4 ms·

It basically comes down to the million monkeys on a million typewriters argument. Any work of art or creation could be created randomly, given an infinity. Pi i

It basically comes down to the million monkeys on a million typewriters argument. Any work of art or creation could be created randomly, given an infinity. Pi is just a sort of random number generator.

gosub100 3y ago
Although every PRNG must eventually repeat, while pi is mathematically proven to never repeat. And real-life RNGs are fundamentally limited by hardware, no? How long would it take to pull multiple terabytes off one? They're not meant for it.
- agent327 3y ago
  Must it? What if you use the seed as an offset into pi, and then just return digits of pi from that point onwards? (of course that will eventually run into a problem with the state of the RNG exceeding available memory, so it will ultimately fail on resource exhaustion, but it won't repeat)
  - gosub100 3y ago
    I think the problem is calculating pi must be done in series, so you can't really get much further than anyone else. contrast that to a hypothetical situation where you could effortlessly start calculating at the nth position of pi. Then you'd have a rock-solid RNG where your real-world entropy source could repesent each digit of the index, so i.e. you get a 500 digit number, then start reciting pi from that position, now you're cooking with gas. Meaning your search space to crack the RNG would be about as difficult as cracking AES-256. but anyway I'm talking above my paygrade here, so no guarantees :)
    - kadoban 3y ago
      > I think the problem is calculating pi must be done in series, so you can't really get much further than anyone else. contrast that to a hypothetical situation where you could effortlessly start calculating at the nth position of pi. There is this: https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80... , so you can calculate later digits of pi without the earlier ones.

gosub100 3y ago

Although every PRNG must eventually repeat, while pi is mathematically proven to never repeat. And real-life RNGs are fundamentally limited by hardware, no? How long would it take to pull multiple terabytes off one? They're not meant for it.

agent327 3y ago
Must it? What if you use the seed as an offset into pi, and then just return digits of pi from that point onwards? (of course that will eventually run into a problem with the state of the RNG exceeding available memory, so it will ultimately fail on resource exhaustion, but it won't repeat)
- gosub100 3y ago
  I think the problem is calculating pi must be done in series, so you can't really get much further than anyone else. contrast that to a hypothetical situation where you could effortlessly start calculating at the nth position of pi. Then you'd have a rock-solid RNG where your real-world entropy source could repesent each digit of the index, so i.e. you get a 500 digit number, then start reciting pi from that position, now you're cooking with gas. Meaning your search space to crack the RNG would be about as difficult as cracking AES-256. but anyway I'm talking above my paygrade here, so no guarantees :)
  - kadoban 3y ago
    > I think the problem is calculating pi must be done in series, so you can't really get much further than anyone else. contrast that to a hypothetical situation where you could effortlessly start calculating at the nth position of pi. There is this: https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80... , so you can calculate later digits of pi without the earlier ones.