# 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:** 3
**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, 8:36pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/41 "2017-03-15T20:36:33Z")
> [@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. Got to be careful here. Clearly there are _programs_ of finite size that spit out the digits of Pi. But the program _plus its working data_ is not finite state. (And the ZL stuff mostly applies to string-in-string out stuff. Vs. Just string out.) The simplest type of Kolmogorov complexity and such addresses program size only. How much memory the program uses isn’t relevant. So you have to careful here. Are you talking finite program or finite state, etc. (Kudos for putting Ziv before Lempel there. How it got perverted into LZ almost everywhere is beyong me. Even worse is “LZW” where the Big Idea was Welch’s. It really should be “WZL”.) We don’t have to restrict ourselves to “merely” computable numbers. E.g., [Chaitin’s constant](https://en.wikipedia.org/wiki/Chaitin's_constant) is an example of an number that has a finite description which isn’t computable but is normal. It is basically (one of) the “densest” numbers in terms of representing useful information per digit. Even if Pi were normal, it couldn’t be anywhere as good as Ω. Given the first 100 digits of Ω and you could rule the world. ---
**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, 9:53pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/42 "2017-03-15T21:53:17Z")
> [@Chronos](#): > > 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. There appears to be a [theoretical way of doing it](https://arxiv.org/pdf/0912.0303.pdf). I only skimmed through it, but it doesn’t appear to be a practical method. ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [March 15, 2017, 10:23pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/43 "2017-03-15T22:23:50Z")
Isn’t 2\*pi encountered more often (in math) than pi? If so, shouldn’t it be more worthy of discussion? ---
**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, 10:29pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/44 "2017-03-15T22:29:11Z")
> [@Crafter\_Man](#): > > Isn’t 2\*pi encountered more often (in math) than pi? If so, shouldn’t it be more worthy of discussion? [So some say.](https://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/) (But that isn’t really relevant to this particular thread. If you want to discuss pi vs. tau, you should probably start a different thread for that.) ---
**Author:** ![D18](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@D18](https://boards.straightdope.com/u/D18)\ **Post date:** [March 16, 2017, 2:49pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/45 "2017-03-16T14:49:29Z")
> [@watchwolf49](#): > > 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 … FWIW - Had some time to kill during a conference call - lefto doesn’t appear in the first two billion digits of pi. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [March 16, 2017, 3:05pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/46 "2017-03-16T15:05:45Z")
> [@D18](#): > > FWIW - Had some time to kill during a conference call - lefto doesn’t appear in the first two billion digits of pi. We need a BIGGER database … ---
**Author:** ![D18](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@D18](https://boards.straightdope.com/u/D18)\ **Post date:** [March 16, 2017, 3:10pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/47 "2017-03-16T15:10:59Z")
Well, an infinite one would answer the question definitively! 😉 ---
**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 16, 2017, 5:07pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/48 "2017-03-16T17:07:19Z")
Mr. Black Hat says “More Power!” ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [March 16, 2017, 5:26pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/49 "2017-03-16T17:26:40Z")
> [@D18](#): > > Well, an infinite one would answer the question definitively! 😉 But your queries would run for an infinite time. I think the normal timeouts in current DBs are already too long. :mad: ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [March 16, 2017, 5:53pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/50 "2017-03-16T17:53:08Z")
Searching pi for English snippets? If God really had used the digits of pi to encode the History of the World in English, mightn’t he have used a Huffman code? We could find desirable strings earlier then. However, even fixing the bit lengths there are still hundreds of quadrillions of ways to assign a Huffman code. I don’t know how we’re supposed to search for a simple limerick, let alone the Meaning of Life. One thing though — long before you find the Bill of Rights encoded in the digits of pi, I’m afraid you’ll find zillions of versions with the N’th Amendment drastically modified. 😛 :smack: ---
**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 16, 2017, 5:57pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/51 "2017-03-16T17:57:45Z")
“It was the best of times, it was the _blurst_ of times”?? You stupid monkey! ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [March 16, 2017, 6:32pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/52 "2017-03-16T18:32:12Z")
But it would be a lot easier to find arbitrary strings if you don’t require that the strings be ASCII codes. Like, you could invent your own code, and search for your string using DorkCode instead of ASCII. And if you find a string that’s pretty close, no problem, just change your definition of DorkCode to make the digits match the string. Easy! And this is how people find secret messages in the Bible. Can’t find a message using the first word of every chapter? Well, how about the 17th letter on alternating pages? No? How about the 16th on even pages and the 27th on odd pages? Oh, that spells out “O-B-A-M-A-S-U-X” God is speaking to us! ---
**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 16, 2017, 7:16pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/53 "2017-03-16T19:16:02Z")
A=3 B=6 C=7 D=8 E=10 F=11 G=5 L=1 S=4 U=9 Y=2 All the rest of the letters have the other obvious values. 3.141592 = 3. **LSLGUY** In other words, pi is all about _ **me** _! CED\* as they say in the (il)logic biz! - **Coincidum Erad Demonstradum** 😃 ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [March 16, 2017, 8:43pm UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/54 "2017-03-16T20:43:49Z")
> [@LSLGuy](#): > > … > E=10 > F=11 > … > L=1 > … Nitpick: This code lacks the prefix property. In particular note that when our OP, **Left Hand of Dorkness** , finds his name in the digits you can laugh and claim that he’s found **Lellt Hand oll Dorkness** instead! ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [March 17, 2017, 3:16am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/55 "2017-03-17T03:16:54Z")
**Chronos** already noted that normality is more than just containing every finite string; it’s containing every finite string of each given length with equal asymptotic frequency. For terminological convenience, I’ll furthermore note that simply containing every finite string is sometimes called being “disjunctive”. Also, I want to say this: often in these discussions it comes up that “almost all” digit-sequences are normal, and therefore we should expect π’s to be normal. Well, it’s true that there is a familiar probability distribution on digit-sequences such that almost all are normal. But it’s just as well true that there is a probability distribution on digit-sequences such that almost all are non-normal. Or 37%, or any other thing. There are a great many probability distributions on digit-sequences. The relevance of any of the aforementioned ones to the plausibility of π’s normality is tenuous. ---
**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 17, 2017, 3:31am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/56 "2017-03-17T03:31:08Z")
What is “asymptotic frequency” please? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [March 17, 2017, 3:46am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/57 "2017-03-17T03:46:10Z")
Given a finite string S and an infinite sequence W, some of the digits in W are the start of S’s, and some of the digits in W are not the start of S’s. At any particular point finitely far into W, some proportion of its finitely many digits so far have been S-starters. This proportion fluctuates as we go further into W; its limit (in the sense of calculus, presuming you are familiar with this notion) as we go arbitrarily far is the asymptotic frequency of S within W. ---
**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 17, 2017, 4:11am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/58 "2017-03-17T04:11:22Z")
Sorry, I don’t speak Math. It goes over my head. My fault, not yours. Thanks for trying. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 17, 2017, 5:24am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/59 "2017-03-17T05:24:32Z")
A bit more simply, perhaps (but less rigorous): You are playing roulette. You expect, if the wheel is fair, that each number on the wheel–from 00 to 36–to come up equally often. For a small number of spins this won’t happen, but if you spin it a million times, a billion times, and so on, you expect them to come up equally. The “asymptotic frequency” is just how often you see each one come up as you spin more and more times. We can also look at “strings”, which is just a way of looking at more than one number in a row. (00, 00) should come up just as often as (23, 34) (in that order!). Likewise for sequences as long as you want (“every finite string”). This is what is meant by “every finite string of each given length [has] equal asymptotic frequency”. All the single numbers come up equally, as well as all the sequences that are a million numbers long. What this means is that even if we knew that pi contained every finite-length string, unless you can prove it’s “normal”, you don’t know that it doesn’t have huge sections of “123123123123” (or whatever) interspersed by more interesting stuff. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [March 17, 2017, 8:12am UTC](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209/60 "2017-03-17T08:12:55Z")
Yeah; although, even π being normal (without any further quantification on the convergence timing of that normality) would technically have no conflict with it having huge strings doing arbitrary weird bizarre stuff at the beginning. Literally nothing we could possibly observe in any finite number of digits of π has any conflict with π being normal or not; the property is independent of anything in any initial finite segment. [Previous page](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209.md?page=2) [Next page](https://boards.straightdope.com/t/is-this-an-accurate-factoid-about-pi/782209.md?page=4)