What kind of "study" would this even be? I thought the point of the infinite monkey thing was to talk about regular distributions and eventualities of every possible string showing up. I don't think anyone claimed that any relatively-long string would show up in any reasonable amount of time necessarily, but it's kind of a bizarre assertion to make.
It's sort of like stating the runtime efficiency of a Bogosort; the runtime efficiency is unbounded. Theoretically any list could be sorted on the first run, but it could also just keep sorting in an unbounded fashion for forever, though given enough time (which could be tens of trillions of years or longer), it will eventually be sorted if we assume regular distribution of random numbers.
I think it is even worse: infinite instances of bogosort are 100% guarantueed to finish instantly, because we are running in parallel here and the ones that are unbounded don't matter at all when at least one of then gets it right. And given the fact that there is a non-zero chance of bogosort getting it right first try, means it there are infinite bogosort instances getting it right first try.
This is also true for the infinite typing monkeys: one of them is getting it right by chance, unless that chance is 0 (and it isn't).
The theorem is called "infinite monkey theorem". That means infinite amount of time. A googol years is not infinite, it's infinite times smaller than that. In an infinite amount of time they will write Shakespeare works (if they type randomly enough and not with some bias like never typing certain combinations of letters)
Also, at least the article could have said what the actual probability is then? Are we talking 1e-500, 1e-1000000, 1 / googolplex, or what?
EDIT: of the above examples 1e-1000000 is the closest I think (in order of magnitude of exponent), based on something like 30^5000000 divided through some amount of years assuming ~5 characters per word. So perhaps "If every atom in the universe was a universe in itself" won't get us there, but recursively repeat that process a million times and we do get there
Reverse Gellman effect: you witness pedants in your own domain surgically tear down a harmless puff piece and immediately know this must be happening 24/7 in every other domain where fun is modestly attempted
Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.
> Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.
I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.
> Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side.
That's a nice thought, but that's giving the average person too much credit when it comes to probability. In my experience, most people's understanding of probability is very poor. For example, few people truly understand the concept of independent events.
Most people believe that after flipping 10 heads in a row, the probability of tails on the next flip is much higher.
I'm sure you could convince a rational individual that the assymetry of the coin makes 50/50 impossible. But I doubt that the average person has ever really considered it.
> the event it describes WILL eventually occur given enough time/trials/etc.
What's the meaning of writing WILL with capitals, and then saying "nobody is talking about the real, actual universe"? What is the value of certainty about what WILL happen in hypothetical universes?
> What is the value of certainty about what WILL happen in hypothetical universes?
Talking about something that would take greater than 1 googol years in our universe has about as much value as talking about something that would take 1 googol years in our universe.
In other words, the fact that something might probably occur right before the heat death of the universe, rather than after, isn't particularly useful either. For that matter, there's about an equal value in talking about something probably "only" a trillion years out, either.
I don't think I've ever heard anyone use the infinite monkey example outside of theoretical mathematics; I'm sure someone has, but when I've heard it, it was to describe regular distribution of random.
I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.
Perhaps not in our observable universe, but in the space of all possible physics that could take place and / or beyond the observable universe if it actually is infinitely big there, perhaps it can? (as in, anything can happen, there will be copies of the Earth with subtle differences somewhere there, Boltzmann brains appearing purely out of quantum fluctuations, etc...)
Yes, I always imagined this being just a silly exercise in pulling out a finite outcome from infinity. It’s not meant to be provable or disprovable, just hard to comprehend because we cannot think in infinite terms.
Yeah, I might be naive, since they're professional mathematicians and I'm not, but their conclusion feels like saying that they "tested" the concept of infinity and found that it's simply unreachable. To me, the infinite monkey theorem is an abstract idea and not something that needs to be "tested", though it's certainly fun to run the numbers.
They didn't "test" the concept of infinity. They said that the results of the infinite monkey theorem are well known, and they wanted to see what happens in the finite case.
"Infinite monkeys" would produce Shakespeare and every other book, document, and all future possible book and document in the amount of time equal to the number of letters in the book and the typing rate of a monkey. It wouldn't take an infinite amount of time. :)
Not the point of the article, but this got me curious...
> Shakespeare’s canon includes 884,647 words – none of them banana.
If this article (1) is accurate, Shakespeare never even knew what a banana is, and he never tried it, since he died ~2 decades before they came to England:
> England got its first glimpse of the banana when herbalist, botanist and merchant Thomas Johnson displayed a bunch in his shop in Holborn, in the City of London, on April 10, 1633.
If you try to write Shakespeare with hurdy-gurdy keys, you're going to get slightly abridged versions, like that famous tragedy A ad Ceaa, or the comedy Ced f E.
> 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 thought the saying was “infinite monkeys..” and in that case you would get the full works of Shakespeare immediately. With an infinite amount of time and one monkey you’d get the full works of Shakespeare in every language supported by the typewriter any number of times in a row you wished. In fact, you’d get anything you wanted as long as the probability was > 0
Edit: after walking my dogs, isn’t the probability of the full works of Shakespeare never being typed out also > 0? (I can’t believe I’m actually spending calories on this..)
I'm picturing scientists in another universe clenching their butts as the monkey goes to type the last letter of Hamlet..... and misses 't' for 'r' and the whole observation hall erupts with loud groans
Sounds to me that the more interesting question would be graphing out the relationship of time and the amount of monkeys needed for one to write Shakespeare.
Kind of embarrassing to even be in this thread spending time here but would it not also be probable, however unlikely, to never get the full works of Shakespeare?
The reporting on this paper is crazy. In the highlights section of the paper’s page on the journal’s website it says “The long-established result of the Infinite Monkeys Theorem is correct, but misleading.” but the Guardian article says “Australian mathematicians call into question the ‘infinite monkey theorem’ in new research on old adage”, which I read as contradictory to what’s in the paper.
I am biased by my religious beliefs, but I've always struggled with the idea that abiogenesis could spontaneously occur in "just" a few billion years on earth. A few billion seems like not enough time. Even the simplest forms of life are mind bogglingly complex.
Of course, it's a few billion years scaled across >1 life-friendly planets (since it only has to happen on 1 of them), but still just seems like not enough monkeys and typewriters in the given timeframe to produce something as astonishingly complex as life, let alone Shakespeare.
So this comes up a lot. I often think about the case of protein structures.
Let's consider a protein of 100 amino acids; although most proteins are in the 200-500 range (IIRC) it makes the maths simpler. Even for such a short sequence, the probability of coming up with one specific sequence at random is incredibly small - 20 to the power of 100 or 1.267651e+130.
The simple answer to this apparent puzzle ('how did proteins evolve from random mutations') is of course that it did not happen like this. Not at all like monkeys typing out scripts and a human checking if they have produced a Shakespeare play yet.
In fact, there are multiple solutions to the same problem - in the analogy, this would be like multiple different versions of the same play being just as good as the other. Even better for evolution, you can - in a sense - put on a version of a play that is pretty bad, but just good enough to put in front of an audience. In other words, some enzymatic functionality can be better than none.
In this way, an evolutionary system can build up complexity by making parts that are _good enough_ and are roughly equivalent to other parts that can be replaced gradually. Combine this with the massive parallelism and the scale of the molecular world, and a billion years can accomplish a lot.
Except abiogenesis didn't occur on Earth in few billion years, but within half to billion years after Earth was habitable. All the other features of life have taken four billion years to arise through evolution. It is like looking at current cars and wondering how they could come from nothing where had to look at the original cars and hundred years of improvement.
Abiogenesis really only need to explain how the first life arose. It could have been really simple since it got out competed by more sophisticated descendant that took over planet and left no trace of original life. We don't know how it happened, if required lots of random chance or if there was a replication step that made if go faster. We know that evolution can make complicated stuff over time.
Where would you get an intuition about how much time a billion years is? Or for what is "mind boggingly complex" and what not? How many eons have you lived? People who claim it is possible have better arguments than "to me it seems". Do you have a number for "this would seem to me as enough time"?
Do you also struggle with the idea of a poll being close to the truth when done on a sample of 1000 persons, out of tens or hundreds of millions? Math and science are often not intuitive. But they work.
Have you ever considered the possibility of supernaturally guided evolution. Always seemed like an interesting possibility to me. So God creates an incredibly beautiful concept that life comes from. Seems like one of the most probable solutions to how astonishingly unlikely abiogenesis would be.
This is a very computer science and not scientific response, but I look at the Game of Life, and it makes me realize that little patterns naturally form everywhere. Biology is just a little pattern that wants to replicate and survive and that doesn't have to mean intelligently.
> Biology is just a little pattern that wants to replicate and survive
I don't really see biology as being a "little" pattern. To me, looking at the jump from replicating molecules in chemical soup to single cell organisms is like looking at the jump from an abacus to an Intel i9 processor.
Who said you had to junp to single celled organisms first? One of the oldest displays at a science museum I remember was very simple. It was basically a rubber sheet attached to the top of a spinning pole resmebling a folded umbrella without the spines. There was a adjustable knob you could play with to adjust the speed that it spun. It would start from zero. Versus interestingly to me, the exhibit demonstrated that at certain speeds the dangling edge of the rubber sheet would form nice sine waves at certain speeds. It might be chaotic at first but eventually, given just the right amount of energy to spin, the wave would appear. If you sped it up or slowed it down, sometimes the wave would collapse, but if you hit another natural frequency, it would eventually snap into a larger or smaller amplitude with a greater or lesser amplitude. My take away was that if there is enough energy and repetition to almost anything, eventually patterns will arise. And if you let them do that long enough, then even in imperfect environments, relatively stable outcomes would occur. Much like life in my opinion. Have enough chemicals and energy thrashing around long enough in a cycle, and enough adverse selection against all those structures, eventually some structures will emerge and self-reinforce. Doesn't gotta start with cells, just molecules.
I would guess that abiogenesis is often framed around randomness as a strategy to argue for its implausibility. Of course, a completely random system is unlikely to produce enough coherence to convince anyone that it could be possible.
But in reality, the universe is full of patterns. The laws of physics are not random. Water behaves in very specific ways. Our planet revolves around the Sun in 365 day intervals. The planet rotates every 24 hours. Even out of these two interlocking patterns, you can see how energy delivery to the surface of the planet could result in mechanical and chemical cycles that may result in non-random mineral formation, concentration gradients, and thermal dynamics.
Scientists argue that abiogenesis is a result of inherently chaotic but non-random processes, not a hypothetical probabilistic scenario like monkeys with typewriters.
> the jump from an abacus to an Intel i9 processor
Call it 75 years (1942 - before electronic computers to 2017 - first i9) which is about 39M minutes. Assume human innovation can work on an minutely cycle[0] and you've got 39M iterations from "no electronic computers" to "Intel i9".
I'd put decent money on there bring several orders of magnitude more chemical reactions than that per second in the primordial soup (good conditions for fast reactions and there was A LOT of it.) And it had about half a billion years (fifteen quadrillion, seven hundred seventy-eight trillion, eight hundred billion seconds) to cook before things really started happening.
Statistically, it was likely.
[0] Obviously optimistic but giving parallelism a chance.
I don't think religion has anything to do with it. Statistics and increasing entropy. Now, where you go from there might take you to religion, and so I'd argue that modern science often has arguably more to do with the religion of atheism than with reason since it's mostly based on certain axioms. I'm not saying we can't derive science off of theories, but as long as the bases are only asserted, you can derive proofs to come to any conclusions and speaking up about this seems to quickly get you disqualified in academia.
What if something in monkey psychology causes them to hit the keyboard with their fist or palm every five minutes or so of typing? What if they regularly lapse into just pressing one key over and over? It seems very unlikely to me that even with infinite monkeys a work would be generated, because they're not actually random number generators.
From the original mathematics paper (open access):
in the long-running television show The Simpsons, the industrialist Charles Montgomery Burns attempted this with multiple monkeys chained to typewriters but gave up when the best one produced was the near-Dickensian “It was the best of times, it was the blurst of times”.
new HN game: predict which order the archive.is link or pedantry comes in. if you get the order right, you get one point. if you get sucked into a pedantic argument, you lose
The basic point is an exercise in at least one older freshman text (Kittel & Kroemer?) but at least this paper does go on beyond and finds some strings (eg "I chimp, therefore I am") that are likely to be typed before the heat death of the universe, if not before extinction of chimpanzees.
If you take it literally, there is a non-zero chance that a monkey types the entire works of Shakespeare. I mean, it has already happened: who is Shakespeare but an intelligent monkey? (don't tell the librarian...)
For that to happen again, a monkey has to evolve into an intelligent specie interested in human history, find the complete works of Shakespeare, and write it. It is more likely than using probabilistic arguments using letter frequencies, or actual monkeys[1].
So let’s say we’ve got 28 possible characters (alphabet + period + space), you have a 1/28 chance of getting the first character right. So it follows that a string of length n is (1/28)^n because you have to hit each character correctly in a row. If we can do x guesses a second, and we know on average how many tries it takes on average to get our string right (28^n), we can divide and get an estimate of time. Though we could do it faster, or slower depending on our luck.
With multiple searchers it’s trickier, but we use the probability complement (probability of all possible events must add to 100%) to figure out the chances that our searchers all miss, and subtract that chance by 1. This gives the chance of at least one agent getting it right. Two searchers looks like 1-(27/28)^2 for the first char, and you can follow the same logic for any length string.
Your answer will heavily depend on your assumptions - how fast the computers guess, what they can guess, etc. But searching in parallel would speed things up dramatically. If you had like 100 computers searching simultaneously, 3 or 4 would likely get the first char right every time, giving you a big speed up on the problem.
> even if all the chimpanzees in the world were given the entire lifespan of the universe
Seems to me like a flawed “study” if the baseline assumption is that chimpanzees would type randomly even when given lifespans through the heat death of the universe, which is estimated at 10^100 (googol) years!
I would argue it is conceivable that given enough time, a monkey or ape species can evolve that is intelligent enough to write Shakespeare’s full works.
Specialists in the business tier, where monkey business usually happens. Members of this clan have a traditional fighting style which involves throwing wrenches at their opponents; this is tolerated because it is not the worst thing that Monkeys have been known to throw.
There is a theory that a finite number of Laughing Monkeys pounding away randomly at a finite number of keyboards will eventually get a clean compile. The existence of the Standard PHP Library would seem to imply that this has already happened.
That's only worth mentioning because the PHP stdlib is mostly written in C. The general proposition (for any language) is trivially true since 93% of ink blobs are valid Perl programs.
Was this seriously a question? I mean, this is something a college student or advanced high schooler could calculate.
The law of large numbers is still correct. Nowhere is there a requirement that the large numbers be smaller than the various physical constants of the universe.p
The paper doesn’t say that either. They only call the original theorem misleading. I understood that their point is the same as yours - that infinity won’t happen in a finite time period.
> The long-established result of the Infinite Monkeys Theorem is correct, but misleading.
> Non-trivial text generation during the lifespan of our universe is almost certainly impossible.
> The Finite Monkeys case shows there will never be sufficient resources to generate Shakespeare.
I don’t see how the original is misleading. The word “infinite” isn’t hidden or anything… unless the definition of infinite is misleading but I think it’s use here is pretty clear.
“Infinity” on its own is clear, but in tandem with monkeys it could get confusing.
If you remember that a monkey here is also a theoretical construct then I guess all is fine. But otherwise monkeys need at least a universe to function and that is finite.
Perhaps it would have been seen as less confusing if it was a demon[1] that enters random letters instead.
You're comparing chalk and cheese to an extent, a perfect copy of Shakespeare's work can exist in exactly one way but DNA isn't required to be copied perfectly, DNA can change without necessarily killing the organism or otherwise rendering it unable to reproduce. Additionally evolution is not a random process, while mutations are random the process by which the mutations are selected is not - it depends on whether the mutation is a reproductive advantage for the organism in the context of their ecological niche. Most mutations are going to be neutral or disadvantageous so they won't be selected. Additionally you're not mutating the whole DNA sequence at once, just parts of it.
I would like to see someone use the most generous parameters possible and simulate the statistics of the first cple amino acids evolving into our homo sapiens sapiens chromosome set randomly over the course of just 4b years.
(selection is irrelevant here; we could even just model it as always-select-for-beneficial-mutation for extra graciousness).
Mind you, even if a beneficient mutation occurs, it is still not guaranteed to be passed onto the next generation. It would have to randomly occur over and over again.
I'm not confident that it's gonna be very convincingly in favour of the random mutation model.
>Mind you, even if a beneficient mutation occurs, it is still not guaranteed to be passed onto the next generation. It would have to randomly occur over and over again.
Why would it have to re-occur again and again? If the mutation is beneficial to the reproductive success of an organism, by definition their mutation will be passed on with no need for it to occur again by chance. The percentage of the population with the mutation would grow, potentially very quickly if it was a strong advantage over the previous generations. You're also characterising evolution as if to get from amoebas to humans you require a series of billions of independent coin-flips which isn't an accurate model, rather each generation is building on that which preceded it. Take the eye as an organ for example, it predates humanity by a very long time and was not independently evolved by humans - there was no need for it to have been since those genes already existed.
The predictions of evolution are generally supported by the available evidence at any rate, if you'd like to overturn it you'll have to propose a theory that explains the evidence more compellingly.
> Why would it have to re-occur again and again? If the mutation is beneficial to the reproductive success of an organism, by definition their mutation will be passed on with no need for it to occur again by chance.
Are you certain this is correct? An individual with a genetic mutation does not necessarily pass it down to its offspring, even if it was beneficial, in my understanding. So there is a probability p of passing it down and 1-p of not doing so.
In the latter case, the beneficial mutation is lost. Now the way evolutionists seem to "solve" this is by conjecturing that since the mutation is beneficial, it will arise in multiple individuals independently and eventually get passed down. Even if I grant this, it makes the statistics once again much more unlikely for this to occur.
> The predictions of evolution are generally supported by the available evidence at any rate ...
Depends which subarea of evolution. No actual speciation based on random mutation has ever been observed (let alone ones predicted by evolution) as far as I'm aware.
Micro-evolution or expression of previously not-expressed but already present genes is a different topic, and not something I have issues with.
All I say is evolution is at best insufficient to explain us. And we haven't even touched consciousness.
>Are you certain this is correct? An individual with a genetic mutation does not necessarily pass it down to its offspring, even if it was beneficial, in my understanding. So there is a probability p of passing it down and 1-p of not doing so.
That value for p is still going to be considerably greater for the gene to be passed on than the probability of that gene arising again randomly through mutation though. Consider the example of eye colour for example, chances are two brown-eyed parents are going to have brown-eyed children too - certainly a greater probability than a random mutation will intervene to make their eyes purple.
>Depends which subarea of evolution. No actual speciation based on random mutation has ever been observed (let alone ones predicted by evolution) as far as I'm aware.
There have been empirical studies of species separating and the mosquitoes on the London Underground are a good example, surface-dwelling mosquitoes cannot interbreed with those from the tunnels. At any rate it's actually quite a difficult thing to study since we're not looking at a binary situation of 'they have gene x now and therefore they're a separate species', that's not how evolution works and I don't think any biologist would claim this to be the case. At the end of the day species are human classifications made based on scientific observation rather than perfect formal categories, we define a species to be that which cannot interbreed with another and produce fertile offspring but that's our classification not nature's - species diverge gradually after taking many different evolutionary paths rather than there being a binary instant they're separate from each-other. The classification of species can only ever be so good because it's attempting to draw a fixed line on a moving canvas.
I think when arguing against the theory of evolution it's tempting to make arguments along the lines that each species is assigned some kind of intangible Platonic form towards which evolution must work but this isn't the case at all, there's no law of nature that says one species has to take x form and another must take y form. There's no Platonic cat which makes a cat a cat rather than a dog or a goldfish, a cat is merely one of the many possible organisms that can fill the ecological niche that cats occupy; and we classify them with our imperfect system of biological classification. I think it's putting the cart before the horse to essentially say that evolution is a flawed theory because our system of categorising species doesn't have the resolution to capture the exact moment species diverge from each-other.
>Micro-evolution or expression of previously not-expressed but already present genes is a different topic, and not something I have issues with.
Micro-evolution versus macro-evolution is a bit of an old canard in my opinion, the idea that they're separate processes rather than a continuum of the same process doesn't really exist outside of creationism which in my opinion is a much more difficult theory of our origins to argue than evolution. I spent some of my early life as a creationist so I'm not unfamiliar with its nuances, but personally I'm yet to hear a creationist argument that is particularly compelling to people who aren't already invested in the existence of a Creator rather than approaching the subject neutrally.
> All I say is evolution is at best insufficient to explain us. And we haven't even touched consciousness.
Consciousness is definitely a much more interesting problem in my opinion, and there's definitely no good theories of consciousness yet as far as I'm concerned. I think the notion of qualia in particular poses a lot of difficulties for a purely materialistic understanding of consciousness for example.
Also wouldn’t a DNA sequence get more likely as time goes on as it builds from the past and is not uniformly random? In the mokey/typewriter thought experiment no previous correct keystroke makes the next keystroke more likely to be correct. However, with DNA/life once it starts the next iteration is more likely to be better since it has the previous success to build upon.
The actual problem is upstream of that at the abiogenesis stage.
For evolutionary selection to occur the machinery for selection must exist. Specifically information storage (DNA/RNA), replication(polymerases) and actioning (transcription) all are needed, and must continue to be able to exist for long enough to matter.
Without selection pressure and inheritance you're just left with requiring a big enough universe and enough time for randomness not to matter.
The critical difference is evolutionary only needs relatively short sequences to be randomly generated, and there’s many valid sequences.
Building a book by generating a single random text string is practically impossible, but if you lock in any given word that’s correct and retry that’ll quickly get something. You’ll have most 8 letter or shorter words correct after 1 trillion runs, and many 9 letter words. It wouldn’t be done, but someone could probably read and understand the work at that point.
Further it’s possible for a few even longer words to match at that point. People think it’s unlikely that specific sequences happened randomly, but what they ignore is all the potential sequences that didn’t occur.
The many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
> You’ll have most 6 letter or shorter words correct after 1 billion tries.
You think that's "quick" for dna which is made up of billions of 6-base-sequences and for a species that can only reproduce sexually once every decade or so at best?
> many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
There’s finite invalid sequences, DNA isn’t infinitely long. It’s also not a question of valid or invalid we live with sub optimal DNA, so yea most people aren’t born with some new beneficial mutation. However, not winning the lottery isn’t the same things a dying, and even smaller wins still benefit us.
As to our long reproductive cycle, there’s a reason we share so much in common with other primates. Most of our DNA has been worked out for a long time. We share 98% of our DNA with pigs, and 85% of it is identical in mice which has practical application in drug development. Of note common ancestors were more closely related to us because both branches diverged.
Hell 60% is shared with chickens, and half of it’s shared with trees.
> only reproduce sexually once every decade or so at best?
Many sperm and fetuses die from harmful mutations, live babies are late in the process here. Also, because order doesn’t matter you get multiple chances to roll the same sequence for every birth.
PS: There’s also quite a bit of viral insertion into our DNA, it’s mostly sexual reproduction but we have some single cell ‘ancestors’ in our recent history.
> The many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
I dont know about the relative numbers but I don't think you do either? Are you begging the question or can you quantify?
> You think that's "quick" for dna which is made up of billions of 6-base-sequences and for a species that can only reproduce sexually once every decade or so at best?
We didn't start from scratch, we are very very late in the game, and the groundwork for us was laid by millions of other species that can replicate quickly, often very quickly.
Unless you believe the Earth is only six thousand years or so old, in which case we might as well leave the discussion where it is.
You are just repeating the point that was being argued against.
If the lifetime of the universe isn't enough to randomly produce Shakespeare, 3-4 billions of years are cute but useless to randomly produce anything even near as sophisticated as our 46 chromosome set.
I imagine Dawkins still just repeats the conjecture "but it's 3-4 billion years, anything can happen!"
A work of Shakespeare is a single specific target, that's why it takes so long to hit it - one letter out doesn't cut it. DNA meanwhile is a general purpose animal kit that has many billions of 'correct answers'. It's not about sophistication.
Just give them a typewriter that records the position of where the key is pressed to a million bits accuracy, convert that to a series of ASCII characters (through a hash function), and the monkeys will type very fast.
That’s really funny. Give the keyboard a big enough buffer to hold Shakespeare and flush it to the screen on startup. With infinite monkeys and therefore infinite buffers the monkeys don’t even have to type!
Yeah exactly, it's a thought experiment about infinities... Is someone going to publish a study concluding that Hilbert's Hotel couldn't be built on Earth too?
Why are people even spending money on this research? What are they trying to prove/disprove?
It's funny that so many people are confused about why this was written. The monkeys argument was originally used against the theory of evolution; "what's the probability that a monkey banging on a typewriter will type out Hamlet? It'll never happen, and that's why evolution is impossible." Then, someone made the counter-argument that given enough time, the monkey will type out Shakespeare. This paper argues that as long as the time is finite on the order of the age of our universe, the monkey will not type out Shakespeare.
I mean this is a really simply thing to work out. There are 30^n strings of length n that can be made by mashing a 30 key keyboard. The time to the heat death of the universe is 10^100 years which is approximately 30^72 seconds. Your odds of getting a string of length n in the lifetime of the universe is
( number of monkeys * typing rate in characters per second * 30^72 ) / 30^n
The authors plugged in 200,000 (=30^3.5) and 1, meaning their odds are 30^75.5 / 30^n = 30^(75.5-n)
For a string of less than 69 characters, the odds are fantastic. For a string of more than 82 characters the odds are abysmal. At 69 the odds of the substring existing are roughly equivalent to losing the lottery, and at 82 the odds are equivalent to winning the lottery.
Shakespeare's shortest sonnet, 126, is a string of 533 characters.
Empirically a monkey did already creat the works of Shakespeare in a mere 13billion years. This is the time it took for the universe to form, earth to evolve to create a monkey that could write all those words down. The entire process from start to finish is way more complicated and random than anyone typing 26 character randomly into the keyboard. But I guess we are talking about uniform distributions here.
You're replacing a hypothetical situation meant to illustrustrate mathematics with something else. The monkeys don't eat, evolve, age, conspire, have agendas or agency, they type randomly as a means to invoke visual imagery of a monkey slamming it's hands down ignorantly on a typewriter. It's chaotic slamming is the "input" that gets eventually distributed in different ways, one of which, if given enough time, will be identical to shakespeare.
Assuming implications to theology or genetic sequencing where none were given is a reflection of your ability to handle rational discussion of the material.
This sub-thread moved on from the original hypothesis as soon as innagadadavida put forward his non-empirical empirical example. Take it up with him, he may also enjoy your evaluation of his rationality.
But universe as we understand it is endless / infinite on time scale, no? [1] has some nice projections how even basic quantum stuff eventually breaks down, yet nothing is really ending, if you don't count matter as we know it.
Granted, the schedule is of maximum generosity. But does it not seem unfair to ask a monkey to compose the entire works of Shakespeare, considering Shakespeare himself might have been incapable of such a feat?
And while it may take an army of them, we know these creatures are at least capable, collectively, of operating the Daily Mail, which is still all pretty early given the time remaining.
I mean, in several models, including the current most-likely one (last I heard) it effectively is finite. Eventually no new planets or stars can get created, and then some time after that, no atoms can exist.
Will the "universe" exist after that? Kind of a philosophical question, but nothing interesting will exist _in_ the universe.
These Mathematicians are very selective about which aspects of the universe they want to regard and which aspects they want ignore. Like, yeah you can take an imaginary situation and imagine that it's possible, or impossible. It can go any way because it's imaginary. No need to waste time on math, you can just imagine any outcome you like.
In reality, however, I think if you had a system that feeds a monkey a treat every time it strikes a letter key that corresponds to the next letter in a Shakespere play displayed on a monitor, you would eventually have some Shakespeare typed out by a monkey.
One could also just have a monkey mash keys for a while, and then after removing all the unnecessary letters you'd be left with a Shakespearian play.
Or, with a group of monkeys and plenty of time one could use natural selection to evolve them into a literate species that could handle the task easily. This is the method currently in use for the typing of Shakespeare. It has already been done, many times over.
> One could also just have a monkey mash keys for a while, and then after removing all the unnecessary letters you'd be left with a Shakespearian play.
What kind of "study" would this even be? I thought the point of the infinite monkey thing was to talk about regular distributions and eventualities of every possible string showing up. I don't think anyone claimed that any relatively-long string would show up in any reasonable amount of time necessarily, but it's kind of a bizarre assertion to make.
It's sort of like stating the runtime efficiency of a Bogosort; the runtime efficiency is unbounded. Theoretically any list could be sorted on the first run, but it could also just keep sorting in an unbounded fashion for forever, though given enough time (which could be tens of trillions of years or longer), it will eventually be sorted if we assume regular distribution of random numbers.
ETA:
Ok, I read through the actual paper, and it's clearly meant more as a joke, which I don't think was made clear in this article: https://www.sciencedirect.com/science/article/pii/S277318632...
I think it is even worse: infinite instances of bogosort are 100% guarantueed to finish instantly, because we are running in parallel here and the ones that are unbounded don't matter at all when at least one of then gets it right. And given the fact that there is a non-zero chance of bogosort getting it right first try, means it there are infinite bogosort instances getting it right first try.
This is also true for the infinite typing monkeys: one of them is getting it right by chance, unless that chance is 0 (and it isn't).
The theorem is called "infinite monkey theorem". That means infinite amount of time. A googol years is not infinite, it's infinite times smaller than that. In an infinite amount of time they will write Shakespeare works (if they type randomly enough and not with some bias like never typing certain combinations of letters)
Also, at least the article could have said what the actual probability is then? Are we talking 1e-500, 1e-1000000, 1 / googolplex, or what?
EDIT: of the above examples 1e-1000000 is the closest I think (in order of magnitude of exponent), based on something like 30^5000000 divided through some amount of years assuming ~5 characters per word. So perhaps "If every atom in the universe was a universe in itself" won't get us there, but recursively repeat that process a million times and we do get there
Reverse Gellman effect: you witness pedants in your own domain surgically tear down a harmless puff piece and immediately know this must be happening 24/7 in every other domain where fun is modestly attempted
Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.
> Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.
I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.
Have you heard of a Boltman Brain? It's the kind of absurdity that happens when people think seriously about this in the real, actual universe.
https://en.wikipedia.org/wiki/Boltzmann_brain
> Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side.
That's a nice thought, but that's giving the average person too much credit when it comes to probability. In my experience, most people's understanding of probability is very poor. For example, few people truly understand the concept of independent events.
Most people believe that after flipping 10 heads in a row, the probability of tails on the next flip is much higher.
I'm sure you could convince a rational individual that the assymetry of the coin makes 50/50 impossible. But I doubt that the average person has ever really considered it.
> the event it describes WILL eventually occur given enough time/trials/etc.
What's the meaning of writing WILL with capitals, and then saying "nobody is talking about the real, actual universe"? What is the value of certainty about what WILL happen in hypothetical universes?
> What is the value of certainty about what WILL happen in hypothetical universes?
Talking about something that would take greater than 1 googol years in our universe has about as much value as talking about something that would take 1 googol years in our universe.
In other words, the fact that something might probably occur right before the heat death of the universe, rather than after, isn't particularly useful either. For that matter, there's about an equal value in talking about something probably "only" a trillion years out, either.
I don't think I've ever heard anyone use the infinite monkey example outside of theoretical mathematics; I'm sure someone has, but when I've heard it, it was to describe regular distribution of random.
I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.
Perhaps not in our observable universe, but in the space of all possible physics that could take place and / or beyond the observable universe if it actually is infinitely big there, perhaps it can? (as in, anything can happen, there will be copies of the Earth with subtle differences somewhere there, Boltzmann brains appearing purely out of quantum fluctuations, etc...)
Yes, I always imagined this being just a silly exercise in pulling out a finite outcome from infinity. It’s not meant to be provable or disprovable, just hard to comprehend because we cannot think in infinite terms.
Relatedly, I wrote an essay that covers this a few years back: https://medium.com/@beadey.teigh/typewriters-29309c8e3b71
Yeah, I might be naive, since they're professional mathematicians and I'm not, but their conclusion feels like saying that they "tested" the concept of infinity and found that it's simply unreachable. To me, the infinite monkey theorem is an abstract idea and not something that needs to be "tested", though it's certainly fun to run the numbers.
They didn't "test" the concept of infinity. They said that the results of the infinite monkey theorem are well known, and they wanted to see what happens in the finite case.
Reminds me of Archimedes calculating the number of grains of sand to fill the universe
"Infinite monkeys" would produce Shakespeare and every other book, document, and all future possible book and document in the amount of time equal to the number of letters in the book and the typing rate of a monkey. It wouldn't take an infinite amount of time. :)
Not the point of the article, but this got me curious...
> Shakespeare’s canon includes 884,647 words – none of them banana.
If this article (1) is accurate, Shakespeare never even knew what a banana is, and he never tried it, since he died ~2 decades before they came to England:
> England got its first glimpse of the banana when herbalist, botanist and merchant Thomas Johnson displayed a bunch in his shop in Holborn, in the City of London, on April 10, 1633.
(1) https://theconversation.com/the-day-bananas-made-their-briti...
A monkey with keyboard already wrote Shakespeare, duh. Other monkeys called it Shakespeare.
In other words: it's "easier" to make better monkeys than to scale up to produce something valuable.
Or in other other words: random generation is highly unlikely to produce something valuable.
Or in other other other words: the amount of useful information in "the library of babel" is miniscule compared to noise.
In other words the only way we know of how significant complexity arises in the universe is (ultimately) through evolution.
pedantry: that monkey was ~250 years before keyboards https://en.wikipedia.org/wiki/Typewriter#Hansen_Writing_Ball
Hurdy gurdys with keyboards have been around long before then.
If you try to write Shakespeare with hurdy-gurdy keys, you're going to get slightly abridged versions, like that famous tragedy A ad Ceaa, or the comedy Ced f E.
Lagniappe: https://www.youtube.com/watch?v=CHxfOZH8cew
I somehow doubt Shakespeare had access to a typewriter...
Someone really needs to go dig up his bones and give him a typewriter. Too bad Halloween was yesterday.
\s
Apes aren't monkeys.
Indeed - that fact was already established 17 years ago ;) https://www.youtube.com/watch?v=--szrOHtR6U
Apes, thank you very much.
Ook!
Did anyone get the number of that donkey cart?
They have arbitrarily shifted the goal posts to fit their conclusion:
> working out that even if all the chimpanzees in the world were given the entire lifespan of the universe, they would “almost certainly” never
Who assumed the original adage had the constraint of the universe’s lifetime.
Just read the paper directly: https://www.sciencedirect.com/science/article/pii/S277318632.... They do no such thing.
Yes, and no…
> 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
But point taken, the article is sensationalizing.
I thought the saying was “infinite monkeys..” and in that case you would get the full works of Shakespeare immediately. With an infinite amount of time and one monkey you’d get the full works of Shakespeare in every language supported by the typewriter any number of times in a row you wished. In fact, you’d get anything you wanted as long as the probability was > 0
Edit: after walking my dogs, isn’t the probability of the full works of Shakespeare never being typed out also > 0? (I can’t believe I’m actually spending calories on this..)
> isn’t the probability of the full works of Shakespeare never being typed out also > 0?
No
I'm picturing scientists in another universe clenching their butts as the monkey goes to type the last letter of Hamlet..... and misses 't' for 'r' and the whole observation hall erupts with loud groans
And wouldn't you also get the next work Shakespeare would have written if he hadn't died/retired first? Fun to consider.
200,000 is quite a bit smaller than infinite.
Clearly not infinite monkeys or infinite time.
If either were truly infinite not only would this be possible, it would be mandatory and would occur infinite times.
Sounds to me that the more interesting question would be graphing out the relationship of time and the amount of monkeys needed for one to write Shakespeare.
That's done in the paper. Using a log(log) scale for time, measured in number of heat deaths of the universe. It's the most amusing part of the study.
Awesome! I really should have checked the paper and skipped the article entirely.
The figure in question: https://www.sciencedirect.com/science/article/pii/S277318632...
Kind of embarrassing to even be in this thread spending time here but would it not also be probable, however unlikely, to never get the full works of Shakespeare?
With fixed tries/time, or without true randomness, yes.
With infinite tries/time and true randomness, no.
The reporting on this paper is crazy. In the highlights section of the paper’s page on the journal’s website it says “The long-established result of the Infinite Monkeys Theorem is correct, but misleading.” but the Guardian article says “Australian mathematicians call into question the ‘infinite monkey theorem’ in new research on old adage”, which I read as contradictory to what’s in the paper.
It calls into question the applicability of the infinite monkeys theorem, so the headline is correct but misleading :)
In graduate school we had to answer this on a test question and it took all of 5 minutes...should have published it, I guess
I was going to say, we went over this in undergrad Statistical Mechanics and Thermodynamics.
I am biased by my religious beliefs, but I've always struggled with the idea that abiogenesis could spontaneously occur in "just" a few billion years on earth. A few billion seems like not enough time. Even the simplest forms of life are mind bogglingly complex.
Of course, it's a few billion years scaled across >1 life-friendly planets (since it only has to happen on 1 of them), but still just seems like not enough monkeys and typewriters in the given timeframe to produce something as astonishingly complex as life, let alone Shakespeare.
So this comes up a lot. I often think about the case of protein structures.
Let's consider a protein of 100 amino acids; although most proteins are in the 200-500 range (IIRC) it makes the maths simpler. Even for such a short sequence, the probability of coming up with one specific sequence at random is incredibly small - 20 to the power of 100 or 1.267651e+130.
The simple answer to this apparent puzzle ('how did proteins evolve from random mutations') is of course that it did not happen like this. Not at all like monkeys typing out scripts and a human checking if they have produced a Shakespeare play yet.
In fact, there are multiple solutions to the same problem - in the analogy, this would be like multiple different versions of the same play being just as good as the other. Even better for evolution, you can - in a sense - put on a version of a play that is pretty bad, but just good enough to put in front of an audience. In other words, some enzymatic functionality can be better than none.
In this way, an evolutionary system can build up complexity by making parts that are _good enough_ and are roughly equivalent to other parts that can be replaced gradually. Combine this with the massive parallelism and the scale of the molecular world, and a billion years can accomplish a lot.
Except abiogenesis didn't occur on Earth in few billion years, but within half to billion years after Earth was habitable. All the other features of life have taken four billion years to arise through evolution. It is like looking at current cars and wondering how they could come from nothing where had to look at the original cars and hundred years of improvement.
Abiogenesis really only need to explain how the first life arose. It could have been really simple since it got out competed by more sophisticated descendant that took over planet and left no trace of original life. We don't know how it happened, if required lots of random chance or if there was a replication step that made if go faster. We know that evolution can make complicated stuff over time.
> A few billion seems like not enough time.
Where would you get an intuition about how much time a billion years is? Or for what is "mind boggingly complex" and what not? How many eons have you lived? People who claim it is possible have better arguments than "to me it seems". Do you have a number for "this would seem to me as enough time"?
Do you also struggle with the idea of a poll being close to the truth when done on a sample of 1000 persons, out of tens or hundreds of millions? Math and science are often not intuitive. But they work.
Have you ever considered the possibility of supernaturally guided evolution. Always seemed like an interesting possibility to me. So God creates an incredibly beautiful concept that life comes from. Seems like one of the most probable solutions to how astonishingly unlikely abiogenesis would be.
This is a very computer science and not scientific response, but I look at the Game of Life, and it makes me realize that little patterns naturally form everywhere. Biology is just a little pattern that wants to replicate and survive and that doesn't have to mean intelligently.
> Biology is just a little pattern that wants to replicate and survive
I don't really see biology as being a "little" pattern. To me, looking at the jump from replicating molecules in chemical soup to single cell organisms is like looking at the jump from an abacus to an Intel i9 processor.
Who said you had to junp to single celled organisms first? One of the oldest displays at a science museum I remember was very simple. It was basically a rubber sheet attached to the top of a spinning pole resmebling a folded umbrella without the spines. There was a adjustable knob you could play with to adjust the speed that it spun. It would start from zero. Versus interestingly to me, the exhibit demonstrated that at certain speeds the dangling edge of the rubber sheet would form nice sine waves at certain speeds. It might be chaotic at first but eventually, given just the right amount of energy to spin, the wave would appear. If you sped it up or slowed it down, sometimes the wave would collapse, but if you hit another natural frequency, it would eventually snap into a larger or smaller amplitude with a greater or lesser amplitude. My take away was that if there is enough energy and repetition to almost anything, eventually patterns will arise. And if you let them do that long enough, then even in imperfect environments, relatively stable outcomes would occur. Much like life in my opinion. Have enough chemicals and energy thrashing around long enough in a cycle, and enough adverse selection against all those structures, eventually some structures will emerge and self-reinforce. Doesn't gotta start with cells, just molecules.
I would guess that abiogenesis is often framed around randomness as a strategy to argue for its implausibility. Of course, a completely random system is unlikely to produce enough coherence to convince anyone that it could be possible.
But in reality, the universe is full of patterns. The laws of physics are not random. Water behaves in very specific ways. Our planet revolves around the Sun in 365 day intervals. The planet rotates every 24 hours. Even out of these two interlocking patterns, you can see how energy delivery to the surface of the planet could result in mechanical and chemical cycles that may result in non-random mineral formation, concentration gradients, and thermal dynamics.
Scientists argue that abiogenesis is a result of inherently chaotic but non-random processes, not a hypothetical probabilistic scenario like monkeys with typewriters.
> the jump from an abacus to an Intel i9 processor
Call it 75 years (1942 - before electronic computers to 2017 - first i9) which is about 39M minutes. Assume human innovation can work on an minutely cycle[0] and you've got 39M iterations from "no electronic computers" to "Intel i9".
I'd put decent money on there bring several orders of magnitude more chemical reactions than that per second in the primordial soup (good conditions for fast reactions and there was A LOT of it.) And it had about half a billion years (fifteen quadrillion, seven hundred seventy-eight trillion, eight hundred billion seconds) to cook before things really started happening.
Statistically, it was likely.
[0] Obviously optimistic but giving parallelism a chance.
We're in the universe where it did happen.
I don't think religion has anything to do with it. Statistics and increasing entropy. Now, where you go from there might take you to religion, and so I'd argue that modern science often has arguably more to do with the religion of atheism than with reason since it's mostly based on certain axioms. I'm not saying we can't derive science off of theories, but as long as the bases are only asserted, you can derive proofs to come to any conclusions and speaking up about this seems to quickly get you disqualified in academia.
Frustrating that we’ve seem to built thousands of assumptions on an unproven base.
Actually, the study doesn't say that it wont happen, but that there's a 6.4 * 10^-7228454 chance of it happening before the Universe ends.
That's an infinitely larger chance than 0!
https://libraryofbabel.info/
it's all there regardless
What if something in monkey psychology causes them to hit the keyboard with their fist or palm every five minutes or so of typing? What if they regularly lapse into just pressing one key over and over? It seems very unlikely to me that even with infinite monkeys a work would be generated, because they're not actually random number generators.
If you had infinite monkies, what is the probability that one of them is actually a random number generator
In the set of all infinite monkies there are infinite monkies that are random number generators
I believe that probability could plausibly be zero.
On an infinite scale it seems unlikely that the probability of anything is actually zero
Near zero, certainly, but not actually zero
I think the number of things that are impossible is far greater than the number of things that are possible, even in an infinite universe.
Oh, but these are idealized monkeys that act like perfect random generators. Almost, but not quite, unlike spherical cows.
it was the best of times, it was the blurst of times!?!?!
Relevant Dankmus: https://www.youtube.com/watch?v=9uYhIiW6lok
Heh reminds me of working with LLMs.
Wrong writer (Dickens).
From the original mathematics paper (open access):
in the long-running television show The Simpsons, the industrialist Charles Montgomery Burns attempted this with multiple monkeys chained to typewriters but gave up when the best one produced was the near-Dickensian “It was the best of times, it was the blurst of times”.
https://www.sciencedirect.com/science/article/pii/S277318632...
“to be, or not to be … that is the gazornenplat??”
yes, i understand the difference between Shakespeare and Dickens, it's a Simpsons reference to the infinite monkey theorem in play here
you must be a devil with the ladies
come for the archive.is link, scroll for the pedantry
theguardian has no paywall
< slow clap >
new HN game: predict which order the archive.is link or pedantry comes in. if you get the order right, you get one point. if you get sucked into a pedantic argument, you lose
[dead]
link to paper: https://www.sciencedirect.com/science/article/pii/S277318632...
The basic point is an exercise in at least one older freshman text (Kittel & Kroemer?) but at least this paper does go on beyond and finds some strings (eg "I chimp, therefore I am") that are likely to be typed before the heat death of the universe, if not before extinction of chimpanzees.
If you take it literally, there is a non-zero chance that a monkey types the entire works of Shakespeare. I mean, it has already happened: who is Shakespeare but an intelligent monkey? (don't tell the librarian...)
For that to happen again, a monkey has to evolve into an intelligent specie interested in human history, find the complete works of Shakespeare, and write it. It is more likely than using probabilistic arguments using letter frequencies, or actual monkeys[1].
[1] https://archive.org/details/NotesTowardsTheCompleteWorksOfSh...
How long would it take a computer or set of computers to pick random characters and generate the complete work
how long for 1 paragraph how long for 1 page how long for 1 chapter
etc etc
Does it get harder/slower by a factor?
would be an interesting exercise
So let’s say we’ve got 28 possible characters (alphabet + period + space), you have a 1/28 chance of getting the first character right. So it follows that a string of length n is (1/28)^n because you have to hit each character correctly in a row. If we can do x guesses a second, and we know on average how many tries it takes on average to get our string right (28^n), we can divide and get an estimate of time. Though we could do it faster, or slower depending on our luck.
With multiple searchers it’s trickier, but we use the probability complement (probability of all possible events must add to 100%) to figure out the chances that our searchers all miss, and subtract that chance by 1. This gives the chance of at least one agent getting it right. Two searchers looks like 1-(27/28)^2 for the first char, and you can follow the same logic for any length string.
Your answer will heavily depend on your assumptions - how fast the computers guess, what they can guess, etc. But searching in parallel would speed things up dramatically. If you had like 100 computers searching simultaneously, 3 or 4 would likely get the first char right every time, giving you a big speed up on the problem.
Yes? The scaling factor is 2^(number of bits).
The universe would die of shame right now if it knew it's humans are spending their time questioning garbage like this.
Next someone will publish a study finding that spherical cows can't survive in the real world.
> even if all the chimpanzees in the world were given the entire lifespan of the universe
Seems to me like a flawed “study” if the baseline assumption is that chimpanzees would type randomly even when given lifespans through the heat death of the universe, which is estimated at 10^100 (googol) years!
More details on the math related to it than you'd like : https://www.youtube.com/watch?v=OjcacSB6_EE
Relevant incremental game: https://www.danneu.com/infinite-monkey-incremental/
It can happen a lot faster with a rigged random number generator:
https://www.pcg-random.org/party-tricks.html
I would argue it is conceivable that given enough time, a monkey or ape species can evolve that is intelligent enough to write Shakespeare’s full works.
we need more monkeys
I was recently reminded of The Codeless Code. In that set of stories, there's the Laughing Monkey Clan.
http://thecodelesscode.com/names/Laughing+Monkey+Clan
I recommend reading from the start ( http://thecodelesscode.com/case/1 ) and checking the links (since they sometimes have background information - http://thecodelesscode.com/names/Elephant%27s+Footprint+Clan ) and remembering image mouseovers.That's only worth mentioning because the PHP stdlib is mostly written in C. The general proposition (for any language) is trivially true since 93% of ink blobs are valid Perl programs.
https://www.mcmillen.dev/sigbovik/
(And wow! Search engines are getting even less useful with time. It's incredible!)
Was this seriously a question? I mean, this is something a college student or advanced high schooler could calculate.
The law of large numbers is still correct. Nowhere is there a requirement that the large numbers be smaller than the various physical constants of the universe.p
Surely it depends on the calibre of monkey we deploy
No-one ever said it would happen within a finite time period, only that it would happen given infinite time.
That’s the whole point.
The paper doesn’t say that either. They only call the original theorem misleading. I understood that their point is the same as yours - that infinity won’t happen in a finite time period.
> The long-established result of the Infinite Monkeys Theorem is correct, but misleading.
> Non-trivial text generation during the lifespan of our universe is almost certainly impossible.
> The Finite Monkeys case shows there will never be sufficient resources to generate Shakespeare.
https://www.sciencedirect.com/science/article/pii/S277318632...
I don’t see how the original is misleading. The word “infinite” isn’t hidden or anything… unless the definition of infinite is misleading but I think it’s use here is pretty clear.
“Infinity” on its own is clear, but in tandem with monkeys it could get confusing.
If you remember that a monkey here is also a theoretical construct then I guess all is fine. But otherwise monkeys need at least a universe to function and that is finite.
Perhaps it would have been seen as less confusing if it was a demon[1] that enters random letters instead.
[1]: https://en.m.wikipedia.org/wiki/Demon_(thought_experiment)
Along an infinite timeline more than one big bang may arise.
Yeah, but now you have another problem: the universe must reinvent monkeys.
Flawed point if it is used to justify the random speciation of evolution.
If they can't type out shakespeare, how can evolution randomly yet correctly type out billions of base sequences of dna in just a cple mil yrs?
You're comparing chalk and cheese to an extent, a perfect copy of Shakespeare's work can exist in exactly one way but DNA isn't required to be copied perfectly, DNA can change without necessarily killing the organism or otherwise rendering it unable to reproduce. Additionally evolution is not a random process, while mutations are random the process by which the mutations are selected is not - it depends on whether the mutation is a reproductive advantage for the organism in the context of their ecological niche. Most mutations are going to be neutral or disadvantageous so they won't be selected. Additionally you're not mutating the whole DNA sequence at once, just parts of it.
I would like to see someone use the most generous parameters possible and simulate the statistics of the first cple amino acids evolving into our homo sapiens sapiens chromosome set randomly over the course of just 4b years.
(selection is irrelevant here; we could even just model it as always-select-for-beneficial-mutation for extra graciousness).
Mind you, even if a beneficient mutation occurs, it is still not guaranteed to be passed onto the next generation. It would have to randomly occur over and over again.
I'm not confident that it's gonna be very convincingly in favour of the random mutation model.
>Mind you, even if a beneficient mutation occurs, it is still not guaranteed to be passed onto the next generation. It would have to randomly occur over and over again.
Why would it have to re-occur again and again? If the mutation is beneficial to the reproductive success of an organism, by definition their mutation will be passed on with no need for it to occur again by chance. The percentage of the population with the mutation would grow, potentially very quickly if it was a strong advantage over the previous generations. You're also characterising evolution as if to get from amoebas to humans you require a series of billions of independent coin-flips which isn't an accurate model, rather each generation is building on that which preceded it. Take the eye as an organ for example, it predates humanity by a very long time and was not independently evolved by humans - there was no need for it to have been since those genes already existed.
The predictions of evolution are generally supported by the available evidence at any rate, if you'd like to overturn it you'll have to propose a theory that explains the evidence more compellingly.
> Why would it have to re-occur again and again? If the mutation is beneficial to the reproductive success of an organism, by definition their mutation will be passed on with no need for it to occur again by chance.
Are you certain this is correct? An individual with a genetic mutation does not necessarily pass it down to its offspring, even if it was beneficial, in my understanding. So there is a probability p of passing it down and 1-p of not doing so.
In the latter case, the beneficial mutation is lost. Now the way evolutionists seem to "solve" this is by conjecturing that since the mutation is beneficial, it will arise in multiple individuals independently and eventually get passed down. Even if I grant this, it makes the statistics once again much more unlikely for this to occur.
> The predictions of evolution are generally supported by the available evidence at any rate ...
Depends which subarea of evolution. No actual speciation based on random mutation has ever been observed (let alone ones predicted by evolution) as far as I'm aware.
Micro-evolution or expression of previously not-expressed but already present genes is a different topic, and not something I have issues with.
All I say is evolution is at best insufficient to explain us. And we haven't even touched consciousness.
>Are you certain this is correct? An individual with a genetic mutation does not necessarily pass it down to its offspring, even if it was beneficial, in my understanding. So there is a probability p of passing it down and 1-p of not doing so.
That value for p is still going to be considerably greater for the gene to be passed on than the probability of that gene arising again randomly through mutation though. Consider the example of eye colour for example, chances are two brown-eyed parents are going to have brown-eyed children too - certainly a greater probability than a random mutation will intervene to make their eyes purple.
>Depends which subarea of evolution. No actual speciation based on random mutation has ever been observed (let alone ones predicted by evolution) as far as I'm aware.
There have been empirical studies of species separating and the mosquitoes on the London Underground are a good example, surface-dwelling mosquitoes cannot interbreed with those from the tunnels. At any rate it's actually quite a difficult thing to study since we're not looking at a binary situation of 'they have gene x now and therefore they're a separate species', that's not how evolution works and I don't think any biologist would claim this to be the case. At the end of the day species are human classifications made based on scientific observation rather than perfect formal categories, we define a species to be that which cannot interbreed with another and produce fertile offspring but that's our classification not nature's - species diverge gradually after taking many different evolutionary paths rather than there being a binary instant they're separate from each-other. The classification of species can only ever be so good because it's attempting to draw a fixed line on a moving canvas.
I think when arguing against the theory of evolution it's tempting to make arguments along the lines that each species is assigned some kind of intangible Platonic form towards which evolution must work but this isn't the case at all, there's no law of nature that says one species has to take x form and another must take y form. There's no Platonic cat which makes a cat a cat rather than a dog or a goldfish, a cat is merely one of the many possible organisms that can fill the ecological niche that cats occupy; and we classify them with our imperfect system of biological classification. I think it's putting the cart before the horse to essentially say that evolution is a flawed theory because our system of categorising species doesn't have the resolution to capture the exact moment species diverge from each-other.
>Micro-evolution or expression of previously not-expressed but already present genes is a different topic, and not something I have issues with.
Micro-evolution versus macro-evolution is a bit of an old canard in my opinion, the idea that they're separate processes rather than a continuum of the same process doesn't really exist outside of creationism which in my opinion is a much more difficult theory of our origins to argue than evolution. I spent some of my early life as a creationist so I'm not unfamiliar with its nuances, but personally I'm yet to hear a creationist argument that is particularly compelling to people who aren't already invested in the existence of a Creator rather than approaching the subject neutrally.
> All I say is evolution is at best insufficient to explain us. And we haven't even touched consciousness.
Consciousness is definitely a much more interesting problem in my opinion, and there's definitely no good theories of consciousness yet as far as I'm concerned. I think the notion of qualia in particular poses a lot of difficulties for a purely materialistic understanding of consciousness for example.
Also wouldn’t a DNA sequence get more likely as time goes on as it builds from the past and is not uniformly random? In the mokey/typewriter thought experiment no previous correct keystroke makes the next keystroke more likely to be correct. However, with DNA/life once it starts the next iteration is more likely to be better since it has the previous success to build upon.
correctly is doing a lot of heavy lifting there, and the selection process in evolution is not random.
The actual problem is upstream of that at the abiogenesis stage.
For evolutionary selection to occur the machinery for selection must exist. Specifically information storage (DNA/RNA), replication(polymerases) and actioning (transcription) all are needed, and must continue to be able to exist for long enough to matter.
Without selection pressure and inheritance you're just left with requiring a big enough universe and enough time for randomness not to matter.
Not the selection itself is random,
but the existence of genetic variants to select from randomly arises due to random genetic mutations according to the theory
The critical difference is evolutionary only needs relatively short sequences to be randomly generated, and there’s many valid sequences.
Building a book by generating a single random text string is practically impossible, but if you lock in any given word that’s correct and retry that’ll quickly get something. You’ll have most 8 letter or shorter words correct after 1 trillion runs, and many 9 letter words. It wouldn’t be done, but someone could probably read and understand the work at that point.
Further it’s possible for a few even longer words to match at that point. People think it’s unlikely that specific sequences happened randomly, but what they ignore is all the potential sequences that didn’t occur.
The many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
> You’ll have most 6 letter or shorter words correct after 1 billion tries.
You think that's "quick" for dna which is made up of billions of 6-base-sequences and for a species that can only reproduce sexually once every decade or so at best?
> many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
There’s finite invalid sequences, DNA isn’t infinitely long. It’s also not a question of valid or invalid we live with sub optimal DNA, so yea most people aren’t born with some new beneficial mutation. However, not winning the lottery isn’t the same things a dying, and even smaller wins still benefit us.
As to our long reproductive cycle, there’s a reason we share so much in common with other primates. Most of our DNA has been worked out for a long time. We share 98% of our DNA with pigs, and 85% of it is identical in mice which has practical application in drug development. Of note common ancestors were more closely related to us because both branches diverged.
Hell 60% is shared with chickens, and half of it’s shared with trees.
> only reproduce sexually once every decade or so at best?
Many sperm and fetuses die from harmful mutations, live babies are late in the process here. Also, because order doesn’t matter you get multiple chances to roll the same sequence for every birth.
PS: There’s also quite a bit of viral insertion into our DNA, it’s mostly sexual reproduction but we have some single cell ‘ancestors’ in our recent history.
> The many valid sequences are relatively nothing compared to the infinitely many invalid ones, right?
I dont know about the relative numbers but I don't think you do either? Are you begging the question or can you quantify?
> You think that's "quick" for dna which is made up of billions of 6-base-sequences and for a species that can only reproduce sexually once every decade or so at best?
We didn't start from scratch, we are very very late in the game, and the groundwork for us was laid by millions of other species that can replicate quickly, often very quickly.
Unless you believe the Earth is only six thousand years or so old, in which case we might as well leave the discussion where it is.
There's no evolutionary pressure to type out Shakespeare.
Life has had 3-4 billions years to evolve on earth.
I suggest you read 'the blind watchmaker' by Dawkins to answer your other question.
You are just repeating the point that was being argued against.
If the lifetime of the universe isn't enough to randomly produce Shakespeare, 3-4 billions of years are cute but useless to randomly produce anything even near as sophisticated as our 46 chromosome set.
I imagine Dawkins still just repeats the conjecture "but it's 3-4 billion years, anything can happen!"
A work of Shakespeare is a single specific target, that's why it takes so long to hit it - one letter out doesn't cut it. DNA meanwhile is a general purpose animal kit that has many billions of 'correct answers'. It's not about sophistication.
it's not about the absolute number of correct answers
it's about the ratio of valid / invalid answers
which is somewhere very close to 0
[citation needed]
What are the numbers?
Well, with an infinite number of monkeys, it could happen in a finite time.
As you say, this paper seems to miss the point.
It's sort of like calculating the probability of a hash collision. The speed at which the monkeys type is also a factor.
How fast do monkeys type?
Just give them a typewriter that records the position of where the key is pressed to a million bits accuracy, convert that to a series of ASCII characters (through a hash function), and the monkeys will type very fast.
That’s really funny. Give the keyboard a big enough buffer to hold Shakespeare and flush it to the screen on startup. With infinite monkeys and therefore infinite buffers the monkeys don’t even have to type!
>> For the timescale calculations, we assume that a monkey typist presses one key per second every second of the day
Yeah exactly, it's a thought experiment about infinities... Is someone going to publish a study concluding that Hilbert's Hotel couldn't be built on Earth too?
Why are people even spending money on this research? What are they trying to prove/disprove?
> Why are people even spending money on this research?
"This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors."
It's funny that so many people are confused about why this was written. The monkeys argument was originally used against the theory of evolution; "what's the probability that a monkey banging on a typewriter will type out Hamlet? It'll never happen, and that's why evolution is impossible." Then, someone made the counter-argument that given enough time, the monkey will type out Shakespeare. This paper argues that as long as the time is finite on the order of the age of our universe, the monkey will not type out Shakespeare.
It doesn't appear that they got any money for this, so I'm more forgiving of mathematicians just dicking around with something for fun.
Still, it's a very bizarre assertion to make; it's like they're trying to debunk something that no one claimed.
ETA:
Maybe they were trying to prevent the Mr Burns' of the world from trying to experiment: https://youtu.be/no_elVGGgW8
> Why are people even spending money on this research? What are they trying to prove/disprove?
That it takes much fewer than infinite humans and infinite time to produce the most pedantic paper possible.
It's just barely possible that this is not an entirely serious paper. Scientists like to have fun too, you know?
Not to mention that frivolous research has been known to pay surprising dividends.
Maybe they are after an Ig Nobel prize?
Franklin Open, whatever it may be, could well have slightly higher standards than Arxiv, but it isn't exactly Nature or Science...
(but try telling that to The Grauniad!)
Perhaps they're finitists, or ultrafinitists?
Many years ago someone complimented me saying I am extra fine; your comment makes me think I'll start identifying as an extrafinitist ╰(∀)╯
Also Zeno’s paradox is clearly untrue because Achilles would just kill the tortoise after a few days of running back and forth, starving.
I suspect that many academic papers are a petty move to win an argument that started one day over lunch.
i disagree rabble rabble rabble rabble
I mean this is a really simply thing to work out. There are 30^n strings of length n that can be made by mashing a 30 key keyboard. The time to the heat death of the universe is 10^100 years which is approximately 30^72 seconds. Your odds of getting a string of length n in the lifetime of the universe is
( number of monkeys * typing rate in characters per second * 30^72 ) / 30^n
The authors plugged in 200,000 (=30^3.5) and 1, meaning their odds are 30^75.5 / 30^n = 30^(75.5-n)
For a string of less than 69 characters, the odds are fantastic. For a string of more than 82 characters the odds are abysmal. At 69 the odds of the substring existing are roughly equivalent to losing the lottery, and at 82 the odds are equivalent to winning the lottery.
Shakespeare's shortest sonnet, 126, is a string of 533 characters.
Empirically a monkey did already creat the works of Shakespeare in a mere 13billion years. This is the time it took for the universe to form, earth to evolve to create a monkey that could write all those words down. The entire process from start to finish is way more complicated and random than anyone typing 26 character randomly into the keyboard. But I guess we are talking about uniform distributions here.
This sequence replaces an infinite God with ~infinite time and then draws the wrong conclusion.
You're replacing a hypothetical situation meant to illustrustrate mathematics with something else. The monkeys don't eat, evolve, age, conspire, have agendas or agency, they type randomly as a means to invoke visual imagery of a monkey slamming it's hands down ignorantly on a typewriter. It's chaotic slamming is the "input" that gets eventually distributed in different ways, one of which, if given enough time, will be identical to shakespeare.
Assuming implications to theology or genetic sequencing where none were given is a reflection of your ability to handle rational discussion of the material.
This sub-thread moved on from the original hypothesis as soon as innagadadavida put forward his non-empirical empirical example. Take it up with him, he may also enjoy your evaluation of his rationality.
But universe as we understand it is endless / infinite on time scale, no? [1] has some nice projections how even basic quantum stuff eventually breaks down, yet nothing is really ending, if you don't count matter as we know it.
[1] https://en.wikipedia.org/wiki/Timeline_of_the_far_future
Bring more monkeys!
Granted, the schedule is of maximum generosity. But does it not seem unfair to ask a monkey to compose the entire works of Shakespeare, considering Shakespeare himself might have been incapable of such a feat?
And while it may take an army of them, we know these creatures are at least capable, collectively, of operating the Daily Mail, which is still all pretty early given the time remaining.
My fingers are crossed and I still have hope
In other news - Life expectancy of the universe is finite
I mean, in several models, including the current most-likely one (last I heard) it effectively is finite. Eventually no new planets or stars can get created, and then some time after that, no atoms can exist.
Will the "universe" exist after that? Kind of a philosophical question, but nothing interesting will exist _in_ the universe.
These Mathematicians are very selective about which aspects of the universe they want to regard and which aspects they want ignore. Like, yeah you can take an imaginary situation and imagine that it's possible, or impossible. It can go any way because it's imaginary. No need to waste time on math, you can just imagine any outcome you like.
In reality, however, I think if you had a system that feeds a monkey a treat every time it strikes a letter key that corresponds to the next letter in a Shakespere play displayed on a monitor, you would eventually have some Shakespeare typed out by a monkey.
One could also just have a monkey mash keys for a while, and then after removing all the unnecessary letters you'd be left with a Shakespearian play.
Or, with a group of monkeys and plenty of time one could use natural selection to evolve them into a literate species that could handle the task easily. This is the method currently in use for the typing of Shakespeare. It has already been done, many times over.
Hey man, remember to type out that play before the universe dies
> One could also just have a monkey mash keys for a while, and then after removing all the unnecessary letters you'd be left with a Shakespearian play.
ChatGPT?
Think an actual monkey might do better!