Saturday, July 29, 2006


Update: This post is a partial review of Stuart Kauffman’s At Home in the Universe: The Search for Laws of Self-Organization and Complexity

cover image of Kauffman's At Home in the UniverseIn At Home in the Universe Kauffman cites the Cambrian explosion—the appearance of an abundance of new life forms during the Cambrian period—as an example of a phenomenon that is difficult to explain using only the theory of natural selection. Natural selection suggests that gradual changes over time slowly accrue, allowing for the development of fitter organisms. This idea, however, is difficult to map onto the relatively rapid appearance of many different body plans during that period. A more selection-friendly period, Kauffman notes, is the rebound from the Permian extinction, when “96 percent of all species disappeared” (13). After the Permian the divergence in body plans, or phyla, basically ended. While there were “many new families, a few new orders, [and] one new class” that appeared at that time, there were no new phyla.

Kauffman refers to the Cambrian explosion as a top-down event—the rapid appearance of many wildly divergent kinds of organisms—while he calls the rebound from the Permian extinction—where there were many changes in the makeup of different organisms, but no new body plans—a bottom-up event (13). This movement from top-down to bottom-up events is typical, according to Kauffman, and is also seen in technological innovations, where an initial period of discovery is followed by an explosion of variations that later settle down into a few distinct, usually optimum, plans. The “branchings of life” that this particular view exhibits follows what Kauffman feels to be a lawful pattern—”dramatic at first, then dwindling to twiddling with details later”, what he calls a “complexity catastrophe” (14, 194). This catastrophe explains how “the more complex an organism, the more difficult it is to make and accumulate useful drastic changes through natural selection”, for “As the number of genes increases, long-jump adaptations becomes less and less fruitful” (194-95).

This process of organization comes from the tendency of “complex chemical systems” to become autocatalytic, that is exhibit a “self-maintaining and self-reproducing metabolism”, and it allows the process of ontogeny, where at division cells differentiate for different purposes (47, 50).

boolean networkIn the first case, Kauffman demonstrates with Boolean networks how autocatalysis occurs naturally in chemical systems. The image on the right shows “a Boolean network with two inputs per node” where “colors represent the state of a node” as being on or off. Using a sparsely-connected network like this to model simple chemical reactions, Kauffman shows that “when the number of different kinds of molecules in a chemical soup passes a certain threshold, a self-sustaining network of reactions”, or autocatalysis, “will suddenly appear” (47). Kauffman argues that his behavior on the part of these chemical systems is completely expected, and therefore not mysterious, as many attempts to explain it imply. Kauffman’s Boolean networks show that “when a large enough number of reactions are catalyzed in a chemical reaction of system, a vast web of catalyzed reactions will suddenly crystallize”, a property that is completely expected (50).

These complex behaviors also explain ontogeny. The tendency of complex chemical systems to organize themselves into auto-catalytic systems leads to those systems settling into a few attractors (see Order for Free for a discussion of attractors in biological systems), a result that allows the cells to differentiate but only in limited ways. As cells branch out to become particular kinds of cells in the organism, their tendency to stay in the basin of the attractor keeps them from becoming disordered, yet allows them to continue to propagate themselves. Order, then, from both the top-down and the bottom-up, is “vast and generative” and “arises naturally” out of common chemical interactions (25).

No comments: