# 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:** 2
**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, 1:51pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/21 "2017-03-15T13:51:08Z")
Yeah, I didn’t mean Kolmogorov complexity as the actual measure (hence the “handwaving” comment.). But I was struggling to think of a better simile. The relationship between Kolmogorov complexity and normal is perhaps caught in the Ziv and Lempel result: _A sequence is normal if and only if it is incompressible by any information lossless finite-state compressor._ If you can find a program that spits out the numbers of Pi that is finite in size, Pi isn’t normal. But you can define Pi in geometric terms very simply. That is what I meant by the information content of the definition. Ratio of diameter to circumference in Euclidian space. There are not a lot of terms needed to produce the _definition_. We can create other definitions as well that can start with the usual Peano’s axioms and work up. They are not _constructive_\*. But they are definitions. That is perhaps the key difference. \*Heck if we start on the question of constructive we may decide Pi isn’t actually a number. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [March 15, 2017, 3:11pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/22 "2017-03-15T15:11:53Z")
There are some practical considerations. If you use the ‘01=A’ scheme you have the problem of pairs. About a third of the letter codes require leading zeros. That includes the 3 most common vowels. Then you need to double up for upper case and add some numbers for space etc. So 'Left Hand of ’ becomes ‘38,05,06,20,53,34,01,14,04,53,30,06,53’. definitely has a 0/3 bias that is likely to continue. Of course you could use a pseudo-random series to select the pairs. That would remove the bias. I’m an addictive number fondler, but I don’t believe this leads anyplace. Crane ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [March 15, 2017, 3:15pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/23 "2017-03-15T15:15:18Z")
Whether any given sequence can be found isn’t “absolutely unknowable” as you might actually find it. Showing that a certain sequence cannot be found is most likely absolutely unprovable. My best guess is that the probability of finding some given sequence is 100%, in fact the probability of finding it infinitely often is 100%, but not certain. That illustrates one difference between infinite sets and finite ones. As an example, choose a real number at random. The chances that it is rational are exactly 0, but that doesn’t mean it couldn’t be rational. Not at all. Blow your mind? It should. But in technical terms it means nothing other than that the measure (in the technical sense) of the set of rationals is 0. Even the set of algebraic numbers (those satisfying a polynomial equation with rational coefficients) has measure 0, as does every other countable set. ---
**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, 3:24pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/24 "2017-03-15T15:24:49Z")
> [@Crane](#): > > There are some practical considerations. If you use the ‘01=A’ scheme you have the problem of pairs. About a third of the letter codes require leading zeros. That includes the 3 most common vowels. Then you need to double up for upper case and add some numbers for space etc. So 'Left Hand of ’ becomes ‘38,05,06,20,53,34,01,14,04,53,30,06,53’. definitely has a 0/3 bias that is likely to continue. I’m not sure that’s relevant though. If pi is indeed normal, then 38050620533401140453300653 is just as likely to appear, or appears just as frequently, as any other sequence of digits of the same length—regardless of the fact that it contains more than the “expected” number of 0’s. ---
**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, 3:37pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/25 "2017-03-15T15:37:41Z")
> [@Thudlow\_Boink](#): > > I’m not sure that’s relevant though. If pi is indeed normal, then 38050620533401140453300653 is just as likely to appear, or appears just as frequently, as any other sequence of digits of the same length—regardless of the fact that it contains more than the “expected” number of 0’s. That’s what I was thinking as well. A lot of this discussion is over my head–I took no math after precal–but I’m trying to keep afloat here :). But yeah, if you suggest that a string with an uneven distribution of digits is not possible, then any string is impossible, since it’s made up of very short strings (one digit long) with uneven distribution of digits. The fact that a particular string is really, really unlikely within any finite larger string is, I think, irrelevant, since we’re not talking about finding it within a finite string. The only important question, as I understand it, is whether pi is normal. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [March 15, 2017, 3:39pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/26 "2017-03-15T15:39:40Z")
> [@watchwolf49](#): > > 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 … “Paul is dead…Paul is dead…” ---
**Author:** ![Fotheringay-Phipps](https://avatars.discourse-cdn.com/v4/letter/f/d9b06d/32.png) [@Fotheringay-Phipps](https://boards.straightdope.com/u/Fotheringay-Phipps)\ **Post date:** [March 15, 2017, 4:11pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/27 "2017-03-15T16:11:17Z")
Seen elsewhere: _An infinite number of rednecks, shooting an infinite number of shotguns, at an infinite number of streetsigns, will eventually produce all Shakepeare’s plays in Braille._ ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [March 15, 2017, 4:18pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/28 "2017-03-15T16:18:37Z")
> [@Left\_Hand\_of\_Dorkness](#): > > That’s what I was thinking as well. A lot of this discussion is over my head–I took no math after precal–but I’m trying to keep afloat here :). > > But yeah, if you suggest that a string with an uneven distribution of digits is not possible, then any string is impossible, since it’s made up of very short strings (one digit long) with uneven distribution of digits. > > The fact that a particular string is really, really unlikely within any finite larger string is, I think, irrelevant, since we’re not talking about finding it within a finite string. The only important question, as I understand it, is whether pi is normal. You might not have taken too much later math, but so far your intuition is spot-on. And yes, whether pi [is/is not] normal is the only significant issue. ---
**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, 6:44pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/29 "2017-03-15T18:44:28Z")
I think I did this right … the first time “Le” appears in pi is starting at the 70,429th digit … I get an error for “Lef” in the first million digits … we’ll need someone with a more robust computer to this I think … ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [March 15, 2017, 6:55pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/30 "2017-03-15T18:55:43Z")
> [@watchwolf49](#): > > I think I did this right … the first time “Le” appears in pi is starting at the 70,429th digit … I get an error for “Lef” in the first million digits … we’ll need someone with a more robust computer to this I think … We’re looking for 125, right? That happens at the 1350th digit after the decimal point. 12520 happens at the 1843rd digit. > **[The Pi-Search Page](https://www.angio.net/pi/)** > > Search for any string of digits in the first 200 million digits of Pi Never mind. I see it’s 01 for A. ---
**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, 7:03pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/31 "2017-03-15T19:03:02Z")
> [@x-ray\_vision](#): > > We’re looking for 125, right? That happens at the 1350th digit after the decimal point. 12520 happens at the 1843rd digit. > > [The Pi-Search Page](http://www.angio.net/pi/) > > Never mind. I see it’s 01 for A. Thanks for the link … “left” occurs at digit 134,962,706 … “lefto” doesn’t in the first 200,000,000 … we need a bigger database … ---
**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:** [March 15, 2017, 7:12pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/32 "2017-03-15T19:12:47Z")
> [@x-ray\_vision](#): > > We’re looking for 125, right? That happens at the 1350th digit after the decimal point. 12520 happens at the 1843rd digit. > > [The Pi-Search Page](http://www.angio.net/pi/) > > Never mind. I see it’s 01 for A. Using the op’s numbering, I find 12 05 06 21 (“left”) at position 32840320. " 1205 (“le”) is in position 3328. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [March 15, 2017, 7:16pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/33 "2017-03-15T19:16:36Z")
To a billion digits: [http://three.onefouronefive.net/](http://three.onefouronefive.net/) ---
**Author:** ![octopus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/octopus/32/3716_2.png) [@octopus](https://boards.straightdope.com/u/octopus)\ **Post date:** [March 15, 2017, 7:57pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/34 "2017-03-15T19:57:46Z")
> [@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. With your example it does have a probability of 1 though. ---
**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, 8:07pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/35 "2017-03-15T20:07:40Z")
> [@](#): > > Quoth **Francis Vaughan** : > > The relationship between Kolmogorov complexity and normal is perhaps caught in the Ziv and Lempel result: > A sequence is normal if and only if it is incompressible by any information lossless finite-state compressor. > > If you can find a program that spits out the numbers of Pi that is finite in size, Pi isn’t normal. That can’t be it, because you can in fact write a finite program that spits out the digits of pi. That’s how people get these lists of the first billion digits of pi, or the like. And the question isn’t quite precisely one of whether pi is normal, either. In a truly normal number, every sequence of digits of a given length shows up, _with equal frequency_ (in other words, 24601 is just as common as 12345 or 86753 or whatever). The OP’s statement didn’t say anything about the frequency, so it’s a slightly weaker condition. ---
**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, 8:14pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/36 "2017-03-15T20:14:41Z")
> [@Chronos](#): > > That can’t be it, because you can in fact write a finite program that spits out the digits of pi. That’s how people get these lists of the first billion digits of pi, or the like. > > And the question isn’t quite precisely one of whether pi is normal, either. In a truly normal number, every sequence of digits of a given length shows up, _with equal frequency_ (in other words, 24601 is just as common as 12345 or 86753 or whatever). The OP’s statement didn’t say anything about the frequency, so it’s a slightly weaker condition. Related question: is it possible to figure out pi’s digits without starting from scratch? That is, let’s say for some reason I want to know the quintillionth digit in pi. Is there any way to find that out without first finding every digit before that one? ---
**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:** [March 15, 2017, 8:18pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/37 "2017-03-15T20:18:15Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Related question: is it possible to figure out pi’s digits without starting from scratch? > > That is, let’s say for some reason I want to know the quintillionth digit in pi. Is there any way to find that out without first finding every digit before that one? [Yes.](https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula) ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [March 15, 2017, 8:19pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/38 "2017-03-15T20:19:39Z")
> [@Left\_Hand\_of\_Dorkness](#): > > That is, let’s say for some reason I want to know the quintillionth digit in pi. Is there any way to find that out without first finding every digit before that one? [https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml](https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml) ---
**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, 8:32pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/39 "2017-03-15T20:32:13Z")
Note that that method only works for base 16 (or for other bases which are a power of 2). No such formula is known for base 10, nor for any other base. I would say that it’s probably impossible, but then, until the discovery of that formula for base 16, I would have said that’s probably impossible, too: I think it’s safe to say that the mathematical world was rather surprised by that one. ---
**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, 8:35pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/40 "2017-03-15T20:35:02Z")
Woah. That’s amazing–and thanks to both of y’all for the cite! However, and pardon my possibly-silly question: this formula seems to give the hexadecimal digit. Is there any way to translate from that to the base-10 digit? Edit: YOU GUYS ARE ANSWERING MY QUESTIONS BEFORE I ASK THEM! [Previous page](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209.md?page=1) [Next page](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209.md?page=3)