[HN Gopher] A numerical evaluation of the Finite Monkeys Theorem
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A numerical evaluation of the Finite Monkeys Theorem
Author : gnabgib
Score : 34 points
Date : 2024-10-31 06:36 UTC (16 hours ago)
(HTM) web link (www.sciencedirect.com)
(TXT) w3m dump (www.sciencedirect.com)
| julian9499 wrote:
| 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.
| adamc wrote:
| 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.
| SideQuark wrote:
| 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)
| bilekas wrote:
| > 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 ?
| bigoljim wrote:
| 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.
| bilekas wrote:
| 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!
| jerf wrote:
| 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")
| mdiesel wrote:
| As long as the implementation still confirms to RFC 2795
| stronglikedan wrote:
| That RFC is for _infinite_. This article discuses _finite_.
| docfort wrote:
| 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.
| jumping_frog wrote:
| How about I define a new language or dictionary where three
| letters written like "aez" is equivalent to all works of
| Shakespeare.
|
| Then job would be easy.
| trhway wrote:
| 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.
| biomcgary wrote:
| I really wish they had done an analysis of finite Planck-scale
| monkeys.
| Xcelerate wrote:
| 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?
| shaftoe444 wrote:
| Have they read Shakespeare?
| Nevermark wrote:
| > 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/
| layer8 wrote:
| 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".
| dhosek wrote:
| 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.
| Nevermark wrote:
| 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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