# Is this an accurate factoid about pi? **URL:** \ **Category:** Factual Questions\ **Created:** [March 15, 2017, 1:36am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209 "2017-03-15T01:36:12Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 15, 2017, 1:36am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/1 "2017-03-15T01:36:12Z")
In honor of pi day, I told my third graders that you could assign a different value to each letter: 01 for A, 02 for B, and so on, up to 26 for Z. Somewhere in pi’s digits is thereby buried the message, “ **Left Hand of Dorkness** , this is a message for you, I’ve hidden it in pi for you, and I am watching you”; this message is repeated elsewhere in pi in every human language from history, and it is repeated for each of my students in every language as well. But beware, for another message is also found in pi’s digits, repeated in every language: “Don’t get too excited, LHOD, because this is just a byproduct of having an infinite, non-repeating number series.” I think this is true, but I worry that I’m missing some mathematical principle that renders it false. Am I? Or is it certain that an infinite non-repeating string will have every possible combination somewhere in it? ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [March 15, 2017, 1:40am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/2 "2017-03-15T01:40:41Z")
Well… it might take awhile. [Probability of Finding Strings In Pi](https://www.angio.net/pi/whynotpi.html) ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [March 15, 2017, 1:49am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/3 "2017-03-15T01:49:58Z")
cool! Next, your third graders should read Borges’ short story “The Library of Babel,” or at least try to find an English sentence in the [virtual version](http://libraryofbabel.info/index.html). ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 15, 2017, 1:52am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/4 "2017-03-15T01:52:59Z")
> [@JKellyMap](#): > > cool! Next, your third graders should read Borges’ short story “The Library of Babel,” or at least try to find an English sentence in the [virtual version](http://libraryofbabel.info/index.html). Thanks–I was trying to remember the title of this story. ---
**Author:** ![gazpacho](https://avatars.discourse-cdn.com/v4/letter/g/6f9a4e/32.png) [@gazpacho](https://boards.straightdope.com/u/gazpacho)\ **Post date:** [March 15, 2017, 1:54am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/5 "2017-03-15T01:54:21Z")
I don’t think that it has been proven that all possible finite length message are in pi. This is asking if pi is a normal number. People think that it is but it has not been proven. ---
**Author:** ![Boozahol\_Squid\_P.I](https://avatars.discourse-cdn.com/v4/letter/b/d9b06d/32.png) [@Boozahol\_Squid\_P.I](https://boards.straightdope.com/u/Boozahol_Squid_P.I)\ **Post date:** [March 15, 2017, 2:01am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/6 "2017-03-15T02:01:04Z")
> [@Left\_Hand\_of\_Dorkness](#): > > But beware, for another message is also found in pi’s digits, repeated in every language: “Don’t get too excited, LHOD, because this is just a byproduct of having an infinite, non-repeating number series.” Pi’s a weird number, and has all sorts of fun twists, but that message actually isn’t true. .12113111411115111116… is another infinite, non-repeating number series that won’t contain your message. ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [March 15, 2017, 2:03am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/7 "2017-03-15T02:03:29Z")
Previous discussions on this topic: > **[Monkeys & Pi](https://boards.straightdope.com/sdmb/showthread.php?t=261353)** > > Okay, stupid subject line. You know that old thing about monkeys typing will eventually churn out Shakespeare? Well, looking at it slightly differently: Pi is an infinte, non-repeating decimal. Does it therefore follow that any finite number string... > **[Why do people say irrational numbers must contain any sequence of numbers?](https://boards.straightdope.com/sdmb/showthread.php?t=635835)** > > Consider the number 0.101001000100001000001… with an increasing number of 0s between the 1s. \[ol\] \[li\]Is this number irrational?\[/li\]\[li\]It does not contain the number “2” or even the sequence “11”\[/li\]\[/ol\] Since this number does not contain the... [http://boards.straightdope.com/sdmb/showthread.php?p=14648059#post14648059](http://boards.straightdope.com/sdmb/showthread.php?p=14648059#post14648059) ---
**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 15, 2017, 2:38am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/8 "2017-03-15T02:38:35Z")
> [@Left\_Hand\_of\_Dorkness](#): > > I think this is true, but I worry that I’m missing some mathematical principle that renders it false. Am I? Or is it certain that an infinite non-repeating string will have every possible combination somewhere in it? It is not true that _any_ infinite non-repeating string will have every possible combination somewhere within it. You could, for example, have an infinite, non-repeating string in which none of the digits are 3’s. As for pi in particular, the correct answer is: > [@gazpacho](#): > > I don’t think that it has been proven that all possible finite length message are in pi. This is asking if pi is a normal number. People think that it is but it has not been proven. [Here’s one cite](http://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations); there are pobably others in those other threads **Peter Morris** linked to. ---
**Author:** ![gazpacho](https://avatars.discourse-cdn.com/v4/letter/g/6f9a4e/32.png) [@gazpacho](https://boards.straightdope.com/u/gazpacho)\ **Post date:** [March 15, 2017, 4:38am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/9 "2017-03-15T04:38:36Z")
I don’t think that any number have been proven to be normal except numbers specifically constructed to be normal like 0.123456789101112131415161718192021222324… ---
**Author:** ![Airman\_Doors\_USAF](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@Airman\_Doors\_USAF](https://boards.straightdope.com/u/Airman_Doors_USAF)\ **Post date:** [March 15, 2017, 4:46am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/10 "2017-03-15T04:46:02Z")
As pi is non-terminating and non-repeating, your assertion isn’t wrong as much as it is absolutely unprovable. Ultimately it’s the million monkeys on a million typewriters with infinite time producing Hamlet question. It’s almost certain to happen at random sooner or later but there is a non-zero possibility that it won’t. ---
**Author:** ![Velocity](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/velocity/32/18006_2.png) [@Velocity](https://boards.straightdope.com/u/Velocity)\ **Post date:** [March 15, 2017, 5:22am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/11 "2017-03-15T05:22:49Z")
Not a mathematician, but I have a hard time buying the idea that if you have an infinite something X, that it will be bound to contain a certain (something Y) inside it. Saying that pi will have “this is a message for you, I’ve hidden it in pi for you, and I am watching you” as a string in it, seems like saying, “If the universe is infinitely large, then somewhere, there is a planet that is made out of 100% amethyst.”) ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 15, 2017, 5:41am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/12 "2017-03-15T05:41:34Z")
> [@Velocity](#): > > Not a mathematician, but I have a hard time buying the idea that if you have an infinite something X, that it will be bound to contain a certain (something Y) inside it. Saying that pi will have “this is a message for you, I’ve hidden it in pi for you, and I am watching you” as a string in it, seems like saying, “If the universe is infinitely large, then somewhere, there is a planet that is made out of 100% amethyst.”) In many ways this is exactly the same as the more technical point above. Are there additional constraints on the sequence that limit the sequences that can occur (just as the universe really is unlikely to allow an Amethyst planet)? The thing is that there is no reason to believe that there is. The universe has lots of rules. Pi has essentially none in comparison. Absent constraints, it is reasonable to assume Pi is normal and all possible sequences are allowed. You need to come up with rules that add constraints to justify Pi not being normal. So far, none are known. Which isn’t to say there are none. ---
**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 15, 2017, 10:21am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/13 "2017-03-15T10:21:40Z")
Pi does not have “essentially no” rules. It’s 100% rules, and we know all of them. We just don’t understand all of the implications of those rules. Now, it is known that the vast majority of numbers are normal, and so most mathematicians take it for granted that any number will be normal unless there’s some specific reason for it not to be. We don’t know of any such reason for pi, so it’s usually guessed that it’s normal. And it might in principle be possible to prove it. But we don’t _know_. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [March 15, 2017, 10:44am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/14 "2017-03-15T10:44:40Z")
> [@Airman\_Doors\_USAF](#): > > As pi is non-terminating and non-repeating, your assertion isn’t wrong as much as it is absolutely unprovable. Ultimately it’s the million monkeys on a million typewriters with infinite time producing Hamlet question. It’s almost certain to happen at random sooner or later but there is a non-zero possibility that it won’t. There’s no obvious repeating, and its certainly not rational, so therefore can’t end in repeat the following “digits”… But its not clear that the patterns aren’t restricted. Eg Only two A’s in 20 letters of the OP’s code… Its possible but the occurrence of the OP’s string is bordering on “no chance” rather than “bound to happen”. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [March 15, 2017, 11:06am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/15 "2017-03-15T11:06:51Z")
> [@Boozahol\_Squid\_P.I](#): > > Pi’s a weird number, and has all sorts of fun twists, but that message actually isn’t true. .12113111411115111116… is another infinite, non-repeating number series that won’t contain your message. Just out of curiosity, how does this one continue after …9111111111…? ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 15, 2017, 11:51am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/16 "2017-03-15T11:51:25Z")
> [@Chronos](#): > > Pi does not have “essentially no” rules. It’s 100% rules, and we know all of them. We just don’t understand all of the implications of those rules I was alluding to the information content of the rules. Pi has a very small amount of information needed to code what it is. The universe needs a great deal more information to code what its rules are, rules that must include the definition of all the initial conditions and constants to enough accuracy to define the way the universe works - certainly enough to know that amethyst planets won’t (or may) happen. This is a sort of handwaving Kolmogorov complexity. By essentially no rules I mean we can define Pi very easily. So much easier than the physical universe that the information content of the rules defining Pi are vanishingly small in comparison. Whenever you want additional structure in something you need more rules - more information in the complexity metric. As Pi has such a low complexity of definition, it is likely that it has very little complexity in its decimal expansion. Which makes it more likely to be normal. ---
**Author:** ![hammos1](https://avatars.discourse-cdn.com/v4/letter/h/ba8739/32.png) [@hammos1](https://boards.straightdope.com/u/hammos1)\ **Post date:** [March 15, 2017, 12:09pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/17 "2017-03-15T12:09:13Z")
> [@chrisk](#): > > Just out of curiosity, how does this one continue after …9111111111…? Presumably 101111111111, which would mean that such a number would in fact contain all the messages described in the OP. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 15, 2017, 12:16pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/18 "2017-03-15T12:16:58Z")
Thanks, all! I learned about normal numbers from this, which is a brand new idea for me. And I think this factoid becomes even weirder if I tell people: it MIGHT be true, but the ratio of a circle’s circumference to its diameter is too mysterious for us to know if it’s true. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [March 15, 2017, 12:39pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/19 "2017-03-15T12:39:28Z")
But 2 has extremely low Kolmogorov complexity and definitely doesn’t have any non-trivial string in it’s decimal expansion. So the heuristic is quite the opposite: Simple (i.e. finite/computable) algorithm or expression for defining a number suggests it’s _not_ normal. Now there are numbers like all strings over an alphabet listed in length/alphabetic order that contain all strings. So it’s certainly not a rule rule. The vast majority of numbers are normal and don’t have a finite specification. So there’s a lot of overlap, to say the least. But not completely. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [March 15, 2017, 1:46pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/20 "2017-03-15T13:46:53Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Thanks, all! I learned about normal numbers from this, which is a brand new idea for me. And I think this factoid becomes even weirder if I tell people: it MIGHT be true, but the ratio of a circle’s circumference to its diameter is too mysterious for us to know if it’s true. While you’re at it … have your students read _War and Peace_ … supposedly there’s a section where every seventeenth word adds up to _The Lord’s Prayer_ … (or was that General Relativity) … either way, it’ll keep them busy 'til the end of the year … [Next page](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209.md?page=2)