Cheaper than printing it out: buy the paperback book.

This set of math techniques that Kauffman, Holland and others devised is still without a proper name, but I'll call it here "net math." Some of the techniques are known informally as parallel distributed processing, Boolean nets, neural nets, spin glasses, cellular automata, classifier systems, genetic algorithms, and swarm computation. Each flavor of net math incorporates the lateral causality of thousands of simultaneous interacting functions. And each type of net math attempts to coordinate massively concurrent events -- the kind of nonlinear happenings ubiquitous in the real world of living beings. Net math is in contradistinction to Newtonian math, a classical math so well suited to most physics problems that it had been seen as the only kind of math a careful scientist needed. Net math is almost impossible to use practically without computers.

The wide variety of swarm systems and net maths got Kauffman to wondering if this kind of weird swarm logic -- and the inevitable order he was sure it birthed -- were more universal than special. For instance, physicists working with magnetic material confronted a vexing problem. Ordinary ferromagnets -- the kind clinging to refrigerator doors and pivoting in compasses -- have particles that orient themselves with cultlike uniformity in the same direction, providing a strong magnetic field. Mildly magnetic "spin glasses," on the other hand, have wishy-washy particles that will magnetically "spin" in a direction that depends in part on which direction their neighbors spin. Their "choice" places more clout on the influence of nearby ones, but pays some attention to distant particles. Tracing the looping interdependent fields of this web produces the familiar tangle of circuits in Kauffman's home image. Spin glasses used a variety of net math to model the material's nonlinear behavior that was later found to work in other swarm models. Kauffman was certain genetic circuitry was similar in its architecture.

Unlike classical mathematics, net math exhibits nonintuitive traits. In general, small variations in input in an interacting swarm can produce huge variations in output. Effects are disproportional to causes -- the butterfly effect.

Even the simplest equations in which intermediate results flow back into them can produce such varied and unexpected turns that little can be deduced about the equations' character merely by studying them. The convoluted connections between parts are so hopelessly tangled, and the calculus describing them so awkward, that the only way to even guess what they might produce is to run the equations out, or in the parlance of computers, to "execute" the equations. The seed of a flower is similarly compressed. So tangled are the chemical pathways stored in it, that inspection of a unknown seed -- no matter how intelligent -- cannot predict the final form of the unpacked plant. The quickest route to describing a seed's output is therefore to sprout it.

Equations are sprouted on computers. Kauffman devised a mathematical model of a genetic system that could sprout on a modest computer. Each of the 10,000 genes in his simulated DNA is a teeny-weeny bit of code that can turn other genes either on or off. What the genes produced and how they were connected were assigned at random.

This was Kauffman's point: that the very topology of such complicated networks would produce order -- spontaneous order! -- no matter what the tasks of the genes.

While he worked on his simulated gene, Kauffman realized that he was constructing a generic model for any kind of swarm system. His program could model any bunch of agents that interact in a massive simultaneous field. They could be cells, genes, business firms, black boxes, or simple rules -- anything that registers input and generates output interpreted as input by a neighbor.

He took this swarm of actors and randomly hooked them up into an interacting network. Once they were connected he let them bounce off one another and recorded their behavior. He imagined each node in the network as a switch able to turn certain neighboring nodes off or on. The state of the neighbor nodes looped back to regulate the initial node. Eventually this gyrating mess of he-turns-her-who-turns-him-on settled down into a stable and measurable state. Kauffman again randomly rearranged the entire net's connections and let the nodes interact until they all settled down. He did that many times, until he had "explored" the space of possible random connections. This told him what the generic behavior of a net was, independent of its contents. An oversimplified analogous experiment would be to take ten thousand corporations and randomly link up the employees in each by telephone networks, and then measure the average effects of these networks, independent of what people said over them.

By running these generic interacting networks tens of thousands of times, Kauffman learned enough about them to paint a rough portrait of how such swarm systems behaved under specific circumstances. In particular, he wanted to know what kind of behavior a generic genome would create. He programmed thousands of randomly assembled genetic systems and then ran these ensembles on a computer -- genes turning off and on and influencing each other. He found they fell into "basins" of a few types of behaviors.

At a slow speed water trickles out of a garden hose in one uneven but consistent pattern. Turn up the tap, and it abruptly sprays out in a chaotic (but describable) torrent. Turn it up full blast, and it gushes out in a third way like a river. Carefully screw the tap to the precise line between one speed and a slower one, and the pattern refuses to stay on the edge but reverts to one state or the other, as if it were attracted to a side, any side. Just as a drop of rain falling on the ridge of a continental divide must eventually find its way down to either the Pacific Basin or the Atlantic Basin, roll down one side or the other it must.

Sooner or later the dynamics of the system would find its way to at least one "basin" that entrapped the shifting motions into a persistent pattern. In Kauffman's view a randomly assembled system would find its way to a stock pattern (a basin); thus, out of chaos, order for free emerges.

As he ran uncounted genetic simulations, Kauffman discovered a rough ratio (the square root) between the number of genes and the number of basins the genes in the system settled into. This proportion was the same as the number of genes in biological cells and the number of cell types (liver cells, blood cells, brain cells) those genes created, a ratio that is roughly constant in all living things.

Kauffman claims this universal ratio across many species suggests that the number of cell types in nature may derive from cellular architecture itself. The number of types of cells in your body, then, may have little to do with natural selection and more to do with the mathematics of complex gene interactions. How many other biological forms, Kauffman gleefully wonders, might also owe little to selection?

He had a hunch about a way to ask the question experimentally. But first he needed a method to cook up random ensembles of life. He decided to simulate the origin of life by generating all possible pools of prelife parts -- at least in simulation. He would let the virtual pool of parts interact randomly. If he could then show that out of this soup order inevitably emerged, he would have a case. The trick would be to allow molecules to converge into a lap game.