# Question about Pi **URL:** \ **Category:** Factual Questions\ **Created:** [March 11, 2021, 6:40pm UTC](https://boards.straightdope.com/t/question-about-pi/937728 "2021-03-11T18:40:39Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Lucas\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lucas_jackson/32/303_2.png) [@Lucas\_Jackson](https://boards.straightdope.com/u/Lucas_Jackson)\ **Post date:** [March 11, 2021, 6:40pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/1 "2021-03-11T18:40:39Z")
(Sorry if this has been asked before - Pi is too short of a search term) If Pi’s decimal representation never ends, it never settles into a permanently repeating pattern and it is infinite, does that mean that every possible combination of numbers would eventually come up? Like for example nine 9’s in a row. Or would it mathematical properties preclude this? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [March 11, 2021, 6:55pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/2 "2021-03-11T18:55:12Z")
That’s [thought to be true](https://en.wikipedia.org/wiki/Pi), but has never been formally proven. > The digits of π have no apparent pattern and have passed tests for statistical randomness, including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often. The conjecture that π is normal has not been proven or disproven. ---
**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:** [March 11, 2021, 6:55pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/3 "2021-03-11T18:55:14Z")
It’s not guaranteed that a non repeating number sequence contains every possible sequence, for example 123112233111222333111122223333… Is non repeating, but never contains the sequence 789 For pi, I belueve its unknown whether it does or not ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [March 11, 2021, 6:57pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/4 "2021-03-11T18:57:20Z")
> [@Lucas\_Jackson](#): > > If Pi’s decimal representation never ends, it never settles into a permanently repeating pattern and it is infinite, does that mean that every possible combination of numbers would eventually come up? It certainly doesn’t follow directly from the “never ends, never repeats” property. The number whose decimal representation is “0.101001000100001000001…” also never ends and never repeats, but doesn’t contain any sequence containing “2” (or even just “11”). The property you are looking for is “[Normality](https://en.wikipedia.org/wiki/Normal_number)”, which I see I’ve been ninjaed on. ---
**Author:** ![TheGunIsMightierThanThePen](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thegunismightierthanthepen/32/2981_2.png) [@TheGunIsMightierThanThePen](https://boards.straightdope.com/u/TheGunIsMightierThanThePen)\ **Post date:** [March 11, 2021, 7:31pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/5 "2021-03-11T19:31:15Z")
For a normal number, the key point is that every possible _finite_ sequence of numbers will be contained within it. So if Pi is normal, it can’t contain other irrational, non-ending numbers like _e_, but it does contain all the works of Shakespeare, as well as _everything humanity has written, or will ever write in its existence_ (assuming the words can be represented as ASCII characters which are converted to their Base-10 representation). Heck, throw in there every piece of digital data humanity has or will ever create. ---
**Author:** ![Saffer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saffer/32/6440_2.png) [@Saffer](https://boards.straightdope.com/u/Saffer)\ **Post date:** [March 11, 2021, 7:57pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/6 "2021-03-11T19:57:42Z")
If pi is normal, and (in principle) can be proven so, then pi contains every possible proof of its own normality, infinitely many times. ---
**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:** [March 11, 2021, 8:18pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/7 "2021-03-11T20:18:09Z")
> [@Lucas\_Jackson](#): > > Pi’s decimal representation never ends, it never settles into a permanently repeating pattern and it is infinite Some people seem to think that this is some special property of the number pi. Actually, this is true of most\* numbers. \*(It’s true of every irrational number, and [most of the real numbers are irrational, in a specific, provable mathematical sense](https://plus.maths.org/content/maths-minute-counting-numbers).) ---
**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:** [March 11, 2021, 8:24pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/8 "2021-03-11T20:24:14Z")
> [@Lucas\_Jackson](#): > > Sorry if this has been asked before And yes, this has come up before. Since the question has been answered, it’s probably not worth searching out earlier answers; but here’s an old thread on a related question that some of us might find interesting: > [@"Messages" (not really) in Pi](https://boards.straightdope.com/t/messages-not-really-in-pi/846073): > > Since Pi is believed to be [normal](https://en.wikipedia.org/wiki/Normal_number) in the sense that any numerical sequence in it’s decimal expansion should appear randomly, and because we currently know the decimal expansion of Pi to [31 trillion digits](https://www.npr.org/2019/03/14/703566696/the-woman-who-calculated-31-trillion-digits-of-pi), then given some suitable scheme for translating digits into letters are there any known short phrases appearing in Pi? Something like “Hello John” for example? ETA: especially if you expressed Pi in base-26 perhaps. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [March 11, 2021, 8:38pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/9 "2021-03-11T20:38:45Z")
> [@Lucas\_Jackson](#): > > Like for example nine 9’s in a row. Sorry, I could only find eight 9s in a row in [this page](https://www.angio.net/pi/) which calls itself the Pi-Search Page. They only seem to use the first 200 Million digits of Pi, but we know several billion by now, and counting. The explaining text reads: > ## Results > > The string **99999999** occurs at position 66780105. This string occurs 1 times in the first 200M digits of Pi. > counting from the first digit after the decimal point. The 3. is not counted. > > The string and surrounding digits: > > 141994430187282261379999999931798954323109584210 You can look up any strings you fancy, if they are shorter than 7 numbers in my experience they usually show up. People seem to try out their birthday often, so did I. Now, how do I prove that the page tells the truth and is not making it all up on the fly? ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [March 11, 2021, 9:05pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/10 "2021-03-11T21:05:42Z")
> [@Pardel-Lux](#): > > Now, how do I prove that the page tells the truth and is not making it all up on the fly? Ask it again. Unless it saves all the requests it won’t know it’s been asked before so it will make something up. It’s highly unlikely it would make up the same thing. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [March 11, 2021, 9:09pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/11 "2021-03-11T21:09:05Z")
That is what I did, and as the answer was the same I felt confident enough to link it. But I cannot prove it. BTW: My birthday appears twice in the first 200 million digits in european notation (DD/MM/YYYY) but none in american notation (MM/DD/YYYY). ---
**Author:** ![blabbermeister](https://avatars.discourse-cdn.com/v4/letter/b/e9a140/32.png) [@blabbermeister](https://boards.straightdope.com/u/blabbermeister)\ **Post date:** [March 11, 2021, 9:12pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/12 "2021-03-11T21:12:23Z")
> [@Pardel-Lux](#): > > The 3. is not counted. Suppose you enter a pi reciting contest, and you’ve memorized the first million digits. You’ve got this! No one can possibly beat you. And then you forget to say “Three point” at the beginning. Would they disqualify you? ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [March 11, 2021, 9:13pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/13 "2021-03-11T21:13:59Z")
What a bummer! ---
**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:** [March 11, 2021, 9:15pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/14 "2021-03-11T21:15:49Z")
In fact, not only is pi believed to be normal, and it is known that most numbers are irrational, it’s even known that most numbers are normal. Which isn’t really as significant as you’d think, because it’s also known that, given any notation system, most numbers can’t even be expressed at all in that notation. Not even if your notation system includes every form of notation human mathematicians ever have or ever will come up with. In other words, every number that we can express is, in some sense, special. And so it’s possible that, for almost all of those cases, that specialness is somehow such that it prevents the number from being normal. Hence, both why we suspect that pi (and e, and sqrt(2), and so on) is normal, and why we’re not actually sure. ---
**Author:** ![Lucas\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lucas_jackson/32/303_2.png) [@Lucas\_Jackson](https://boards.straightdope.com/u/Lucas_Jackson)\ **Post date:** [March 12, 2021, 3:01am UTC](https://boards.straightdope.com/t/question-about-pi/937728/15 "2021-03-12T03:01:33Z")
> [@Pardel-Lux](#): > > You can look up any strings you fancy, if they are shorter than 7 numbers in my experience they usually show up. People seem to try out their birthday often, so did I Thanks for that link. My grandson turned 11 on November 11, 2011 so I looked up 11/11/11 (that’s 11/11/11 for you non-Americans). It comes up 191 times in the first 200 million places. ---
**Author:** ![penultima\_thule](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/penultima_thule/32/3833_2.png) [@penultima\_thule](https://boards.straightdope.com/u/penultima_thule)\ **Post date:** [March 12, 2021, 5:08am UTC](https://boards.straightdope.com/t/question-about-pi/937728/16 "2021-03-12T05:08:33Z")
> [@Lucas\_Jackson](#): > > (that’s 11/11/11 for you non-Americans) That is just plain damn hospitable and considerate of you. Ta muchly. 🙃 ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [March 12, 2021, 7:26am UTC](https://boards.straightdope.com/t/question-about-pi/937728/17 "2021-03-12T07:26:47Z")
It would seem to me that if your grandson turned 11, you should have looked for 11111111. Which comes up three times. Lucky number! For your grandson, anyway. Glad I could help 🥳 Looking for Pi in the emojis I only found a Japanese variant ⛩ and a musical one 🎵. Strange omission. ---
**Author:** ![Yllaria](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yllaria/32/3452_2.png) [@Yllaria](https://boards.straightdope.com/u/Yllaria)\ **Post date:** [March 12, 2021, 6:23pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/18 "2021-03-12T18:23:44Z")
> [@TheGunIsMightierThanThePen](#): > > but it does contain all the works of Shakespeare, as well as _everything humanity has written, or will ever write in its existence_ (assuming the words can be represented as ASCII characters which are converted to their Base-10 representation) So somewhere it say “Help, I’m trapped in a universe-creating factory!” ---
**Author:** ![TheGunIsMightierThanThePen](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thegunismightierthanthepen/32/2981_2.png) [@TheGunIsMightierThanThePen](https://boards.straightdope.com/u/TheGunIsMightierThanThePen)\ **Post date:** [March 12, 2021, 6:40pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/19 "2021-03-12T18:40:27Z")
> [@Yllaria](#): > > So somewhere it say “Help, I’m trapped in a universe-creating factory!” Yep, it’s guaranteed to be in there, but we just don’t know where the index is. It could be past 100 trillion digits, past Tree(3) digits, or even past a Loader’s number of digits. The point is, when compared to infinity, even these massive numbers are _nothing_. If the universe could be simulated by 1s and 0s, it will also have a simulation of the entire history of the observable universe (since that is finite) from the moment of the Big Bang. ---
**Author:** ![blabbermeister](https://avatars.discourse-cdn.com/v4/letter/b/e9a140/32.png) [@blabbermeister](https://boards.straightdope.com/u/blabbermeister)\ **Post date:** [March 12, 2021, 7:35pm UTC](https://boards.straightdope.com/t/question-about-pi/937728/20 "2021-03-12T19:35:55Z")
> [@Yllaria](#): > > So somewhere it say “Help, I’m trapped in a universe-creating factory!” Somewhere it says “Please disregard all of the following digits.” [Next page](https://boards.straightdope.com/t/question-about-pi/937728.md?page=2)