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Mathematical Darwinian Absurdities

When I was growing up my father (who is the most brilliant scientist I have ever known — he worked on the Manhattan A-bomb project, was the founder and director of an experimental nuclear reactor at Washington State University, and developed the Ph.D. program in chemical physics at WSU) delighted in giving me puzzles to figure out.

One in particular I remember: He asked if I would rather be given a million dollars, or be given a penny one day, two pennies the next day, four pennies the next day, and doubled pennies for a month.

Of course, I knew it was a trick question, so I did the math. The doubled pennies would be worth 10 million dollars in a 30-day month, and more than 20 million dollars in a 31-day month.

Later in life (after I was awakened from my Darwinian stupor) I took my dad’s mathematical admonitions to heart. Even given the most generous assumptions about populations, mutation rates, reproductive events, etc. (i.e., probabilistic resources) the notion that Darwinian mechanisms can account for what is credited to them is perhaps the most transparently mathematically absurd proposition ever advanced in the name of science.

This is not hard to figure out. In fact, it’s a completely trivial exercise.

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31 Responses to Mathematical Darwinian Absurdities

  1. I thought Darwin hated maths.

  2. Gil,

    Even given the most generous assumptions about populations, mutation rates, reproductive events, etc. (i.e., probabilistic resources) the notion that Darwinian mechanisms can account for what is credited to them is perhaps the most transparently mathematically absurd proposition ever advanced in the name of science.

    I’m really curious, do have something we can look at where you’ve worked some of this out? I’d just like to see how you did it, what parameters and constants you used, etc.

  3. 3

    Even for everyone their is a instinctive and intuitive sense that its absurd or quite impossible by the math to have the great complexity interacting with each other and the basic substance of biology HAVING come from selection on mistakes .
    Its stupid and always was.
    THere is not just no evidence for evolutionary claims but its impossible .
    Bubbles to buffalos never happened or could happen.

    They just wanted it to be true to explain biology.
    They dismissed the religious ideas and simply it had to be from some mechanism in nature without a God creating or controlling it.
    darwin came and they said AHA thats it IT must be IT.
    Only now is serious attention being made to its claims.
    It was always sustained by the need to have some idea and reject the popular and important religious ideas which had ruled civilization for a long time.
    Evolution is always said to have changed morte then a few ideas in biology but to have attacked religious truth.
    The scopes trial is just another fact this is what evolution was needed for.
    christianity really was and is the most important motivational movement in human history.
    target number one by many.

  4. 4

    Gil, you are right:
    But, a good darwinist is 100% convinced that a God would not do a world so badly and with infinite amount of evil. So the probability of God for them is 0%, then an evolution by chance, probability 10^-100000000000000000 is something sure, a Fact (without facts).

    That is their logic.

  5. Here’s a calculation that’s fairly typical:

    Let see how long it would take to get a specific protein that is 100 amino acids long – something along the lines of cytochrome c.

    There are 20 amino acids, so the total number of combinations is 20 taken 100 at a time, 20 to the 100th power, which in base 10 is 1.27 x 10^130.

    Now to make things simple, let’s assume that the entire mass of the earth is amino acids, and let’s take the simplest one, glycine. The mass of the earth is about 6 x 10^27 grams and glycine has a mass of 75 grams per mole.
    A mole is 6.023 x 10^23 particles (glycine molecules in this case), so the total number of glycine molecules would be:
    (6 x 10^27 / 75) * 6.023 x 10^23 = 4.82 x 10^49.
    And thus the total number of proteins that could be made of
    100 amino acids would be 4.82 x 10^47.

    So now let’s assume that the earth has been creating a new set 4.82 x 10^47 proteins 100 times per second for 5 billion
    years. The total number of seconds in 5 billion years is:
    5 x 10^9 years * 365.25 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 1.58 x 10^18 seconds.
    So the total number of proteins that could have been created in that time would be:
    4.82 x 10^47 * 100 * 1.58 x 10^18 = 7.62 x 10^67.

    Now let’s assume that there are a trillion earth-like planets in our galaxy, and that there are a trillion galaxies in the universe. Then the total number of 100 amino acid proteins that could have been created would be:
    7.62 x 10^67 * 10^9 * 10^9 – 7.62 x 10^85.

    And one final assumption. Assume there are a billion different proteins that have some sort of function or use that are 100 amino acids long. So that would mean that the probability of finding a single useful protein in all of the universe would be:
    1.27 x 10^130 / 10^9 / 7.62 x 10^85 = 1.67 x 10^35.

  6. Slight typo:

    7.62 x 10^67 * 10^9 * 10^9 – 7.62 x 10^85.

    should have an equals sign instead of a minus sign:

    7.62 x 10^67 * 10^9 * 10^9 = 7.62 x 10^85.

  7. snelldl

    please excuse me if i come arcoss a little naive here, but what does all that say?

  8. The final number indicates the odds of creating one functional protein that is 100 amino acids long in the last 5 billion years in the entire universe. The ^ indidcates “to the power of”, so:

    7.62 x 10^85

    means 1 chance in about 10 followed by 85 zeroes (rounding up).

  9. Dang! I did it again. Copied the wrong line.

    That should be

    1.67 x 10^35, so 1 chance in about 10 followed by 35 zeroes.

  10. Oh boy.

    1 chance in about 10 followed by 34 zeroes (rounding down).

  11. Except that large & complex proteins were likely built from the bottom up, i.e. from smaller folding units, over eons of evolutionary history.

  12. “likely” = we haven’t got a clue

  13. No, it’s an open question, but it’s not that we don’t have a clue. See for example, Lang et al. Science 2000, 289, 1546. The authors provide structural evidence the (beta/alpha)8-barrel proteins, a widespread and complex fold, arose by a process of gene duplication and fusion.

  14. I could just as easily say that a 4 barrel carburator “arose” by a process of duplication from a single barrel carburator.

  15. snelldl,

    Thanks for showing us an actual calculation. I wish more participants in this debate were willing to discuss the issues at a nuts-and-bolts level, as you’re doing.

    Your calculation hinges on a number of assumptions, including the following:

    A) 99.99999999999999999999
    9999999999999999999999999
    9999999999999999999999999
    9999999999999999999999999
    999999999999999999999999% of all potential 100-amino-acid proteins are useless.

    and B) All 100-amino-acid proteins are realized from an unbiased distribution of 10^130 potential outcomes. That is, they’re produced by maximum-entropy random processes, like tornadoes in junkyards.

    With regards to the first assumption, it doesn’t seem to satisfy Gil’s “given the most generous assumptions” condition. Even Yockey allows for far more than a billion functional 100-amino-acid proteins, IIRC.

    But that issue is negligible compared to the second assumption, which you didn’t explicitly state, much less justify. This shows that you are not, in fact, demonstrating a “mathematical Darwinian absurdity”, since your model has nothing to do with Darwinism.

  16. RObb:

    The “unbiased distributor” is called God.

  17. Sorry, 16 should read:

    The “biased distributor” is called God.

  18. RObb:

    You’re correct about the calculation not being about Darwinism. It’s obviously related to origin of information/structures in the first cell.

    Perhaps the work of Douglas Axe is more of what the OP was referring to.

  19. RObb:

    Looking at the calculation again, I divided by a billion (10^9) to include the final assumption. That’s not correct. I should have subtracted a billion to do that. So if we take that out, we’d end up with:

    1.67 x 10^44

    That would be the probability for any individual sequence.

  20. RObb:

    Not to keep flogging this horse, but here I go anyway…

    I recall reading on talkorigins probably a decade or more ago, that of the 1.27 x 10^130 combinations of 100 amino acids, 10^67 would be some form of cytochrome c. I don’t know where he got that number from.

    Assuming it’s correct, if we subtract those 2 number, we get:

    1.26666666….00000…0 x 10^130. (i’m too lazy to count).

    So it really doesn’t affect the calculation, because the search space is so large.

  21. snelldl:

    Looking at the calculation again, I divided by a billion (10^9) to include the final assumption. That’s not correct.

    Actually, it looks right to me. The probability of at least one success in n tries is 1-(1-p)^n which is approx n*p for small p. If p = 1e9 / 1e130 and n = 7e85, then the resulting probability is 7e85 * 1e9 / 1e130, as you said.

    I’m curious to see Gil’s math. I personally don’t see how accurately modeling biological evolution can be considered a “completely trivial exercise”. On another blog, he made reference to some “simple probability calculations” and he was repeatedly asked to share them with us. As far as I know, he never did, but maybe he’ll do so now.

  22. The probabilistic calculations are utterly trivial to figure out, given the inherent nature of the combinatorial explosion of nucleotide sequences. The nature of combinatorial explosion was the theme of my post. Darwinists never address this question.

    The notion that random errors (whether or not filtered by natural selection) could transform Lucy into Liszt, a microbe into Mozart, or a hippo into a whale, is so statistically absurd that anyone with an IQ above room temperature should be able to figure out that this thinking can only be held by people who have completely lost contact with reality.

    The really weird and pathetic thing is that people who have lost contact with reality want the rest of us to believe that they are promoting rationality and science, when, in fact, they are doing the exact opposite.

    And they do it with a cult-like religious passion, using the legal system to suppress any dissent from Darwinian orthodoxy in public education, no matter how rational or evidence-based such dissent might be.

    If the evidence was available, that random errors filtered by natural selection had the statistical creative powers to transform a microbe into Mozart, I would be more than happy to accept such a proposition.

    But I’m not sufficiently stupid, uneducated, or irrational to accept such transparent idiocy.

  23. Gil:

    The probabilistic calculations are utterly trivial to figure out, given the inherent nature of the combinatorial explosion of nucleotide sequences.

    The size of a combinatorial space does not, by itself, tell us what the probabilities are. If it did, then we would be surprised every time our offspring turned out to be human.

    Why is it that when you’re asked to show us these calculations, you respond by telling us again that they’re “utterly trivial”? If they’re so trivial, what is preventing you from posting them?

  24. Gil,

    I want to see your calculations to see what probablility measures you are using. I can’t agree or desagree with you until I see your scientific reasoning. She us what you’re talking about.

  25. Probability calculations are meaningless because no one can demonstrate that a probability exists wrt accumulations of random mutations and the construction of new, useful multi-protein configurations requiring more than two new protein-to-protein binding sites.

    IOW just by including/ discussing probailities gives evos something that is undeserved.

    That means THEY need to step up and demonstrate a probability exists. Good luck with that…

  26. Joe,

    IOW just by including/ discussing probailities gives evos something that is undeserved.

    Not quite sure what you’re getting at. Gil feels he has a solid probabilistic argument and I’d just like to be clear what it is. I can’t say why he hasn’t responded as of yet . . . perhaps he’s very busy, but I hope he does.

    That means THEY need to step up and demonstrate a probability exists. Good luck with that…

    That’s the trouble with random events!! Even so certain general rates of mutation have been studied but I think you’re looking for something that doesn’t exist. In it’s specifics.

    I believe the origination of life of earth via natural processes is highly unlikely. But, in order for us to be here discussing it we would have to be on a planet, conducive to life where that improbable event had occurred. I can’t say how improbable it was partly ’cause I don’t know how it happened. But I’m willing to concede it was very improbable.

    I’m sure the advent of two new protein-to-protein binding sites is also unlikely. But, if a population is big enough and the ‘gene pool’ is stirred well enough then the probability of the necessary mutations developing, perhaps in separate individuals, and then meeting is less improbable than it happening linearly.

  27. Jerad:

    Not quite sure what you’re getting at. Gil feels he has a solid probabilistic argument and I’d just like to be clear what it is.

    No one needs a “probability argument” because no one can even demonstrate a feasibility.

  28. Gil,

    Aside from the fact that that post doesn’t directly address the point of this thread (I admit I haven’t read the whole thread) Darwinism doesn’t say that natural selection is a random process nor does it acknowledge islands of function. Given a first, basic replicator which leaves descendants with a smattering of mutations/modifications (many of which are unviable, a few which are), the viable descendants are ‘fitter’ and evolution flows, slowly, towards increased complexity and function tiny steps at a time. There is much waste and death of course. I realise you do address the notion of the probabilities of common descent with modification but without the calculations you said were simplistic. And remember, if there are potentially billions of planets which could harbour life it only has to happen once for us to be here. I agree that the origin of life IS highly unlikely. After that I think the probabilities change dramatically. Not for there to be humans but for there to be higher intelligence.

    Joe,

    Gil brought up the probability argument, not me. I’m just asking him to lay it out in the same way he’d ask me to uphold any assertion I made. Surely that’s fair and reasonable. I don’t want to misinterpret him after all.

  29. Gil, are you referring to your calculation of the number of unique 66-character strings from an alphabet of 26 symbols? You weren’t kidding when you said it’s trivial.

    Like snelldl’s calculation, this has nothing to do with Darwinism. Unlike snelldl, you don’t even bother calculating a probability, and your calculation isn’t about anything biological.

    So, contrary to the title of the OP, you don’t really have any mathematical Darwinian absurdities to show us, do you? A good start would have been to model an actual Darwinian process, as your colleagues at the Evo Info Lab did when they modeled Weasel as a birth/death Markov chain. Of course, this is a far, far cry from modeling real biology, but at least it deals with a simple Darwinian mechanism.

  30. R0bb-

    Darwinism IS a mathematical absurdity and no one can model real biology….

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