A numerical evaluation of the Finite Monkeys Theorem | Hacker News Reader

A numerical evaluation of the Finite Monkeys Theorem

sciencedirect.com

41 pointsgnabgib22 comments

> Given the expected time until the heat death of the universe, we demonstrate that the widely-accepted conclusion from the Infinite Monkeys Theorem is, in fact, misleading in our finite universe

Maybe I'm missing something here, but wasn't the analogy used to describe the nature of infinity ?

The paper is pretty cool, but it gives a weird correlation between infinity as a principle and the heat death of the universe ?

I was also confused until I read the abstract. This is the FINITE Monkeys Theorem.

>Here, we consider the Finite Monkeys Theorem and look at the probability of a given string being typed by one of a finite number of monkeys within a finite time allocation consistent with estimates for the lifespan of our universe.

I misread finite as infinite multiple times.

Now I just feel infinitely silly. I didn't pay enough attention in the end but still seems like a cool mental excersize more than anything else!

A somewhat popular variant I've seen of this problem of the infinite limit versus the real physical reality is people calculating the probabilities of some event occurring in some game with a fixed seed, as was popular in old games. Someone might start computing the probability that this monster has its rare variant AND the boss gets the maximum HP roll AND the awesome sword gets its lowest damage variant AND so on and so on... but if the game has a 32-bit seed that determines everything and the resulting probability is, say, one in a trillion, then the real probability is likely a straight zero, because none of the finite number of seeds will have the calculated outcome, even if a hypothetical variation of the game with a large random state space could.

Similarly, if you use a psuedo-random number generator and start trying to calculate how long it will be before it produces some string substantially larger than the side of its internal state, your answer will likely be incorrect as the answer is it will never produce the longer string, a flat zero.

Not consequential errors in most cases because it's fairly rare to exhaust the entire state space of a random number generator and be concerned about the result. (Unless you're a speedrunner. Or in the case of one recent YouTuber, just insane, in that good ol' hacker way: https://www.youtube.com/watch?v=jNMWkD5VsZ8 "Beating every possible game of Pokemon Platinum at the same time")

It's too bad that they took the physicality of the monkeys into account, but assumed the key probabilities were IID. It would have been nice to see the effect of keyboard layout on the overall probabilities. Key mashing would clearly make nearby keys much more likely to be pressed in a sequence, implying that there might be an optimal keyboard layout for each phrase. And that’s before considering soft keyboards with autocomplete.

How about I define a new language or dictionary where three letters written like "αηζ" is equivalent to all works of Shakespeare.

Then job would be easy.

I always like these sort of papers. They signify some form of humanity among researchers. It is explainable to people outside of the research community and explores a comical topic while applying the scientific method.

It always makes for great examples of how to apply the scientific method.

Yes, and I think of them as examples to grab interest, particularly of young people. Which is good, the world needs not only more scientists, but more people who understand and appreciate how it works.

Or how not to apply …

Ok, but what is the probability that a monkey types a string such that when the string is provided as input to a universal Turing machine that maximally compresses all written works except Shakespeare, the output of the machine is the works of Shakespeare?

Yes, but as monkeys->inf then P(Shakespeare generated) -> 1 almost certainly (also in math sense).

The result depends on the relative rates that things go to infinity, just like lim (x,y)->(inf, inf) of x/y completely depends on the path (x,y) takes to (inf, inf)

As long as the implementation still confirms to RFC 2795

That RFC is for infinite. This article discuses finite.

One can only wonder what can be faster - the monkeys would produce a work of Shakespeare or Google pays the fine of $20,000,000,000,000,000,000,000,000,000,000,000 that the Russian court imposed on Google for blocking Russian state propaganda on Youtube. At least in case of monkey the monkeys can learn and improve from their previous output while Russia isn't even willing to.

I really wish they had done an analysis of finite Planck-scale monkeys.

log(log(Universe deaths)) is an interesting graph axis unit.

They deserve ignobel prize.

Have they read Shakespeare?

> To quote Hamlet, Act 3, Scene 3, Line 87: “No”.

I can see I have hardly been availing myself enough of the plethora of short phrase quality literature quoting opportunities.

"Indeed"

-- Master Shakespeare, The Passionate Pilgrim, Poem 20, Line 29, Word 6 [0]

[0] https://nosweatshakespeare.com/poems/the-passionate-pilgrim/

The art is in finding a line/sentence that consists of only the word in question, in other words a complete utterance. That’s the case for the “No”, but not for your “Indeed”.

The difference here is that “No” (actually “No!” in my text) is the entirety of Hamlet III.iii.87 without need to sample less than a line.

I believe that might be a difference in degree, not really in kind.

And selecting (and documenting) a single word extraction was part of the light hearted point. I was careful not to include a period inside the quote. :)

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