Universe would die before monkey with keyboard writes Shakespeare, study finds
theguardian.com
theguardian.com
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...
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).
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
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.
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.
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.
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?
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.
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.
Relatedly, I wrote an essay that covers this a few years back: https://medium.com/@beadey.teigh/typewriters-29309c8e3b71
> 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...
\s
Lagniappe: https://www.youtube.com/watch?v=CHxfOZH8cew
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.
> 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.
> 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.
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..)
No
If either were truly infinite not only would this be possible, it would be mandatory and would occur infinite times.
The figure in question: https://www.sciencedirect.com/science/article/pii/S277318632...
With infinite tries/time and true randomness, no.
it's all there regardless
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.
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.
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.
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.
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.
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.
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.
That's an infinitely larger chance than 0!
Assuming implications to theology or genetic sequencing where none were given is a reflection of your ability to handle rational discussion of the material.
you must be a devil with the ladies
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...
[1] https://en.wikipedia.org/wiki/Timeline_of_the_far_future
In the set of all infinite monkies there are infinite monkies that are random number generators
Near zero, certainly, but not actually zero
That’s the whole point.
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.
"This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors."
Not to mention that frivolous research has been known to pay surprising dividends.
(but try telling that to The Grauniad!)
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
> 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...
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)
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?
but the existence of genetic variants to select from randomly arises due to random genetic mutations according to the theory
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.
> 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?
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.
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.
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.
I suggest you read 'the blind watchmaker' by Dawkins to answer your other question.
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!"
it's about the ratio of valid / invalid answers
which is somewhere very close to 0
What are the numbers?
(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.
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.
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.
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.
As you say, this paper seems to miss the point.
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 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
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.
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
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!
http://thecodelesscode.com/names/Laughing+Monkey+Clan
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.
https://www.mcmillen.dev/sigbovik/
(And wow! Search engines are getting even less useful with time. It's incredible!)
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
( 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.
Will the "universe" exist after that? Kind of a philosophical question, but nothing interesting will exist _in_ the universe.
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.
ChatGPT?
Think an actual monkey might do better!