Paulos on Creationist Math

Mathematician John Allen Paulos offers these worthy thoughts on the subject of creationist arguments based on probability theory:

But there’s another contributing factor to this opposition to evolution that I’d like to discuss here. It is the concerted attempt by creationists to dress up in the garb of mathematics fundamentalist claims about human origins and to focus criticism on what they take to be the minuscule probability of evolutionary development. (Even the conservative television pundit and ace biologist Ann Coulter has lent her perspicacity to this mathematical endeavor in her recent book.)

Sadly, I know from personal experience that this is true. I attended an ID conference in Kansas City a few years ago. One of the speakers was from the right-wing Heritage Foundation, and he spoke about probability theory a la William Dembski. At one point he whipped out some numbers, multiplied them all together, and then claimed that the tiny number that emrged represented the probability of some complex structure evolving.

During the ensuing Q&A one young man, with a look on his face that can only be described as comically serious, asked something like, “When atheistic scientists are confronted with probabilities that small,” dramatic pause, “how can they do anything except stare helplessly at it?” Heritage guy agreed that this was very puzzling.

So I raised my hand and informed the previous questioner that scientists respond by challenging the assumptions that went into the calculation, which in this case were universally false. I also mentioned several other variables that would have to be taken into consideration to have any hope of performing a meaningful calculation. The previous questioner gave me a look of such malevolence I decided not to pursue the issue any further. Heritage guy dodged the question and then went on to someone else.

This was hardly the only time that happened. When I attended the major young-Earth conference in Lynchburg last year, one of the best received talks was an attempt to use information theory to refute evolution. As I pointed out in my report on the conference, he received a standing ovation despite the fact that his arguments were utterly incoherent. The fact is that mathematics is unique in its ability to bamboozle lay audiences, which makes it well-suited to creationist ends.

Anyway, Paulos makes the central point:

This line of argument, however, is deeply flawed.

Leaving aside the issue of independent events, which is too extensive to discuss here, I note that there are always a fantastically huge number of evolutionary paths that might be taken by an organism (or a process) over time. I also note that there is only one that actually will be taken.

So if, after the fact, we observe the particular evolutionary path actually taken and then calculate the a priori probability of its being taken, we will get the minuscule probability that creationists mistakenly attach to the process as a whole.

Misunderstanding this tiny probability, they reject outright the evolutionary process.

Well said!

Comments

  1. #1 David Heddle
    September 6, 2006

    I agree that creationists often misuse probability, especially when creating those long chains of events. However, the naive rebuttal, which is essentially the one Paulos is making, and which usually goes like this: “any card hand, even a royal flush, is equally likely” misses the boat. Because while any card hand is equally likely, most are losing hands. That needs to be considered in his argument. His assertion “a fantastically huge number of evolutionary paths that might be taken by an organism” is not beyond challenge. Exactly how many is a “fantastically huge number?” He cannot know, because he cannot test how many of those countless imaginable evolutionary pathways would have been successful.

  2. #2 bmkmd
    September 6, 2006

    The thing missing from these arguments about probability is that evolution is cumulative. AFter the first branch in the tree, all the possibilities on the branch not taken are no longer possibilities during the second step of natural selection.

    It is the tinyest probability only when viewed from the very begining step, without reference to the lessening range of choices with each step of mutations, and with each step of selection, a racheting mechanism (with or without a designer).

    It would only be so if you could go back, retrace your steps, unevolve, and start over the second and third and forth time, ad infinitum.

  3. #3 Ryan S.
    September 6, 2006

    “That needs to be considered in his argument. His assertion “a fantastically huge number of evolutionary paths that might be taken by an organism” is not beyond challenge. Exactly how many is a “fantastically huge number?” He cannot know, because he cannot test how many of those countless imaginable evolutionary pathways would have been successful.”

    Yes, thats what we call an extinct organism.

  4. #4 FhnuZoag
    September 6, 2006

    But what, pray tell, is success?

    What is needed for ID to succeed is, by analogy, the existence of rules in the game. Until ID shows that there is an universal and objective criteria which narrows down the set of all possibilities and yet is independent of the evolutionary process, then their argument is meaningless.

    But the thing is, the existence of such an universal ‘purpose’ to life that a design would fulfill implies the existence of God.

    ID hence is simply a circular argument. If life has a supreme, divine purpose, then a god exists to assign the purpose. If God designed life, then life is designed by God.

  5. #5 TomS
    September 6, 2006

    Whenever I hear the “probability” argument, the first thing that I think of is not the
    faults in the calculation, nor the validity of the presuppositionss.

    The first thing that I think of is “what is the probability under your alternative explanation?”

    An “intelligent designer” is capable of doing everything that ordinary natural processes can do, as well as a whole lot more. That means that the probability of a given outcome is far less, if intelligent designers are involved. Not to mention: if there is an omnipotent designer, then anything is possible, which means the probability of any one outcome is effectively zero.

  6. #6 Dave S.
    September 6, 2006

    David Heddle says:

    However, the naive rebuttal, which is essentially the one Paulos is making, and which usually goes like this: “any card hand, even a royal flush, is equally likely” misses the boat. Because while any card hand is equally likely, most are losing hands.

    But a “losing” hand depends on what the game you’re playing. A Royal Flush is only an unbeatable hand (in most games, in a game like Lowball it loses to many other hands) because we defined it that way. We could as easily define 4h5c6c8sJd as an unbeatable hand instead of 10hJhQhKhAh.

  7. #7 Fred
    September 6, 2006

    Here’s a little game about probability that shows how amazingly often it is that seemingly impossible things happen:

    Go outside and stand on a street corner. Take a look at the driver of the first car that goes by. Now, what are the chances, with all the places you’ve been, and all the time that’s gone by in your life that you just happened to be there at the exact right time to see that person drive by? Imagine all of the decisions and events that led to your being there. It’s overwhelming. You certainly couldn’t have done it if you tried.

    If I came to you when you were 5 years old and told you that you had to manipulate your life so as to be in this exact spot at this exact time in order to see that person drive by, what are the chances you could have done it? And yet somehow, against probability, you did do it. (Let alone the events that led up to that person being there in the car at that moment…)

    Of course, I’m sure you see the glaring error in all of this, which is that neither you nor the driver *were* told to try to generate this outcome, it was just the result of millions of random events. It just *looked* amazing when I told you it was important outcome (seeing the person). I made it a coincidence, or whatever, merely by stating that it was.

    Well the same goes for the probability argument against evolution. You can look at the result and say it was improbable, but if things were different today, like that we had four arms, six eyes and were green, scaly and cold-blooded, you’d *still* say it was improbable.

    Unless you predict the result very far in advance, or if only one result is viable, you can’t say it’s improbable. There’s nothing inherently special or “better” about the results of evolution that we see today. In fact, as has been well noted, human beings are pretty poorly “designed,” so there are other roads that evolution could have taken that would have been far better.

    Besides, if we’re improbable, how probable is God? Or how probable is it that life arose on some other planet and its inhabitants eventually got so advanced that they designed life here? If your own theory falls apart with the same argument you’re making against another theory, then your theory is no better. At all.

    So to sum up, evolution was not aiming at anything specific, so *any* outcome– and there will always be an outcome– is just as likely as another. And probability in hindsight is the wrong way of looking at things.

  8. #8 Badger3k
    September 6, 2006

    Addition to Dave S point:
    “But a “losing” hand depends on what the game you’re playing. A Royal Flush is only an unbeatable hand (in most games, in a game like Lowball it loses to many other hands) because we defined it that way. We could as easily define 4h5c6c8sJd as an unbeatable hand instead of 10hJhQhKhAh.”

    In many hands, a simple high card can wind. In that situation, there are a huge number of possible winners, but looking back on it afterwards, we have only one actual winnner. In evolutionary theory, the “winner” (ie the one that succeeds in passing it’s genes on to the next generation”) merely needs to be better than the other players, not have an unbeatable hand. I rarely play poker, especially for money, but my largest win was with a pair.

  9. #9 Dave S.
    September 6, 2006

    Fred –

    I’ve used a similar exercise in the past. Of all the eggs ever produced by my mother (10,000+) and all the sperm by by father (hundreds of millions), only 1 pair could have made me. The same holds true for my father and mother, and their parents, and so on. What is the probability starting say even 200 years ago, that all the necessary people would meet and procreate and all the right sperms and eggs and other biological factors would fall into place to make moi, 166 years later?

  10. #10 Jim Ramsey
    September 6, 2006

    I always get the feeling that Dembski is playing 10**18 card Monty.

  11. #11 Steven
    September 6, 2006

    Jason,

    I think that we should take up a collection to pay for a bodyguard to accompany you to some of these creationism/ID conferences. You should have the freedom to ask any questions and make any points that you deem to be appropriate. What do you think?

  12. #12 FCB
    September 7, 2006

    It has amazed me for years that people argue probability. I think that it is a 100% probability that we exist.
    The problem with most people trying to prove that God exists is that they use natural means to try to explain a supernatural being. God is superior to nature. The physical laws do not apply to Him.
    I have been asked to prove that God created everything. Look around, do you see things? They exist. I believe God created them. I will ask you (anyone here) how did the universe come into existense? Did it come from nothing or did it always exist? If it came from nothing, how can that happen? If it always existed, how can that be?

    The universe exists. It was created by some means either natural or supernatural. I believe a supernatural God created it. You believe that nature or natural means created it. Who or what created those natural means?

  13. #13 Fred
    September 7, 2006

    FCB, I have two replies for you:

    1) If the universe is so amazing to you that it could not have come about naturally, isn’t a God who could create something so amazing even *more* amazing, and therefore could not have just come about on his own? So saying “God is the origin” is not an answer, because it just stops at God, and doesn’t explain where God came from. Just like the answer to the origin of man is not “my parents.”

    2) We don’t know what created the laws of the universe or where the material for the big bang came from, or what existed before the big bang. But we don’t believe the answer is to make up fairy tales about some magical being. Where’s the basis for that belief? If you can believe that “God just *is* and has always *been*,” how is “matter (or energy) has, in some form, in some way, always existed” any less believable? If you lose your car keys do you assume a natural explanation, like they fell under the couch, or do you assume that God, or “a God,” took them?

    3) If we do accept the supernatural, where do we stop? Is there one God or thousands of Gods? Is God still here? Is he the same God or “God’s son” or something? How can you know *anything*? Accepting the supernatural means accepting anything and everything.

  14. #14 bmkmd
    September 7, 2006

    Why do you ask “who” created the universe, assuming it needed creating. The “who” assumes that it was a person- like something with a mind, a “bodyless mind” and intent and consciousness created it. Doesn’t that sound a lot like a human being up there without a body?

    Asking the question as “who” created the world/universe begs the question.

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