4 ms·

There is a dead post in this thread talking about what if "at 101T digits we find an infinite series of 000000000". I just wanted to point out that this is imp

by schoen 4y ago

There is a dead post in this thread talking about what if "at 101T digits we find an infinite series of 000000000". I just wanted to point out that this is impossible, because in that case pi would be a rational number. However, it's been proven to be a transcendental number, which is a stronger condition than just being irrational. So, it's not possible that pi ends with any infinitely repeating sequence.

ISL 4y ago
It is almost certain that pi does contain sequences of zeroes of arbitrary length, but that following those zeroes are other numbers.
- 6gvONxR4sf7o 4y ago
  Isn’t that still just a conjecture that pi’s digits are random-ish?
  - pvg 4y ago
    If you're talking about whether pi is 'normal', it's more than 'just a conjecture' but not something that's been proved. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
    - hansvm 4y ago
      Wtf is there between a conjecture and something which has been proven?
      - pvg 4y ago
        Intermediate results, on which eventual proofs often end up relying.
      - sbierwagen 4y ago
        Fortunately, Philip J. Davis wrote a paper on this exact topic in 1985: https://www.gwern.net/docs/www/www.maa.org/9230a8f2614ddd74b52c556fe0364fbcc24e1a30.pdf https://www.gwern.net/docs/www/www.maa.org/9230a8f2614ddd74b... He listed at least 21 states between "conjecture" and "proof".
ianai 4y ago
But more weirdly, it's possible to find any string of digits within the digits of pi. So there are going to be quite a few zeros in there, followed by ever more non-zeros. Transcendental numbers are truly awesome.
- mb7733 4y ago
  Small note, this is believed to be true but has not been proven.
madars 4y ago
Fun fact: Mahler famously showed that if p/q is a rational number then |\pi - p/q| > 1/q^42. So we can't have a string of 4242T zeros after first 101T digits :-) The exponent 42 has since been improved by a series of works to 7.1032 - https://arxiv.org/abs/1912.06345 https://arxiv.org/abs/1912.06345
- jgeralnik 4y ago
  You can't have a string of 4242T zeroes immediately after the first 101T digits but presumably you could have them sometime later (say after another 10000T digits)
f0e4c2f7 4y ago
I seem to remember reading a sci-fi story quite a long time ago where the characters discover a message embedded in pi but only after many digits were calculated. I think the implication was something about simulations or maybe instructions on how to build a device. Can't quite remember the details.
- LegitShady 4y ago
  That sounds like Contact by Carl Sagan
  - cpeterso 4y ago
    In Northern Exposure season 4 episode 3 ("Nothing's Perfect"), a grad student comes to Cicely to study Pi. "I just have this feeling if I take pi, well past all this static, take pi to 10 million, 20 million digits, that I'll find something really incredible. Not just a pattern, not just an order, but a sign. A mathematical sign." https://moosechick.com/43.html https://moosechick.com/43.html
deleted 4y ago
[deleted]

by schoen 4y ago

ISL 4y ago

It is almost certain that pi does contain sequences of zeroes of arbitrary length, but that following those zeroes are other numbers.

6gvONxR4sf7o 4y ago
Isn’t that still just a conjecture that pi’s digits are random-ish?
- pvg 4y ago
  If you're talking about whether pi is 'normal', it's more than 'just a conjecture' but not something that's been proved. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
  - hansvm 4y ago
    Wtf is there between a conjecture and something which has been proven?
    - pvg 4y ago
      Intermediate results, on which eventual proofs often end up relying.
    - sbierwagen 4y ago
      Fortunately, Philip J. Davis wrote a paper on this exact topic in 1985: https://www.gwern.net/docs/www/www.maa.org/9230a8f2614ddd74b52c556fe0364fbcc24e1a30.pdf https://www.gwern.net/docs/www/www.maa.org/9230a8f2614ddd74b... He listed at least 21 states between "conjecture" and "proof".

ianai 4y ago

But more weirdly, it's possible to find any string of digits within the digits of pi. So there are going to be quite a few zeros in there, followed by ever more non-zeros. Transcendental numbers are truly awesome.

mb7733 4y ago
Small note, this is believed to be true but has not been proven.

madars 4y ago

Fun fact: Mahler famously showed that if p/q is a rational number then |\pi - p/q| > 1/q^42. So we can't have a string of 4242T zeros after first 101T digits :-) The exponent 42 has since been improved by a series of works to 7.1032 - https://arxiv.org/abs/1912.06345 https://arxiv.org/abs/1912.06345

jgeralnik 4y ago
You can't have a string of 4242T zeroes immediately after the first 101T digits but presumably you could have them sometime later (say after another 10000T digits)

f0e4c2f7 4y ago

I seem to remember reading a sci-fi story quite a long time ago where the characters discover a message embedded in pi but only after many digits were calculated. I think the implication was something about simulations or maybe instructions on how to build a device. Can't quite remember the details.

LegitShady 4y ago
That sounds like Contact by Carl Sagan
- cpeterso 4y ago
  In Northern Exposure season 4 episode 3 ("Nothing's Perfect"), a grad student comes to Cicely to study Pi. "I just have this feeling if I take pi, well past all this static, take pi to 10 million, 20 million digits, that I'll find something really incredible. Not just a pattern, not just an order, but a sign. A mathematical sign." https://moosechick.com/43.html https://moosechick.com/43.html

deleted 4y ago

[deleted]