Returning now to my radio debate with Sean Pitman, another issue that arose involved the use of probability theory in understanding evolution. Sean argued, indeed, it was really his only argument, that natural selection was incapable in principle of crafting complex adaptations. He chided me for not including in my book any probability calculations to show that natural selection can do what I say it can do. I replied that probability theory was simply the wrong tool for that particular job. Sean was aghast, suggesting, bizarrely, that this somehow rendered evolution unscientific.

In his own blog post about our debate, Sean wrote this:

However, as I read through the book, I was disappointed to discover that Dr. Rosenhouse had not included a single mathematical/probability argument in favor of the creative potential of the evolutionary mechanism of random mutations and natural selection. In fact, as is almost always the case for modern neo-Darwinists, he claimed, in his book and during our debate, that the modern Theory of Evolution is not dependent upon mathematical arguments or statistical analysis at all. In this, he seemed to argue that his own field of expertise is effective irrelevant to the discussion – that, “It is the wrong tool to use.” Beyond this, he also explained that he wasn’t a biologist or a geneticist and that any discussion of biology would require bringing in someone with more expertise and knowledge of the field of biology than he had.

At this point I began to wonder why we were having a debate at all if his own field of expertise was, according to him, effectively irrelevant to the conversation and that he was not prepared to present arguments from biology or genetics regarding the main topic at hand – i.e., the potential and/or limits of the evolutionary mechanism of random mutations combined with natural selection.

This is all very muddled, and it pretty badly distorts what I said. Probability is the wrong tool for the job of determining whether natural selection can craft a complex adaptation like, say, a bacterial flagellum. That is a very long way from saying that mathematics in general, or probability theory in particular, is irrelevant to discussions of evolution. Moreover, it is very unclear what it means to say, “the modern Theory of Evolution is not dependent upon mathematical arguments or statistical analysis at all.” I certainly made no such claim. The modern theory of evolution receives contributions from many different disciplines, and mathematics is one of them. The field of population genetics is largely about applying probability theory to evolution, for example, and phylogenetic reconstruction relies heavily on statistics and combinatorics.

The question of whether natural selection can craft complex adaptions, which Sean is so keen to discuss, is actually both trivial and unimportant. Of course it *can* craft complexity, what on earth is the reason for thinking it cannot? Proofs of concept are easy to come by. The important question is whether it *did* craft complex adaptations in natural history. There is rather a lot of evidence to suggest that it did, as I discuss briefly at the end of this post. Not the least of that evidence are the routine successes of adaptationist reasoning in biology.

It is typical of how these discussions play out. Creationists sit on the sidelines making bold confident claims about what is possible and what is not. These claims are supported by nothing more than handwaving and misapplied jargon. Meanwhile, scientists go into the field and the lab, apply evolutionary reasoning to their work, and in this way they solve problems and get results. As I noted during the debate, if massive amounts of physical evidence say something happened, but some abstract mathematical model says it cannot happen, then it is the model and not the evidence that should be discarded.

There are three obvious reasons why probability theory has no role to play in validating the creative abilities of natural selection. The first is that there are so many unquantifiable variables in natural history that a meaningful calculation would simply be impossible. Probability calculations take place in the context of a properly defined probability space. This means that you must have a grasp on all the things that might have happened in lieu of the event you are studying, and you must have some basis for assigning a probability distribution to that collection of events.

(For example, if you want to know the probability of rolling a one with a six-sided die, you need to know not only that there are six possible outcomes, but also that the die is not loaded in a way that makes certain outcomes more likely than others).

Good luck trying to define the appropriate probability space for studying the long-term development of natural history.

The second reason is that it is not clear what you should be finding the probability of. Should we determine the probability of evolving the modern vertebrate eye, or do we care instead about the probability of evolving *some* kind of organ for using light to glean information about the environment? Any specific adaptation might have a very small probability, but the probability of evolving some representative of a class to which that adaptation belongs could be rather large. So even if you could define an appropriate space, you would still have the problem of determining the relevant event within the space.

(As an aside, this is known as the reference class problem, and it arises in many attempts to apply probability theory to practical situations. This is especially the case when taking a frequentist approach to probability.)

This leads naturally into the third problem. Let us suppose you could perform a relevant probability calculation and the result was a very small number. So what? What would that prove? Unlikely events occur all the time, after all. Any particular outcome of billions of years of evolution likely occurs with very small probability, but that is simply irrelevant to determining the credibility of evolution. The particular sequence of heads and tails you get when flipping a coin five hundred times is extremely unlikely, but *something* had to happen. The endpoints of eons of evolution are very much like that.

Now, this is the point where ID folks might point to William Dembski, and start going on about “complex specified information.” They might argue that while certain events are of the “something had to happen” sort, others are not. If five hundred heads came up, you would reject the hypothesis that a fair coin had been flipped in a fair manner. Indeed, but that is simply a bad analogy. Dembski’s attempts to define his notion of “specificity” in a useful, non-vague way that can be applied to biology (or much of anything for that matter) have been entirely unsuccessful. The relentless use of the term “complex specified information” by ID proponents, as though this term actually meant anything, is an example of what I meant in saying that evolution’s critics rely frequently on misapplied jargon.

So that’s the problem. We have no way of defining a relevant probability space. Even if we did, we would still have no way of selecting the relevant event. And even if we could get past those two problems, the number produced by our calculation would tell us nothing. And that is why probability theory is not helpful in this context.

I don’t know why Sean makes such a fetish of probability. During the debate he said that my refusal to supply a probability calculation somehow rendered evolution unscientific, which is rather bizarre. Probability theory is wonderful stuff (my first book was mostly about probability theory) but it is hardly the last word on what is science and what is not.

I certainly agree that natural selection has never been observed to produce something as complex as the vertebrate eye. Intelligent agents have never been observed to bring universes into being or to create life from scratch, but Sean has no trouble believing *that* occurred. The fact remains that there is voluminous circumstantial evidence supporting the claim that natural selection can in principle and has in natural history produced complex adaptations. When you contrast this with the perfect vacuum of evidence supporting the existence of intelligent designers who can do what ID folks say they can do, it becomes clear why scientists are all but unanimous in preferring evolution over intelligent design.