Gene Expression

Math and Creation

I don’t speak that much about the Evolution-Creation debate in comparison to other Science Bloggers. Fundamentally, it is because I find the elucidation of the fact of evolution far more fascinating at this point in my life than an analysis of the meta-scientific and cultural issues revolving around the Creationist response to evolutionary science. But today I checked the genetics & evolution query on google news as is my habit, and I stumbled upon this blog entry, Mathematicians and Evolution by Casey Luskin. Most of you probably know him, and I’ll leave it to others to appraise this individual.

But, I will make two points. Mathematicians play an essential role in evolutionary science, both R.A. Fisher and J.B.S. Haldane took degrees in mathematics, not biology (Haldane also took a classics). Fisher outlined the core of the Neo-Darwian Synthesis with his genetical theory of natural selection. Obviously mathematicians have been crucial to the foundation of evolutionary biology, and they will continue to be. But, both Fisher and Haldane were evolutionary biologists, their colleagues were empirical biologists, field workers and laboratory experimentalists. Both were steeped in the culture of evolutionary biology and so their mathematical expertise was applied to the greatest effect. The problem of course emerges when individuals comment on evolutionary biology in passing. A facility with modeling and deductive formalism does not endow one with magical powers to just “drop in” and speak ex cathedra, the main problem being that mathematical models by their nature simplify reality, and the selection of relevant parameters and the discarding of variables is contingent on biological, not mathematical, considerations.

Second, this quote from Stanislaw Ulam is staggering:

“[I]t seems to require many thousands, perhaps millions, of successive mutations to produce even the easiest complexity we see in life now. It appears, naively at least, that no matter how large the probability of a single mutation is, should it be even as great as one-half, you would get this probability raised to a millionth power, which is so very close to zero that the chances of such a chain seem to be practically non-existent.”

!?!?#@!?!?#@!@$@!!#!@!!

Comments

  1. #1 John Emerson
    July 12, 2006

    People are always saying that mathematicians and physicists are the smartest people, and they are as far as mental quickness goes, but as I’ve said, they don’t necessarily figure out exactly where they are when they venture out of their own fields.

  2. #2 DarwinCatholic
    July 12, 2006

    It seems a bizzar case of thinking about the problem from the result backwards. Certainly, if you imagine that the original state was somehow trying to achieve the final state through a specific set of mutations, it would be very difficult, but that’s not what evolutionary biology suggests.

    It would be impossible to look at a completed nine hole game of golf, calculate the probability of each stroke sending the ball exactly where it did, and then reproduce each stroke exactly. The odds or successfully producing an identical reenactment of a game of golf as such as to make it impossible. But that didn’t keep the original sequence of strokes from taking place, because each time the golfer hit the ball, it had to go somewhere.

  3. #3 razib
    July 12, 2006

    what do you know, are you a mathematician?

  4. #4 DarwinCatholic
    July 12, 2006

    Just a data analyst and database programmer with a classical education and a lot of opinions… :-)

    But I do think one of the key problems the ID folks run into again and again in their thinking (typified by the bit you quoted) is that they calculate the likelihood of getting to a specific end point (say the human eye) via a long series of mutations, without considering that the human eye was by no means a necessary outcome.

  5. #5 razib
    July 12, 2006

    what databases do you do? (e.g. mysql, postgresql, sql server)

  6. #6 DarwinCatholic
    July 12, 2006

    MySQL (favorite), SAS (ugh), SQL Server, and what I should be doing right now unfortunately: Access (blah)

  7. #7 FhnuZoag
    July 12, 2006

    Er, yeah. I am a mathematician.

    Ulam’s (alleged) statement seems staggeringly stupid – to the existent that it seems very likely to me that he is being quoted out of context. After all, the article this is from is asking “How to Formulate Mathematically Problems of Rate of Evolution”, and I’d hope that in the following parts of the article, he goes on to discuss how the above view is in fact simplistic and fallacious.

    It isn’t true to say that Ulam didn’t have any connection with biology – in fact, he went on to help develop highly useful tools for investigating evolution. e.g. the link below details lectures he gave in 1972 (6 years after the quote) on mathematical attempts to formulate evolution in terms of cellular automata.

    http://www-hto.usc.edu/papers/msw_papers/msw-065.pdf

    It seems that he was smart enough to get over any intuitive objections, and was smart enough to actually become part of evolutionary theory. So a creationist has been misquoting people again.

    Quelle surprise.

  8. #8 razib
    July 12, 2006

    thanks, i assumed as much, but i don’t this field.

  9. #9 razib
    July 12, 2006

    access, ouch :) i work in the former.

  10. #10 Alan Kellogg
    July 13, 2006

    Having a 3 billion to one chance of something happening doesn’t mean the event effectively cannot occur, it means that out of three billion occasions it might occur it will typically occur once.

    Now, when you have billions upon billions of life forms around you’re going to have those 3 billion opportunities showing up very frequently. Even with 3 billion to one odds, at the end of the day you’re going to have it happening a shitload of times.

  11. #11 Maria
    July 13, 2006

    Mark Chu-Carroll’s point about the odds of any one card shuffle (I can’t find a link) is quite straightforward. If there are 54 cards in a deck, there are 54! = 2×10^71 possible shuffles. And you can get any one of them yourself.

  12. #12 FhnuZoag
    July 13, 2006

    Kellogg et al, you are kinda missing the point. The quote is killed by two points:

    1. There is no such thing as a minimal, or even a canonical eye. The ‘eye’ is defined evolutionary not in terms of specific DNA bullseye, but a distributed and very numerous selection of genetic situations that would produce *some sort of* organ that detects EM radiation.

    2. There is such a thing as inheritance. In probability, we take powers of factors in order to find the probability of X *and* Y and so on happening on the same try. That’s what the example does with a coin toss model.

    But in evolution modelled as a series of coin tosses, just because we fail to land a head at a given point does not mean that we start again from the beginning. Instead, we keep the chain of heads that we have already obtained, and keep tossing the coin until we get another head. (This is assuming a very strong selection factor, and a single target. The former increases probability, the latter decreases probability) This lets us avoid the multiplicative law and instead get an additive law – we ask, how many times out of our n tosses do we manage to advance the chain? If we take a target of 1 million, then we see that after two million generations, we have a probability of 1/2 that the eye has already been evolved – we’d have discovered eyeballs before multicellular life.

  13. #13 FhnuZoag
    July 16, 2006

    As a heads up, David Wilson has dug up the proper context of the quote in the comments at

    http://scienceblogs.com/evolutionblog/2006/07/are_mathematicians_qualified_t_1.php#comment-171411

    And woohoo, it says exactly what I said. More evidence of barefaced lying from the DI people. (Though I suspect Luskin isn’t aware of the lie himself, merely parroting the claims of the arch manipulators at the top, or the ones lost in the mists of internet history.)

  14. #14 shiva
    July 16, 2006

    DarwinCatholic It would be impossible to look at a completed nine hole game of golf, calculate the probability of each stroke sending the ball exactly where it did, and then reproduce each stroke exactly.

    But that’s a case of specified complexity paid for with intelligence!