1993-08-08: Antichaos and Adaptation

Antichaos and Adaptation (Scientific American, August 1991)

by Stuart A. Kauffman (-)

In this article, Kauffman describes the organization (self-organization) of random boolean networks (RBNs).  These are networks of boolean elements with various patterns of interconnection.  Kauffman uses them as a model of the expression of genes within an organism.  Ken Karakotsias expects to use them as a model of the expression of memes in a culture.

Kauffman uses the term ‘boolean’ to mean elements with two states (on/off), and expresses the state function of any element as a boolean function of its inputs.  He classifies RBNs as NK networks, having N elements, each of which has K inputs.  All inputs come from other elements of the network (no outside stimulus).  Another classification criterion is the type of function; biased functions can affect the dynamics of such a network.

Kauffman finds that some networks exhibit chaotic behavior, with a relatively small number of attractors, relatively small state-cycles around the attractors, and a certain robustness against either changes of state of elements or ‘mutations’ in the network structure (element connectivity or function).

The model seems to predict roughly the right number of cell-types in organisms as a function of the number of genes, allowing some fudging of parameters, and some other features, such as the branching processes of ontogeny.

The model seems less well-suited for modeling behavior.  For one thing, I fear it doesn’t allow for inhibition by active elements of other active elements; I think this is crucial to allowing for selection of a single behavior in the face of conflicting desires.  I think this could be remedied by using a model with binary elements, but allowing the state function to be a more complex function, along the lines of neural nets, with positive and negative connection weights.  I think a suitable model could be based on ternary (-1, 0 or -1) weights.

Nonetheless, the idea of attractors, state-cycles and branching development may have merit.


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