A number of years ago I attended an ID conference near Kansas City. One of the breakout sessions featured a fellow from the Heritage Foundation (an ultra-right-wing political think tank) presenting a lecture about probability and evolution. His talk was mostly just a watered-down version of William Dembski’s standard talking points. His triumphant conclusion was that the probability of something or other having evolved by natural processes was one over something enormous, from which he concluded that evolution had been refuted.

There were only about fifteen of us in the room. During the subsequent question period, one older gentleman said something very close to this: “When scientists are confronted with a probability that small…” He paused here, as though struggling to accept just how small a number it was. “What else can they do but just stare at it helplessly?”

I was the next to speak. I said, “I think I can tell you how they would react to that calculation. They would question the legitimacy of the assumptions that went into it.” I then rattled off three implausible assumptions underlying the calculation. The other fellow just stared at me. The speaker, incredibly, replied that this was just a popular level presentation, and then rattled off several additional points of disanalogy between his calculation and reality. He seemed to think that was a good answer.

I replied that the problem wasn’t simply that certain details had been left out of the calculation to keep it manageable. It was that the variables that were missing could not be quantified with any accuracy. Consequently, absolutely nothing like what he was doing could be made to work. He just shrugged and went on to the next question.

Creationists love probability. If you are a speaker trying to bamboozle a lay audience, there is no better way than to drop in a back-of-the-envelope calculation. The trouble is that the things they are trying to quantify are inherently unquantifiable. There is no way to calculate the probability of an eye, for example, evolving over the course of millions of years of evolution by natural selection.

The young-Earthers typically try to circumvent this point by ignoring the role of selection. They typically toss off combinatorial arguments in which the probability of evolving some complex molecule, like hemoglobin, is taken to be one over the number of ways of arranging the amino acids in that molecule. Sadly, that only works if all of those arrangements are equiprobable, but the continuing action of natural selection ensures that they are not. The ID folks try to gum up the works with blather about specificity or universal probability bounds. But when it comes time to perform specific probability calculations (something they almost never do) they inevitably invoke “irreducible complexity” as an excuse for ignoring the role of natural selection. That is not a reasonable thing to do, to put it kindly.

I was thinking about this while reading this post over at Uncommon Descent. Jonathan M. writes:

A couple months ago, I took an online “moodle” class with the Center for Inquiry on the topic of the evolution debate. The instructor was the renowned philosopher and evolutionary biologist, Massimo Pigliucci. I entered into an exchange of dialogue with Pigliucci and the other students on the evidence for the efficacy of naturalistic evolution, as well as presenting some counter-arguments against it and for ID.

During the course of our discussion, Pigliucci made some claims which astonished me — especially as arguments coming from a trained philosopher and world-renowned evolutionary theorist. To my surprise, when I articulated the numerous probabilistic hurdles — hurdles which are so pervasive at every level — which Darwinism has to overcome in order to be considered a viable paradigm, he wrote,

No evolutionary biologist I know…actually attaches probabilities to specific evolutionary events of the type you are talking about. There is no way to do that. Similarly, there is no way to attach probabilities to the set of physical laws regulating our universe, for the simple reason that we have no sample population to draw from (which is why typically you estimate probabilities).

Let’s pause here. One suspects that the key phrase in Pigliucici’s statement is, “of the sort you are talking about.” Assuming that Jonathan M.’s vague reference to the probabilistic hurdles facing evolution involves the sorts of things ID folks usually say, then Pigliucci’s statement is exactly right. When an ID proponent starts applying probability language to questions regarding the fine-tuning of the universe or to specific biological structures, it’s a pretty safe bet they are talking through their hats.

But Jonathan M. demurs. He continues:

This struck me at the time as a very strange argument to be making given the fact that many Darwinists (Dawkins & Futuyma spring to mind) say that the brilliance of Darwin was to reduce the improbability of getting complex, design-like systems. What was the whole point of “Climbing Mount Improbable”? The point was that probability didn’t have to jump up the sheer face of the cliff. It could meander up the gently sloping rear side, in small probability increments. But if we can’t assign probabilities to the events, exactly what has Darwin’s theory done?

The image of probability jumping up the sheer face of a cliff is amusing, but otherwise I fail to understand how any of this relates to what Pigliucci said. After all, he certainly did not say that you must never, ever use probability language in the context of evolution.

In context, it is perfectly clear what Dawkins and Futuyma have in mind. If we naively think of every possible genotype having the same probability as every other possible genotype, and then imagine evolution proceeding by selecting genotypes entirely at random, then the probability is vanishingly small that we shall ever find one that produces a functional, complex organism. But when we factor natural selection into the process it becomes clear that we should not be treating all possible genotypes as equiprobable. Instead, most of those genotypes have a probability close to zero of ever occurring, because they will be weeded out by selection. The handful of functional genotypes will be favored by selection. In this way it is meaningful to say that natural selection changes the probabilities of evolving various structures.

Notice, though, that neither Dawkins nor Futuyma tried to calculate a precise number representing the probability of evolving some particular complex system. That’s precisely the sort of calculation Pigliucci was describing as impossible.

Jonathan M. now writes:

In response to Massimo, I cited several attempts by Darwinists — many of which feature in the peer-reviewed literature — which attempt to demonstrate the efficacy of the Darwinian mechanism by virtue of probabilistic arguments. I wrote…

He now unloads a long list of examples in which evolutionists employ probabilistic arguments. Follow the link to the post for the details. He concludes his list with:

But this should be sufficient to refute your [Pigliucci's] claim that evolutionary biologists are not interested in evaluating probabilistic feasibility.

He now protests that he never got a reply from Pigliucci. I’m not surprised, since Jonathan M. is completely confused about what the issue is. Pigliucci certainly never claimed that biologists are not interested in evaluating probabilistic feasibility (whatever that even means). He said simply that evolutionary biologists do not assign probabilities to specific events in the way that ID folks would like.

For example, Jonathan M. points to a calculation in which biologist Sean Carroll estimated the probability of obtaining the same mutation four times independently in different orders of birds. In such a narrowly defined situation the problem has more to do with combinatorics than probability, and we can be confident that all of the relevant variables can be approximated with reasonable accuracy.

He also points to a paper by Durrett and Schmidt, in which they evaluated the probability of obtaining two particular mutations in at least one individual of a population. Once again, in such a narrowly defined situation it is possible to get a grip on all of the relevant variables. But notice that neither they, nor Carroll, were trying to calculate the probability of evolving a flagellum or anything remotely like that.

In the remaining examples the authors don’t explicitly calculate the probability of anything. Jonathan M. mentions Dawkins’ “weasel” experiment, presented in his book *The Blind Watchmaker.* But Dawkins was merely illustrating the power of cumulative selection versus random selection. He was not calculating probabilities. This paper by Wilf and Ewens, also mentioned in the post, puts some mathematical meat on the bones of Dawkins’ suggestion. They are working with probabilities only indirectly, and certainly were not trying to assign precise numerical values to specific evolutionary events. The final reference is to the Avida simulation, but this too had nothing to do with working out the probabilities of specific evolutionary events.

The basic point here is very simple. A proper probability calculation begins with the definition of a probability space, which means roughly that you must have a grasp on all of the things that might happen and also on the probabilities with which those events occur. There are many contexts in evolutionary biology where that can be done. In population genetics, for example, we typically narrow our focus to small numbers of loci over short periods of time, which permits us to get a grip on all of the relevant variables. This is far different from trying to work out precise probabilities for specific structures that evolved over vast stretches of time. In such situations we have no hope of getting a grip on everything.

But ID folks forge ahead regardless. More precisely, since they almost never carry out actual calculations, they simply claim that such things can be done and that when they are the result is bad news for evolution. Pointing out that this sort of thing is not feasible even in principle, as PIgliucci quite sensibly did, hardly implies that probability does not have useful roles to play in evolutionary theory.