3 ms·

Pick a digit, repeat, don't stop.

by tantalor 10mo ago

markusde 10mo ago
Exactly right. You can pick and use real numbers, as long as they are only queried to finite precision. There are lots of super cool algorithms for doing this!
- jibal 10mo ago
  That's just saying that you can pick and use rational numbers (which are a subset of the reals.)
  - skulk 10mo ago
    Not really. You can simulate a probability of 1/x by expanding 1/x in binary and flipping a coin repeatedly, once for each digit, until the coin matches the digit (assign heads and tails to 0 and 1 consistently). If the match happened on 1, then it's a positive result, otherwise negative. This only requires arbitrary but finite precision but the probability is exactly equal to 1/x which isn't rational.
    - jibal 10mo ago
      No, it isn't ... an infinite expansion isn't possible.
  - markusde 10mo ago
    Kind of, but you're not just picking rationals, you're picking rationals that are known to converge to a real number with some continuous property. You might be interested in this paper [1] which builds on top of this approach to simulate arbitrarily precise samples from the continuous normal distribution. [1] https://dl.acm.org/doi/10.1145/2710016 https://dl.acm.org/doi/10.1145/2710016
techas 10mo ago
And don’t die.
jibal 10mo ago
At no point will your number be transcendental (or even irrational).
- tantalor 10mo ago
  That's why you can't stop.
  - jibal 10mo ago
    That's irrelevant. It's like saying that you can count to infinity if you never stop counting ... but no, every number in the count is finite.
    - tantalor 10mo ago
      That's how limits at infinity work.
      - jibal 10mo ago
        No, it certainly isn't.
      - IAmBroom 10mo ago
        You seem to be positing that Maxwell's Demon can be reassigned to another impossible task, but that isn't a proper use of his "powers". Infinities defy simple assumptions about maths, while Maxwell's Demon only needs to ignore the Laws of Thermodynamics. I'm being serious, not glib, here. "And then do it infinitely many times" doesn't automatically enable any possible outcome, any more than the "multiverse of all possible outcomes" enables hot dog fingers on Jamie Curtis.

Pick a digit, repeat, don't stop.

Exactly right. You can pick and use real numbers, as long as they are only queried to finite precision. There are lots of super cool algorithms for doing this!

jibal 10mo ago
That's just saying that you can pick and use rational numbers (which are a subset of the reals.)
- skulk 10mo ago
  Not really. You can simulate a probability of 1/x by expanding 1/x in binary and flipping a coin repeatedly, once for each digit, until the coin matches the digit (assign heads and tails to 0 and 1 consistently). If the match happened on 1, then it's a positive result, otherwise negative. This only requires arbitrary but finite precision but the probability is exactly equal to 1/x which isn't rational.
  - jibal 10mo ago
    No, it isn't ... an infinite expansion isn't possible.
- markusde 10mo ago
  Kind of, but you're not just picking rationals, you're picking rationals that are known to converge to a real number with some continuous property. You might be interested in this paper [1] which builds on top of this approach to simulate arbitrarily precise samples from the continuous normal distribution. [1] https://dl.acm.org/doi/10.1145/2710016 https://dl.acm.org/doi/10.1145/2710016

techas 10mo ago

And don’t die.

jibal 10mo ago

At no point will your number be transcendental (or even irrational).

tantalor 10mo ago
That's why you can't stop.
- jibal 10mo ago
  That's irrelevant. It's like saying that you can count to infinity if you never stop counting ... but no, every number in the count is finite.
  - tantalor 10mo ago
    That's how limits at infinity work.
    - jibal 10mo ago
      No, it certainly isn't.
    - IAmBroom 10mo ago
      You seem to be positing that Maxwell's Demon can be reassigned to another impossible task, but that isn't a proper use of his "powers". Infinities defy simple assumptions about maths, while Maxwell's Demon only needs to ignore the Laws of Thermodynamics. I'm being serious, not glib, here. "And then do it infinitely many times" doesn't automatically enable any possible outcome, any more than the "multiverse of all possible outcomes" enables hot dog fingers on Jamie Curtis.