Probability Theory, Intelligent Design, and the Monty Hall Problem

27Dec09

I think I have just eaten Dembski’s probabilitistic lunch, but I need someone who knows more about probability theory than I do to check my work.

I will try to explain in a way normal mortals can understand. :P

In his book on intelligent design, Dembski argues, among other things, that certain biological structures cannot have happened by chance because the probability that they would appear by chance in nature (presumably, he means “at all anywhere ever”) is less than 1 in 10^150. (I have issues with how he got this number that are too complicated to go into here*, so for the sake of this argument, we’ll go with 1 in 10^150.)

My first instinct was that this was wrong, because it overlooks that certain structures are meaningful to us.

A very simple illustration: say you can make a protein from a series of building blocks, which are chosen by random flips of a coin. Dembski argues, for example, that HTTHTHTHTHTHTHHHTHTH could not occur randomly in nature because the chances of that sequence happening randomly in nature fall below 1 in 10^150. (This is just an illustration; I haven’t even tried to do the math to demonstrate the probability of flipping HTTHTHTHTHTHTHHHTHTH. My excuse is that Dembski doesn’t do it either.) My first problem with this is that we only give a shit about HTTHTHTHTHTHTHHHTHTH in the first place because it is meaningful to us; the probability of hitting HTTHTHTHTHTHTHHHTHTH on the first try** is susceptible to the position of the observer (us) as to whether HTTHTHTHTHTHTHHHTHTH is significant.

I had absolutely no way of articulating this until I remembered the Monty Hall Problem. The Monty Hall Problem (you may remember this from some recent movie with math geeks in it; I know I saw it there but I can’t remember which movie – I’m thinking either 21 or Good Will Hunting) goes like this:

Imagine you are on a game show. The point of the game show is to win a car. In front of you are three doors, marked 1, 2, and 3, which are closed. You know there is a car behind one door and goats behind the other two doors.

The host (who knows what is behind each door) asks you to pick a door. For illustration, you pick Door No. 1. The host then opens Door No. 2 and shows you the goat behind it. Then, the host asks if you want to keep Door No. 1 or switch to Door No. 3. What do you do?

The answer, counterintuitively, is that you switch. Because if you switch, you have a 2 in 3 chance of winning the car, whereas if you stick, your chance of winning is only 1 in 3. It’s counterintuitive because, once you know what is behind Door No. 2, you’d think your chance of winning the car is only 50/50: after all, there are only two closed doors left, and you know that one door is car and the other is goat.

But what skews the odds is not that you don’t know what’s behind 1 or 3, but that the host does, and more importantly, that the host did not show you the car. The probability that you’ll win the car has changed not because the numbers have, but because of the influence of the host’s knowledge on the numbers.

To maybe make it clearer: say that, instead of three doors, there are a hundred doors. You pick Door No. 1, and the host opens all the other doors *except* Door No. 49. You’d switch, instantly, because it’s obvious the host knows something you don’t about about Door No. 49 – say, that there’s a car behind it. (Yes, it is possible that the host picked No. 49 arbitrarily and you had the car in the first place. It’s also true that, in the original problem, the host picked No. 2 arbitrarily and you had the car in the first place. That’s why your chance of winning if you switch is only 2 in 3, not 3 in 3.)

Dembski’s argument is predicated on the idea that all possible combinations (say, of proteins) are equally likely, and that therefore any one of the equally-likely combinations cannot have happened by chance. But (overlooking the vast array of external pressures for the moment, because Dembski does) the combinations aren’t all equally likely. Like the host, we’ve eliminated a huge number of zonk combinations because we know they do not work. And our chances of landing on the few that do work thus increase. I haven’t crunched the numbers, but I would bet they increase well over Dembski’s “probabilitistic threshold” of 1 in 10^150.

That’s as clear as I can make it right now, unfortunately.

And of course, even if this flaw exists, the entire notion of “design theory” suffers from another a priori flaw that renders this one moot: it unnecessarily compounds the postulate. There is simply no need to postulate a Creator Intelligence, Dembski’s “probabilitistic threshold” notwithstanding. What’s hilarious is that Dembski even admits as much, albeit not in so many words.

*Dembski comes up with 1 in 10^150 by multiplying the estimated number of elementary particles in the universe by the estimated number of units of Planck time that have passed since the universe began. I still suspect that anything that could occur beneath a threshold consisting of the smallest possible bit of matter multiplied by the smallest measurable unit of time could not “occur” in any meaningful sense at all, but I have no way of demonstrating it just yet.

**Dembski does seem to think we ought to hit on a working biological structure on the first try, or never. I also think he’s wrong about this because he fails to account for the amount of time available for biological structures to respond to adaptive and other pressures.



2 Responses to “Probability Theory, Intelligent Design, and the Monty Hall Problem”

  1. 1 Joe Jensen

    The Monty Hall Problem isn’t applicable to the probability of proteins forming by random action. The actions are random, no intelligent selection is possible, therefore the odds don’t change.
    Dempski allows for the continuous production of non-functioning proteins throughout the universes history, there isn’t as you describe, a requirement for a working protein on the first try or never. The odds he describes takes into account a continuous juggling of particles throughout the 15 billions years of the universes existence, in other words, many tries.
    Dempski’s thought exercise is to illustrate the futility of expecting random actions to not only make one functioning protein, but the collection of many different functioning proteins required to have even 1 organism capable of reproduction and subject to the adaptation pressures you mention.
    In every other field of science, evidence for intelligence would be acknowledged. I can only assume your bias blinds you to maintain the mantra of the creative power of random chemistry. Your theory is much LESS probable, and can only be described as belief in Magic.
    A true scientist, follows the data wherever it leads, without fear. Dempski’s argument doesn’t require a belief in a Christian God, just creative intelligence. It might be aliens, it might be robots from the future……etc. The data doesn’t say, but we will never learn the actual truth, if we’re too afraid to look.


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