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Comment by stevebmark | Hacker News Reader

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.

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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

wonder if e is normal

> 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.

> 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.

> While √2, π, ln(2), and e are strongly conjectured to be normal, it is still not known whether they are normal or not.

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.

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).

> 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.

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.

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