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Math

Australian Mathematicians Debunk 'Infinite Monkey Theorem' 77

Posted by msmash from the tough-luck dept.
Australian mathematicians have proven the famous "infinite monkey theorem" impossible within the universe's lifespan. The theorem suggests monkeys typing randomly would eventually produce Shakespeare's complete works. Scientists Stephen Woodcock and Jay Falletta calculated that even 200,000 chimpanzees typing one character per second until the universe's heat death would fail to reproduce Shakespeare's writings.

A single chimp has only a 5% chance of typing "bananas" in its lifetime, with more complex phrases facing astronomically lower odds. "This finding places the theorem among other probability puzzles and paradoxes... where using the idea of infinite resources gives results that don't match up with what we get when we consider the constraints of our universe," Associate Prof Woodcock was quoted as saying by BBC.

Australian Mathematicians Debunk 'Infinite Monkey Theorem' More | Reply

Australian Mathematicians Debunk 'Infinite Monkey Theorem'

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  • Oh really? (Score:5, Funny)

    by i kan reed ( 749298 ) on Friday November 01, 2024 @10:03AM (#64911759) Homepage Journal

    There's a difference between the mathematical concept of infinity and what's practical in the real world?

    No one has ever had that insight before. Academia has proven its value once again.

    • Re: Oh really? (Score:5, Interesting)

      by barlevg ( 2111272 ) on Friday November 01, 2024 @10:06AM (#64911781)
      The problem isn't academia, it's scientific reporting. Putting probability values to the Infinite Monkeys concept is fine. Reporting breathlessly that "this disproves the Infinite Monkeys hypothesis!" is absurd.

      • Re: (Score:3)

        by 0xG ( 712423 )

        The problem isn't academia, it's scientific reporting.

        If you're going to be pedantic, it's *science* reporting.
        Scientific reporting would be something quite different.

      • No, I'm going to say that the problem is academia. The infinite monkey theorem works on the concept of infinity. I'll quote Wikipedia here which is always a risk, but "The theorem can be generalized to state that any sequence of events that has a non-zero probability of happening will almost certainly occur an infinite number of times, given an infinite amount of time or a universe that is infinite in size." The whole point of the theorem is to illustrate the difference between "highly improbable but not
    • No, it was always based on a misrepresentation of infinity. Think of it this way, if you have a pattern 1, 3, 5, 7, 9, ... it goes forever... it's infinite.... but you will NEVER have an even number.

      • You're articulating the other objection based on realism to the pointless thought experiment, that monkeys are non-random.

      • Re: (Score:3)

        by dskoll ( 99328 )

        That is not true. From a finite subset of a sequence, it's impossible to tell what comes next.

        The fifth-degree polynomial y = 0.258333x^5 - 3.875x^4 + 21.958333x^3 - 58.125x^2 + 72.78333x - 32 passes through the points (1,1), (2,3), (3,5), (4,7), (5,9), (6,42) which allows me to state with absolute confidence that the next number in the sequence is 42.

    • Re: (Score:3)

      by Dr. Tom ( 23206 )

      I don't think they showed that the universe is not infinite

    • Re:Oh really? (Score:5, Insightful)

      by Joce640k ( 829181 ) on Friday November 01, 2024 @10:24AM (#64911881) Homepage

      Breaking: "Mathematician" doesn't know the difference between 200,000 and infinity.

      PS: Chimps aren't monkeys.

  • Boltzmann Brains (Score:4, Informative)

    by Jamu ( 852752 ) on Friday November 01, 2024 @10:03AM (#64911765)
    Ah, so it only works with infinite Boltzmann monkey brains attached to Boltzmann typewriters.

  • This Infinite (Score:4, Funny)

    by stooo ( 2202012 ) on Friday November 01, 2024 @10:06AM (#64911775) Homepage

    This word you use "Infinite"
    It does not mean what you thing it means.

    • This word you use "Infinite"
      It does not mean what you thing it means.

      But if it's not real, if infinite time isn't real, let me introduce monkey Shakespeare, he can write the entire works of original Shakespeare in a few weeks recalled from his perfect cyborg memory and fragments of Shakespeare's brain only limited by the speed of his typewriter. Or a programmable typewriter with the entire works of Shakespeare ready to go with one bug button. None of that's real either, but hey it could happen right?

    • Well I do. Wouldn't infinite monkeys collapse into a black hole?

  • infinity != 200k (Score:4, Funny)

    by Sloppy ( 14984 ) on Friday November 01, 2024 @10:09AM (#64911793) Homepage Journal

    "Send more chimps." - Zombie in Return of the Living Dead #27528226

    • Re: (Score:2)

      by Njovich ( 553857 )

      As far as numbers go 200k is pretty low too

      • Re: (Score:2)

        by Falos ( 2905315 )

        I had more grief with the buttonmashing being one character/second, but suppose the army size balances it out.

        Not that either matter given infinite time. Someone go upside the journalist's head with a bat labeled "Mathematicians debunk FINITE monkey theorem".

      • They also assume the universe ends. If it just reboots everytime, it is going to happen some day. Do they have to get the ISBN number right?

    • 200k is larger than infinity, for small values of infinity

  • 200k is a low value for "infinite" (Score:5, Funny)

    by ihadafivedigituid ( 8391795 ) on Friday November 01, 2024 @10:12AM (#64911811)
    I thought "infinite" meant at least a million!

    Did they major in remedial math or something?

  • These "mathematicians" are weak (Score:3)

    by Night Goat ( 18437 ) on Friday November 01, 2024 @10:13AM (#64911821) Homepage Journal

    You'd think a mathematician would understand the concept of infinity. The heat death of the universe is not the value of infinity! Universe transplant, bionic monkeys. Easy solution.

    • You'd think a mathematician would understand the concept of infinity. The heat death of the universe is not the value of infinity! Universe transplant, bionic monkeys. Easy solution.

      The easy solution is to ignore the simplified problem they presented and return to the original problem, an infinite number of moneys. Time is the wrong variable.

  • a billion primates typing random shit on a billion keyboards have given us social media, slashdot, fanfiction, and Microsoft windows. Fear the monkey fingers

    • Re: (Score:2)

      by Dr. Tom ( 23206 )

      The Hive Mind has awoken.

      We all predicted this.

      The connection of all computers and all human knowledge.

      It's ChatGPT, monkey brain

  • Yes, the Mandelbrot set is infinitely complex, with infinite detail, but you still get bored, looking at it after a while. It's not gonna look like a monkey, ever. Mostly elephants

    • That's because you've not looked far enough, or deep enough. There's monkeys there, somewhere... and humans, and three armed moties too.

  • I read it yesterday and do t completely recall it now, but my understanding is that by showing that under finite but theoretically possible conditions the end state cannot be achieved, they can reclassify the Infinite Monkey problem as a paradox.

    Doesn't make sense to me, but I assume it's a mathematician's definition of 'paradox'.

    Quantifying the ranges of monkeys and time required and comparing that to what is actually possible in reality is interesting.

    • Considering the basic statement is about the nature of infinity itself, proving that a non-infinite situation cannot produce the result is about as useful as proving that a gerbil has never given birth to a sperm whale. And even for a non-infinite thing, the Universe can be surprisingly small. There are actual still-finite numbers whose values are so large that the number itself cannot be represented within the Universe. And those numbers, as mathematicians who study this stuff will usually tell you, are
  • From chim-pan-a to chim-pan-z.
  • So in Australia, 200,000 is about the same as infinite? Is their phd equivalent to a fifth grade education in the test of the works?

    • Re: (Score:2)

      by rossdee ( 243626 )

      If you put even a googol of monkeys into the space of Australia, it would immediately collapse into a black hole, so you're never going to see a result.

  • Infinity is larger than 200k (Score:4, Insightful)

    by trybywrench ( 584843 ) on Friday November 01, 2024 @10:33AM (#64911931)
    Infinite monkeys is much larger than 200k monkeys. Seems like infinite monkeys would produce the full works of Shakespeare on the first try.

  • Apes together, strong!

  • Well if you combine it with the many worlds theory and quantum suicide, then everybody can be a famous author if they want.

  • "Get your stinking paws off me you damned dirty ape! Start typing!"

    That's pretty close to the original quote.

  • Even though monkeys may never write prose tapping the keyboard hastens the heat death. This makes them an orchestra of their demise along with the humans. So, they do write poetry in their way. Shakespeare is just a distraction.

  • Simpsons [youtube.com]

  • It wouldn't take that long for them to evolve into humans and at least one of them to reach the intelligence level required to produce the literature - especially with the exponential population growth over time from the initial 200k - perhaps to a number a bit nearer to infinity.

    Take your stinking paws off my typewriter, you damned dirty ape!

  • What's the difference betweenthe Infinite Monkey Theorem and Neural Network Training? Granted, one has a fitness function that helps it move in the right direction but given an infinite amount of time should that really matter?

  • infinite trolls (Score:5, Funny)

    by awwshit ( 6214476 ) on Friday November 01, 2024 @10:56AM (#64912023)

    Slashdot has infinite trolls, they have yet to type out the works of Shakespeare. They may have typed out every known conspiracy theory.

  • Mr. Burns got close [youtube.com], and he only had 1000 monkeys!

  • They didn't debunk anything (Score:3)

    by jpatters ( 883 ) on Friday November 01, 2024 @11:00AM (#64912037)

    The thought experiment is about an infinite number of monkeys for an infinite about of time. Nobody who understands the statistics behind this has claimed that you can get the works of Shakespeare using 1000 monkeys in some finite amount of time, even the lifespan of the universe, or even that you could somehow do useful writing work with monkeys randomly typing and somehow filtering the results.

    • Re: (Score:2)

      by ceoyoyo ( 59147 )

      You can do it with 1000 moneys in a finite amount of time. It's much, much longer than the lifespan of the universe, but you can pick any probability and number of monkeys and the time will be finite. Presumably they did calculate it and that's what the actual story is about.

      The infinite monkeys thing is unfortunately a poor illustration of infinity. If you have infinite monkeys you definitely get the works of Shakespeare, and everything else written or not yet written or never-will-be-written, on the first

  • There's no time limit on the infinite monkey theorem. What is being "debunked"? A trillion-trillion monkeys will probably not type Shakespeare before heat death. Honestly the BBC article has a better title "Monkeys will never type Shakespeare, study finds". It does sound like a funny study.

  • The article directly says the theorem is mathematically valid. Nobody claimed it applied to the universe. Logic is a symbolic substrate, not the thing being described by it.
  • Sure, if you're using chimps. But what about Capuchins? Can someone rerun this important study with Capuchin monkeys? How about it "mathematicians"?
  • If you're going to take this thought experiment, a theoretical problem, and bring various other scientific beliefs to bear on it, like to limit the duration to a finite period due to scientists estimate of the end of the universe, then shouldn't you also include other scientific processes that are widely held?

    For instance, if you believe that humans evolved from lower life forms, then wouldn't it be likely that monkeys would evolve into more intelligent beings over the millions of years as they are typing

  • feels like if you accept the idea of infinite monkeys, you should also accept infinite time for them to work in... but also accept that with infinite monkeys, there is a stupidly small, but non zero chance of a monkey randomly hitting enough random keys to match Shakespeare's works...

    as far as i understood the statement didn't come with an asterisk/caveat... *infinite shall here forth mean 200,000, and time shall be limited to the heat death of the universe with the current understanding of thermal dynamic

    • Apparently we must add: assume an infinite number of electrons, neutrons, and protons in the universe to comprise the infinite monkeys, as there are always estimates of the number of electrons in the universe being a finite number, which, when you ponder it, is odd if all electrons are the same single electron throughout the electron field as is popular nowadays in some physics circles.

  • Now if they had asked whether infinite monkeys could produce the works of Sir Francis Bacon, they'd be on to something.

  • Wow - this post sure generated at lot of responses quickly.

    But, y'all are being too pedantic.

    In reality, if you had all those monkeys banging the keys, there'd be so much poop flying around that the keyboards would get all fudged up, the paper smeared to opacity, so even if one did accidentally type Hamlet, you'd never know it.

    Want a tangible expressible problem to work out the statistics on? Derive how, as the typewriters stink up and drop offline, the exponential decline in bandwidth changes the primary

  • This article has to be bait. I don't know how to view the actual study, but the claim that they've disproved anything involving an infinite number of monkeys (in which case infinite time isn't even important) is so far off the mark that it's Not Even Wrong. I'd be willing to bet that the actual study contextualizes itself a bit better than this.

  • Its immediately obvious that the probability of typing the entire works of Shakespeare randomly is far too low to happen in the history of the universe - that's not at all unusual for statistical calculations. The works contain a few million characters, and 26^(1,000,000) is obviously larger than an countable thing (like the number of plank-times X plank-volumes X age_of_universe. This isn't "math" its a 5 minute undergrad level statistics problem.
  • Isn't it just an old adage about randomness and luck?

    If a monkey gets lucky, that blows up all their math. The point of being random is that the monkeys could write Shakespeare today or never. In that view these 'mathematicians' didn't debunk shit.
  • So... would 200 000 monkeys be able to write a research paper about debunking the infinite monkey theorem? I guess that uses a bit less characters.

  • The impossibility of the "monkey problem" has been known for a long time.

    I remember, as an undergraduate in mathematics and physics, taking a 2nd-year statistical/thermal physics course out of Charles Kittel's excellent text. One of the side-notes in the text was about the "monkey problem" -- raised in the context of how extremely large numbers can be counter-intuitive. The side-note calculated that the expected amount of time a moderate number of monkeys (a hundred I think?) would need to write just Shakes

  • Just rent another super cluster in the next simulation over.
  • My issue with this has always been that monkeys, even an infinite number of monkeys, are not going to be running through permutations on the keyboard. They're just going to be banging away at it. And people would say "well, sure but on an infinite timeline everything is inevitable." I disagree, I think on an infinite timeline infinite monkeys would just type "ALJFLDSJF:OJSDGPOSJFG" infinitely.
  • I was not aware that the word banana was anywhere in the works of Shakespeare. Also, I was not aware that 20,000 approximates infinity. I was thinking more like a sequence 20 trillion then 20 quadrillion then 20 quintillion then 20 sextillion then 20 septillion then 20 octillion then 20 nonillion then 20 decillion monkeys might start revealing the shape of the curve for proper curve fitting to gain some insight of where the curve was headed as the number of monkeys approaches positive infinity.

  • You don’t need infinite time anyway, all you really need is infinite monkeys. That way it will only take as long as it takes to type the longest word.

  • We'll be balancing angels on the head of a pin.

    ...as soon as we find some angels.

  • This seems like a good place to link the Library of Babel [libraryofbabel.info]. It has every possible combination of 1.3 million or fewer English characters including space, comma, and period. This very comment is in there, although it's practically impossible to provide the reference as that would change the location.
  • Choose a shorter work... lets say, just the sonnets?

    I know my cousins and a monkey's work is never done.
    Never, I say!

    Never implies infinity, so .. yep, those monkeys will get the job done... eventually
    OR maybe right a way because that is a possibility if they type randomly.
    Maybe they'll bang it out on the first try.
    Prove me wrong.

  • Just take different Monkeys!!

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