Saturday, July 29, 2006

Order for free

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

In At Home in the Universe: The Search for Laws of Self-Organization and Complexity (1995) Stuart Kauffman argues that traditional notions of how order arises are at best incomplete. Traditionally, it is assumed that Darwinian forces—“Random variation, selection-sifting”—were responsible for all the order we see in the universe (8). However, Kauffman demonstrates that random variation alone isn’t enough to explain the origin of order. By themselves, variation and selection are susceptible to two problems which counteract their organizing properties: if it proceeds towards an evolutionary dead end it can become “trapped” there and, even when it doesn’t run into this problem it is prone to “error catastrophes” (184). Kauffman derives this information from statistical models called fitness landscapes that map all the possible ways a particular environment can evolve. When the landscape is too rough the environment becomes “trapped or frozen into local regions” preventing further development. This problem is not solved by finding solutions with less peaks and troughs, for “on smooth landscapes” selection “suffers the error catastrophe and melts off peaks,” a process which would leave the genotype “less fit” (184-85). When an error catastrophe occurs, “the useful genetic information built up in the population is lost as the population diffuses away from the peak” (184); that is, whatever fitness the population may have demonstrated would be lost because the mechanism of selection is not capable of surveying a fitness landscape to find the best possible niches for the organism. This leads to Kauffman’s realization that “there appears to be a limit on the complexity of a genome that can be assembled by mutation and natural selection”, and, in turn, that there is not just a “singular source” of order in the universe—natural selection—but rather there must be another source as well, one that limits selection into useful areas of fitness (185, 71).

Kauffman calls this other source of order “self-organization”, and he argues that because of it, “vast veins of spontaneous order lie at hand” (8). Self-organization is a product of “extremely complex webs of interacting elements [that] are sparsely coupled” (84). When enough of these interacting elements are brought together and their ability to communicate is limited—Kauffman has shown that one optimum number is two connections each—they can organize themselves into regular patterns. These patterns are analogous to the attractors in complex mathematical systems, and systems that exhibit the behavior of strange attractors provide the complex qualities that Kauffman describes.

Additionally, Kauffman notes that these attractors often occur on the border between stable and chaotic behavior or “poised between order and chaos” (26). It is during the phase transition between the stable and the unstable that systems display organized behavior, what Kauffman calls “order for free” (106). This order is what makes natural selection possible, for it limits the action of complex systems—which often display more states than could be cycled through in the life of the universe—from all possible states to a few attractors, making ordered behavior not improbable but expected.

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