Thursday, March 10, 2005

Maser developer has difficulty understanding conditional probability

I heard the interview linked from this post's title on Morning Edition on National Public Radio this morning, and for a bit, thought I was still semi-conscious. The story was about Dr. Charles Townes who, along with Dr. Arthur Schawlow, developed the maser (microwave amplification by stimulated emission) -- the longer-wavelength precursor to the laser. Dr. Townes shared the 1964 Nobel Prize in Physics for this work.

Now, what stood out as unusual was that the story was about his receiving the "Templeton Prize" for his work in the field of religion.

This prize is awarded by the John Templeton Foundation, an organization devoted to the intersection between science and religion. I've looked through their web site, and they don't seem on the surface to be religious right crazies (if someone ever reads this and knows more, please drop me a line or add a comment). According to this June 2004 article, Townes is on the Templeton Foundation Board of Advisors.

What stuck out in my mind was Townes' comments on what one might call "cosmological intelligent design" (see the last paragraph of this Cornell news story. Basically, like aficionados of "intelligent design" as a stealth way of inserting religion into the biology curriculum, he reasons that the universe must have been designed with life in mind, because it is so improbable that the universe's physical laws would turn out "just right" for life to arise. In fact, it is true that physicists don't currently know why various underlying physical constants have the values they do, thought only fairly narrow ranges would produce universes suitable for life.

This is an old argument against science in general and evolution in particular: that since we can't explain everything right now, that must mean that God set things up. Besides the logical fallacy, there is a fundamental probabilistic fallacy in this. Let's imagine that many, many universes could be created, and only a small fraction would have physical laws suitable for life. to make things concrete, I'll use 0.0001 as a small probability, but any number would work. So, the probability of a suitable universe is P(S) = 0.0001. Let's also assume that, even if the universe is suitable, the probability of life arising is small, too (again, the number actually doesn't matter). This is a conditional probability, the probability of life given we know the universe is suitable, P(L|S) = 0.0001. We also know that life cannot arise if the universe is not suitable, P(L|~S) = 0. So, the a priori probability of life occurring in a universe, before we checked to see if the universe is suitable, is P(L) = P(S) P(L|S) = 10^-8.

What we want to know is the probability that the universe is suitable, given that there is life in it. This is exactly what Townes is having a problem with -- we've already seen that P(S) and P(L) are very small, so there's no way that this suitable universe could have happened "by chance". (Of course, we don't know that it was by chance, but that's beside my point here.) Actually, however, that is not true -- given that we exist (otherwise, we wouldn't be around to be amazed by this improbable-seeming universe), the probability that the universe is suitable is 100%, P(S|L)=1. There are a variety of ways of arriving at this; I'll use Bayes' rule (not the simplest way to do it), but it's really a tautology of the math.

Bayes' rule allows us to reason from evidence back to cause, given that we understand ahead of time how the cause relates to the evidence. For our suitable universe, the rule is:
P(S|L) = P(L|S) P(S)/P(L) = (0.0001)(0.0001)/(10^-8) = 1

As we can see now, the numbers don't matter because P(L) = P(L|S) P(S), which is true because P(L|~S) = 0. In other words, of course we see that the universe is suitable for life; if it weren't suitable, we wouldn't be here! The same reasoning can be applied to evolution. It doesn't matter how improbable the evolution of intelligence is, the fact is that only intelligent life can ponder such matters, and so all such conditional probabilities are actually certainties.

Note added 3/11/2005: There's a great FAQ on the "Anthropic Principle" that you should read, if you're interested in this sort of thing.

4 comments:

  1. No. Townes refers to P(S), not P(S|L). Thus, you are grappling with a strawman. Please leave probability to those of us who are qualified to speak on the topic (engineers who like to play sycophant to pseudo-scientists like Paul Myers most certainly do not qualify).

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  2. Robert O'Brien said:
    No. Townes refers to P(S), not P(S|L).
    True, he refers to P(S), but his statement is actually about P(S|L), because it is predicated on his own existence. My point is that P(S) is irrelevant, which is exactly what you admit in terming the argument a straw man. Only it's Townes' straw man, not mine.

    Robert O'Brien said:
    Please leave probability to those of us who are qualified to speak on the topic..
    Actually, probability is used extensively in Computer Science. Probabilistic reasoning is a core part of Artificial Intelligence research, which is not too distant from my own area (Neural Networks). So, though I admit it isn't my own area, I believe I'm qualified to speak of it. In any event, your criticism had nothing to do with probability theory.

    Hey, man, thanks for posting a comment!

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  3. True, he refers to P(S), but his statement is actually about P(S|L), because it is predicated on his own existence.I disagree.

    Actually, probability is used extensively in Computer Science. Probabilistic reasoning is a core part of Artificial Intelligence research, which is not too distant from my own area (Neural Networks).Yeah, I know some people at Iowa State who work in AI.

    Hey, man, thanks for posting a comment!You are welcome (from one West Coast sojourner in Gainesville to another).

    Please forgive my choleric parenthetical afterthought. My absolute contempt for Myers tends to cloud my perceptions of those he attracts to his blog (most of whom are his sycophants).

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  4. Please forgive my choleric parenthetical afterthought. My absolute contempt for Myers tends to cloud my perceptions of those he attracts to his blog (most of whom are his sycophants).Please don't misunderstand me, I am one of his sycophants. I think Prof. Myers has an excellent, informed blog. (For the record, I should probably add this link to the relevant post in his blog.) I also think that the future of science belongs to the biologists -- that's where the action is. As for your post in your own blog, let me say the following:

    1. The University of Minnesota Morris may not be a "Research I" university campus, but then again, not everyone wants to work at such a place. From what I can see, Morris looks like a very nice town and university campus, very much in line with other liberal arts schools. Keep in mind that there are many people who would make similar comments about Gainesville that you've made about Morris. (Note: I've never been to Minnesota.)

    2. If you're going to critique what other people write, it might be better to stick to factual statements. Scientific truth does not depend on the fame or reputation of people or institutions. And most individual results of individual research projects at even Research I schools isn't terribly significant.

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