Australian Mathematicians Debunk 'Infinite Monkey Theorem' 96
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.
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.
Oh really? (Score:5, Funny)
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)
Re: (Score:3)
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.
Re: (Score:3)
Re: (Score:2)
Adding constraints is ridiculous. Nobody ever thought, "a bunch of monkeys will reproduce Shakespeare in X years." because that'd be absurd.
They have disproven nothing, and I'm pretty sure they would know that, which makes me wonder if they actually claimed to. This may have just been a humorous setting of bounds, and
Re: (Score:2)
Ah but you can put limits on it. Compute the probability that all monkeys become extinct before the all the works of Shakespeare are reproduced, and that working typewriters will exist throughout that time period! The thought experiment assumes that this particular family of mammals will exist in a state to be able to use a typewriter. Even if monkeys and typewriters last a couple billion more years, there is no difference of that to infinity than the support period of Windows 8.
Re: (Score:2)
Re: (Score:2)
You're articulating the other objection based on realism to the pointless thought experiment, that monkeys are non-random.
Re:Oh really? (Score:4, Insightful)
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.
What number comes next? (Score:2)
That is not true. From a finite subset of a sequence, it's impossible to tell what comes next.
Thank you for pointing this out! I so often see brainteaser / puzzle / IQ type of questions that show a series of numbers and ask what number comes next. I keep telling people these is no correct answer to any such question.
In fact, for any given starting sequence of numbers, it's possible to derive a formula that makes the next number any number you want. It's beyond my own abilities, but I have a mathematician friend who has demonstrated this for me.
For example, suppose you're asked "What is the next numb
Re: (Score:2)
I don't think that's a good example. Going to what someone else quoted from Wikipedia on the subject, "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 probability of an even number appearing in your sequence is zero, so the fact that your sequence has not end has no bearing on whether an even number will appear in it.
Re: (Score:2)
The probability of an even number appearing in your sequence is zero
Incorrect.
Do you think there does not exist a function that can produce the series 1, 3, 5, 7, 9, 10?
This is a pretty common misconception that people are disabused of at the beginning of high school Analytical Math, lovingly called anal math.
Re: (Score:3)
I don't think they showed that the universe is not infinite
Re:Oh really? (Score:5, Insightful)
Breaking: "Mathematician" doesn't know the difference between 200,000 and infinity.
PS: Chimps aren't monkeys.
Re: (Score:2)
> PS: Chimps aren't monkeys.
Lol
Re: (Score:2)
PPS: The supposed difference between apes and monkeys is solely an English language problem, an verbal inconsistency. In other languages, there is no difference between apes and monkeys. In French, both are called singes, in German Affen.
Molson Canadian Monkeys (Score:2)
Re: Oh really? (Score:1)
Boltzmann Brains (Score:5, Informative)
Re: (Score:2)
They also have to be spherical monkeys of uniform mass.
This Infinite (Score:5, Funny)
This word you use "Infinite"
It does not mean what you thing it means.
Re: (Score:1)
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?
Re: (Score:2)
Re: (Score:2)
Monkeys are not that dumb to cuddle so close.
Re: (Score:2)
If they monkeys are spread out evenly across space, infinitely in all directions, the the gravitational force of all the monkeys would hold them in place. They could not cuddle even if they wanted to. However, should one monkey sneeze and ever so slightly change its position then the entire monkey-verse would begin to collapse, eventually resulting in what would be known as the Big Crunch of Infinite Duration.
Re: (Score:2)
Inconceiveable!
infinity != 200k (Score:4, Funny)
"Send more chimps." - Zombie in Return of the Living Dead #27528226
Re: (Score:2)
As far as numbers go 200k is pretty low too
Re: (Score:2)
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".
Re: infinity != 200k (Score:2)
Re: (Score:1)
200k is larger than infinity, for small values of infinity
200k is a low value for "infinite" (Score:5, Funny)
Did they major in remedial math or something?
Re: (Score:1)
Re: (Score:2)
I will give that mathematician $200K if he gives me a million dollars.
Re: (Score:2)
These "mathematicians" are weak (Score:3)
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.
Infinite monkeys not infinite time (Score:2)
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.
internet (Score:1)
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)
The Hive Mind has awoken.
We all predicted this.
The connection of all computers and all human knowledge.
It's ChatGPT, monkey brain
Mandelbrot set (Score:2)
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
Re: (Score:2)
Bad title, interesting study (Score:2)
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.
theoretically possible =/= infinite (Score:2)
I hate every ape I see (Score:2)
Australian math (Score:2)
Re: (Score:2)
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)
Re:Infinity is larger than 200k (Score:4, Insightful)
>>Seems like infinite monkeys would produce the full works of Shakespeare on the first try.
Not just one copy, but an infinite number of copies. As well as every other work of literature in every language (that can be typed on typewriter) including those that haven't been written yet. Also the source code for every version of every program that has ever been written or ever will be. Such is the staggering power of infinite monkeys.
Re: (Score:2)
Re: (Score:2)
That would be bananas.
Re: (Score:2)
Infinite monkeys is much larger than 200k monkeys.
They redefined the word "infinite" around the same time as they invented "unlimited" mobile plans in the U.S.
Re: (Score:2)
Infinite monkeys is much larger than 200k monkeys. Seems like infinite monkeys would produce the full works of Shakespeare on the first try.
To be precise, the normal statement of the theorem is that a single monkey hitting keys for an infinite amount of time will produce the works of Shakespeare somewhere in the stream of output. They picked 200k because that's the approximate global population of chimpanzees (which aren't actually monkeys).
In any case, the "debunking" is nothing of the sort. Which, of course, the mathematicians acknowledged, because mathematicians are precise; it was the slashdot editor who called it a "debunking". From th
Oh Yeah?! Well Infinity + 1!! (Score:2)
Apes together, strong!
Many worlds theory (Score:2)
Mandatory ape quote (Score:2)
"Get your stinking paws off me you damned dirty ape! Start typing!"
That's pretty close to the original quote.
What is the point (Score:2)
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.
Planet of the Apes (Score:2)
Simpsons [youtube.com]
Already been done... (Score:2)
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? (Score:2)
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?
Re: What's the difference? (Score:2)
Lots of meta heuristics have proofs of eventual optimality which come from the infinite monkey theorem: genetic algorithms, simulated annealing, etc.
infinite trolls (Score:5, Funny)
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 (Score:2)
They didn't debunk anything (Score:3)
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)
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
Re: (Score:2)
You can do it with 1000 moneys in a finite amount of time
With a finite number of monkeys and a finite amount of time, the probability would never reach 1. You really need either infinite monkeys or infinite time to achieve certainty.
you can pick any probability and number of monkeys and the time will be finite.
Any probability less than 1.
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 try, no need for infinite time at all.
Well, the normal formulation is one monkey for infinite time. Infinite monkeys for finite time also works, as long as you give the monkeys enough time to produce the required number of characters.
Re: (Score:2)
The thought experiment is about an infinite number of monkeys for an infinite about of time.
"Strictly speaking, one immortal monkey would suffice." -- Jose Luis Borges.
Also, it's an easily-proved theorem, not just a thought experiment.
Only need one monkey (Score:2)
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.
Another post conflating math and physics? (Score:2)
What About Capuchin Monkeys? (Score:1)
Including science?? (Score:2)
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
if you accept infinite monkeys, you should also... (Score:2)
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
Re: (Score:2)
Wrong hypothesis (Score:2)
Now if they had asked whether infinite monkeys could produce the works of Sir Francis Bacon, they'd be on to something.
Professor Poopflinger says .. (Score:2)
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
Bait (Score:2)
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.
No one every thought that was a serious suggestion (Score:2)
When did this become a Theorem? It's about luck. (Score:2)
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.
Infinite monkey theorem part deux (Score:2)
This is not news (Score:2)
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
constraints of this universe? (Score:2)
Infinite Garbage (Score:1)
non sequitur and tiniest infinity ever (Score:2)
Re: (Score:2)
I was not aware that the word banana was anywhere in the works of Shakespeare.
It isn't. [theguardian.com] (The Guardian's take on the same story.)
This is fine (Score:2)
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.
For our next trick! (Score:2)
We'll be balancing angels on the head of a pin.
Library of Babel (Score:1)
simple solution (Score:2)
I know my cousins and a monkey's work is never done.
Never, I say!
Never implies infinity, so
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.
Easy! (Score:2)
Just take different Monkeys!!
Not only possible. It happened already. (Score:1)
Re: US Election? (Score:2)
The Universe Itself (Score:2)
The Universe Itself took 13 billion years to create the complete works of Shakespeare and it had to create it's own typewriter.