A Tiny Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]

Nutters.org ^ | 13-Dec-1995 | Brett Watson

[Southack]

There is a recurring claim among a certain group which goes along the lines of "software programs can self-form on their own if you leave enough computers on long enough" or "DNA will self-form given enough time" or even that a million monkeys typing randomly on a million keyboards for a million years will eventually produce the collected works of Shakespeare.

This mathematical proof goes a short distance toward showing in math what Nobel Prize winner Illya Prigogine first said in 1987 (see Order Out of Chaos), that the maximum possible "order" self-forming randomly in any system is the most improbable.

This particular math proof deals with the organized data in only the very first sentence of Hamlet self-forming. After one examines this proof, it should be readily apparent that even more complex forms of order, such as a short story, computer program, or DNA for a fox, are vastly more improbable.

So without further adue, here's the math:

[Southack]

Water evaporation isn't more complicated [than gene sequences in DNA or in monkeys typing the first sentence of Hamlet] because it does NOT depend upon any set, specific sequence of water molecules. - Southack

"First, the end process in my example was rain, not evaporation. Try to keep up." - Dan Day

Acting petty and pedantic fails to promote a scientific discussion (yes, I know, you've got some quips and retorts about just how "scientific" this discussion has become - because you are utterly predictable). Moreover, my point was valid for evaporation and is still also valid for condensation (i.e. rain). - Southack

"Second, the point is that it most certainly *does* take a very unlikely specific configuration of water molecules if, like the author of the original post, you foolishly make your calculations without taking into account all the physical processes at work." - Dan Day

That's ridiculous. Rain is NOT dependent upon any specific sequence of ordered molecules of H2O, and because it is NOT dependent upon sequence, its processes are less complicated, less complex, and more probable than are actions which require large amounts of specificly sequenced data (e.g. the ordered characters of the alphabet which comprise the first sentence of Hamlet, the ordered sequence of base pairs which comprise a functioning gene, et al).

[Southack]

However, the first sentence of Hamlet ABSOLUTELY depends upon a set, specific sequence of characters, - Southack

...which is one of the many reasons it's an invalid analogy... - Dan Day

as does every gene depend upon a set, specific sequence of base pairs. - Southack

Gee, really? Then you must have new information to rebut all those biologists who have found huge numbers of alternate forms of various genetic sequences in various species, all performing the same function. - Dan Day

I said nothing about the sequence of genes, even though you've managed to falsely infer that point from my posts. Surely you can comprehend that the sequence of base pairs INSIDE a gene is seperate and distinct from any potential sequence (if any) of genes themselves.

The sequence of base pairs is absolutely critical. Changing the sequence will impact the output of the specific gene in question.

Of course, like any good programming language, there will always be more than one way to achieve the same eventual functionality, so it is entirely possible for two radically different sequence of codons to achieve something remarkably similar, but the path taken to reach the final result WILL be different (certainly so if the sequences of codons are different, rearranged, or changed).

And contrary to your bizarre claim above in the blockquote, that fact does NOT invalidate my analogy.

You'll have to do far better than that if you want to appear even the least bit persuasive (something that you've utterly failed at up to this point).

[Dan Day]

Oh good grief. Did I really have to specify the smallest gene to achieve replication?

Well you certainly need to learn to say what you mean.

You asked:

How many DNA codons would we expect to see in the simplist known gene? Since we know that there are only four DNA codons (also called "letters" on this thread), we can calculate the precise probability / improbability of the natural, unaided self-formation of the data for a single gene once we agree upon how many codons are in a gene

You asked a reasonably clear question, I gave you the answer. If you wanted something else, you should have asked something else.

We were discussing abiogenesis and evolution weren't we?

Yes we were, but you did not clarify *which* of the two you were focusing on with that question. Furthermore, you muddled the issue by asking about *genes*. Genes, as such, most likely developed long after the first replicator -- they're a more advanced mechanism than was likely present at first.

Your question was like asking about jet engines while attempting to pose a question about the very first airplane.

No matter, consider myself to be corrected. What is the smallest possible gene size to achieve replication (i.e., to actually be germaine to this debate)?

No one knows for certain, of course, but one good candidate is a self-replicating peptide from the Ghadiri group, which is 32 amino acids long (sequence RMKQLEEKVYELLSKVACLEYEVARLKKVGE) and is an enzyme, a peptide ligase that makes a copy of itself from two 16 amino acid long subunits. It is also of a size and composition that is ideally suited to be formed by abiotic peptide synthesis. The fact that it is a self replicator is an added irony.

Oh, and the probability formula that you are going to want from me will probably end up being 1/4096^number that you give to respond to that question (4 possible valid bases ^ 2 = potential # of base pairs combinations ^ 3 base pairs per codon),

Well, there are a few problems with that..

1. It only applies to DNA sequences, and not to any of the many, many, many other possible forms of a "first replicator. I repeat, creationists like to reduce things to grade school level -- the chemistry is much more complex than that.

2. Even when applied to DNA sequences, your calculation presumes that any of the four possible bases can link up with any of the other four when making a base pair (this is obvious in your "4^2" term). However, even schoolchildren who have taken a basic Biology course know that the whole reason that the double-stranded DNA is a workable replicator is the fact that the bases *CAN'T* link up any damn way they please -- each possible base can *only* be linked to its complementary base. Nice try.

3. I *told* you that (1/4)^N wasn't going to cut it. Your equation is just a thinly disguised form of it. After correcting your erroneous "^2" term, your equation can be written as: (1/4)^(3*C), where 3*C (three times the codon count) is just another way of expressing N (the base pair count).

The reason that this is a bogus calculation is that the first replicator almost certainly wasn't DNA-based. DNA-based biology evolved from humbler beginnings, and your calculation doesn't do jack to model those other scenarios.

a probability that will decrease subtantially faster than that of the math for the monkeys typing the same length of Hamlet characters.

You have a monkey fixation, don't you? Ok, I'm going to dispose of it once and for all.

Several people, including myself, have pointed out the many things wrong with trying to use the silly "monkey typists" analogy to make any sort of conclusion about evolution (or even abiogenesis).

But hey, I'll *give* you the Shakespeare problem. Let's say that the formation of the first replicator was as hard as monkeys kicking out Shakespeare. But let's take out the science fiction aspect of it, we don't need monkeys on Mars, and various other outer space locations, as the silly author put it.

Let's move all the monkeys to just our own planet. And because we're trying to make analogies to molecular processes, let's shrink the monkeys down to molecular size.

Suddenly, you'll find something that chemists and biologists have long known, but creationists have yet to snap to: There's a *LOT* of room down there.

There are 3.3 x 10^25 molecules in a single liter of water. There are about 1 x 10^24 liters of water in the ocean. That's a total of 3.3 x 10^49 monkeys. Excuse me, molecules.

Furthermore, molecular reactions are *fast* -- typically on the order of a million per second.

And to be more realistic, let's not make every molecule be it's own typing monkey, we'll just let its current orientation represent a single "bit" of message, constantly changing as it vibrates around, jostling its neighbors.

So how long would it take a given 41 character * 5 bits/character = 205-bit sentence to be produced, like the Shakespeare example, using the oceans as a computer instead of monkeys on distant galaxies?

5.14x10^61 / (3.3x10^49 / 205) / 1,000,000 = 319303030 seconds / 3600 / 24 / 365 = 10.12 years.

Yeah, that's right, if we used water molecules instead of monkeys, we could produce the preferred Shakespeare line in about ten years, tops (5, on average). Not billions and billions of years using all available stars in the universe...

Furthermore, since 10 years would be enough time to generate a number of random sequences equal to the *total* number of 41-character strings, we would have produced, in the same 10 years, not just "to be or not to be, that is the question", but also *every* other 41-character sequence from *all* of Shakespeare's works.

And not only *that*, we would have produced *ALL* 41-character sequences from *ALL* books, newspapers, or internet postings *ever* published (including this one), or ever *to* be published.

Now that I've shown this using YOUR OWN CHOSEN NUMBERS, when you try to claim that the Earth's oceans couldn't have by chance concocted a single self-replicating molecule in a BILLION or so years, don't you feel a bit like a monkey yourself?

Class dismissed, I'm going to bed.

[Dan Day]

Acting petty and pedantic fails to promote a scientific discussion (yes, I know, you've got some quips and retorts about just how "scientific" this discussion has become -

I'll stop if you will.

Moreover, my point was valid for evaporation and is still also valid for condensation (i.e. rain).

You totally miss the point of the example, but I'm not going to explain it to you any more. Go back and reread it until it sinks in.

That's ridiculous. Rain is NOT dependent upon any specific sequence of ordered molecules of H2O, and because it is NOT dependent upon sequence, its processes are less complicated, less complex, and more probable than are actions which require large amounts of specificly sequenced data

Totally misses the point of the example, do feel free to try again.

Hint: Garbage in, garbage out.

[Dan Day]

I said nothing about the sequence of genes,

Neither did I.

even though you've managed to falsely infer that point from my posts.

Nope.

Surely you can comprehend that the sequence of base pairs INSIDE a gene is seperate and distinct from any potential sequence (if any) of genes themselves.

Yes, I most surely can, which is why I was talking about that very issue.

Hint: "Genetic sequence" means "the sequence of base pairs within the gene".

It wouldn't hurt you to become familiar with biological terms before you try to discuss biology.

The sequence of base pairs is absolutely critical.

Not as much as you'd think, no.

Changing the sequence will impact the output of the specific gene in question.

Sometimes it does, sometimes it doesn't. Sometimes it will make no effect whatsoever on the result (the "neutral mutations" we were discussing earlier in the thread), sometimes it makes a difference but not a critical one and the function of the gene is almost entirely what it was before.

Your implication that this is not the case is ludicrous.

This is Genetics 101 -- why don't you know this already?

Of course, like any good programming language, there will always be more than one way to achieve the same eventual functionality, so it is entirely possible for two radically different sequence of codons to achieve something remarkably similar, but the path taken to reach the final result WILL be different (certainly so if the sequences of codons are different, rearranged, or changed).

That too. But configurations that are slightly mutated from each other very often perform identically or nearly so.

And contrary to your bizarre claim above in the blockquote, that fact does NOT invalidate my analogy.

That "bizarre claim" is research results, sorry if you can't accept where the evidence leads.

You'll have to do far better than that if you want to appear even the least bit persuasive (something that you've utterly failed at up to this point).

...which brings us right back to one of my original statements in this thread:

Sure I can, son. But first I'll have to become convinced that it's worth my time to do so. That is, that you'll have any idea what I'm talking about, and that you're intellectually honest enough to accept when you're wrong.

I could tell from your posts before I even jumped in here that you were unlikely to a) understand most of the rebuttals to you and b) be able to admit to yourself when you were shown to be mistaken.

So yeah, I fully expected you to remain unpersuaded. You're unpersuadable. Your mind was made up, long before you actually bothered to really learn the subject, and you're not about to start now.

I'm not writing for your benefit, I'm writing for the benefit of the lurkers.

I did you the courtesy of spending a great deal of time dealing with your original post and all your questions. Now it's your turn. You clearly didn't bother to read this the first time I suggested that you try to come up to speed on the subject, why don't you give it a shot now, then get back to us once you've learned a bit more about the topic?

I've pretty well spent all the time I can spare introducing you to the basics of this complex field, time for you to do your own homework.

[Southack]

"So how long would it take a given 41 character * 5 bits/character = 205-bit sentence to be produced, like the Shakespeare example, using the oceans as a computer instead of monkeys on distant galaxies?

5.14x10^61 / (3.3x10^49 / 205) / 1,000,000 = 319303030 seconds / 3600 / 24 / 365 = 10.12 years.

Yeah, that's right, if we used water molecules instead of monkeys, we could produce the preferred Shakespeare line in about ten years, tops (5, on average). Not billions and billions of years using all available stars in the universe..."

You do need to go to bed, and I certainly hope that you aren't teaching poor defenseless children ANYTHING in a classroom, because you've completely botched your own feeble attempt at science.

Your equation, based upon a 5 bits per character "natural" environment, would mean that your random vibrations of molecules could ONLY vibrate in a sum total of two directions (bits being equal to on/off, a binary, two-part world).

The bigger problem, of course, is that your world presumes that every possible "movement" of a water molecule is a VALID part of a potential sequence, as well as that each movement of each water molecule is a new, valid bit of data. Each and every conceivable movement of water is equal to valid data, oh come on!

Moreover, such a world would mean that the vibrations of one molecule would not interrupt of otherwise be destructive to any other part of the system (lest our sequential chain be broken), and then

This new inanimate world of yours would actually have to "know" that it had reached the desired output.

But wait, there's more, even if your bizarre little world managed your incredulous feat, you still haven't explained how it would procede to animate itself.

After all, even when we have a valid DNA sequence from a dead organism, we still don't know how to animate it into a living, replicating, controlling process (at least not yet, and at least not without using other currently living/animated processes to provide such a jump-start or clone).

In short, you've managed to conjure up a world in which the sum total of your inanimate binary MOVEMENT would equal the number of random/natural guesses required to sequence the first sentence of Shakespeare's Hamlet, but that's a far cry from actually being a viable world in which realistic guesses were being made by currently-known natural processes.

Gee, you've shown that the sum total of all Earth's water molecules can vibrate 5.14x10^61 times in a decade, except, that has absolutely no bearing on how DNA self-formed in useful sequences of data, much less how it managed to become self-animated (a REQUIREMENT for any non-intelligent environment).

Nice try, but that sort of psuedo-science will hardly fool very many people (except perhaps those who don't want to believe anything else).

[Southack]

"Now that I've shown this using YOUR OWN CHOSEN NUMBERS, when you try to claim that the Earth's oceans couldn't have by chance concocted a single self-replicating molecule in a BILLION or so years, don't you feel a bit like a monkey yourself?"

No, but you should feel silly for daring to think that your "all Earth's water molecules" scribe would somehow invalidate the math and/or the simile used by the author for this thread.

You haven't even touched it (at least not honestly).

[Southack]

"3. I *told* you that (1/4)^N wasn't going to cut it. Your equation is just a thinly disguised form of it. After correcting your erroneous "^2" term, your equation can be written as: (1/4)^(3*C), where 3*C (three times the codon count) is just another way of expressing N (the base pair count). The reason that this is a bogus calculation is that the first replicator almost certainly wasn't DNA-based. DNA-based biology evolved from humbler beginnings, and your calculation doesn't do jack to model those other scenarios."

My calculation wasn't SUPPOSED to model any other scenarios. Thus, your "reason" given for it being bogus is in error.

Ergo, my point (and my calculation) still stands: it is LESS probable for DNA sequences to self-form naturally than it is for phenomenally large numbers of monkeys to type out the first 41 characters (in sequence) of Shakespeare's Hamlet...in 17 billion years.

And the math for the monkeys is covered in exhaustive fashion in the very first post on this thread. In fact, that what this thread is all about.

[Southack]

And contrary to your bizarre claim above in the blockquote, that fact does NOT invalidate my analogy. - Southack

"That "bizarre claim" is research results, sorry if you can't accept where the evidence leads." - Dan Day

No apology is required. The evidence at hand supports my analogy; it does not invalidate it. The sequence of base pairs inside a gene is critical to its final output, and this can be confirmed by randomly rearranging large numbers of codons in any animated gene and then watching the output.

[Southack]

Back to my point about the sequence of base pairs being critical, it's probably worth pointing out to you that the entire Human Genome Project is about mapping, sequencing, and identifying what the genes do.

Ergo, even Evolutionists, at least the modern ones, should know that sequencing is critical to our understanding of genes as well as to the performance of those genes.

[gore3000]

DNA is a molecule. There is no such thing as animation of DNA anymore than there is an animation of common table salt.

An interesting statement for a materialist! So if the molecules of DNA are not that thing we call 'life' then what is?

[gore3000]

In a population of a million those having the mutation will be 1/1,000,000 of the population even in cases where the population increases.-me-

No, look up "Genetic Drift".

Nope, in a situation where there is no selective advantage as here where there is a neutral mutation, the mutation does not spread. Genetic drift only changes allele frequency when new groups intermingle. Then in a sense a new larger group arises including the new members and this results in new allele frequencies of the new group. However in the case here of a single mutation occurring in one individual, it has no effect at all.

Look up "Genetic Drift" -- there's a surprisingly good chance that a neutral mutation will spread to the entire population.

Nope, the laws of Mendelian genetics are quite strict. The 50% chance of an allele reproducing is set in stone. Because all alleles have the same chance, the proportion of incidence of an allele in a population does not change when it does not have a selective advantage as is the case here.

In short, what I am telling you very simply is that the concept of neutral drift is absolute malarkey. This is proven by the persistence of recessive genetic defects. Because the carriers of the defect do not suffer from the defect, the defect remains in the population in spite of its deleterious effects on the progeny.

Also, as the population interbreeds, the various mutations in the population get "mixed and matched" very rapidly, the "2nd, 3rd, etc." mutations don't have to occur in any direct descendant of the individual with the "1st" mutation. If they occur *anywhere* in the population they can get shuffled together at any subsequent generation.

Not so, and again this is precluded by Mendelian genetics (that is why it is such a killer for evolution!). The mutations cannot get shuffled. Let say that individual A has a mutation, and individual B has a mutation, that they mate and both mutations are passed to the descendant. What will happen is that mutation A will be in one allele and mutation B will be in another allele, the alleles will not mix and create a new AB mutation. This is fairly simple genetics and it shows the impossibility of the propositions made by evolutionists.

[js1138]

In your post 451, you seem to be arguing that, since ID has changed its claims, it is an invalid concept. I hope you don't mean that, because the theory of evolution has changed pretty frequently as well.

The mechanisms of evolution were unknown in Darwin's time. He worked before the theory of genetics, and nearly a hundred year before DNA was discovered. The general theory of variation, overproduction and selection has never been altered, nor has the assumption that this takes place without guidance from outside the system.

[js1138]

Inanimate DNA is found in every dead organism.

So cloning DNA from a dead organism is impossible?

[js1138]

It matters whether in your heart of hearts you think we are cosmic accidents or images of God. It effects how kind or nasty one is. In that sense, even if evolution is true, believing it is true produces a coarser, meaner society, while believing the opposite produces a kinder, more respectful, and loving society.

If belief in God produced moral behavior, Islam would be paradise on earth. If belief in Jesus produced moral behavior the atrocities of the middle ages would not have happened.

[js1138]

This new inanimate world of yours would actually have to "know" that it had reached the desired output.

Again you show yourself completely incapable of understanding the concept of natural selection. there is no "desired" output. Only what survives. A survivable form in one environment can be lethal in another.

[js1138]

So if the molecules of DNA are not that thing we call 'life' then what is?

That is a truely interesting question. I might add that this question was posed to my freshman biology class on the first day of lab. Wouldn't you like to know what we came up with for the answer?

[VadeRetro]

David Niven

Cary Grant! Next time, Cary Grant!

;)

[Southack]

"So cloning DNA from a dead organism is impossible?"

No. Why would you think that way?

Animating inanimate DNA is not only possible, it is axiomatic.

The issue, of course, is HOW that inanimate DNA becomes animated (e.g. via a completely natural process or via an intelligent intervention such as human-directed cloning).

[Southack]

"Again you show yourself completely incapable of understanding the concept of natural selection. there is no "desired" output. Only what survives. A survivable form in one environment can be lethal in another."

Nothing survived in Dan Day's water world.

Nothing. Not a single valid sequence survived for more than the tiniest fraction of a second.

One of the many reasons that I asked him how his system would "know" if it achieved the correct output was because the correct output, under his conditions and playing by his rules, would only last until the next water molecule vibrated, and if you notice his precursor conditions to that world, they vibrated pretty frequently.

So how would that temporary "correct" sequence survive or how would the system "know" to keep that one correct output that survived for a fraction of a second once every decade?

Nor was there any "natural selection" in Dan Day's water world. In fact, it was a completely lifeless world that he created and was referring to.

Would you like to explain how a completely lifeless world is going to implement natural selection, especially his lifeless world in question?