Pertinent Probabilities

At first sight, this looks very powerful, since, given the time available for the evolution of life on earth (four billion or so years), it seems extremely improbable that the clotting mechanism could have evolved through natural selection.

Yet we should think carefully about the ways in which the pertinent probabilities are calculated. Behe is relying on two general ideas about probabil- ity. One is the thought that, when events are independent of one another, the probability that both will occur is the product of the individual probabili- ties—if you toss a fair die twice, then the chance of getting two sixes is 1 in 36; for, on each toss, the probability is 1 in 6, and, since the tosses are inde- pendent of one another, you multiply. The other idea is that, when you have a range of alternatives and don’t have any reasons for thinking that one is more likely to occur than another, each of the possibilities has an equal chance. This idea, the notorious “principle of indifference,” is known to be problematic, but, judiciously employed, it serves us well in some everyday contexts—as, for example, when we conclude that each side of the die has the same probability of falling uppermost.

Even in ordinary life, however, there are occasions on which applications of these principles would lead us to obviously unacceptable conclusions, so that we would rethink our computations. Consider a humdrum phenomenon sug- gested by Behe’s analogy with bridge. You take a standard deck of cards and deal 13 to yourself. What is the probability that you get exactly those cards in exactly that order? The answer is 1 in 4 � 1021. Suppose you repeat the process 10 times. You’ll now have received 10 standard bridge hands, 10 sets of 13 cards, each one delivered in a particular order. Scrupulously, you record just the order in which all these cards were received, and calculate the chance that this event occurs. The probability; you claim, is 1 in 410 � 10210, which is approxi- mately 1 in 10216—notice that this denominator is enormously larger than Behe’s 1018. It must be really improbable that you (or anyone else) would ever receive just those cards in just that order in the entire history of the universe. But you did, and you have witnesses to testify that your records are correct. Ex- citedly, you contact Michael Behe to announce this quite miraculous event, surely evidence of some kind of Intelligence at work in the universe.

Your report would not be well received. Like everyone else, Behe knows how to understand this commonplace occurrence. Given the way in which the cards were initially arranged, the first deal was bound to go as it did. Given the shuffling that produced the ordering prior to the second deal, that deal, too, was sure to give rise to just those cards in that order; and so on. So there was a perspective, unknown to you, from which the probability of that sequence of cards wasn’t some infinitesimally small number, but one (as high as chances go). If you describe events that actually occur from a perspective that lacks crucial items of knowledge, you can make them look improbable. We know enough about card dealing and coin tossing to understand this, and to see the calculation I attributed to you as perverse—for, although you don’t know what the initial setup was, you should have recognized that there was some initial setup that would determine the sequence. Hence you should have known that application of the two general principles of proba- bility in this context would provide a misleading view of the chance that this particular sequence would result.