Six Nines in Pi | Hacker News Reader

Six Nines in Pi

en.wikipedia.org

60 pointsphonebucket39 comments

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Somewhat related:

https://github.com/philipl/pifs

If the expansion of pi is normal then all your data is already in it

And you can compress any data as the index at which it occurs in pi!!!1!

Can the index be reliably represented in fewer bytes than the data itself?

this 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.

In fact, no compression scheme can reliably compress data to fewer bytes than it started as, thanks to the pigeonhole principle.

Nope. On average it takes much more information to represent the index than the data itself. "Compress" is definitely a misnomer here.

https://dilbert.com/strip/2001-10-25

These two belong together: https://xkcd.com/221/

Also really interesting to think about that you shared a comic that's almost 20 years old. Where did time go?

Sony did the same thing with the ps3

The first missing prime in the first million digits of pi is 100057 ( https://primes.utm.edu/curios/page.php?short=100057).

Is 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?

See https://en.wikipedia.org/wiki/Normal_number Answer: No one knows, but we assume Pi is normal.

Wow, 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.

It's a common misconception

The probability that that's the case is 1, but that's not the same as a proof.

Not 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.

Pi 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.ht...

This reminds me of Borges' Library of Babel: https://libraryofbabel.info/libraryofbabel.html

Yes, there's no mathematical significance, but finding such a thing so early is emotionally intriguing to some humans, myself included.

Gets me thinking about then ending of the book version of Contact.

A more numinous ending at that.

I 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?

There'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

17,387,594,880 http://mathworld.wolfram.com/PiDigits.html

I 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!

Using this website:

https://www.angio.net/pi/digits.html

I can search for the sequence 0123456789. It is not found in the first 200M digits.

Lo! Technology: https://www.angio.net/pi/

It surely does appear somewhere. But it isn't within the first 2 billion digits.

The 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/

I love how Wikipedia contains these weird little nuggets of knowledge, and I love how they keep showing up on Hacker News.

would be cool to have the same thing for other bases

I wondered the same thing, surprised it wasn’t mentioned in the Wikipedia article.

Yeah. It doesn't seem like pi is meant to be base10

This kind of trivia is my favorite thing to find on HN

The digits "360" are centered at the 360th digit. [Edit: if you include the leading 3 before the decimal, which Wikipedia doesn't.]

All my passwords are conveniently stored in the constant Pi

Now I'm adding √-1 to all my passwords.

Now that's one complex password, I'd imagine.

Hmmm, on second thought, maybe i shouldn't be involved.

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