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It’s a common logical error. Infinity doesn’t mean all possibilities. An infinite universe doesn’t have infinite copies of someone. Pi doesn’t have everyone’s s

It’s a common logical error. Infinity doesn’t mean all possibilities. An infinite universe doesn’t have infinite copies of someone. Pi doesn’t have everyone’s source code. There an infinite number of infinite random digit series that don’t contain anyone’s source code.

ghosty141 3y ago
Since pi never repeats it should actually contain any sequence of numbers possible though, right? So if you encode your source code as number thet argument should hold up.
- orangecat 3y ago
  Since pi never repeats it should actually contain any sequence of numbers possible though, right? Simple counterexample: 0.101001000100001... which is 1 followed by one 0, then 1 followed by two 0s, then 1 followed by three 0s, and so on. It never repeats, but "11" will never appear. "Almost all" real numbers do contain all finite sequences, but it hasn't been proven for pi (https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number).
lucas_membrane 3y ago
But if my source code has length n in binary, and I had an infinite number of monkeys typing on an infinite number of terminals, they could find it in pi or any similar digit sequence within (((n * n) * n) * n)! years. Finding a jpeg of the Titanic sinking autographed by the captain might take a little longer, but Fox News is working on that.
SamBam 3y ago
GP didn't say "infinite," they said "normal" [1]. If Pi is normal, as conjectured, then it does contain every possible sequence. 1. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
- m463 3y ago
  wonder if e is normal
crazygringo 3y ago
> Pi doesn’t have everyone’s source code. This isn't actually proven though, as far as I know. There are plenty of infinite non-repeating sequences that we know that don't contain a given sequence. (E.g. 0.1101001000100001000001...) But pi is not among them. It might very well have everyone's source code. It also might not.
- d3w4s9 3y ago
  > In mathematics, a real number is said to be simply normal in an integer base b[1] if its infinite sequence of digits is *distributed uniformly* in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b^−n.
  - crazygringo 3y ago
    > While √2, π, ln(2), and e are strongly conjectured to be normal, it is still not known whether they are normal or not.
mr_toad 3y ago
> An infinite universe doesn’t have infinite copies of someone. Depends on the uniformity of matter and energy and physical laws in the universe. If matter and energy are uniformly distributed with no large scale variation, and the laws of physics are constant then eventually somewhere in the universe you’d be able to find an Earth arbitrarily close to ours.

ghosty141 3y ago

Since pi never repeats it should actually contain any sequence of numbers possible though, right? So if you encode your source code as number thet argument should hold up.

orangecat 3y ago
Since pi never repeats it should actually contain any sequence of numbers possible though, right? Simple counterexample: 0.101001000100001... which is 1 followed by one 0, then 1 followed by two 0s, then 1 followed by three 0s, and so on. It never repeats, but "11" will never appear. "Almost all" real numbers do contain all finite sequences, but it hasn't been proven for pi (https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number).

lucas_membrane 3y ago

But if my source code has length n in binary, and I had an infinite number of monkeys typing on an infinite number of terminals, they could find it in pi or any similar digit sequence within (((n * n) * n) * n)! years. Finding a jpeg of the Titanic sinking autographed by the captain might take a little longer, but Fox News is working on that.

SamBam 3y ago

GP didn't say "infinite," they said "normal" [1]. If Pi is normal, as conjectured, then it does contain every possible sequence. 1. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number

m463 3y ago
wonder if e is normal

crazygringo 3y ago

> Pi doesn’t have everyone’s source code. This isn't actually proven though, as far as I know. There are plenty of infinite non-repeating sequences that we know that don't contain a given sequence. (E.g. 0.1101001000100001000001...) But pi is not among them. It might very well have everyone's source code. It also might not.

d3w4s9 3y ago
> In mathematics, a real number is said to be simply normal in an integer base b[1] if its infinite sequence of digits is *distributed uniformly* in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b^−n.
- crazygringo 3y ago
  > While √2, π, ln(2), and e are strongly conjectured to be normal, it is still not known whether they are normal or not.

mr_toad 3y ago

> An infinite universe doesn’t have infinite copies of someone. Depends on the uniformity of matter and energy and physical laws in the universe. If matter and energy are uniformly distributed with no large scale variation, and the laws of physics are constant then eventually somewhere in the universe you’d be able to find an Earth arbitrarily close to ours.