Sunday, 9 September 2012

Why Richard Dawkins’ typing monkey theorem is a load of nonsense

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.

Evolutionary biologist Richard Dawkins employs the typing monkey concept in his book The Blind Watchmaker to demonstrate the ability of natural selection to produce biological complexity out of random mutations.

I have often heard this argument advanced by atheists in debates but in fact it does not survive deeper scrutiny.

Philosopher and former atheist Antony Flew, who became a theist in later life, explains how he changed his mind on whether the origin of life pointed to the activity of a creative Intelligence. It was in a debate in 2004 at New York University with Israeli scientist Gerald Schroeder that he announced he now accepted the existence of a God.

Flew explains his thinking in his book ‘There is a God’, which I finally got around to reading earlier this year. He argues on pp75-8 as follows:

‘I have embraced since the beginning of my philosophical life of following the argument no matter where it leads.

I was particularly impressed with Gerry Schroeders's point-by-point refutation of what I call the "monkey theorem." This idea, which has been presented in a number of forms and variations, defends the possibility of life arising by chance using the analogy of a multitude of monkeys banging away on computer keyboards and eventually ending up writing a Shakesparearean sonnet.

Schroeder first referred to an experiment conducted by the British National Council of Arts. A computer was placed in a cage with six monkeys. After one month of hammering away at it (as well as using it as a bathroom!), the monkeys produced fifty typed pages - but no a single word. Schroeder noted that this was the case even though the shortest work in the English language is one letter (a or I). A is a word only if there is a space on either side of it. If we take it that the keyboard has thirty characters (the 26 letters and other symbols), then the likelihood of getting a one-letter world is 30 x 30 x 30, which is 27,000. The likelihood of a getting a one-letter word is one chance of 27,000

Schroeder then applied the probabilities to the sonnet analogy. "What's the chance of getting a Shakespearean sonnet?" he asked, He continued....

•All the sonnets are the same length. They're by definition fourteen lines long. I picked the one I knew the opening line for, "Shall I compare thee to a summer's day?" I counted the number of letters; there are 488 letters in the sonnet. What's the likelihood of hammering away and getting 488 letters in exact sequence as in "Shall I campare thee to a summer's day? What you end up with is 26 multiplied by itself 488 times - or 26 to the 488th power. Or, in other words, in base 10,10 to the 690th.

•Now the number of particles in the universe - not grains of sand, I'm talking about protons, electrons, and neutrons - is 10 to the 80th . Ten to the 80th is 1 with 80 zeros after it. Ten to 690th is 1 with 690 zeros after it. There are not enough particles in the universe to write down the trials; you'd be off by a factor of 10 to the 600th.

•If you took the entire universe and converted it to computer chips - forget the monkeys - each one weighing a millionth of a gram and had each computer chip able to spin out 288 trials at, say, a million times a second; if you turn the entire universe into these microcomputer chips and these chips were spinning a million times a second (producing) random letters, the number of trials you would get since the beginning of time would be 10 to the 90th trials. It would be off again by a factor of 10 to the 600th. You will never get a sonnet by chance. The universe would have to be 10 to the 600th time larger. Yet the world just thinks monkeys can do it every time.


After hearing Schroeder's presentation, I told him that he had very satisfactorily and decisively established that the 'monkey theorem' was a load of rubbish, and that it was particularly good to do it with just a sonnet; the theorem is sometimes proposed using the works of Shakespeare or a single play, such as Hamlet. If the theorem won't work for a single sonnet, then of course it's simply absurd to suggest that the more elaborate feat of the origin of life could have been achieved by chance.’

41 comments:

  1. Thanks Peter.

    I particularly like John Lennox's book, "God's Undertaker". Looking at the various natural theories on the evolution of 'code' for the passing on of genetic information, Lennox argues that those put forward (particularly by Dawkins) are front-loaded to give the appearance of code from nothing. It is very hard to make long periods of time (or monkeys!) account for the information we find in nature. His argument is that just as the universe cannot come from nothing, neither can information it seems. I find this very plausible.

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  2. Whilst I'm not a young-earth creationist, I do believe that the dogmatism of some biologists could be holding the subject back. I don't know how much you know about epigenetics, but perhaps positive adaptation (as opposed to random mutation) may be responsible for the relatively rapid speed of evolution?

    I believe that if he wished, God could create life simply by setting the laws of the Universe. Is it not a greater testament to his genius that he could do that millions of years in advance, rather than creating us as we are?

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    1. Well said. Science does not fall apart if one believes in a God who created AND sustains the universe in each moment from eternity. It actually adds to it - because you don't just appreciate how things work, but ultimately why they work.

      I feel that Dawkins believes it would somehow be 'cheating' for God to create a purposeful universe - to load the dice, so to speak. To accept the alternative, is to embark on the dead-end road that we have seen oft-trodden in recent years: huge amounts of emotional and physical effort to make science do the thing it could never, by definition, be capable of doing which is to comment difinitively on the existance of God. Dawkins will exhaust himself trying, and rather than destroying God (as others have tried) he could destroy himself, I fear... even if he does turn out to be right!

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  3. You and Mr Schroeder have a misunderstanding of the concept of infinity. Infinity covers all possible outcomes of an infinite amount of monkeys bashing away at a keyboard; including all works of shakespeare, even all of them in order, even everything ever written by anyone.

    You would be correct in saying that it doesn't technically support the validity of anything that happens by chance in nature, as infinity doesn't ever present itself as a measurable quantity in nature. So if you're a pedant, a poor analogy.

    However the number of permutations of random gene mutations required for evolution to occur without the influence of a deity has definitely presented itself in the few billion years it's had to work.

    Such a shame that a god has to be thrown into it, it's a beautiful mechanism on its own.

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    1. I think the point is that since the universe hasn't been around for an infinite amount of time, then infinite typing monkeys for an infinite amount of time is a poor illustration. Mr. Dawkins (and possibly you as well?) have given random selection far more time to work than has ever existed.

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    2. It's a variant on Zeno's paradox. Having all eternity doesn't make it any more likely.

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    3. "Infinity covers all possible outcomes of an infinite amount of monkeys bashing away at a keyboard; including all works of shakespeare, even all of them in order, even everything ever written by anyone."
      - I agree, but would it actually 'mean' anything? - wouldn't it just be a series of characters without meaning unless there was something to compare it with or someone to interpret it?

      "Such a shame that a god has to be thrown into it, it's a beautiful mechanism on its own."
      - I think it would be a beautiful mechanism whether God is thrown into it or not. God could maintain such a process, yet the pickle is where does the information come from?

      Lennox quotes William Dembski saying that although natural processes involving only chance and necessity can effectively transmit complex specified information, they cannot generate it. And so the problem of the origin of life, says Berdn-Olaf Kuppers, is clearly basically equivalent to the problem of the origin of information. Would you agree with that?

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    4. I think all of you actually need to go read the source. Evolution is NOT a random process, and the analogy does not suggest so. Although the genetic mutations that occur (one source of variation) are indeed random, the process of natural selection is precisely not random. The continuation of the monkey analogy assumes this. Dawkins does not suggest the monkeys would hammer out the works of Shakespeare. In fact, Blind Watchmaker follows much of the same mathematical logic that is followed here. The rest of the analogy and its explanation quite clearly express this. Go read it.

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    5. Brent, You are entirely wrong. As postulated Evolution is a random process because it relies on the random events to generate traits, the random events that generate the environment and the random events that place the subject in that environment.

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  4. The thing that I've never understood about the monkey theorum is not only do you need the monkeys and the typewriters to generate the code but also you need a language for them to type in and therefore someone to understand the language and recognise that they've written a sonnet or a play. Even if the code was possible, surely everything else isn't.

    So not only do you need the DNA code, you also need the mRNA and ribosomes to understand the code, and everything involved with DNA to be able to write the code in the first place.

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  5. Firstly, you clearly don't get the idea of a theory...........who said it was fact? It's just an excuse tohave a go at someone, in this case Dawkins.

    Secondly, the above critique is proof of any god how? When scientific peer reviewed evidence of ANY god appears, someone might take you seriously......

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    1. The point of the article is to demonstrate that chance and necessity alone are not adequate to explain specified complexity (such as a Shakespearean play or a DNA sequence coding for a functioning protein).

      Flew concluded that you need design as well, but unlike Flew many people are not willing to 'follow the argument no matter where it leads'. They cannot allow for the possibility of a divine footprint.

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    2. "When scientific peer reviewed evidence of ANY god appears, someone might take you seriously......"

      But as I mentioned above science, by definition, cannot offer such evidence - nor its negation. Don't you agree? However, as Peter said, we can attempt an inference to some explanation for what we observe.

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  6. Thankfully, the fact that Schroeder's belief that Jesus Christ was a fraud and deserved to be crucified is as much a nonsense of his treatment of the Monkey Theorem.

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  7. "former atheist Antony Flew, who became a theist in later life ..."

    Oh no he didn't. At best, Flew became a deist. Read the article at

    http://www.nytimes.com/2010/04/17/arts/17flew.html?_r=1

    An excerpt:
    " A long article in The New York Times Magazine by Mark Oppenheimer suggested that Mr. Flew, his mental faculties in decline, had been manipulated by his co-author [Varghese] and other Christian proselytizers. Mr. Flew, in a statement issued through his publisher, reaffirmed the views expressed in the book, which did not include belief in an afterlife.

    “I want to be dead when I’m dead and that’s an end to it,” he told The Sunday Times of London. “I don’t want an unending life. I don’t want anything without end.”

    Antony Flew did not become a theist and more than likely, the onset of dementia enabled christians to manipulate his worldviews (who would have thought it possible) to their ends.

    If you have read the book, you will notice an aged English public school boy using the word cookies for biscuits and baseball metaphors. Flew, in fact, had admitted that the book was written by Varghese.

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  8. I've read Schroeder's analysis which is printed above. I cannot find any element of (natural) selection within the analysis.

    I only see probabilities.

    Can you please point to where the mechanism of selection in Schroeder's analysis appears so that there is actually some form of "deeper scrutiny" enabling you to conclude that Schroeder has "very satisfactorily and decisively established that the 'monkey theorem' was a load of rubbish"?

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    1. According to Dawkins, Natural Selection operates on the variations of life that occur after random mutations (chance errors) produce those variations. This article does not attack Natural Selection (something that happens independent of Dawkin's theory of how variation occurs). According to Dawkins, those variations are random. Randomness is measured using probability, therefore the mathematics (not religion or faith) strongly disagree with Dawkin's position.

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  9. "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare."

    True enough. This is what the theorem says - enough trials, any result possible.

    "Evolutionary biologist Richard Dawkins employs the typing monkey concept in his book The Blind Watchmaker to demonstrate the ability of natural selection to produce biological complexity out of random mutations."

    Well, again, he uses "a" typing monkey concept - indeed with a selection element - to illustrate how complexity can eventually, with small incremental "improvements", arise.

    But these two paragraphs differ in a substantial way.

    Dawkins' use of a monkey typing out "Methinks it is a weasel" does not use infinity as a boundary to arrive at the complex result. He uses ... SELECTION! The driving force of evolution.

    I shall explain; let's say we wish to explain the occurrence of the sentence:

    SAUNDERS IS A DISINGENUOUS LIAR

    First, the monkey starts hammering away on a special typewriter until suddenly the letter D appears in the fifth position. It gets "selected" by the environment - it "fits". It doesn't need to change any more - it works - and the probability of finding the remaining letters is subsequently and dramatically reduced. Then, as the monkey continues typing, other letters start appearing in the required positions - another D in the 15th position, an S in the first and so on, each letter that "fits" being selected until, eventually, the specified complexity is arrived at.

    Schroeder seems to avoid this selection mechanism in his analysis.

    Saunders doesn't seem to realise it either but is happy to pronounce the process as "nonsense".

    What an idiot Dawkins must be!

    And Saunders is so much more clever.

    I wonder if Saunders will withdraw the post now that he knows that it is not Dawkins' mechanism but his own analysis that is rubbish.

    An apology would be a good, christian act too.


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    1. I only apologise for mistakes and I'm afraid that Dawkins has hoodwinked you.

      He would have us believe that each letter as it appears is 'selected'.

      And yet he also wants us to believe that blind chance does this selecting, that blind chance can read, that blind chance understands the language and that blind chance knows and recognises the target phrase and every step towards it.

      But these kinds of processes require an intelligent mind.

      Or are you suggesting that each string of letters, each nonsense sentence on the way to the target phrase has a meaning that confers some kind of adapative advantage which results in its 'natural selection'?

      I'm afraid biology is just not like that. Change one critical base pair in the DNA code resulting in one different amino acid and your protein will not function at all.

      It is indeed astonishing that Dawkins is unable to see that he has actually introduced into his analogy an intelligent mind, the very thing he is trying to disprove.

      Chance and necessity alone cannot produce specified complexity. It takes design, and design requires an intelligent mind.

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  10. "I only apologise for mistakes and I'm afraid that Dawkins has hoodwinked you."

    You should really apologise then for the mistake of using Schroeder's analysis - a probability assessment - on Dawkins' analogy which uses a selection element to overcome the problems of low possibilities. If I have five dice and I must continually use all five to throw five sixes in one throw, it will indeed take me - on probability - a long time. If I am allowed to leave any six that appears on each throw and use the remaining dice to build up my five sixes, it will take considerably less time. You've used the first method to rubbish the high possibility of the second method.

    Admit it. Go on, be a good christian and admit you are mistaken and apologise to your readers.

    "He would have us believe that each letter as it appears is 'selected'."

    Yes, that is the idea. The idea that you failed to understand when you applied Schroeder's analysis which lacks any element of selection. And whether you think Dawkins' analogy accounts for complexity arising from non-complexity is irrelevant. You have erroneously and falsely rubbished someone's work. You should acknowledge this, withdraw your position, apologise and if you want to, have another go, using suitable analysis, to dismantle Dawkins' analogy.

    "And yet he also wants us to believe that blind chance does this selecting .."

    I think you have some sort of reading and intelligibility problem. "Blind chance does this selecting"? ARE YOU SERIOUS? How can you possibly infer this stupidity from anything that anyone has ever written? Now try to understand some basic Darwinism: "Blind" chance delivers the mutation, the trial, the new letter that the monkey has typed. The first part. Natural selection - WHICH IS ANYTHING OTHER THAN CHANCE OR RANDOM - does the selecting and delivers the complexity and the fitness. How can "blind chance do[es] the selecting"?!!!!! You don't even comprehend what you are trying to rubbish.

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  11. Peter Saunders writes:

    "I'm afraid biology is just not like that. Change one critical base pair in the DNA code resulting in one different amino acid and your protein will not function at all."

    That's not usually the case. Most mutations are neutral. But, sure, it's often the case that a mutation will more likely be deleterious in effect than beneficial.

    Now, Peter, can you see how this in fact illustrates Dawkins' point and refutes your claim that natural selection is a "random" process? If you understood evolutionary theory, you would.

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  12. Well, I'm a geneticist and I work with DNA and mutations every day. Shroeder's analysis and Peter's hamfisted effort at an apology for it are catastrophically wrong. Dawkins does not employ the "infinite monkey" as an argument - indeed, he shows it's inadequacy. "The Blind Watchmaker" is not an expensive or difficult book. Buy it, read it, learn something.
    As for John Lennox, he is funny and uses big words, but he has a very poor grasp of science, philosophy and history. "God's Undertaker" is an embarrassment.

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    1. Dawkins' use of this analogy to show how meaningful DNA sequences might develop purely by chance and necessity is fundamentally flawed because he introduces into it a selection process involving retention of 'correct' letters, a 'language' and a 'target phrase'.

      But these things require the involvement of an intelligent mind in order to yield results within the given time frame.

      The great tragedy is that Dawkins and his adoring followers appear to lack Flew's ability to see this or his courage and integrity in being willing to follow the argument to its conclusion.

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    2. Tragic misrepresentation there, Peter. Charitably I'll suggest you simply don't understand the argument and have not read "The Blind Watchmaker". If you had, you would know that Dawkins points out the failure of the monkey model, its inapplicability to the issue of origins, and how information can actually arise given selection. You would not be the first to disingenuously misrepresent the issue, which is why I suggest your readers check out what Dawkins ACTUALLY says in The Blind Watchmaker, rather than accepting the word of a monkey like yourself banging away uncomprehendingly on a keyboard.

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    3. Shane you seem to have advanced three arguments here:

      1. You are a geneticist and you work with DNA mutations every day (the appeal to authority). So are many others who do not share your views about biological complexity being the blind product of chance and necessity alone.

      2. Schroeder and I are catastrophically wrong (no reasons given). Please explain why.

      3. Read Dawkins book. Another lazy appeal to authority. Why not try to explain his position to readers here and let them make their own judgement. You can't just denounce views not agreeing with your own without giving reasons. Show me the flaws in my argument.

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    4. "As for John Lennox, he is funny and uses big words, but he has a very poor grasp of science, philosophy and history. "God's Undertaker" is an embarrassment."

      Here endeth the lesson.

      And I agree, he is funny, although Dawkins failed to see the funny side during their debates when Lennox didn't have to try very hard to make HIM look like the one with a poor grasp of science (or indeed philosophy, history or Dawkins' chosen specialist subject: religionology)... now that was an embarrassment. Your criticism of Lennox (a Mathematician and a Philosopher of Science) is by extension a criticism of Dawkins who, with due respect to the monkeys, hasn't convinced me that he knows what he's talking about - although I'm not a Geneticist.

      Seriously though, when you stop saying silly things, I'll stop saying silly things. Deal?

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  13. I see Saunders continues to ignore what has been pointed out to him that he is mistaken in using Schroeders´ analysis to debunk Dawkins´ `Methinks it is a weasel` analogy.

    In point 2 of his post on 19th September at, he thinks that the argument that Schroeder is wrong is being advanced and says that no reasons are given!

    Can´t Saunders read?

    I have pointed out to him on two occasions that Schroeder's analysis DOES NOT APPLY to Dawkins's analogy and I have explained why and given him a simply analogy to explain it.

    Schroeder is probably not wrong. It's just that his analogy does not apply to what Dawkins wrote.

    Saunders continues to embarass and disgrace himself by not understanding that the his central argument - the subject of the post - does nothing to refute what Dawkins wrote.

    Saunders, if he had a shred of decency, should retract his position and apologise for misleading his readers.

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  14. The proper context of the infinite monkey theorem is of course the "Boeing 747 in a junkyard" argument from Fred Hoyle. Hoyle likened the chance of complex life arising to the chance of a hurricane blowing through a junkyard and assembling a 747 intact.

    Schroeders' analysis would of course support that thinking.

    But Dawkins' analogy was written after Hoyle's argument and was constructed to expose just how natural selection overcomes low probability events.

    That's right. Dawkins constructed an analogy to expose just how Hoyle's and Schroeders arguments when applied to evolution and natural selection are just rubbish.

    And Saunders has put the horse before the cart.

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  15. Saunders: "The great tragedy is that Dawkins and ... appear[s] to lack Flew's ability to see this "

    I see that Saunders had not responded to my pointing out how christians abused Flew in his old age.

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  16. Saunders: "Dawkins' use of this analogy to show how meaningful DNA sequences might develop purely by chance and necessity is fundamentally flawed because he introduces into it a selection process involving retention of 'correct' letters, a 'language' and a 'target phrase'. "

    It's funny that serious scientists haven't pointed out this fundamental flaw. Nor has Dawkins admitted as such.

    Only an ignoramus like Saunders thinks there are flaws in it.

    For those who actually want to learn something: "correct letters" are those letters, i.e., characteristics of the organism that is evolving, that are favoured by the environment. "Language" is not the spoken language but physical, natural mechanisms. The "target phrase" is a misnomer. Evolution has no target - humans and other organisms ended up the way they are because they contain successful, "fit for purpose" genes and Dawkins was at pains to point out that the analogy he developed indeed uses a "directed" evolution to which natural selection does not apply.

    Saunders: you are a liar or an idiot.

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  17. It's one thing to copy something, I.e. reproducing words by accident. But Shakespeare never produced anything by accident, his works had meaning and intention, something missing from the monkey business!!!

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  18. I readily admit I am no philosopher, no geneticist and no scientist of any sort but as I read these posts and others like these, I am struck by something I heard a few years ago. Evolutionists use the terms "chance" and "necessity" as though they were active causal forces which bear on matter in processes to move from simplicity to complexity. This strikes me as impossible.

    To my simple mind "chance and necessity" are only adjectives. They are descriptors not prescriptors. These words only have meaning when they describe a thing other than themselves. "Chance" is no more an active causal force than is either "Blue" or "Large". One would be thought an imbecile to say that "Blue" caused this or that. Similarly, to say that "chance" causes anything is hopelessly ridiculous. Even more so when coupled with "necessity" or "it fits". WHOSE need? WHAT does it fit? Chance's, Blue's?

    I have also never encountered a satisfactory natural explanation for "everything from nothing". As I understand it in broad terms the theory looks like this: "Nothing + Big Bang = Everything." Am I missing something here???

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    1. Why is Nothing + God = Everything more satisfying? You are still left with What caused God, who cannot be examined, so you are left at a dead end when looking for answers. The thing is, every previously unexplainable dead end in science, has been explained with a rational and logical scientific answer. All these answers build on what has been previously known, pushing the "need" for God further and further into the background. And quite frankly, at the point that it was undeniable that the Earth is Billions of years old and was not created in one week a few thousand years ago, the bible stopped being able to be taken seriously. It is wrong, in the opening chapters of the first book. Nothing that happens after that can be taken as fact.

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  19. i am aware of a world renowned specialist in human genetics who does not believe in macro evolution. Among his reasons is the fact that having treated and discovered a vast number of genetic flaws he has NEVER found one that is beneficial. The chances of such an event happening is so remote that itmay be disregarded.

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    1. http://www.biomedcentral.com/1471-2148/9/302

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  20. "If you took the entire universe and converted it to computer chips (..) You will never get a sonnet by chance"

    Actually, apparently it's already been done:

    http://www.jesse-anderson.com/2011/10/a-few-million-monkeys-randomly-recreate-every-work-of-shakespeare/

    Sincerely, a born-again Christian

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    1. You do realize that his entire method is completely flawed, right? He wasn't doing even close to what the actual challenge is.

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  21. http://www.telegraph.co.uk/technology/news/8789894/Monkeys-at-typewriters-close-to-reproducing-Shakespeare.html

    Here is a closer look at monkeys producing Shakespearean sonnets. Apparently they were successful in achieving this because "small" useful parts they produced were plucked out or selected.

    Applying the same analogy to Darwinism, there seems to be a definitive process of natural selection which does all the sorting. But this process deemed as "survival of the fittest" betrays any full fledged explanation of human phenomena. Human mind with all its morals,senses and everything is a much more complex thing and needs something more than just a "survival" process. I won't jump to a God directly but there is a need for biologists to look in another direction if there are to tackle the increasing number of questions.

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