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All possible permutations
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this post was submitted on 01 Jun 2024
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Right, the logic is this. First, out of 26 letters in both upper and lower cases, 10 Arabic numerals, whitespace and various common punctuation marks, there are dozens of symbols that can be typed at any time. Let's call it a nice round number like 50.
So when any of them has equal odds the likelihood that the next symbol you randomly type is any specific character, like the lowercase 'g', is 1 in 50. The liklihood that the letter after that is a lowercase 'o' is also 1 in 50. So the liklihood of both the 'g' and then the 'o' being pressed in succession to spell the work "go" is 1 in 50^2, i.e. 1 in 2,500. The liklihood of any specific 3, 4, and 5 characters would be 1 in 125,000, 1 in 6,250,000, and 1 in 312,500,000, respectively. As you can guess, to write a play like Hamlet with 130,000 letters in it, the odds would be astronomical. 1 in 50^130,000, to be specific.
You can't even comprehend how big a number 50^130,000 is. You can't even conceive of something at that scale. When I say that that number is more than all of the nanoseconds since the big bang multiplied by the number of molecules in the observable universe, that is such an understatement that it is funny. That doesn't actually even put a dent into how big that number is.
So then the chances of writing Hamlet may feel, intuitively, like the odds are actually 0. Something with such unbelievably low odds simply cannot practically happen, right? But that is not the case and I can prove it. Imagine a random letter generator that puts out a random series of letters, numbers, whitespace and punctuation. Imagine it had to output a selection of 130,000 characters. What does the output look like in your head? Probably a random mess of gibberish, right? The odds are good of that, after all. But, wait. What are the odds that the SPECIFIC mess of gibberish, that specific set of letters, was selected? Well, obviously, it would be 1 in 50^130,000. The exact same odds as Hamlet. The thing that feels literally impossible. That exact string of meaningless nonsense and the masterpiece by Shakespeare have the exact same odds of happening, and one of them already did. If one can happen, so can the other.
I posted this in a different thread recently:
=====
it is to illustrate the vastness of infinity not the efficacy of monkeys
assuming one infinite monkey:
sonnet 18 has 592 characters- or a chance of 4.3x10^-848
For scale - the universe is 1.3x10^10 years old.
And the ^-848 was 14 lines, a onehundredth of a single percent of the complete works.
However, it's infinite monkeys, so the time it would take is effectively how every long it takes for one monkey to type that many lines. A few days? A week? In an infinite monkey cage it's done at the first attempt: that's the size of infinity.
If you converted all the mass in the universe to energy, and all the time until it's heat death and could combine them into one machine: probably not enough to clear Titus Andronicus.