[ My dialogue piece responding to Stephen M. Barr, from Divine Action and Natural Selection, pp. 479-80. ]

Much of what Dr. Barr says is theological. I have no competence to comment on how it fits in with his particular religious tradition. It also strikes me as irrelevant to those not already committed to his tradition; it certainly has little bearing on scientific matters.

That being said, I think there is some confusion about randomness exhibited throughout the article, and that might be worth pointing out. I do not by this mean issues concerning philosophical interpretations of probability; like most physicists, I am also perfectly happy to set those aside for pragmatic reasons. What I suspect is that Barr does not give algorithmic randomness as defined by Kolmogorov/Martin-Löf/Chaitin its due as a rigorous definition that captures most of our intuitions about randomness, including lack of correlations.

For example, Barr states that “a non-random process (like computing the digits of pi) can generate a sequence that passes all statistical tests for randomness.” This is false. Indeed the notion of sequences that pass all possible statistical tests has been historically important in developing the concept of algorithmic randomness. The digits of pi, or, for that matter, the output of pseudorandom number generators, only pass a limited set of statistical tests and are therefore useful in certain circumstances. They certainly do not pass all tests.

In this context, speaking of randomness is not purely a matter of choosing a pragmatic label. Since almost all (in a measure-theoretic sense) integer functions (or digit sequences, or any number of equivalent descriptions) are random, it makes sense to allow for randomness in physical models. Moreover, exactly all sequences can be expressed by combining algorithms and random functions. It would be surprising if we did not find randomness in fundamental physics.

The main significance of randomness in nature for debates over claims such as intelligent design is the way we build models by recognizing patterns in finite data. Randomness is equivalent to a complete lack of pattern; hence, random data alone cannot support inferences such as a causal structure. For example, if random variation and selection is sufficient to explain adaptive change in the history of life, then that history cannot be used to infer an intelligent designer. This does not, however, preclude an inference to a designer that does not depend on data from biology.

I am not offering these observations as a correction to Dr. Barr, only as a clarification. He does not defend intelligent design (at least not explicitly). And his examples of how randomness can result from design underline the point that the inference to design in these cases has to rely on information that goes beyond the patternless sequence under discussion. Nevertheless, all this does raise the question of what extra information is available that is relevant to biology. Merely stating that certain forms of theology are compatible with evolution is not controversial. But it may also be empty—even fundamentalist views can be compatible with any amount of data, depending on how much we are willing to massage interpretations of religion on one hand and proposed scientific models on the other. Barr does not tell us why his views of divine design are plausible explanations rather than just being minimally compatible metaphysical glosses.