5 ms·
Six Nines in Pi
- nategri 7y agoGets me thinking about then ending of the book version of Contact.
- 0xdeadbeefbabe 7y agoA more numinous ending at that.
- nvusuvu 7y agoI wonder what the longest known streak of identical digits is in pi. Also, does the sequence 0123456789 happen any in location of the known digits of pi?
- hx2a 7y agoUsing this website: https://www.angio.net/pi/digits.html https://www.angio.net/pi/digits.html I can search for the sequence 0123456789. It is not found in the first 200M digits.
- dmurray 7y agoThere's a sequence of thirteen eights, and twelve of each of the other digits, documented at [0] which covers the first 2.7 trillion digits. Based on that you can be all but certain any given ten-digit sequence, including 0123456789, has also been found. [0] https://bellard.org/pi/pi2700e9/pidigits.html https://bellard.org/pi/pi2700e9/pidigits.html
- ksaj 7y agoIt surely does appear somewhere. But it isn't within the first 2 billion digits.
- snagglegaggle 7y agoLo! Technology: https://www.angio.net/pi/ https://www.angio.net/pi/
- BlackLotus89 7y ago17,387,594,880 http://mathworld.wolfram.com/PiDigits.html http://mathworld.wolfram.com/PiDigits.html
- klyrs 7y agoI dunno about "known" but you can get a billion digits pretty easy. $ wget https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt $ grep -ob 012345678 pi-billion.txt 956753746:012345678 $ grep -ob 0123456789 pi-billion.txt $ So close, and amusingly close to the end of the file!
- hx2a 7y agoI love how Wikipedia contains these weird little nuggets of knowledge, and I love how they keep showing up on Hacker News.
- vadansky 7y agoSomewhat related: https://github.com/philipl/pifs https://github.com/philipl/pifs If the expansion of pi is normal then all your data is already in it
- 0-_-0 7y agoAnd you can compress any data as the index at which it occurs in pi!!!1!
- jacobkg 7y agoCan the index be reliably represented in fewer bytes than the data itself?
- jameshart 7y agothis question is equivalent to asking a physicist about a machine, ‘but can it reliably do more work than you put in to it?’ The equivalent of the law of thermodynamics in this case is the pigeonhole principle.
- ramshorns 7y agoIn fact, no compression scheme can reliably compress data to fewer bytes than it started as, thanks to the pigeonhole principle.
- CydeWeys 7y agoNope. On average it takes much more information to represent the index than the data itself. "Compress" is definitely a misnomer here.
- deleted 7y ago[deleted]
- ashton314 7y agoIs there a proof that says that any arbitrary finite sequence of digits will appear somewhere in the digits of pi? Are there finite sequences known to never appear?
- marktani 7y agoWow, your question led to some Wikipedia research on my end, and I found this: 'In particular, the popular claim "every string of numbers eventually occurs in π" has not been proven.' I think I claimed this before. Oops! Quote from https://en.m.wikipedia.org/wiki/Normal_number https://en.m.wikipedia.org/wiki/Normal_number.
- im3w1l 7y agoIt's a common misconception
- ars 7y agoSee https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number Answer: No one knows, but we assume Pi is normal.
- AlexCoventry 7y agoThe probability that that's the case is 1, but that's not the same as a proof.
- nine_k 7y agoNot in digits of pi necessarily (needs a proof), but indeed in any truly random character sequence with independent probabilities of characters; you can easily calculate the probability of it, exponentially decreasing with number of characters in the desired sequence.
- jokoon 7y agowould be cool to have the same thing for other bases
- jeffwass 7y agoI wondered the same thing, surprised it wasn’t mentioned in the Wikipedia article.
- stOneskull 7y agoYeah. It doesn't seem like pi is meant to be base10
- _bxg1 7y agoThis kind of trivia is my favorite thing to find on HN
- sp332 7y agoThe digits "360" are centered at the 360th digit. [Edit: if you include the leading 3 before the decimal, which Wikipedia doesn't.]
- sp332 7y agohttps://dilbert.com/strip/2001-10-25 https://dilbert.com/strip/2001-10-25
- Aperocky 7y agoAll my passwords are conveniently stored in the constant Pi
- hinkley 7y agoNow I'm adding √-1 to all my passwords.
- codesushi42 7y agoNow that's one complex password, I'd imagine.
- hinkley 7y agoHmmm, on second thought, maybe i shouldn't be involved.
- gblanchette 7y agoThe first missing prime in the first million digits of pi is 100057 ( https://primes.utm.edu/curios/page.php?short=100057 https://primes.utm.edu/curios/page.php?short=100057).
- dvt 7y agoPi is conjectured[1], though not proved, to be normal. If true (likely), we can expect to find Moby Dick in its entirety somewhere in 𝛑, along with tomorrow's news of the day. Eventually, we'll find a string of digits nnnn....nnnn that's going to be longer than the number of particles in our universe. Of course, there's also a lot of gibberish. [1] http://info.sjc.ox.ac.uk/users/gualtieri/Is%20Pi%20normal.htm http://info.sjc.ox.ac.uk/users/gualtieri/Is%20Pi%20normal.ht...
- dantondwa 7y agoThis reminds me of Borges' Library of Babel: https://libraryofbabel.info/libraryofbabel.html https://libraryofbabel.info/libraryofbabel.html
- happytoexplain 7y agoYes, there's no mathematical significance, but finding such a thing so early is emotionally intriguing to some humans, myself included.
- 8bitsrule 7y agoThe people who produced 800-1160-digit approximations of pi before computers ... back in the late 1940s (e.g. Wrench & Smith) ... used electro-mechanical calculators (e.g. Marchant). That (doomed) technology is well-documented here: http://www.vintagecalculators.com/ http://www.vintagecalculators.com/