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So the researchers didn’t refute the assumption “given an infinite amount of time,” and instead chose to address the long finite-time case, which is fundamentally different.
Wasn’t the saying an infinite number of monkeys on an infinite number of typewriters? If so then they’d write Hamlet and indeed every other book written or ever will be written in however long it would conceivably take to type them out if you were copying them.
I don’t really know how this myth? paradox is supposed to work? I know infinity isn’t a number but a concept and in theory I understand what it’s trying to say, but if I have an infinite amount of scrap yards and infinite amount of tornadoes, they can go on forever, but they’ll never assemble a Boing 747.
An infinite number of monkeys typing randomly on an infinite number of typewriters, so long as the writing is truly random, will eventually write every novel. Once you factor in the infinite number of monkeys, every novel in existence will not only be written, it will be written an infinite number of times.
It’s like saying if you had a random number generator and gave it an infinite amount of time generating 16 numbers at a time, it would eventually generate every bank card number ever an infinite number of times. Give that task to an infinite number of random number generators and they will generate every bank card number an infinite number of times instantaneously.
Come to think of it, if the tornado throws around junk completely randomly, and provided there’s enough material in every junkyard to assemble a plane, the tornado will eventually assemble it. That’s the power of infinity and randomness.
Once you factor in the infinite number of monkeys, every novel in existence will not only be written, it will be written an infinite number of times.
You don’t need an infinite number of monkeys to ensure that. The cardinality of an infinite collection of 2-tuples (monkey, char) is the same as the cardinality of an infinite sequence of characters, just as the cardinality of the rational numbers is the same as the cardinality of the integers.
And in a countably infinite sequence of uniformly random characters, there is no assurance that any particular finite sequence will occur only a finite number of times.
🤓
Not the same the monkeys have all the capabilities and tools to cohesively combine letters words and white space. A tornado cannot weld and program controllers and solder. But a monkey can type randomly even wacking randomly. The idea is that given an infinite truly random output of text by the nature of infinity the text of Shakespeare will be outputted in its entirety eventually
The idea is that given an infinite truly random output of text by the nature of infinity the text of Shakespeare will be outputted in its entirety eventually
Only for a certain kind of randomness. For example, it’s possible to construct a random process that at each step emits a uniformly distributed character, but which also includes a filter that blocks the emission of the string “Falstaff” if it occurs. Such a process cannot ever produce the complete works of Shakespeare, since the complete works include that string, though it will still contain (for example) every lost work of Aristotle, as well as an infinite number of false and corrupted versions of those works.
But yeah, an unconstrained uniform-random-distributed countably infinite sequence of printable English characters and whitespace cannot be proven to not contain the complete works of Shakespeare, or any other finite sequence. I believe it’s also impossible to exclude any countably infinite sequence, but I might be wrong on that part, since my mathematics education happened a very long time ago.
I guess that was kinda what I was trying to convey in the truly random part. Truly random in which you have no idea what character will be next, no filter. In that case yes which I believe is what most people think of when they think of random
You know it? That’s nice. A lot of people think they know a lot of things that aren’t really true.
Now prove it.
Same way in the infinite random non repeating numbers of Pi is the binary of a 4k resolution photo of Betty White nude holding a snake on a tiger.
It’s random forever and eventually the 1s and 0s fall into place. The problem is the monkeys repeating themselves.
The problem here is the implied entropic outcomes of each system.
If the monkeys were replaced with true-random number generators, then you’d eventually get shakespear. But they aren’t RNG engines, and they aren’t quantumly random.
Instead, the monkeys have a large-ish but very finite number of logical branches that they can take in their decision-making processes, with slight variations within a fixed genetic scope. They will slam away at the typewriters in a very specific monkey kind of way.
At the end of the thought experiment, you will end up with an infinite amount of monkey-gibberish and a slightly smaller infinite amount of soiled or destroyed typewriters.
If the monkeys’ probability distribution function can be transformed to a uniform distribution by a continuous function, the outcomes are equivalent enough for this exercise. (There are probably some discontinous functions that’d also work). So, unless there’s some genetic weirdness in monkeys that prevents their ever hitting certain keys, they’re adequate RNG engines. But at that point, you’re really tweaking the assumptions based on how realistically you think monkeys are portrayed in the thought experiment.
And I don’t believe “quantumly random” is a necessary condition here.
The study found a finite number of monkeys in a finite amount of time would not write all the works of Shakespeare.
Which is not what the common saying said.
I think their research is empirically falsified already. If chimp = monkey, then “simian” is reasonable generalisation of “monkey” - also that reflects a lot of real english speakers usage of the words.
A less than infinite number of simians have already done it once.
Not to mention that I think they’re assuming no evolution. Fucking chriatian fundamentalists.
Not to mention that I think they’re assuming no evolution. Fucking chriatian fundamentalists.
Wut.
I’m not christian and I assumed the experiment didn’t allow for evolution as it was not specified in its parameters. I assumed that the monkeys were a horrible (and very wrong) analogy for random number generators, were immortal, and had no time for making offspring as they were all trained and consumed with typewriting, or physically separated from one another.
The monkeys would produce wildly more limited results than a random number generator mind you, and they are essentially frozen in evolutionary time, so they are not going to be writing shakespear.
A less than infinite number of simians have already done it once.
And how likely is it that it’ll be done again identically by a finite set of simians?
Next they’re going to tell us that a bird sharpening its beak every thousand years wouldn’t wear out a mountain made of diamond.
It’s soft tissue from benares touching a mountain every century, right? A kalpa IIRC.
A monkey already wrote Shakespeare. Anything it’s possible.
I chimp, therefore I am.
Yes, a different cuestion usually has a different answer
A stupid article akin to someone on Lemmy misunderstanding an idium and going “well actually…”.
And that’s coming from me, a person who likes knowing how insanely unlikely it is a guess ever longer and longer pass phrases. A computer trying to brute force Hamlet would also fail before the heat death of the universe (probably, anyway- do the math and you too can publish junk!).
To quote the theme song of a science show on BBC radio:
If infinite monkeys type every day
They may accidentally write ‘Hamlet’ the play
But they’ll probably shit on it and throw it away
In the Infinite Monkey Cage
This doesn’t bode well for my typewriting monkey startup
Aka most AI startups.
Basic information theory.
insane that THIS gets headlines which is literally just recording a monkey with a keyboard and running 3 lines of python, purposely missing the point of the saying.
Yeah, no, using a finite number to try and disprove a theory that is all specifically about infinite numbers isn’t poking holes in anything…
It’s more a “yeah, but…” than a refutation.
the time it would take for a typing monkey to replicate Shakespeare’s plays, sonnets and poems would be longer than the lifespan of our universe.
Which means that while mathematically true, the theorem is “misleading”, they said.
Gotta read the articles 👍
If there are an infinite number of trials (either infinite monkeys or infinite time), the outcome is truly random, and the desired text is finite, it must necessarily happen at some point. In fact, it’d happen an infinite number of times.
The original thought experiment clearly states infinite. As soon as you bound that in any way (such as not infinite monkeys, but 1 monkey for every atom in the universe) you’re talking about another experiment entirely. Infinite means infinite, not really really big. Gotta use some critical thinking 👍
If you have infinite time, you don’t also need infinite monkeys.
The theorem is not misleading, it literally states infinite monkeys. Not 200k monkeys or even 200 decillion monkeys, infinite. If it’s possible for the monkeys to press the keys in the right order, then the time it will take for one of them to write Shakespeare’s complete works will be limited only by their typing speed.
The “theorem”, if we wanna call it that, says that, given an infinite amount of monkeys and time, they could write Shakespeare.
This doesn’t mean it’s actually possible in the real world, it’s just to say that random events can seem, from the outside, like intelligent creations. Like a cloud that looks like a pig, no one actually created it to look like that, it was just random happenstance.
Gotta read the articles 👍
No, you…
As well as looking at the abilities of a single monkey, the study also did a series of calculations based on the current global population of chimpanzees, which is roughly 200,000.
(E: never mind that, as has already been suggested to you, the theoretical thought experiment in question specifies not only infinite monkeys, but infinite time too, so they’ve not stuck to either parameter)
(E: never mind that, as has already been suggested to you, the theoretical thought experiment in question specifies not only infinite monkeys, but infinite time too, so they’ve not stuck to either parameter)
Whoah, whoah, whoah… Big critical thinker here thinks the paper is about disproving a thought experiment?
You understand that this is impossible? Even if it were attempted, such a venture is more a philosophical one, not a mathematicians forte.
Obviously the paper is not looking at that, it’s doing math
“Yes, it is true that given infinite resources, any text of any length would inevitably be produced eventually. While true, this also has no relevance to our own universe, as ‘reaching infinity’ in resources is not something which can ever happen.”
That needing to be pointed out to you is… Well you’ll have to excuse me if I don’t waste my energy “critically thinking” yet 👍
What exactly is misleading about the theorem? Does anyone actually expect to setup some monkeys and typewriters and get something legible?
The theorem states that given an infinite amount of time, which is outside the realm of the life of the universe.
Trash “research” and trash journalism covering it. First they find that monkeys would write Shakespeare, it would just take on average longer than the entire existence of the universe. They then try to infer that how long it takes is relevant. It is not. The calculation is vaguely interesting as a curio but the shoehorned “discussion” and interpretation to get attention is crap and another example of bad science misleading people.
It’s pointless and stupid - the thought experiment itself is that infinite monkeys typing would eventually type the whole of Shakespeare. Not how long it would take. The whole point of it is that in a truly random system all known patterns should eventually emerge somewhere within it. The length of time it takes for the pattern to emerge is irrelevant as the idea is based in infinity. So for example if there is a truly random infinite multiverse then in theory all imaginable possibilities would exist somewhere within it at some point.
The whole point of it is that in a truly random system all known patterns should eventually emerge somewhere within it.
So pi (probably) has this property. There are some joke compression programs around this (they don’t really work because it takes up more space to store where something in pi is, than storing the thing itself). But it is funny, to think that pi could theoretically hold every past, present, and future piece of information within those digits after the decimal.
https://github.com/philipl/pifs
https://ntietz.com/blog/why-we-cant-compress-messages-with-pi/
Also interesting is the notion of ‘Kolmogorov Complexity’ - what is the shortest programme that could produce a given output? Worst case for a truly random sequence would just be to copy it out, but a programme that outputs eg. a million digits of pi can actually be quite short. As can a programme that outputs a particular block cypher for an empty input. In general, it is very difficult to decide how long a programme is needed to produce a given output, and what the upper limit of compression could be.
