3 ms·

OK cool. But... Finding random numbers repeating is a simple brute force problem. It is cool, but slightly boring. Related to this, what I cannot wrap my head

OK cool. But... Finding random numbers repeating is a simple brute force problem. It is cool, but slightly boring. Related to this, what I cannot wrap my head across, is the Infinite monkey theorem. Is it not possible that we keep expanding the numbers and never reach a complex enough set of values?

clueless 2y ago
in a pure infinite monkey scenario, works of Shakespeare would be generated at some point
- ryanmcbride 2y ago
  You can't guarantee that monkeys are typing perfectly randomly. We may never see better than "it was the best of times it was the blurst of times"
  - scarmig 2y ago
    It doesn't need to be perfectly random; you just need every sequence to have a nonzero probability of being generated. "to be or not to be" may be more likely for a monkey on a keyboard to generate than a random string, actually. The keys to generate it are highly repetitive and relatively close together. That's true for any NL string: the lower entropy of NL strings are reflected in the keyboard layout. If the monkeys switch to Dvorak, they could probably generate Shakespeare even faster.
  - tacoooooooo 2y ago
    you misunderstand infinity
    - clueless 2y ago
      how so?
    - chowells 2y ago
      So if I randomly type letters from the top row of my keyboard forever, I'll eventually type the entire works of Shakespeare? Of course not. There are lots of ways you can bias random that remain random, but prevent every possible output from being generated. That's all GP was saying. You can't just say "infinite time", you need to rule out biases that would prevent the desired result.
      - recursive 2y ago
        You don't need "perfect randomness". The claim was about "perfect randomness". You just need a non-zero probability for the outcomes in question. And you need independence between subsequent random events.
  - deathanatos 2y ago
    What, you egg? [He stabs him.] (from Macbeth) Are you certain the real thing isn't "the blurst of times" already?
  - mauvehaus 2y ago
    Your monkeys are pretty bad at Shakespeare if the best they come up with "it was the best of times it was the blurst of times".
    - qingcharles 2y ago
      Their typewriters are kinda janky, TBH. https://preview.redd.it/it-was-the-best-of-times-it-was-the-blurst-of-times-v0-uq7ix310nl5a1.jpg?width=640&crop=smart&auto=webp&s=867b3d5845acdf7437b3c4a1ba5b57774de0e922 https://preview.redd.it/it-was-the-best-of-times-it-was-the-...
    - mr_toad 2y ago
      > Your monkeys are pretty bad at Shakespeare Worse, they can’t even tell their Shakespeare from their Dickens (It’s the opening line of A Tale of Two Cities).
- crtified 2y ago
  If you have infinite monkeys, then (at least) one of the monkeys is Shakespeare.
  - dmurray 2y ago
    If you have finite monkeys, let's say they number M, but infinite time, then for small values of M it would be faster to breed the monkeys until one of them evolves into Shakespeare.
sponaugle 2y ago
It is, as far as being a math problem, somewhat boring. The numbers themselves are equivalent to a random number. There is certainly no significance to the numbers themselves, especially as this is all in the decimal representation, which is very 'us' specific. It does represent something 'interesting' that is easy to observe and wonder about, and for the non-math person it leads to slightly better understanding of 'normal' numbers, of the difference in representation ( these answers are base specific), and a very small amount of simple computer science. The notion of world record is of course tongue in cheek. No one really needs to know these numbers, nor will they rememeber them! But at least there is an entry in OEIS!
- bee_rider 2y ago
  WRT significance, do people ever find the position of socially significant numbers in pi? For example I recall quite a while ago, there was a leak of the key that was used to encrypt blue rays. Hypothetically that could be found in pi, right? Of course, it ended up being spread widely enough that they gave up on trying to police it. But maybe there are some other not-allowed numbers that could be distributed as a position in pi? I’m not sure what the point would be, mostly just to make a point I guess.
  - zimpenfish 2y ago
    https://www.angio.net/pi/ https://www.angio.net/pi/ lets you search for sequences of up to 120 digit in the first 200M digits of pi. I'm sure there's others knocking around that might go further.

clueless 2y ago

in a pure infinite monkey scenario, works of Shakespeare would be generated at some point

ryanmcbride 2y ago
You can't guarantee that monkeys are typing perfectly randomly. We may never see better than "it was the best of times it was the blurst of times"
- scarmig 2y ago
  It doesn't need to be perfectly random; you just need every sequence to have a nonzero probability of being generated. "to be or not to be" may be more likely for a monkey on a keyboard to generate than a random string, actually. The keys to generate it are highly repetitive and relatively close together. That's true for any NL string: the lower entropy of NL strings are reflected in the keyboard layout. If the monkeys switch to Dvorak, they could probably generate Shakespeare even faster.
- tacoooooooo 2y ago
  you misunderstand infinity
  - clueless 2y ago
    how so?
  - chowells 2y ago
    So if I randomly type letters from the top row of my keyboard forever, I'll eventually type the entire works of Shakespeare? Of course not. There are lots of ways you can bias random that remain random, but prevent every possible output from being generated. That's all GP was saying. You can't just say "infinite time", you need to rule out biases that would prevent the desired result.
    - recursive 2y ago
      You don't need "perfect randomness". The claim was about "perfect randomness". You just need a non-zero probability for the outcomes in question. And you need independence between subsequent random events.
- deathanatos 2y ago
  What, you egg? [He stabs him.] (from Macbeth) Are you certain the real thing isn't "the blurst of times" already?
- mauvehaus 2y ago
  Your monkeys are pretty bad at Shakespeare if the best they come up with "it was the best of times it was the blurst of times".
  - qingcharles 2y ago
    Their typewriters are kinda janky, TBH. https://preview.redd.it/it-was-the-best-of-times-it-was-the-blurst-of-times-v0-uq7ix310nl5a1.jpg?width=640&crop=smart&auto=webp&s=867b3d5845acdf7437b3c4a1ba5b57774de0e922 https://preview.redd.it/it-was-the-best-of-times-it-was-the-...
  - mr_toad 2y ago
    > Your monkeys are pretty bad at Shakespeare Worse, they can’t even tell their Shakespeare from their Dickens (It’s the opening line of A Tale of Two Cities).
crtified 2y ago
If you have infinite monkeys, then (at least) one of the monkeys is Shakespeare.
- dmurray 2y ago
  If you have finite monkeys, let's say they number M, but infinite time, then for small values of M it would be faster to breed the monkeys until one of them evolves into Shakespeare.

sponaugle 2y ago

It is, as far as being a math problem, somewhat boring. The numbers themselves are equivalent to a random number. There is certainly no significance to the numbers themselves, especially as this is all in the decimal representation, which is very 'us' specific. It does represent something 'interesting' that is easy to observe and wonder about, and for the non-math person it leads to slightly better understanding of 'normal' numbers, of the difference in representation ( these answers are base specific), and a very small amount of simple computer science. The notion of world record is of course tongue in cheek. No one really needs to know these numbers, nor will they rememeber them! But at least there is an entry in OEIS!

bee_rider 2y ago
WRT significance, do people ever find the position of socially significant numbers in pi? For example I recall quite a while ago, there was a leak of the key that was used to encrypt blue rays. Hypothetically that could be found in pi, right? Of course, it ended up being spread widely enough that they gave up on trying to police it. But maybe there are some other not-allowed numbers that could be distributed as a position in pi? I’m not sure what the point would be, mostly just to make a point I guess.
- zimpenfish 2y ago
  https://www.angio.net/pi/ https://www.angio.net/pi/ lets you search for sequences of up to 120 digit in the first 200M digits of pi. I'm sure there's others knocking around that might go further.