# Could I get a piece of pi? **URL:** \ **Category:** Factual Questions\ **Created:** [December 17, 2011, 3:48pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542 "2011-12-17T15:48:32Z")\ **Posts on this page:** 14\ **Page:** 2
**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:** [December 17, 2011, 8:59pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/21 "2011-12-17T20:59:12Z")
> [@Czarcasm](#): > > Very interesting. The string “11111111” occurs at position 159,090,113. Can I assume that 9 "1"s are the max? If I understand correctly, pi being normal (which is widely believed but not known) would mean there is no max: a string of 1’s of _any_ particular length would appear somewhere within the digits of pi. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 17, 2011, 9:56pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/22 "2011-12-17T21:56:06Z")
> [@Czarcasm](#): > > Very interesting. The string “11111111” occurs at position 159,090,113. Can I assume that 9 "1"s are the max? Why would you assume that? ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 18, 2011, 10:13am UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/23 "2011-12-18T10:13:39Z")
Referring to finding 236592 in there somewhere: > [@Snarky\_Kong](#): > > **Walton Firm** , that’s the brute force method. First compile digits of pi, then search for the sequence. Well, the brute force method would be compile the digits until you get to the sequence you want, but that’s close enough. **Walt** was simply responding to post #2 above, in which **DCnDC** says: [QUOTE=DCnDC] For what it’s worth, I didn’t find “236592” in there, but I’m assuming that was just a number you chose arbitrarily. [/quote] Yes, 236592 is too in there, and not all that far in either. ---
**Author:** ![Walton\_Firm](https://avatars.discourse-cdn.com/v4/letter/w/45deac/32.png) [@Walton\_Firm](https://boards.straightdope.com/u/Walton_Firm)\ **Post date:** [December 18, 2011, 1:36pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/24 "2011-12-18T13:36:26Z")
Indeed, I’m aware that the OP is asking for a non-bruteforce method; I just thought that since the consensus seems to be that no such method is known or likely to exist, some people in this thread might find that site interesting… ---
**Author:** ![AaronX](https://avatars.discourse-cdn.com/v4/letter/a/7bcc69/32.png) [@AaronX](https://boards.straightdope.com/u/AaronX)\ **Post date:** [December 18, 2011, 2:42pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/25 "2011-12-18T14:42:50Z")
I wonder - what’s the longest string that has the same value as the position of its starting digit? So far I got “5”. Hmm… ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [December 18, 2011, 3:50pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/26 "2011-12-18T15:50:40Z")
So you’d need the string “143” to start in the 143rd place? 90 two-digit strings, so a 1 - 0.99^90 = 0.59527 chance of there being at least one. 900 three-digit strings, so a 1 - 0.999^900 = 0.59631 chance of there being at least one. etc. Apparently converging to 1 - exp(-0.9) That’s using Octave, and I don’t know if it’s handling the rounding off correctly, but if it is, it looks like about a 59% chance for each string length. That’s ignoring strings beginning with a leading 0. Including those, it goes up to 63% chance for each string length. ---
**Author:** ![kaltkalt](https://avatars.discourse-cdn.com/v4/letter/k/bb73d2/32.png) [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)\ **Post date:** [December 18, 2011, 6:15pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/27 "2011-12-18T18:15:52Z")
There is no evidence that pi is fractal. In fact, quite the contrary - if it were fractal it would not be an irrational number, as there would be a pattern to it. The premise of the post linked to in the OP is the same premise behind the old notion that if you give an infinite number of monkeys an infinite number of typewriters one of them will eventually write Hamlet, or War and Peace, or type out the meaning of life. It seems right but it’s not, and it’s just a product of the human mind’s inability to truly grasp the concept of infinity. Pi is infinitely long (this can be proven). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 18, 2011, 7:49pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/28 "2011-12-18T19:49:52Z")
> [@kaltkalt](#): > > There is no evidence that pi is fractal. In fact, quite the contrary - if it were fractal it would not be an irrational number, as there would be a pattern to it. A) What do you mean by “fractal”? B) There’s nothing preventing digit-sequences with patterns to them from representing irrational numbers; they just can’t be of the particular form of eventually-cyclic patterns. E.g., as noted above, numbers such as 0.012345678910111213141516… or 0.101001000100001000001… have a very clear pattern to them, but are irrational all the same. > [@](#): > > The premise of the post linked to in the OP is the same premise behind the old notion that if you give an infinite number of monkeys an infinite number of typewriters one of them will eventually write Hamlet, or War and Peace, or type out the meaning of life. It seems right but it’s not, and it’s just a product of the human mind’s inability to truly grasp the concept of infinity. Pi is infinitely long (this can be proven). What’s that got to do with anything? Of course pi’s decimal sequence is “infinitely long” (i.e., does not eventually become constantly 0); that’s part of what fuels the OP’s hope that every particular finite decimal string appears within it. Why do you say “It seems right but it’s not”? It’s certainly plausible that every finite decimal string appears in the expansion of pi somewhere; indeed, it’s never been disproven and is near-universally believed to be true, even by mathematicians (though, granted, it’s never actually been proven either). ---
**Author:** ![kaltkalt](https://avatars.discourse-cdn.com/v4/letter/k/bb73d2/32.png) [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)\ **Post date:** [December 18, 2011, 10:11pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/29 "2011-12-18T22:11:54Z")
By fractal I mean it has an internal grand scheme of underlying patterns, something an irrational number does not have. Picking a random string of 15 digits out of said irrational number and saying it has a pattern proves nothing. And I do not believe an infinite number of chimps (or an infinitely long, random string of numbers) would ever produce/contain the words to the novel War and Peace (consider it a specific string of 20 million numbers, or however many individual characters are in that novel, including numbers, punctuation and spaces. It would take an infinite amount of time for that to happen, thus it would never happen. Not after a billion years, not after a billion billion years. But that’s another debate, probably for ‘great debates’ I’m just saying the post cited by the OP is derivative of this question. The infinitely long string of pi can be the combined output of the infinite number of monkeys, etc. ---
**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:** [December 18, 2011, 10:48pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/30 "2011-12-18T22:48:58Z")
> [@kaltkalt](#): > > By fractal I mean it has an internal grand scheme of underlying patterns, something an irrational number does not have. Patterns (or their absence) are not part of the definition of what makes an irrational number. Irrational numbers are just those that cannot be represented by simple fractions, for example, 22/7 is an approximation of pi, but 22/7 is a rational number (a ratio), whereas pi isn’t. > [@](#): > > And I do not believe an infinite number of chimps (or an infinitely long, random string of numbers) would ever produce/contain the words to the novel War and Peace (consider it a specific string of 20 million numbers, or however many individual characters are in that novel, including numbers, punctuation and spaces. It would take an infinite amount of time for that to happen, thus it would never happen. Not after a billion years, not after a billion billion years. But that’s another debate, probably for ‘great debates’ I’m just saying the post cited by the OP is derivative of this question. The infinitely long string of pi can be the combined output of the infinite number of monkeys, etc. The monkeys/typewriters thing is a finite task - just a very big one. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [December 18, 2011, 10:50pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/31 "2011-12-18T22:50:00Z")
> [@kaltkalt](#): > > By fractal I mean it has an internal grand scheme of underlying patterns, something an irrational number does not have. Picking a random string of 15 digits out of said irrational number and saying it has a pattern proves nothing. Two comments: [ol] [li]Don’t use the word fractal that way, because no one will know what the hell you’re talking about.[/li][li]Irrational numbers can have patterns, just not repeating decimal expansions. For instance, any irrational number which satisfies a quadratic equation with integer coefficients has a [periodic continued fraction expansion](https://en.wikipedia.org/wiki/Periodic_continued_fraction).[/li][/ol] ---
**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:** [December 18, 2011, 10:59pm UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/32 "2011-12-18T22:59:15Z")
> [@kaltkalt](#): > > By fractal I mean it has an internal grand scheme of underlying patterns, something an irrational number does not have. Picking a random string of 15 digits out of said irrational number and saying it has a pattern proves nothing. Pi is irrational. “An irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number.” Irrational has nothing to do with internal patterns. It means only that it cannot be expressed by a terminating or repeated decimal. > [@](#): > > And I do not believe an infinite number of chimps (or an infinitely long, random string of numbers) would ever produce/contain the words to the novel War and Peace (consider it a specific string of 20 million numbers, or however many individual characters are in that novel, including numbers, punctuation and spaces. It would take an infinite amount of time for that to happen, thus it would never happen. Not after a billion years, not after a billion billion years. But that’s another debate, probably for ‘great debates’ I’m just saying the post cited by the OP is derivative of this question. The infinitely long string of pi can be the combined output of the infinite number of monkeys, etc. This is not debatable. It’s pure math. If the expression of pi exists as generally understood, if not proven, today then it will contain any specific string of 20 million numbers.\* It will do so at a finite place in the expansion. That may be very far out but not infinitely so. In fact, there’s no such thing as infinitely far out. Infinite means endless. Any place in an expansion you can define is finite, and can be reached in finite time and expressed in a finite amount of symbols. That’s definitional, the way irrational is definitional. - More than that. You can find any definite string of 20 million number repeated 20 million times in a row and also find it repeated 20 million times followed by a 9 and then repeated 20 million more times. And anything else you can define. Yet all of these will be found a finite number of digits into the expansion. Infinity is mind-blowing and yet well-defined. ---
**Author:** ![kaltkalt](https://avatars.discourse-cdn.com/v4/letter/k/bb73d2/32.png) [@kaltkalt](https://boards.straightdope.com/u/kaltkalt)\ **Post date:** [December 19, 2011, 6:21am UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/33 "2011-12-19T06:21:38Z")
FWIW I meant to say pi is a transcendental number rather (or in addition to) an irrational one. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 19, 2011, 6:34am UTC](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542/34 "2011-12-19T06:34:03Z")
Being a transcendental number does not rule out having a pattern to one’s digits. E.g., [Champernowne’s constant](http://en.wikipedia.org/wiki/Champernowne_constant), 0.123456789101112131415…, whose digits follow quite a simple pattern indeed, is transcendental. (In case you are not aware of the actual definition of “transcendental”, it is this: a number is called “algebraic” if it is a root of some nonzero polynomial with integer coefficients. And “transcendental” is a fancy word for “non-algebraic”.) [Previous page](https://boards.straightdope.com/t/could-i-get-a-piece-of-pi/606542.md?page=1)