Chance, Progress and Complexity in Biological Evolution

The idea of continuous progress occupies an essential place in the personal metaphysics of many of our contemporaries. It is so embedded in their minds that they would have a hard time living without it. This is why the reminder of what evolution owes to chance, coming from certain contemporary biologists and paleontologists like Stephen Jay Gould, is salutory. The recent book by the latter, Full House, forces us to reexamine the applications of the notion of chance in the domain of biological evolution.

This said, we must recognize that the specificity of the living creature, by incorporating in its very genome the history of the presumably victorious variations of its ancestors, draws the evolution of each separately considered branch along a precise trajectory, subject to constraints rooted in its history. If we must repudiate the idea of progress as too tainted by ideology, mustn't we conclude that these trajectories carry certain living creatures toward an accrued complexity, and across certain thresholds from which they cannot turn back, thereby creating new, emerging qualities?

Mathematical Chance and its Applications in Biology

In order to decide whether a physical or biological phenomenon is the result of chance, we must have a rigorous definition of this notion, as well as a method for deciding if the phenomenon fits this definition. Unfortunately, objective chance (which applies to things themselves, as opposed to ignorant chance or subjective chance) is a notion for which it is impossible to come up with a universal, operational definition. We cannot define chance, except in its lack, its negative form, by the absence of order.

The notion of disorder is easily characterized by the unpredictability associated with it. The outcome of a roll of the dice or the flip of a coin cannot be guessed in advance. It can also be said that the results of a long series of coin flipping is very complex, meaning that once again the sequence is unpredictable. But what does this mean in concrete terms? If we think about it, we would agree that this sequence cannot be described in a more simple way than by the statement of each of the events that comprise it; there is no way to shorten its description, to condense the account. In fact, this is the conclusion reached by three mathematicians specializing in chance: Solomonoff, Kolmogorov and Chaitin. The three have proposed the following definition for chance: "the workings of chance cannot be summarized" (Chaitain, 1975). Thus, in order to prove that a series of heads or tails or a series equivalent to "0" and "1" (more easily manipulated in a computer, which can interpret it as a series of binary instructions) is truly chance, one must prove that there is no shorter algorithmic program capable of reproducing it on a computer. Intuitively, we can see the difficulty of this enterprise. Gödel's Theorem establishes its impossibility: it cannot be proved that a sequence is pure chance, as defined above, when its length exceeds that of the binary information contained in all the founding axioms. Thus "chance" is a horizon whose positive definition will always elude us.

The parallel between the notions of chance and of complexity can be further clarified. The notion of a minimal program for describing a phenomenon in fact allows us to define its complexity. One could say that the complexity of a series of numbers or of a machine designed by an engineer is measured by the length of the minimal program (expressed in information "bits") required to produce it. From the foregoing, one can guess that the larger the place left to chance in the architecture of the functioning of a system, the greater its complexity, understood in this sense.

However, a mathematical definition of complexity is not completely appropriate for biology; one could say that it is not "complex" enough, in the sense that it certainly does not correspond to what a biologist means when he marvels at the complexity of...