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

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

[Dan Day]

"No, it very most certainly does not."

Nonsense! Of course "feedback" implies intelligence.

I'm sorry, your declaring it and adding an exclamation point simply does not make it so.

Tell me, what sort of intelligence is involved when a microphone picks up the sound from a too-close loudspeaker, and squawking results? (And if you say, "because someone had to invent the microphone, I'm going to have to write you off entirely.) There's also feedback in purely natural processes, such as the way that waves pile sand near a beach, and then the new shape of the sand affects the waves, which affects the sand, which... Where's the "intelligence" in that?

Feedback is simply when the results of a process are not fully isolated from the "inputs" of the same process and affects the future input. This happens by accident far more often than by intelligence intervention.

Are you sure you have any grasp of the concepts you're preaching about?

Heck, try a dictionary even:

feed-back (feed'bak ) n.

1. a. the return of part of the output of a circuit, system, or device to the input, either purposely or unintentionally, as in the reflux of sound from a loudspeaker to a microphone in a public-address system.

-- Random House Webster's, College Edition

If the monkeys in the math simile for this thread are compelled to read a dictionary and select their output based upon its "fitness", then you have injected intelligence into the math proof both with the dictionary (which takes intelligence to compile) as well as with the monkeys (who would have to determine what part of their output is to be kept and built upon with future keystrokes).

Wow, what a lame "proof" of your point. Yes, if the monkeys were intelligent, then that would involve intelligence in the one particular example of feedback you chose to describe.

That's hardly the same as demonstrating that feedback is impossible without intelligence, though. Nice try. Get a good book on Logic 101 sometime, it'll help you learn how to forumalate valid arguments.

You did read the post #100, its predecessors, and its replies, didn't you?

Yup, sure did. It was just you stamping your feet and declaring that feedback can't happen without intelligence, again without supporting argument.

Well, at least read post #444.

Been there, done that. I'll dismantle it in my forthcoming post. See you there.

You are recovering old, long disproven ground in this thread.

No, I'm re-covering old ground where people previously pointed out the flaws in your position but you failed to accept it (or even understand it, many times).

Thus my earlier post about wondering if it would be worth taking the time to spell things out for you, or whether you'll just declare "is so!" again.

[Southack]

A Reactionary Rant by The Famous Brett Watson, 12-Jan-2002.

---

The Mathematics of Monkeys and Shakespeare still ranks as the most popular document of all time on Nutters.org. It's probably been getting more hits per week than everything else combined. I've written more on the subject before, in the form of More Monkey Business, but that document is way too long and involved for most tastes. I'll try to learn a lesson from this and specifically not attempt to address every possible objection to every possible argument this time.

Although nobody has ever pointed out a flaw in my mathematics, many people leap on the "conclusion" of The Mathematics of Monkeys and Shakespeare as being unsupported by the corpus of the essay, and to a large extent, this is quite true. The essay was originally an email to a person that I met on the 'net. He put to me the difficult question as to what evidence I thought there was for the existence of God. Why believe in God at all? From an evidential perspective, I believe that the argument from probability makes a strong case for believing in God. This conclusion is not inescapable, however, and I admit as much in the "Postscript" of my essay, which I reproduce here for your information.

If you read the thesis above, you will agree at least that if the universe did arise by chance, it must be truly infinite and in the continuous process of trying out new alternatives. That, and the universe as we know it is an incomprhensibly unlikely fluke. I find it much simpler (and much more "natural", I might say) to suppose that there is a God who is greater than the universe who made it, much like I made this document.

You can believe that the universe is an accident if you want to, and nobody is ever likely to be able to prove you wrong on that point. The mathematics I present is simply intended to put that belief into perspective for those who are still deciding whether or not God exists. Of course, if you're already committed to a naturalistic world view, where everything that happens happens because of the laws of physics, then you've already written "God" pretty much out of the picture, and any non-zero probability will do to fill in the gap, no matter how small.

It's people who have taken this stance of committed naturalism who most often criticise my essay. Most such criticisms arrive by email, but some are published on the web. I'm going to pick on one particular web-published criticism today, mostly for the sake of my own convenience. It's fairly representative of the kinds of objections that I get, and it's called Statistical Monkey Business, by Aaron Krowne.

Before getting down to the business of addressing the specific points raised in Aaron's critique, I'd like to point out a debating technique that I've seen evolutionists employ — probably unwittingly more often than not — in arguments against creationists or apologists for anything other than naturalism generally. I don't have a clever name for the technique, so I'll describe it here.

I first noticed the technique when I read some responses to Michael Behe's excellent and thorough work, "Darwin's Black Box". In this work, Behe carefully describes the biochemical details of certain vital functions, like blood-clotting. He shows how amazingly complex such apparently simple systems are at the biochemical level, and how breaking any one link in the biochemical chain can have catastrophic results for the biological function in question. He puts forth the challenge to evolutionists generally to explain how such a system (where a complex system is in place, and the disruption any one link can break the function) can arise one piece at a time in a slow and gradual manner.

This would seem like a knock-out blow to me. Can evolutionists show a viable biochemical sequence of small steps between distinct but supposedly related biological systems? The typical answer is to dismiss Behe as having overlooked the obvious. They don't need a linear set of modifications between one and the other, they say, because it may not have happened that way. In the same way that an arch requires scaffolding when it is being built, but supports its own weight when complete, these biochemical systems may well have had scaffolding around them in the past which rendered this objection irrelevant.

What they never ever do, of course, is provide details how that scaffolding could have worked at the biochemical level. It's like Behe has given them a really hard challenge, saying, "you claim this has happened; here are the facts of the matter, now explain how your system worked." In response, they claim that the process happened by some much more round-about method, and omit the explanation part. In my opinion, this is a magician's technique: distraction. It's a way of preventing people from noticing that you haven't really answered the question, and it's certainly not good science. I claim that Aaron Krowne's critique of my essay also contains such distractions. I leave it to you, dear reader, to judge the extent to which that claim is valid.

Aaron's first objection is that of "probabilistic independence of events". My hypothetical monkeys are strictly independent of each other, and one keypress is strictly independent of the next, but in the physical universe nothing is perfectly independent in this way. I note in the first instance that this doesn't stop statisticians from taking themselves perfectly seriously when they use the same kind of "independent event" model in their calculations. Why is this so? Because, in many cases, whatever "dependence" exists between the two events is so small as to be negligible. Dependence can be validly ignored when it doesn't have a significant impact on the outcome. It's fair to point out that I've used a model of independent events, but this in itself is no big deal unless dependence is significant to the results.

The exact nature of the objection is somewhat confused by Aaron's example of a baby learning to speak. If we consider a baby as a random event generator (like the monkeys in my essay), then the chances of it ever uttering a Shakespearean quotation is pretty darn low. But it would be very odd to consider a baby as a random event generator, because they aren't even remotely like that. Real live monkeys aren't all that much like random event generators either, but for the purposes of illustrating a mathematical problem using something other than numbers, monkeys and typewriters are a reasonable choice, I think.

A human baby, on the other hand, has spectacular learning capacity. We expect a human baby to pick up language as a matter of course, because that's what human babies do. We would be inclined to think that there was something wrong with a human baby that did not pick up language skills. We don't expect a baby chimpanzee to learn to talk (or type, for that matter), despite whatever other similarities may exist with human babies.

A human baby does, as Aaron suggests, reside in an environment where it experiences dependent events and feedback, but this would be irrelevant if it weren't for its innate capacity to react to that feedback in a manner that allowed it to acquire language abilities. Every other object in the baby's environment is exposed to the same kind of stimuli as the baby, but only the baby reacts to those stimuli in such a way that it eventually acquires the ability to publish essays on the Internet.

Aaron has completely ignored the "intelligence" involved in his example, concluding instead that "we have significantly accelerated how fast complex patterns like communication can arise in a dependent universe." Dependence is a factor in his example, no doubt, but is it the key factor? Replace the human baby with a chimpanzee and you get all the same dependencies but none of the results. I would argue that the example shows how intelligence can be a vital ingredient to the production of "complex patterns like communication".

Others have suggested that I'm ignoring the effects of "Natural Selection", which may have been what Aaron was really driving at here. This is true, but Natural Selection (in the form of "differential reproduction") only applies to things which can reproduce. My mathematical objections are still completely valid, even with the omission of Natural Selection, when applied to "chemical evolution", being that stage of the process that goes from non-life to life.

It's entirely likely that the kinds of events necessary for chemical evolution would have a large number of dependencies, and that a model of "independent events", such as I have used, is not a very good model of the process. Dependencies would change matters, either for better or worse, but it's unlikely that they would change the fundamentally exponential nature of the problem. Rather than speculate about it, however, I would like to actually perform a mathematical analysis of the probabilities in chemical evolution, but the supposed process of chemical evolution has never been defined in sufficient detail to analyse mathematically! I will be happy to include dependencies in my analysis if anyone can specify exactly what those dependencies are.

Aaron's second objection is that "improbable does not equal impossible". This objection comes in two parts: a semantic quibble, and an attack on my underlying assumptions. I dismiss the semantic quibble as immaterial. Aaron (and others who have raised this objection) would have me use "impossible" only in the strict sense of "having a probability of zero", or "can not happen under any circumstances". As the objectors have rightly noted, I have here used it in the slightly less strict sense of, "cannot reasonably be expected to happen", or "utterly impracticable". This distinction does not affect my conclusion, and the dictionaries of the English language which I have checked recognise such usage. Even so, I anticipated that I would face pedantic objections of this sort, and carefully weighed up the use of the word at the time, ultimately deciding that "impossible" was necessary to drive the point home.

The objection relating to my underlying assumptions is a little more interesting. Aaron correctly identifies that my argument "assumes that all useful analysis of life belongs within the scale of 17 billion years." As Aaron concedes, I didn't pick this number entirely arbitrarily: it is the approximate "age of the universe" as currently accepted by mainstream (evolutionary) science. Yet Aaron declares the age of the universe to be irrelevant on the grounds that we can speculate about as much additional time and space (in the form of other universes) as is needed to solve the problem. Astute readers will notice that I allowed for this kind of "out" in my Postscript (quoted earlier) in the form of an "infinite universe", although "arbitrarily many universes" will do just as well.

Granted, I do make the assumption that Aaron suggests. Why do I make that assumption? I make it because it's as generous as I can be with the figures relating to available time and space whilst staying within the bounds of "science". I don't necessarily believe that the scientific mainstream is right about the age of the universe, but I'm taking what they claim is a fact of science ("the universe is about seventeen billion years old") and applying it to another alleged fact of science ("life evolved without the input of an intelligent creator"), and hoping to demonstrate that the two are somewhat incongruous.

Surely an appeal to other universes beyond the reach of scientific knowledge cannot be considered a scientific objection to my thesis? It's metaphysical — pure speculation. I recognise that many people hold this belief, which is why I spoke of committed naturalists earlier, but I can see no compelling reason to prefer a naturalistic view over a supernaturalistic one, particularly when discussing matters that the parties agree is beyond the ken of science! Aaron states that the possibility of multiple universes with differing laws of physics is "not ruled out by known science", but the same applies to the possibility that the universe was created by divine fiat, so how does this help his argument?

In conclusion, Aaron criticises the lack of connection between my conclusion and the corpus of my work, whilst at the same time making the passing comment that, "science is a process - the only sure process - for gaining knowledge about the world." This is a statement of belief, not logically connected with the corpus of his work, not supported by facts in the corpus of his work, and not even strictly adhered to in the corpus of his work. Aaron has demonstrated some degree of epistemological awareness in another essay, so this apparent lapse is disappointing.

As to whether or not Aaron's objections really do expose flaws in my argument, let the reader be the judge.

[Southack]

"That's hardly the same as demonstrating that feedback is impossible without intelligence, though. Nice try. Get a good book on Logic 101 sometime, it'll help you learn how to forumalate valid arguments."

What you've failed to comprehend is that I NEVER said that natural feedback was "impossible".

What I said was that INJECTING the kind of feedback mentioned by the poster (circa Post #100 & #104) was adding aided intelligence into what was otherwise an unaided process.

The poster in #100 (or thereabouts) wanted the monkeys to read a dictionary and then choose which of their outputs should be kept or discarded. Well, that ADDS intelligence into a process (both via the dictionary as well as in the monkeys having to make an intelligent choice).

Thus, that sort of feeback implies intelligence. QED.

[Dan Day]

Just to be clear, a "fitness test" implies intelligent intervention.

And just to be clear, you're still wrong.

Organisms endure their "fitness test" by living their lives and reproducing successfully, *or* dying early and/or failing to mate and produce offspring (or similarly, by producing more offspring than their fellow organisms).

There's no intelligence involved at all. Their "fitness" is weighed and measured simply by the difficulties of survival in the wild. They either manage to survive and reproduce against what Mother Nature and Lady Luck have in store for them, or they don't.

No intelligence needed for such a fitness test, Southack.

Whether you are talking about the intelligently-derived dictionary for the monkeys

Invalid analogy, evolution does not proceed by "checking a dictionary" or any other reference material.

or whether you are talking about a "process" that can determine which DNA guesses are worth building upon (as opposed to never trying again),

Oh, puh-LEAZE. This is the sort of "missing the point" stuff that demonstrates that you don't even understand the basics of the theory of evolution well enough to describe it properly, MUCH LESS understand it well enough to point out any flaws it may have.

Evolution is *NOT* about "determining which DNA guesses are worth building on". I don't know what you're trying to talk about here, but it ain't evolution. If *this* is your skewed understanding of evolution, then it's no surprise that it looks unbelievable to you. But you're engaging (perhaps unintentionally) in a Straw Man fallacy here.

What evolution actually consists of is not that it ever determines what's "worth building on", it that it ends up doing "trial and error" building on whatever already happens to be in the DNA. That's a *far* different thing than your version.

And the "trials" (mutations and recombinations) are undirected ("random" if you will) but the "errors" are statistically weeded out by the "school of hard knocks".

Over time (and generations), the lucky improvements persist and propagate, the mistakes die off. Over enough time, improvements have piled upon improvements to the point where large cumulative changes have resulted.

you are getting AWAY from the pure mathematical odds of random chance

This half you have exactly right -- this is why your original post was in error, it counts *ONLY the "pure mathematical odds of random chance".

due to the intelligence in such "fitness check" processes.

*EERRNNTT*. Thanks for playing.

Of course, that's the whole point of the math for this thread: to demonstrate that something MORE than mere random chance must be in play, that a "fitness check" or other form of intelligent intervention is REQUIRED.

You're *close*, but you keep crashing to the ground with the "intelligent intervention" presumption.

It takes no intelligence whatsoever for a slower mosquito to be eaten more often by a dragonfly than the faster mosquito. It takes no intelligence for the hawk with better eyesight to prosper more than the hawk without.

Natural selection happens just fine naturally.

Re-read the math in the article. It's all there. Left unsaid is only what the math means.

You're right in that it (trivially) demonstrates that things don't happen "purely randomly". But it's a huge mistake to leap from that obvious observation to "it was designed, I tell you!!"

[Southack]

"Natural selection happens just fine naturally."

Perhaps, but even if natural selection does actually occur in the wild, it still fails to explain evolution.

Natural selection merely culls an existing species or allows an existing species to prosper/multiply.

Natural selection per se adds no mutations to DNA nor does it create distinct new DNA from whole cloth; instead, natural selection only applies to existing species as they stand, leaving science to still answer the question as to the origin of those species.

[Southack]

"And just to be clear, you're still wrong. Organisms endure their "fitness test" by living their lives and reproducing successfully, *or* dying early and/or failing to mate and produce offspring (or similarly, by producing more offspring than their fellow organisms). There's no intelligence involved at all. Their "fitness" is weighed and measured simply by the difficulties of survival in the wild. They either manage to survive and reproduce against what Mother Nature and Lady Luck have in store for them, or they don't. No intelligence needed for such a fitness test, Southack."

That's fine, but you've missed the point.

The poster was claiming that the creation of the first valid, useful DNA strand could be explained by an intelligent "fitness" process, not that there were fitness processes in existence which did not require intelligence.

[Dan Day]

"And what mathematical calculation do you plan to use to arrive at this probability? If you were going to say "(1/4)^N", you're wrong."

I'm fine with you inventing a strawman calculation that I never wrote, only to "knock it down" yourself,

Excuse me while I roll my eyes. I did nothing of the sort, and if this is the best sort of discussion you can manage, my patience with you is coming to an end. I said "if", Bucko. I never represented it as your actual position, which is a prerequisite for a Straw Man fallacy. I was merly pointing out that that's the probability calculation most creationists use when they try to address this issue, so I was heading it off at the pass if that's the direction you might have been going.

if you will at least post your own calculation for the probability in question.

Wow, what a lame dodge. I asked *you* for *your* calculation, Southack. Feel free to present it.

What is your calculation? You do have one, right??

Well *you* clearly don't, given how clumsily you tried to divert attention from *me* asking you for *yours*.

In fact, you claimed to have a calcuation so definite that it could calculate the "precise" (your word) probability of the formation of a gene given *only* one single piece of information: How many codons are in a gene.

Here, let me refresh your memory:

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.

So since you claim to know that it's possible to make a "precise" probability calculation given only this one number (how many codons in a gene), *surely* you must have the calculation at hand.

So let's see it. Now.

Or admit that you were talking out of your rear end.

[Southack]

For me to provide you with an acceptable probability formula, you will have to first state how many codons are in the minimum complexity gene?

Also, nice dodge on your part. Not only did you not provide your own mathematical formula for the probability of genes forming naturally, but you also didn't provide a single example of where the math for this thread was in error.

Nor can you.

[Dan Day]

Is there a single tangible, incontravertible example of such an intermediate gene in all of science?

Sure, thousands. You're not keeping up with the literature, are you? Here are three for you to look into:

Ohno S. (1984 Apr). Birth of a unique enzyme from an alternative reading frame of the preexisted, internally repetitious coding sequence. Proc Natl Acad Sci U S A, 81, 2421-5.

Nurminsky DI, Nurminskaya MV, De Aguiar D, and Hartl DL. (1998 Dec 10). Selective sweep of a newly evolved sperm-specific gene in Drosophila Nature, 396, 572-5.

Park IS, et al. Gain of D-alanyl-D-lactate or D-lactyl-D-alanine synthetase activities in three active-site mutants of the Escherichia coli D-alanyl-D-alanine ligase B. Biochemistry. 1996 Aug 13;35(32):10464-71.

Also, how do you explain the existence/non-existence of incomplete genes?

I'm sorry, could I have that question again in English?

[Dan Day]

And you'll find that the math in question for this thread DOES have a good sort of idea for the process that it is modelling

No, actually, as I pointed out previously, it's a grade-school-level approach to a complex issue.

And you can't model chemical synthesis reactions with the simple independent-event probability calculation you learned on the first day of probability class.

[Dan Day]

Either you can show the errors (that you ALREADY claimed exist) in the math for this thread, or else you can't. Nor is it a matter of time, because taking you at your word means that you've already spotted the errors. Thus, if you don't show those specific errors, it can only mean that you weren't being honest.

I already told you my reasons. Documenting errors (not seeing them, explaining them properly) takes time, and it's not worth doing if your audience isn't going to bother to listen.

Your attempt here to make a flying leap from that observation to a conclusion of calling me dishonest only reinforces my opinion that you're more interested in rhetorical games than actual rational discussion.

Try again.

[Southack]

"Ohno S. (1984 Apr). Birth of a unique enzyme from an alternative reading frame of the preexisted, internally repetitious coding sequence. Proc Natl Acad Sci U S A, 81, 2421-5."

Did Ohno actually state that the alternative reading frame was due to a natural, non-intelligent process?

[Dan Day]

many people leap on the "conclusion" of The Mathematics of Monkeys and Shakespeare as being unsupported by the corpus of the essay, and to a large extent, this is quite true.

Bingo. It's so nice when the author admits his own errors.

[Southack]

And you'll find that the math in question for this thread DOES have a good sort of idea for the process that it is modelling - Southack

"No, actually, as I pointed out previously, it's a grade-school-level approach to a complex issue." - Dan Day

Even IF you were correct, your point fails to invalidate my statement above.

Nor have you managed to show a flaw in the math for this thread, even though YOU CLAIMED that the math was in error.

Surely gradeschool math (your definition, per above) isn't beyond your abilities...

[Southack]

"I already told you my reasons. Documenting errors (not seeing them, explaining them properly) takes time, and it's not worth doing if your audience isn't going to bother to listen."

Nonsense.

I called your bluff.

You have been dishonest. Contrary to your wild-eyed claims, you physically CAN NOT show a flaw in the math for this thread.

Typical.

[Southack]

"Bingo. It's so nice when the author admits his own errors."

If you actually believe your own claim, then you've failed to grasp his overriding point about his conclusion.

[Southack]

"And don't point to the original post, it's full of errors, unsupported presumptions, and overestimations." - Dan Day

Just a little reminder (above) that you were making some pretty wild, unsupportable claims back in post #486.

Where are those math errors, Dan?!

[silence. nothing but the sound of crickets...]

[Dan Day]

What you've failed to comprehend is that I NEVER said that natural feedback was "impossible".

You kept insisting that feedback in a system "implies intelligence":

"Feedback" implies intelligent intervention into the process. (Post 98)

Nonsense! Of course "feedback" implies intelligence. (Post 489)

But hey, if you want to back off that position and agree that natural feedback is quite possible, I'll accept that.

What I said was that INJECTING the kind of feedback mentioned by the poster (circa Post #100 & #104) was adding aided intelligence into what was otherwise an unaided process.

And this is a non sequitur.

The poster in #100 (or thereabouts) wanted the monkeys to read a dictionary and then choose which of their outputs should be kept or discarded.

No, actually, he didn't. The dictionary and having the monkeys do the filtering was *your* idea.

Well, that ADDS intelligence into a process (both via the dictionary as well as in the monkeys having to make an intelligent choice).

This overcomplication of the selection process was your own, so I'm hardly impressed by your jumping up and down and pointing out how complicated it is.

[Dan Day]

Perhaps, but even if natural selection does actually occur in the wild, it still fails to explain evolution.

Let's check your reasoning, shall we?

Natural selection merely culls an existing species or allows an existing species to prosper/multiply.

Sure, but you're *really* underestimating all the nuances and consequences when you try to dismiss that as "merely".

Natural selection per se adds no mutations to DNA nor does it create distinct new DNA from whole cloth;

Correct, it's the *mutations* that add the mutations to DNA and create distinct new DNA from whole cloth.

How could you possibly have overlooked that?

Even a children's primer to evolution points out that at its most fundamental evolution arises from the interaction of *TWO* processes: Variation (via mutation and other mechanisms) and natural selection.

So why are you now acting befuddled about how natural selection *alone* can't produce evolution? That's correct, but trivially so. It's natural selection in tandem with varation which runs the engine of evolution.

Were you not aware of this? Are you so ignorant of basic evolutionary theory? Are you so willing to denounce and "disprove" it even without knowing even the most basic things about it?

instead, natural selection only applies to existing species as they stand, leaving science to still answer the question as to the origin of those species.

Sigh. See above. I have led you to water, I can't make you drink.

[Godebert]

"Of course it only took one monkey to come up with Earth in the Balance."

A Monkey? And all this time I thought it was written by a Jackass.