# Monkeys & Pi **URL:** \ **Category:** Factual Questions\ **Created:** [June 13, 2004, 5:56pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147 "2004-06-13T17:56:50Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![flex727](https://avatars.discourse-cdn.com/v4/letter/f/258eb7/32.png) [@flex727](https://boards.straightdope.com/u/flex727)\ **Post date:** [June 13, 2004, 5:56pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/1 "2004-06-13T17:56:50Z")
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 will occur somewhere in Pi? Interesting tidbit: [Pi to one million digits](http://3.141592653589793238462643383279502884197169399375105820974944592.com/) Don’t you just love that URL? ---
**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:** [June 13, 2004, 6:04pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/2 "2004-06-13T18:04:26Z")
Yes, the concept that if the digits in pi are random and normally distributed then all finite sequences are encoded in it has been bandied around for quite a while. There is a good discussion of it [here](http://sprott.physics.wisc.edu/pickover/pimatrix.html). ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 13, 2004, 6:11pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/3 "2004-06-13T18:11:19Z")
> [@flex727](#): > > Pi is an infinte, non-repeating decimal. Does it therefore follow that any finite number string will occur somewhere in Pi? No. Pi may have that property, but it doesn’t follow from what you’ve stated. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [June 13, 2004, 6:21pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/4 "2004-06-13T18:21:38Z")
[You can search for your number in the first 100 million digits of pi.](http://www.angio.net/pi/piquery) It seems like pretty much any 7-digit number you can think of is within these digits. ---
**Author:** ![carterba](https://avatars.discourse-cdn.com/v4/letter/c/85e7bf/32.png) [@carterba](https://boards.straightdope.com/u/carterba)\ **Post date:** [June 13, 2004, 10:14pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/5 "2004-06-13T22:14:24Z")
I searched for the first 10 digits of e (2.718281828). No match. Is there a page that lets me search for number strings in e? I Googled “e-search”, but that returned all kinds of spurious matches… ---
**Author:** ![Garfield226](https://avatars.discourse-cdn.com/v4/letter/g/9e8a1a/32.png) [@Garfield226](https://boards.straightdope.com/u/Garfield226)\ **Post date:** [June 13, 2004, 10:25pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/6 "2004-06-13T22:25:32Z")
> [@carterba](#): > > I searched for the first 10 digits of e (2.718281828). No match. According to [this page](http://www.angio.net/pi/piquery#likely), there’s only about a 1% likelyhood of finding any 10-digit string in the first 100 million digits of Pi. Additionally, if you chop off the last two digits and just search for 27182818, it’s there. ---
**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:** [June 13, 2004, 11:42pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/7 "2004-06-13T23:42:29Z")
> [@ultrafilter](#): > > No. Pi may have that property, but it doesn’t follow from what you’ve stated. For example, 0.1 0 1 00 1 000 1 0000 1 00000 1 000000 1 … [spaces added to make the pattern easier to recognize] is an infinite, non-repeating decimal (i.e. an irrational number), but it’s pretty easy to think of finite number strings that do not appear within its digits! ---
**Author:** ![Trigonal\_Planar](https://avatars.discourse-cdn.com/v4/letter/t/0ea827/32.png) [@Trigonal\_Planar](https://boards.straightdope.com/u/Trigonal_Planar)\ **Post date:** [June 14, 2004, 2:27am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/8 "2004-06-14T02:27:24Z")
Similar to the above post, one way you could think of it is that its entirely possible that pi “degenerates” into a series of 1’s and 0’s. In this case, there would be many strings that could not occur. ---
**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:** [June 14, 2004, 2:56am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/9 "2004-06-14T02:56:38Z")
> [@Exapno Mapcase](#): > > Yes, the concept that if the digits in pi are random and normally distributed then all finite sequences are encoded in it has been bandied around for quite a while. There is a good discussion of it [here](http://sprott.physics.wisc.edu/pickover/pimatrix.html). Hmm, Carl Sagan’s book \* contact\* finishes with the heroine finding a message from God coded into the digits of Pi. Does this mean that the message really is in there, somewhere? And _I, the jury_ by Mickey Spillane? The New York Telephone directory? ---
**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:** [June 14, 2004, 3:00am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/10 "2004-06-14T03:00:22Z")
I answered what the OP meant, and not what was written. If you don’t do that you can’t get anything done around this place. 🙂 It’s true that nobody knows if pi - or any other math constant - is normal. But there’s been some progress in the investigation, as [this article](http://www.lbl.gov/Science-Articles/Archive/pi-random.html) indicates. Newer links to Bailey and Crandall work can be found on [Bailey’s web site](http://crd.lbl.gov/~dhbailey/). And you can now [search for your name in pi](http://pisearch.lbl.gov/). ---
**Author:** ![Meeko](https://avatars.discourse-cdn.com/v4/letter/m/e495f1/32.png) [@Meeko](https://boards.straightdope.com/u/Meeko)\ **Post date:** [June 14, 2004, 4:29am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/11 "2004-06-14T04:29:09Z")
Ok, get your can of worms at the ready… On Pi being a ‘random’ number; Isn’t Pi the number of times the length of the diameter of circle ‘A’ can divide evenly into the length of the circumference of circle ‘A’ ? By defintion, since we “know” that Pi has to have this characteristic, isn’t its value preset? Therefore, Pi can not be random; We can never know the exact value of Pi, yet it is not “random”, it is simply unknown (in full). ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [June 14, 2004, 4:44am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/12 "2004-06-14T04:44:01Z")
> [@carterba](#): > > Is there a page that lets me search for number strings in e? I Googled “e-search”, but that returned all kinds of spurious matches… I couldn’t find one either. I found one that converted _e_ to base 27 and lets you search for your [name](http://www.angelfire.com/mt/ofolives/esearch.html) in it, but it appears to be broken. If I can find a site with a list of the first few million digits of _e_, I can slap together a PHP or Perl script to search through it. ---
**Author:** ![JimOfAllTrades](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@JimOfAllTrades](https://boards.straightdope.com/u/JimOfAllTrades)\ **Post date:** [June 14, 2004, 8:15am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/13 "2004-06-14T08:15:29Z")
> [@Meeko](#): > > Ok, get your can of worms at the ready… > > On Pi being a ‘random’ number; > > Isn’t Pi the number of times the length of the diameter of circle ‘A’ can divide evenly into the length of the circumference of circle ‘A’ ? > > By defintion, since we “know” that Pi has to have this characteristic, isn’t its value preset? > > Therefore, Pi can not be random; We can never know the exact value of Pi, yet it is not “random”, it is simply unknown (in full). Disclaimer: I’m not a mathematician. My formal training in math stopped about 30 years ago, just after trig and before calculus. So if I screw something up, I hope one of the real math people will correct me. I don’t think anyone is saying that pi is a random number. I think they’re saying that while the value of pi is known, the expression of that value in base 10 involves an infinite string of the digits 0 through 9 in what approximates a random pattern. In other words the digits 0 through 9 all appear with about the same frequency, no patterns are apparent, and we can’t predict what the next digit will be based on the digits already appearing (we can always calculate the next digit of course, but we can’t predict it based on any pattern). ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [June 14, 2004, 8:21am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/14 "2004-06-14T08:21:23Z")
> [@Peter Morris](#): > > Hmm, Carl Sagan’s book \* contact\* finishes with the heroine finding a message from God coded into the digits of Pi. Does this mean that the message really is in there, somewhere? She was looking for sequences that are grossly above random chance. IIRC, the pattern she found was something like over 100 digits of 1’s and 0’s arranged into a circle. Not something that is likely to appear in any random sequence we could search through in our lifetimes. ---
**Author:** ![InvidiousCourgette](https://avatars.discourse-cdn.com/v4/letter/i/e47c2d/32.png) [@InvidiousCourgette](https://boards.straightdope.com/u/InvidiousCourgette)\ **Post date:** [June 14, 2004, 10:27am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/15 "2004-06-14T10:27:21Z")
As the link \*\*Exapno Mapcase \*\* indicates, you can expect to find, on average, 1 instance of \*every \* N digit number in the first 10^N digits of pi. The complete works of Shakespeare contains something like 800 000 words of text. We could express those words with a 12 800 000 digit number, say. So that means we can expect to find the complete works of Shakespeare, with no errors, in the first 10^12 800 000 digits of pi! ---
**Author:** ![bienville](https://avatars.discourse-cdn.com/v4/letter/b/4bbf92/32.png) [@bienville](https://boards.straightdope.com/u/bienville)\ **Post date:** [June 14, 2004, 11:08am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/16 "2004-06-14T11:08:08Z")
14 replies and no one has said it. Wow. On one hand this could mean we are evolving and maturing as a community. Still, there is something to be said for tradition. When come back, bring **Pi**! ---
**Author:** ![bienville](https://avatars.discourse-cdn.com/v4/letter/b/4bbf92/32.png) [@bienville](https://boards.straightdope.com/u/bienville)\ **Post date:** [June 14, 2004, 11:10am UTC](https://boards.straightdope.com/t/monkeys-pi/250147/17 "2004-06-14T11:10:13Z")
P.S. Silver is not the color to use if you want the text to be cleverly invisible. :smack: Slate Gray? Dim Gray? Regular Gray? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 14, 2004, 1:22pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/18 "2004-06-14T13:22:58Z")
> [@Meeko](#): > > Ok, get your can of worms at the ready… > > On Pi being a ‘random’ number; > > Isn’t Pi the number of times the length of the diameter of circle ‘A’ can divide evenly into the length of the circumference of circle ‘A’ ? > > By defintion, since we “know” that Pi has to have this characteristic, isn’t its value preset? > > Therefore, Pi can not be random; We can never know the exact value of Pi, yet it is not “random”, it is simply unknown (in full). What does “random” mean again? ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [June 14, 2004, 1:59pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/19 "2004-06-14T13:59:03Z")
Just to make a tiny contribution… [Mathworld](http://mathworld.wolfram.com/NormalNumber.html) has an entry on _normal_ numbers that might be illuminating. ---
**Author:** ![asterion](https://avatars.discourse-cdn.com/v4/letter/a/4da419/32.png) [@asterion](https://boards.straightdope.com/u/asterion)\ **Post date:** [June 14, 2004, 2:04pm UTC](https://boards.straightdope.com/t/monkeys-pi/250147/20 "2004-06-14T14:04:23Z")
> [@pulykamell](#): > > [You can search for your number in the first 100 million digits of pi.](http://www.angio.net/pi/piquery) It seems like pretty much any 7-digit number you can think of is within these digits. Neat. I found my phone numbers but it couldn’t handle the area code. [Next page](https://boards.straightdope.com/t/monkeys-pi/250147.md?page=2)