, so it should at least be included in the "Related statistics" section. Gurrka (talk) 09:30, 15 March 2013 (UTC)[reply]

The fact is, the notability of the Feynman Point rests entirely on its statistical unlikelihood (by various measures). Nutty or not, the corresponding point in 2π is in the exact same position (actually, one position earlier), but with yet another 9. It is deeply related to the Feynman Point, yet significantly more notable by every measure by which the Feynman Point is notable, with the notable exception that Feynman himself failed to note it.jjgignac (talk) 22:59, 07 June 2013 (UTC)[reply]

I agree. It's an unlikely coincidence in pi and an even MORE unlikely coincidence in Tau. (10 times more unlikely). For completeness sake, the article should mention it.50.157.226.255 (talk) 17:26, 14 July 2015 (UTC)[reply]

There's nothing unlikely about the 9's in tau; in fact it's the very opposite of unlikely. The fact that pi contains a sequence of 9's FORCES 2*pi to have approximately the same number of 9's in approximately the same position. Same as would happen with any other real number containing a sequence of 9's. The tau nonsense really has nothing to do with this article and should be deleted. Mnudelman (talk) 19:20, 19 December 2015 (UTC)[reply]

I disagree with Mnudelman, as per 50.157.226.255's comment above. cmɢʟee⎆τaʟκ 01:28, 1 January 2016 (UTC)[reply]

I don't understand what you are disagreeing with. Are you claiming that there are real numbers whose decimal representation includes a string of 9's but where double that number does NOT contain a string of 9's in approximately the same place? Can you give an example of such a number? Mnudelman (talk) 23:51, 2 January 2016 (UTC)[reply]

@Mnudelman: I disagree with "There's nothing unlikely about the 9's in tau" and "The tau nonsense really has nothing to do with this article and should be deleted.". Please see my reply to Gap9551 below. Ta, cmɢʟee⎆τaʟκ 13:21, 4 January 2016 (UTC)[reply]

I agree with IP 50.157.226.255 and others that the sequence of seven 9's in tau is noteworthy. Obviously it is strongly related to the sequence of six 9's in pi and nobody here claims that both sequences are independent coincidences. But the extra 9 in tau, which is quite a noteworthy constant in itself despite not being widely accepted, adds to the coincidence in the sequence in pi. In general the sequence in the double number can also be the same length as, or one shorter than, the sequence in an original number. Since the whole article is about the sequence in pi and how unlikely it is, the tau sequence should be (briefly) mentioned too. Gap9551 (talk) 00:42, 3 January 2016 (UTC)[reply]

I've tabulated for the substring 2 × …x999y… where x and y are not 9 (otherwise it would just make it a longer run) both with and without a carry of 1 (the most that's possible by multiplying 2) — let me know if I missed any other cases:

Legend:   shorter run (49.4%)   same length shifted (6.2%)   same length at same place (39.5%)   longer run (4.9%)

without carry
y x	0	1	2	3	4	5	6	7	8
0	…19980…	…19982…	…19984…	…19986…	…19988…	…19990…	…19992…	…19994…	…19996…
1	…39980…	…39982…	…39984…	…39986…	…39988…	…39990…	…39992…	…39994…	…39996…
2	…59980…	…59982…	…59984…	…59986…	…59988…	…59990…	…59992…	…59994…	…59996…
3	…79980…	…79982…	…79984…	…79986…	…79988…	…79990…	…79992…	…79994…	…79996…
4	…99980…	…99982…	…99984…	…99986…	…99988…	…99990…	…99992…	…99994…	…99996…
5	…19980…	…19982…	…19984…	…19986…	…19988…	…19990…	…19992…	…19994…	…19996…
6	…39980…	…39982…	…39984…	…39986…	…39988…	…39990…	…39992…	…39994…	…39996…
7	…59980…	…59982…	…59984…	…59986…	…59988…	…59990…	…59992…	…59994…	…59996…
8	…79980…	…79982…	…79984…	…79986…	…79988…	…79990…	…79992…	…79994…	…79996…
with carry
y x	0	1	2	3	4	5	6	7	8
0	…19981…	…19983…	…19985…	…19987…	…19989…	…19991…	…19993…	…19995…	…19997…
1	…39981…	…39983…	…39985…	…39987…	…39989…	…39991…	…39993…	…39995…	…39997…
2	…59981…	…59983…	…59985…	…59987…	…59989…	…59991…	…59993…	…59995…	…59997…
3	…79981…	…79983…	…79985…	…79987…	…79989…	…79991…	…79993…	…79995…	…79997…
4	…99981…	…99983…	…99985…	…99987…	…99989…	…99991…	…99993…	…99995…	…99997…
5	…19981…	…19983…	…19985…	…19987…	…19989…	…19991…	…19993…	…19995…	…19997…
6	…39981…	…39983…	…39985…	…39987…	…39989…	…39991…	…39993…	…39995…	…39997…
7	…59981…	…59983…	…59985…	…59987…	…59989…	…59991…	…59993…	…59995…	…59997…
8	…79981…	…79983…	…79985…	…79987…	…79989…	…79991…	…79993…	…79995…	…79997…

Only 8 (4.9%) of the 162 cases have an extra 9. Therefore, that 𝜏's run has one more 9 is actually unusual and noteworthy. Cheers, cmɢʟee⎆τaʟκ 13:21, 4 January 2016 (UTC)[reply]

Thanks for the thorough analysis, Cmglee. This clearly shows that the string of 9s in tau adds significantly to the coincidence, even though obviously the coincidence already provided by the string in pi is larger. Gap9551 (talk) 15:58, 4 January 2016 (UTC)[reply]

MUCH larger. The probability of the six 9s in pi at that position is 0.0001%, 50,000 times smaller than the probability of the extra 9 in tau. The latter hardly seems noteworthy in comparison. It's comparable to the difference between tossing a coin and getting 17 heads in a row, versus tossing it once and getting heads once. Mnudelman (talk) 16:50, 4 January 2016 (UTC)[reply]

No, the probability at exactly that location isn't relevant here, neither the fact that they are 9s or another digits (the probability of a sequence of any 6 identical digits at the location would already be 0.001%). A long sequence earlier in the sequences would be relevant too. In the article it says: For a randomly chosen normal number, the probability of a specific sequence of six digits occurring this early in the decimal representation is usually only about 0.08%. This probability is only 61 times smaller than the 4.9% mentioned above. Gap9551 (talk) 17:00, 4 January 2016 (UTC)[reply]

By the way, I think that the participants in this discussion have a good grasp on what probabilities mean; comparisons with coins are not necessary, I think. Gap9551 (talk) 17:03, 4 January 2016 (UTC)[reply]

${\displaystyle 1\leq n\leq 393\;\Rightarrow \;\lfloor n\tau /128\cdot 10^{767}\rfloor \equiv -1{\pmod {10^{\nu _{2}(n)-[n=256]}}}}$ 89.244.26.202 (talk) 08:41, 27 October 2019 (UTC)[reply]

I readded this after coming across the OEIS entry; it does seem significant enough to mention (but both bits of numerology are equally random and only notable to the extent they are referenced by others). – SJ + 15:09, 2 May 2023 (UTC)[reply]

Obviously enough, base ten is no "special snowflake", as the fact we prefer to use it more than likely merely stems from our anatomy. How about represetations of Pi in other bases, can we observe a similar phenomenon? — Preceding unsigned comment added by 89.70.16.131 (talk) 01:35, 24 December 2016 (UTC)[reply]

Nope. It's been tried. But you make a good point .... there are probably a lot of other coincidences like this out there in base 9, base 8, etc.... just not for pi specifically. —Soap— 12:23, 18 July 2020 (UTC)[reply]

Would you have a source on that? This is fascinating, should be readily available, and yet my searches are spoilt by trivial questions about the transcendance of pi. 85.31.132.219 (talk) 17:39, 17 May 2021 (UTC)[reply]

A 9x12 table layout seems highly irregular, with the added difficulty to easily find specific digit positions. As a minimum, I'm sure with a slight mod to the text size, a 10x10 grouping would have fit the page. Alternatively, the graphic at the top of the article could have been used, perhaps with modification into groupings of 10 digits rather than 5, with the bonus interactive capability of the mouse tag providing the specific digit position. SquashEngineer (talk) 13:24, 14 March 2017 (UTC)[reply]

I have removed the jpeg illustration because (a) the text duplicates it, (b) it was color coded clear down to the two-digit pairs, creating a hard-to-read mess, and (c) it also showed results for "tau", a distraction that can imply to casual readers that there are two six-number strings in pi.

Others, of course, may disagree. - DavidWBrooks (talk) 18:53, 19 March 2018 (UTC)[reply]

Thanks -- I had cleaned most of the silly tau references out of the text some time ago, but obviously missed that it was in the figure. I agree with the removal on all grounds cited. --JBL (talk) 20:22, 19 March 2018 (UTC)[reply]

In a reversion of a recent edit,

  and terminates at the 761st digit (which, in its terminating form, would be 5 instead of 4.)

User:DavidWBrooks said that “Sorry, but that's not what it implies at all.” But I think the reason for the reversion is incorrect, because that is exactly what “4999999 and so on” implies: 5 with a bunch of zeros ad infinitum. (In math, the decimal numbers 0.49999999999999 ... and 0.5 are the same.) -- Roger Hui (talk) 14:48, 30 December 2018 (UTC)[reply]

Yes, the removed statement is correct. Maybe it can be reinstated as a footnote at least. Gap9551 (talk) 14:58, 30 December 2018 (UTC)[reply]

Yes, it is correct - I misread it. I have returned it elsewhere in the article, as it seems to me to be more detail than we need to bring up on first reference about what the error implies. - DavidWBrooks (talk) 15:10, 30 December 2018 (UTC)[reply]

I object to efforts to explain the joke in the absence of a secondary source that does so. I suggest removing both the sentence the IP was editing and the new sentence. (Many things logically follow from the false statement that pi is rational, but so what?) --JBL (talk) 15:42, 30 December 2018 (UTC)[reply]

Oh, I don’t know; I think the new (current) sentence is harmless and perhaps even useful. Useful in helping the non-cognoscenti “get” the joke. (FYI: I did not do the reverted sentence nor the new sentence.) -- Roger Hui (talk) 15:51, 30 December 2018 (UTC)[reply]

I have added a "definition needed" tag on "a randomly chosen normal number", since it is not clear to me what is the probability distribution the text is talking about. Is there a natural definition for normal numbers? The normal number page does say anything about it. --Lucha (talk) 22:04, 25 October 2019 (UTC)[reply]

The article seems to contradict itself: "while strings of nine 9's next occur at position 590,331,982 and 640,787,382" vs "the positions of the first occurrence of a string of 1, 2, 3, 4, 5, 6, 7, 8, and 9 consecutive 9's in the decimal expansion are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206, respectively". Does a sequence of 9 digits 9 appear both at the position 564,665,206 and 590,331,982, or did somebody miscount the digits (e.g. count EOL characters as well)? - Mike Rosoft (talk) 07:13, 17 April 2021 (UTC)[reply]

Removed the first of these claims. —Kusma (talk) 14:49, 27 November 2022 (UTC)[reply]

In MathWorld as of 1999; perhaps the first use of the name online? Someone might ask Weisstein where he got his initial list of terms. The later citation in MathWorld (to the Penguin Dictionary) notes the sequence but doesn't name it. – SJ + 15:09, 2 May 2023 (UTC)[reply]