Cheaper than printing it out: buy the paperback book.

Stuart Kauffman's simulations are as rigorous, original, and well- respected among scientists as any mathematical model can be. Maybe more so, because he is using a real (computer) network to model a hypothetical network, rather than the usual reverse of using a hypothetical to model the real. I grant, though, it is a bit of a stretch to apply the results of a pure mathematical abstraction to irregular arrangements of reality. Nothing could be more irregular than online networks, biological genetic networks, or international economic networks. But Stuart Kauffman is himself eager to extrapolate the behavior of his generic test-bed to real life. The grand comparison between complex real-world networks and his own mathematical simulations running in the heart of silicon is nothing less than Kauffman's holy grail. He says his models "smell like they are true." Swarmlike networks, he bets, all behave similarly on one level. Kauffman is fond of speculating that "IBM and E. coli both see the world in the same way."

I'm inclined to bet in his favor. We own the technology to connect everyone to everyone, but those of us who have tried living that way are finding that we are disconnecting to get anything done. We live in an age of accelerating connectivity; in essence we are steadily climbing Kauffman's hill. But we have little to stop us from going over the top and sliding into a descent of increasing connectivity but diminishing adaptability. Disconnection is a brake to hold the system from overconnection, to keep our cultural system poised on the edge of maximal evolvability.

The art of evolution is the art of managing dynamic complexity. Connecting things is not difficult; the art is finding ways for them to connect in an organized, indirect, and limited way.

From his experiments in artificial life in swarm models, Chris Langton, Kauffman's Santa Fe Institute colleague, derived an abstract quality (called the lambda parameter) that predicts the likelihood that a particular set of rules for a swarm will produce a "sweet spot" of interesting behavior. Systems built upon values outside this sweet spot tend to stall in two ways. They either repeat patterns in a crystalline fashion, or else space out into white noise. Those values within the range of the lambda sweet spot generate the longest runs of interesting behavior.

By tuning the lambda parameter Langton can tune a world so that evolution or learning can unroll most easily. Langton describes the threshold between a frozen repetitious state and a gaseous noise state as a "phase transition" -- the same term physicists use to describe the transition from liquid to gas or liquid to solid. The most startling result, though, is Langton's contention that as the lambda parameter approaches that phase transition -- the sweet spot of maximum adaptability -- it slows down. That is, the system tends to dwell on the edge instead of zooming through it. As it nears the place it can evolve the most from, it lingers. The image Langton likes to raise is that of a system surfing on an endless perfect wave in slow motion; the more perfect the ride, the slower time goes.

This critical slowing down at the "edge" could help explain why a precarious embryonic vivisystem could keep evolving. As a random system neared the phase transition, it would be "pulled in" to rest at that sweet spot where it would undergo evolution and would then seek to maintain that spot. This is the homeostatic feedback loop making a lap for itself. Except that since there is little "static" about the spot, the feedback loop might be better named "homeodynamic."

Stuart Kauffman also speaks of "tuning" the parameters of his simulated genetic networks to the "sweet spot." Out of all the uncountable ways to connect a million genes, or a million neurons, some relatively few setups are far more likely to encourage learning and adaptation throughout the network. Systems balanced to this evolutionary sweet spot learn fastest, adapt more readily, or evolve the easiest. If Langton and Kauffman are right, an evolving system will find that spot on its own.

Langton discovered a clue as to how that may happen. He found that this spot teeters right on the edge of chaotic behavior. He says that systems that are most adaptive are so loose they are a hairsbreadth away from being out of control. Life, then, is a system that is neither stagnant with noncommunication nor grid-locked with too much communication. Rather life is a vivisystem tuned "to the edge of chaos" -- that lambda point where there is just enough information flow to make everything dangerous.

Rigid systems can always do better by loosening up a bit, and turbulent systems can always improve by getting themselves a little more organized. Mitch Waldrop explains Langton's notion in his book Complexity, thusly: if an adaptive system is not riding on the happy middle road, you would expect brute efficiency to push it toward that sweet spot. And if a system rests on the crest balanced between rigidity and chaos, then you'd expect its adaptive nature to pull it back onto the edge if it starts to drift away. "In other words," writes Waldrop, "you'd expect learning and evolution to make the edge of chaos stable." A self-reinforcing sweet spot. We might call it dynamically stable, since its home migrates. Lynn Margulis calls this fluxing, dynamically persistent state "homeorhesis" -- the honing in on a moving point. It is the same forever almost-falling that poises the chemical pathways of the Earth's biosphere in purposeful disequilibrium.

Kauffman takes up the theme by calling systems set up in the lambda value range "poised systems." They are poised on the edge between chaos and rigid order. Once you begin to look around, poised systems can be found throughout the universe, even outside of biology. Many cosmologists, such as John Barrow, believe the universe itself to be a poised system, precariously balanced on a string of remarkably delicate values (such as the strength of gravity, or the mass of an electron) that if varied by a fraction as insignificant as 0.000001 percent would have collapsed in its early genesis, or failed to condense matter. The list of these "coincidences" is so long they fill books. According to mathematical physicist Paul Davies, the coincidences "taken together...provide impressive evidence that life as we know it depends very sensitively on the form of the laws of physics, and on some seemingly fortuitous accidents in the actual values that nature has chosen for various particle masses, force strengths, and so on." In brief, the universe and life as we know are poised on the edge of chaos.

What if poised systems could tune themselves, instead of being tuned by creators? There would be tremendous evolutionary advantage in biology for a complex system that was auto-poised. It could evolve faster, learn more quickly, and adapt more readily. If evolution selects for a self-tuning function, Kauffman says, then "the capacity to evolve and adapt may itself be an achievement of evolution." Indeed, a self-tuning function would inevitably be selected for at higher levels of evolution. Kauffman proposes that gene systems do indeed tune themselves by regulating the number of links, size of genome, and so on, in their own systems for optimal flexibility.

Self-tuning may be the mysterious key to evolution that doesn't stop -- the holy grail of open-ended evolution. Chris Langton formally describes open-ended evolution as a system that succeeds in ceaselessly self-tuning itself to higher and higher levels of complexity, or in his imagery, a system that succeeds in gaining control over more and more parameters affecting its evolvability and staying balanced on the edge.

In Langton's and Kauffman's framework, nature begins as a pool of interacting polymers that catalyze themselves into new sets of interacting polymers in such a networked way that maximal evolution can occur. This evolution-rich environment produces cells that also learn to tune their internal connectivity to keep the system at optimal evolvability. Each step extends the stance at the edge of chaos, poised on the thin path of optimal flexibility, which pumps up its complexity. As long as the system rides this upwelling crest of evolvability, it surfs along.

What you want in artificial systems, Langton says, is something similar. The primary goal that any system seeks is survival. The secondary search is for the ideal parameters to keep the system tuned for maximal flexibility. But it is the third order search that is most exciting: the search for strategies and feedback mechanisms that will increasingly self-tune the system each step on the way. Kauffman's hypothesis is that if systems constructed to self-tune "can adapt most readily, then they may be the inevitable target of natural selection. The ability to take advantage of natural selection would be one of the first traits selected."

As Langton and colleagues explore the space of possible worlds searching for that sweet spot where life seems poised on the edge, I've heard them call themselves surfers on an endless summer, scouting for that slo-mo wave.

Rich Bageley, another Santa Fe Institute fellow, told me "What I'm looking for are things that I can almost predict, but not quite." He explained further that it was not regular but not chaotic either. Some almost-out-of-control and dangerous edge in between.

"Yeah," replied Langton who overheard our conversation. "Exactly. Just like ocean waves in the surf. They go thump, thump, thump, steady as a heartbeat. Then suddenly, WHUUUMP, an unexpected big one. That's what we are all looking for. That's the place we want to find."