What does the ‘infinite monkey theorem’ suggest about the anthropic principle?

[Arete]

23 hours ago, joigus said:

Point 1) I think what Arete's point is that Nature is much less forgiving to "mistyping" DNA than the monkey theorem suggests. Monkeys that mistype too much are removed (see below).

The point *should* be a pretty simple statistical point.

In English, each set is comprised of a combination of 26 characters, of any length until a monkey pushes the space key -effectively meaning there are infinite sets. There are approximately 470,000 words in the English language, so that many sets are translatable, the rest are not. 

In DNA, sets are a combination of 4 characters in lengths of three, meaning there are 64 possible sets. All are translatable to a suite of 21 meanings. 

These two probability landscapes are incredibly different. One is like searching for a needle in a haystack, the other is like searching for a needle somewhere in the universe. 

23 hours ago, joigus said:

Point 2) give the monkeys a chance to make some typing mistakes, as different codons give rise to same protein. Proofreading processes give the monkeys another shot too. This is equivalent to letting the monkeys disregard certain typographic rules, e.g.: ignore capitals, spell words phonetically, etc. We don't have infinitely many monkeys in our typing bench!

This point has to do with redundancy. The phrase "Call me Ishmael" has no redundancy - either all the letters are correct or the phrase is wrong. 

The genetic code has lots of redundancy. All amino acids have at least two of the 64 codons that encode them. Seven have completely redundant third positions - if the first two letters encode the correct amino acid, the third base pair doesn't matter - theoretically a full third of the nucleotides in the gene/genome could be entirely different from the "right" sequence, but the encoded protein translation identical.  All of a sudden, there are a thousand needles in the haystack and you only need to find one. 

 

On 6/14/2021 at 4:14 PM, joigus said:

point 3), while connecting with the OP's analogy of the typing monkeys; it is as if every now and then, when a monkey makes a typing mistake that's too bad to be forgiven, some directing process kicks him off the team of typing monkeys and lets other monkeys take his job.

Not quite - selection quickly fixes beneficial or "correct" sequences in the gene pool of a population. So, once a monkey gets a genetic "word" correct, it will tell all the other monkeys about it. In all subsequent iterations of the gene/genome the monkeys uniformly get that word right, iteratively shrinking the parameter space left to search. The monkeys are burning the straw as the search and the haystack iteratively shrinks. Not so for a random smashing of literary keys in search of a phrase in English.  

[exchemist]

9 hours ago, Arete said:

The point *should* be a pretty simple statistical point.

In English, each set is comprised of a combination of 26 characters, of any length until a monkey pushes the space key -effectively meaning there are infinite sets. There are approximately 470,000 words in the English language, so that many sets are translatable, the rest are not. 

In DNA, sets are a combination of 4 characters in lengths of three, meaning there are 64 possible sets. All are translatable to a suite of 21 meanings. 

These two probability landscapes are incredibly different. One is like searching for a needle in a haystack, the other is like searching for a needle somewhere in the universe. 

This point has to do with redundancy. The phrase "Call me Ishmael" has no redundancy - either all the letters are correct or the phrase is wrong. 

The genetic code has lots of redundancy. All amino acids have at least two of the 64 codons that encode them. Seven have completely redundant third positions - if the first two letters encode the correct amino acid, the third base pair doesn't matter - theoretically a full third of the nucleotides in the gene/genome could be entirely different from the "right" sequence, but the encoded protein translation identical.  All of a sudden, there are a thousand needles in the haystack and you only need to find one. 

 

Not quite - selection quickly fixes beneficial or "correct" sequences in the gene pool of a population. So, once a monkey gets a genetic "word" correct, it will tell all the other monkeys about it. In all subsequent iterations of the gene/genome the monkeys uniformly get that word right, iteratively shrinking the parameter space left to search. The monkeys are burning the straw as the search and the haystack iteratively shrinks. Not so for a random smashing of literary keys in search of a phrase in English.  

While everything you have said is illuminating (to me, anyway), it presupposes an already high degree of order in living things, viz. a system of heredity, mediated by codes of bases on a long molecule. So it seems to me it can't address the fundamental argument in the (creationist) claim recited in the OP. Though I suppose it does address the issue of the probabilities involved in how more complex life arises from simple life through variation (and selection), once an RNA or DNA type replication system is up and running.   

[swansont]

1 hour ago, exchemist said:

While everything you have said is illuminating (to me, anyway), it presupposes an already high degree of order in living things, viz. a system of heredity, mediated by codes of bases on a long molecule. So it seems to me it can't address the fundamental argument in the (creationist) claim recited in the OP. Though I suppose it does address the issue of the probabilities involved in how more complex life arises from simple life through variation (and selection), once an RNA or DNA type replication system is up and running.

The context of the OP's argument is often "evolution can't happen because randomness" and then showing the big numbers as the conclusion. This ignores the point that chemistry isn't random (as we've brought up a few times), and is falsified by the Miller-Urey experiment (and yes, while it's true that the conditions of that experiment are likely not those of early earth, it demolishes the notion that such probability calculations are relevant, because you would calculate a low probability of those amino acids being formed, and you would predict the formation of molecules that don't form.)

One part of the rebuttal to the OP is that only the creationists are asserting that all aspects of evolution are random, and you should never cite a creationist as a credible source of information about evolution.

[studiot]

On 6/15/2021 at 12:14 AM, joigus said:

This connects very much with point 3) by @Arete. Point 3), I think, is essential.

Well Arete is making the point specifically about genetic processes, which are heavily multifactorial.

I'm glad Arete chimed in because (s)he knows so much more about this than I do, which is why I was waffling generalities.

But yes the monkeys are an elementary (unitary or single factor) process and evolution, which depends upon genetics, is very multifactorial.

And, of course, the statistics of multifactorial processes is quite different from that of elementary ones, due to interactions between the factors.

Swansont has also pointed this out, but I disagree with his interpretation of 'infinite' as applied to monkeys.

As I understand this it is a classic statement of the probability which is a limit to infinity of repeated trials of a single factor. ie infinite trials.

It is not infinite monkeys all typing at once.

This difference clearly shows up in statistics, which does not take the time for a trial into account  - rather like thermodynamics not taking the rate of a chemical reaction into account.

@MarkE It is a misuse of statistics to make the mistake of infinite repetitions to measure time, as is the direct comparison of elementary and multifactorial processes timewise.

 

Out of interest I said 'random' is an adjective and needs a noun to complete its definition of use.

An example is the difference of use in the two phrases

A random process

A random number

 

 

 

[swansont]

46 minutes ago, studiot said:

As I understand this it is a classic statement of the probability which is a limit to infinity of repeated trials of a single factor. ie infinite trials.

It is not infinite monkeys all typing at once.

The link provided by the OP suggests it is, or at least can be. 

 

Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence.

...

For n = 1 million, Xn is roughly 0.9999, but for n = 10 billion Xn is roughly 0.53 and for n = 100 billion it is roughly 0.0017. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as is desired,[2][a] and the chance of typing banana approaches 100%.

The same argument shows why at least one of infinitely many monkeys will produce a text as quickly as it would be produced by a perfectly accurate human typist copying it from the original.

[studiot]

1 hour ago, swansont said:

The link provided by the OP suggests it is, or at least can be. 

 

Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence.

...

For n = 1 million, Xn is roughly 0.9999, but for n = 10 billion Xn is roughly 0.53 and for n = 100 billion it is roughly 0.0017. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as is desired,[2][a] and the chance of typing banana approaches 100%.

The same argument shows why at least one of infinitely many monkeys will produce a text as quickly as it would be produced by a perfectly accurate human typist copying it from the original.

It's only a passing point since we all seem agreed that it is an inappropriate example, for various reasons.

I thought it was pointing out that any number of trials from 2 to infinity are not necessarily equivalent if they comprise n repetitions of the same trial by the same agents or n attempts at one trial by different n different agents.

[joigus]

On 6/16/2021 at 1:32 AM, Arete said:

Not quite - selection quickly fixes beneficial or "correct" sequences in the gene pool of a population. So, once a monkey gets a genetic "word" correct, it will tell all the other monkeys about it. In all subsequent iterations of the gene/genome the monkeys uniformly get that word right, iteratively shrinking the parameter space left to search. The monkeys are burning the straw as the search and the haystack iteratively shrinks. Not so for a random smashing of literary keys in search of a phrase in English.  

I'm not following your analogy here. Are the monkeys individuals, or genetic sequences, or the background chemical processes, in the analogy? Either way: How does the monkey "tell the other monkeys" once that particular sequence works, that it does and they must use it?

I think we agree in most everything else and that we have established that evolution is not random.

23 hours ago, studiot said:

Well Arete is making the point specifically about genetic processes, which are heavily multifactorial.

Yes it's true that most phenotypes  are multifactorial. A well-known example is size. But when stochastic variables depend on many other independent stochastic variables the central-limit theorem guarantees that they will conform to a Gaussian. Something that in the case of size seems to be satisfied very well.

This is a question about what particular probability distribution does the phenotype fit; not really about whether the selection process is random or not.

The key question in evolution is that the throwing of the dice is one of a very quick step-by-step change (genetics) against a much, much slower erratic change (climate, competitors, etc.). And I think we all basically agree that the monkey model doesn't fit the bill.

[studiot]

7 hours ago, joigus said:

Yes it's true that most phenotypes  are multifactorial. A well-known example is size. But when stochastic variables depend on many other independent stochastic variables the central-limit theorem guarantees that they will conform to a Gaussian. Something that in the case of size seems to be satisfied very well.

This is a question about what particular probability distribution does the phenotype fit; not really about whether the selection process is random or not.

The key question in evolution is that the throwing of the dice is one of a very quick step-by-step change (genetics) against a much, much slower erratic change (climate, competitors, etc.). And I think we all basically agree that the monkey model doesn't fit the bill.

Remember we are discussing the proposition that the Universe is not old enough to have evolved the complexity of life we observe.

This proposition is supported by a very elementary calculation of the most probably time it would take to type out a simple phrase in English, by hitting the keys at random.

On 6/14/2021 at 11:21 AM, MarkE said:

Given fifty-eight possible keys, it would be 58 x 58 x 58 x 58 ... fifteen times over, which is about 283 trillion trillion attempts.

 

No one has yet point out the most elementary flaw in this argument.

The phrase being

Quote

Call me Ishmael

Which has 15 characters.

The chance of this occuring as the first 15 characters typed is exactly the same as the chance of it being the (283 x 10¹⁸ to (283 x 10¹⁸ +15)) characters.

So just like the person who wins the lottery with their first ever ticket, the Universe could be lucky and not need to wait at all.

 

I would observe that the central limit theorem does not apply to chemical reaction rates or times.

[Arete]

On 6/17/2021 at 6:19 AM, joigus said:

I'm not following your analogy here. Are the monkeys individuals, or genetic sequences, or the background chemical processes, in the analogy? Either way: How does the monkey "tell the other monkeys" once that particular sequence works, that it does and they must use it?

I think we agree in most everything else and that we have established that evolution is not random.

Apologies - I think the complication stems from the fact that in reality organisms are self replicating and there's nothing analogous to the "monkeys". The point is simply that in the analogy, the typing monkeys are searching the parameter space in a blind, random fashion. In an evolving population, be it genes, organisms, genomes, the probability of fixation or extinction of a mutation is governed by its selection coefficient in the prior generation. Ergo, the parameter space is searched in a directed manner, rather than a random one. 

Ultimately the big numbers game is not really a compelling argument. It would only take me a short time to roll a six sided dice 100 times. The possibility of getting a particular sequence is 1.53^-78. However, just by performing the action you will get a sequence. Saying you couldn't get the specific sequence you did because of the low probability is negated by the fact that if you roll a dice 100 times, there is a 100% chance you will get an improbable result. 

[swansont]

7 minutes ago, Arete said:

Saying you couldn't get the specific sequence you did because of the low probability is negated by the fact that if you roll a dice 100 times, there is a 100% chance you will get an improbable result. 

An excellent point, which serves to show that the monkey argument carries a hidden, unsupported, and probably very bad assumption that life could only arise through one particular path.

[Kartazion]

On 6/14/2021 at 12:21 PM, MarkE said:

If you agree with the author:
This would imply that complexity can’t be the result of randomness. But if it’s not randomness that could have determined the path of our evolution, which would lead to us, human beings, what’s the non-random factor directing this evolution, then? Or consider of the universe at large, and the 'anthropic principle'. If our Solar System, and its place in a fine-tuned universe, can't be the result of complete randomness, what's this supposed 'non-random factor', then, if it exists at all?

Nature uses a subtle selection of random combinations.

If each typist monkey created a universe for each of them, then the result of the likelihood of finding a combination comparable to our human brain would be unlikely.

Indeed, nature follows a well-defined pattern. Which one is it?

[dimreepr]

56 minutes ago, Kartazion said:

Nature uses a subtle selection of random combinations.

If each typist monkey created a universe for each of them, then the result of the likelihood of finding a combination comparable to our human brain would be unlikely.

Indeed, nature follows a well-defined pattern. Which one is it?

That doesn't mean the problem is soluble...

Infinate monkey's couldn't possibly re-write Hamlet...

Our time is so limited... 😉

[swansont]

2 hours ago, dimreepr said:

Infinate monkey's couldn't possibly re-write Hamlet...

Our time is so limited... 😉

Infinite monkeys would re-write Hamlet in the time it takes a typist going at the same rate to type out Hamlet, per the link in the OP