# "Messages" (not really) in Pi **URL:** \ **Category:** Factual Questions\ **Created:** [January 7, 2020, 4:04pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073 "2020-01-07T16:04:53Z")\ **Posts on this page:** 16\ **Page:** 4
**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:** [January 12, 2020, 7:16pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/61 "2020-01-12T19:16:57Z")
> [@Chronos](#): > > Huh, based on my understanding of how JPEG works, I would have thought that any defect introduced by a changed byte would be limited to a single 8x8 pixel square. I suppose that I might have learned an older version of the encoding, and it’s now more sophisticated. The DCT step is 8x8 (which is lossy), then a bunch of tricks are thrown in that are lossless including RLE and Huffman. Those two have issues with byte errors depending on where the error is. DCT not so much. ---
**Author:** ![steepone](https://avatars.discourse-cdn.com/v4/letter/s/977dab/32.png) [@steepone](https://boards.straightdope.com/u/steepone)\ **Post date:** [January 13, 2020, 2:19am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/62 "2020-01-13T02:19:24Z")
> [@markn\_1](#): > > I looked out to a billion digits. > Hello (0805121215) appears at position 390,990,395. > John (10150814) appears 12 times in the first billion digits. > God (071504) first appears at 386,707, then at 396,745, 1,222,168, 1,735,723, etc. I count 1007 occurrences of God in the first billion digits. That guy is always scribbling his name on everything. In fact, YHVH (25082208) occurs 8 times too. And Allah (0112120108) appears once at 596,539,269. > Of the people posting in this thread, only DPRK appears, at positions 16,285,229 and 93,869,933. Re the first example ( Hello), can I ask what rule you used to decide the sequence 121215 meant LLO and not ABABAE or even AUUE ---
**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:** [January 13, 2020, 3:09am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/63 "2020-01-13T03:09:06Z")
I’m guessing that it’s the obvious alphabetical one: a = 01, b = 02, etc. ---
**Author:** ![RioRico](https://avatars.discourse-cdn.com/v4/letter/r/f04885/32.png) [@RioRico](https://boards.straightdope.com/u/RioRico)\ **Post date:** [January 13, 2020, 3:29am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/64 "2020-01-13T03:29:39Z")
If the Creators of the Universe embedded a message in Pi, it was not meant for we mere humans on our peripheral planet during our brief window of literacy. So the trick is to decipher who it’s meant for, and how to deal with them if/when they arrive here, guided by our primitive EMF emissions. ---
**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:** [January 13, 2020, 1:05pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/65 "2020-01-13T13:05:08Z")
> [@Dewey\_Finn](#): > > About twenty years ago, there was an [Internet program](https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Random_document_generation) that you could run to simulate a large number of monkeys typing randomly to see if any random string corresponded with text from Shakespeare’s plays. After a ridiculous amount of simulated time (billions of years) passed, the best result was about 24 characters. Here’s a long-running website that simulates Borges’ short story “The Library of Babel”: [https://libraryofbabel.info/](https://libraryofbabel.info/) (Chronos mentioned this story in post #49). It automatically highlights any English words that happen to arise among the gibberish. ---
**Author:** ![davidm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidm/32/225_2.png) [@davidm](https://boards.straightdope.com/u/davidm)\ **Post date:** [January 13, 2020, 1:27pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/66 "2020-01-13T13:27:35Z")
> [@Keeve](#): > > The OP is a major plot point in the novel _Contact_ by Carl Sagan. IIRC they discovered, in a binary expansion of Pi, a statistically unlikely long string of zeroes with a smaller number of ones interspersed. Someone realized that the length of this string was a square number. When they arranged the string in an X by X square the ones formed a perfect circle. I don’t seriously entertain the idea that some higher power could hide a message in Pi, but if I did this is the type of thing I’d expect, rather then something in a human language. ---
**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:** [January 13, 2020, 2:20pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/67 "2020-01-13T14:20:58Z")
> [@davidm](#): > > IIRC they discovered, in a binary expansion of Pi, a statistically unlikely long string of zeroes with a smaller number of ones interspersed. Someone realized that the length of this string was a square number. When they arranged the string in an X by X square the ones formed a perfect circle. > > I don’t seriously entertain the idea that some higher power could hide a message in Pi, but if I did this is the type of thing I’d expect,… As you imply, Sagan was careful to point out that the pattern was certain to occur eventually; the surprise was how early in pi’s expansion it did occur. The simple fraction 16/113 approximates the fractional part of pi to better than 1 part in 10 million. I think over 99.9% of random real numbers will lack such a good approximation. **Coincidence?** _I report, you decide._ √(ln(262537412640768745)^2/163) approximates pi to better than 1 part in 14 trillion quadrillion. **Coincidence?** _I report, you decide._ It might seem impossible for a Higher Power to influence such a pure mathematical constant. But maybe Mathematics is _itself_ the Higher Power! > [@davidm](#): > > rather then something in a human language. Have the Board’s Klingon experts weighed in? ---
**Author:** ![davidm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidm/32/225_2.png) [@davidm](https://boards.straightdope.com/u/davidm)\ **Post date:** [January 13, 2020, 6:14pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/68 "2020-01-13T18:14:34Z")
> [@septimus](#): > > As you imply, Sagan was careful to point out that the pattern was certain to occur eventually; the surprise was how early in pi’s expansion it did occur. > > … Yes, that’s what I meant. I should have stated that explicitly. I also should have used “than” rather than “then”. I do know better, so I’ll just blame it on autocorrect. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [January 13, 2020, 6:25pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/69 "2020-01-13T18:25:19Z")
> [@steepone](#): > > Re the first example ( Hello), can I ask what rule you used to decide the sequence 121215 meant LLO and not ABABAE or even AUUE > [@Chronos](#): > > I’m guessing that it’s the obvious alphabetical one: a = 01, b = 02, etc. Yes, I was using the obvious code, mentioned in post #5 just before my post. Note that using this coding, almost 3/4 of the digit pairs will not code for any letter. So a 10 digit sequence that codes to ANY five characters, even if it’s not a meaningful word, is pretty rare (only occurring on average once in 842 ten-digit sequences). ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [January 13, 2020, 6:30pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/70 "2020-01-13T18:30:06Z")
> [@Dewey\_Finn](#): > > About twenty years ago, there was an [Internet program](https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Random_document_generation) that you could run to simulate a large number of monkeys typing randomly to see if any random string corresponded with text from Shakespeare’s plays. After a ridiculous amount of simulated time (billions of years) passed, the best result was about 24 characters. I never quite grokked the appeal of getting Shakespeare from the million monkeys. We already _got_ Shakespeare. Some due wrote it, I forgot their name. Surely the true fantasy is getting a completely random but transcendentally profound masterwork of random origin ? ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [January 13, 2020, 6:38pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/71 "2020-01-13T18:38:30Z")
Thing about messages in pi is that they are always going to be about as far into the number as your encoding system takes up digits. Unless you are incredibly lucky, “How are you” will be somewhere within 10x of 22 digits in. You ,right get lucky, you might get unlucky. But generally, the index to your your encoded message will be at least as long as the message itself. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 16, 2022, 5:06am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/72 "2022-11-16T05:06:30Z")
> [@Judge\_Phred\_1](#): > > Given that the digits of Pi are infinite, non-repeating and normal, doesn’t that mean that “any” given word, sentence, or entire book are represented in there somewhere? In fact, all words ever written, in any and every order must be in there somewhere. Including this post and also what is written next! Such is the nature of infinity Well, _eventually_ of course. But randomness being what it is, it’s like wondering how long you’d have to stare at a screen of random “snow” before the Mona Lisa appeared momentarily. A mere 10^14 digits of Pi isn’t much to work with. ---
**Author:** ![Bootb](https://avatars.discourse-cdn.com/v4/letter/b/e19b73/32.png) [@Bootb](https://boards.straightdope.com/u/Bootb)\ **Post date:** [November 16, 2022, 5:27am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/73 "2022-11-16T05:27:39Z")
> [@Kobal2](#): > > I never quite grokked the appeal of getting Shakespeare from the million monkeys. We already _got_ Shakespeare. Some due wrote it, I forgot their name. Surely the true fantasy is getting a completely random but transcendentally profound masterwork of random origin ? But if it’s not Shakespeare, how would we be able to tell if it’s any good? ---
**Author:** ![Wallaby](https://avatars.discourse-cdn.com/v4/letter/w/dc4da7/32.png) [@Wallaby](https://boards.straightdope.com/u/Wallaby)\ **Post date:** [November 17, 2022, 4:38am UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/74 "2022-11-17T04:38:45Z")
There are still experimenttal programs underway, to see if endless random typing by barely sentient creatures could produce any useful original works or meaningful insights. The programs have seemingly random names like Twitter, Facebook and Instagram. So far the results are not promising. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [November 19, 2022, 12:58pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/75 "2022-11-19T12:58:46Z")
> [@Judge\_Phred\_1](#): > > Given that the digits of Pi are infinite, non-repeating and normal, doesn’t that mean that “any” given word, sentence, or entire book are represented in there somewhere? In fact, all words ever written, in any and every order must be in there somewhere. NO, not guaranteed, I think there may be words that are impossible to find in pi ? For example, its known the decimal representation favours runs of 9’s, eg the 999 999 starting at the 762th position, This suggests other patterns, like runs of 5’s, may be disfavoured to impossible. ---
**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:** [November 19, 2022, 1:21pm UTC](https://boards.straightdope.com/t/messages-not-really-in-pi/846073/76 "2022-11-19T13:21:15Z")
Pi is believed to be normal. If that’s so, then in the long run, it doesn’t favor runs of 9s, or any other pattern. It so happens that there is a run of six 9s fairly early on, but then, by that sort of argument, you could also say that it favors 3s, 1s, and 4s, since it goes on for a number of digits using nothing but those. That said, however, it is not proven to be normal. It’s known that almost all irrational numbers are normal, but it’s been proven for very few specific irrational numbers, mostly just for ones that were explicitly constructed for that purpose. And there also certainly exist some numbers that aren’t normal, and for all we know, pi (or e or sqrt(2) or phi) might be one of those. [Previous page](https://boards.straightdope.com/t/messages-not-really-in-pi/846073.md?page=3)