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Out of Control

"We've got to get used to dealing in billions of things!" Kauffman once told an audience of scientists. Huge multitudes of anything are different: the more polymers, the exponentially more possible interactions where one polymer can trigger the manufacture of yet another polymer. Therefore, at some point, a droplet loaded up with increasing diversity and numbers of polymers will reach a threshold where a certain number of polymers in the set will suddenly fall out into a spontaneous lap circle. They will form an auto-generated, self-sustaining, self-transforming network of chemical pathways. As long as energy flows in, the network hums, and the loop stands.

Codes, chemicals, or inventions can in the right circumstances produce new codes, chemicals, or inventions. It is clear this is the model of life. An organism produces new organisms which in turn create newer organisms. One small invention (the transistor) produces other inventions (the computer) which in turn permit yet other inventions (virtual reality). Kauffman wants to generalize this process mathematically to say that functions in general spawn newer functions which in turn birth yet other functions.

"Five years ago," recalls Kauffman, "Brian Goodwin [an evolutionary biologist] and I were sitting in some World War I bunker in northern Italy during a rainstorm talking about autocatalytic sets. I had this profound sense then that there's a deep similarity between natural selection -- what Darwin told us -- and the wealth of nations -- what Adam Smith told us. Both have an invisible hand. But I didn't know how to proceed any further until I saw Walter Fontana's work with autocatalytic sets, which is gorgeous."

I mentioned to Kauffman the controversial idea that in any society with the proper strength of communication and information connection, democracy becomes inevitable. Where ideas are free to flow and generate new ideas, the political organization will eventually head toward democracy as an unavoidable self-organizing strong attractor. Kauffman agreed with the parallel: "When I was a sophomore in '58 or '59 I wrote a paper in philosophy that I labored over with much passion. I was trying to figure out why democracy worked. It's obvious that democracy doesn't work because it's the rule of the majority. Now, 33 years later, I see that democracy is a device that allows conflicting minorities to reach relative fluid compromises. It keeps subgroups from getting stuck on some locally good but globally inferior solution."

It is not difficult to imagine Kauffman's networks of Boolean logic and random genomes mirroring the workings of town halls and state capitals. By structuring miniconflicts and microrevolutions as a continuous process at the local level, large scale macro- and mega-revolutions are avoided, and the whole system is neither chaotic nor stagnant. Perpetual change is fought out in small towns, while the nation remains admirably stable -- thus creating a climate to keep the small towns in ceaseless compromise-seeking modes. That circular support is another lap game, and an indication that such systems are similar in dynamics to the self-supporting vivisystems.

"This is just intuitive," Kauffman cautions me, "but you can feel your way from Fontana's 'string-begets-string-begets-string' to 'invention-begets-invention-begets-invention' to cultural evolution and then to the wealth of nations." Kauffman makes no bones about the scale of his ambition: "I am looking for the self-consistent big picture that ties everything together, from the origin of life, as a self-organized system, to the emergence of spontaneous order in genomic regulatory systems, to the emergence of systems that are able to adapt, to nonequilibrium price formation which optimizes trade among organisms, to this unknown analog of the second law of thermodynamics. It is all one picture. I really feel it is. But the image I'm pushing on is this: Can we prove that a finite set of functions generates this infinite set of possibilities?"

Whew. I call that a "Kauffman machine." A small but well-chosen set of functions that connect into an auto-generating ring and produce an infinite jet of more complex functions. Nature is full of Kauffman machines. An egg cell producing the body of a whale is one. An evolution machine generating a flamingo over a billion years from a bacterial blob is another. Can we make an artificial Kauffman machine? This may more properly be called a von Neumann machine because von Neumann asked the same question in the early 1940s. He wondered, Can a machine make another machine more complex that itself? Whatever it is called, the question is the same: How does complexity build itself up?

"You can't ask the experimental question until, roughly speaking, the intellectual framework is in place. So the critical thing is asking important questions," Kauffman warned me. Often during our conversations, I'd catch Kauffman thinking aloud. He'd spin off wild speculations and then seize one and twirl it around to examine it from various directions. "How do you ask that question?" he asked himself rhetorically. His quest was for the Question of All Questions rather than the Answer of All Answers. "Once you've asked the question," he said, "there's a good chance of finding some sort of answer.

A Question Worth Asking. That's what Kauffman thought of his notion of self-organized order in evolutionary systems. Kauffman confided to me: "Somehow, each of us in our own heart is able to ask questions that we think are profound in the sense that the answer would be truly important. The enormous puzzle is why in the world any of us ask the questions that we do."

There were many times when I felt that Stuart Kauffman, medical doctor, philosopher, mathematician, theoretical biologist, and MacArthur Award recipient, was embarrassed by the wild question he had been dealt. "Order for free" flies in the face of a conservative science that has rejected every past theory of creative order hidden in the universe. It would probably reject his. While the rest of the contemporary scientific world sees butterflies of random chance sowing out-of-control, nonlinear effects in every facet of the universe, Kauffman asks if perhaps the butterflies of chaos sleep. He wakes the possibility of an overarching design dwelling within creation, quieting disorder and birthing an ordered stillness. It's a notion that for many sounds like mysticism. At the same time, the pursuit and framing of this single huge question is the quasar source of Kauffman's considerable pride and energy: "I would be lying if I didn't tell you that when I was 23 and started wondering how in the world a genome with 100,000 genes controls the emergence of different cell types, I felt that I had found something profound, I had found a profound question. And I still feel that way. I think God was very nice to me."

"If you write something about this," Kauffman says softly, "make sure you say that this is only something crazy that people are thinking about. But wouldn't it be wonderful if somehow there are laws that make laws that make laws, so that the universe is, in John Wheeler's words, something that is looking in at itself!? The universe posts its own rules and emerges out of a self-consistent thing. Maybe that's not impossible, this notion that quarks and gluons and atoms and elementary particles have invented the laws by which they transform one another."

Deep down Kauffman felt that his systems built themselves. In some way he hoped to discover, evolutionary systems controlled their own structure. From the first glimpse of his visionary network image, he had a hunch that in those connections lay the answer to evolution's self-governance. He was not content to show that order emerged spontaneously and inevitably. He also felt that control of that order also emerged spontaneously. To that end he charted thousands of runs of random ensembles in computer simulation to see which type of connections permitted a swarm to be most adaptable. "Adaptable" means the ability of system to adjust its internal links so that it fits its environment over time. Kauffman views an organism, a fruitfly say, as adjusting the network of its genes over time so that the result of the genetic network -- a fly body -- best fits its changing surroundings of food, shelter, and predators. The Question Worth Asking was: what controlled the evolvability of the system? Could the organism itself control its evolvability?

The prime variable Kauffman played with was the connectivity of the network. In a sparsely connected network, each node would on average only connect to one other node, or less. In a richly connected network, each node would link to ten or a hundred or a thousand or a million other nodes. In theory the limit to the number of connections per node is simply the total number of nodes, minus one. A million-headed network could have a million-minus-one connections at each node; every node is connected to every other node. To continue our rough analogy, every employee of GM could be directly linked to all 749,999 other employees of GM.

As Kauffman varied this connectivity parameter in his generic networks, he discovered something that would not surprise the CEO of GM. A system where few agents influenced other agents was not very adaptable. The soup of connections was too thin to transmit an innovation. The system would fail to evolve. As Kauffman increased the average number of links between nodes, the system became more resilient, "bouncing back" when perturbed. The system could maintain stability while the environment changed. It would evolve. The completely unexpected finding was that beyond a certain level of linking density, continued connectivity would only decrease the adaptability of the system as a whole.

Kauffman graphed this effect as a hill. The top of the hill was optimal flexibility to change. One low side of the hill was a sparsely connected system: flat-footed and stagnant. The other low side was an overly connected system: a frozen grid-lock of a thousand mutual pulls. So many conflicting influences came to bear on one node that whole sections of the system sank into rigid paralysis. Kauffman called this second extreme a "complexity catastrophe." Much to everyone's surprise, you could have too much connectivity. In the long run, an overly linked system was as debilitating as a mob of uncoordinated loners.

Somewhere in the middle was a peak of just-right connectivity that gave the network its maximal nimbleness. Kauffman found this measurable "Goldilocks'" point in his model networks. His colleagues had trouble believing his maximal value at first because it seemed counterintuitive at the time. The optimal connectivity for the distilled systems Kauffman studied was very low, "somewhere in the single digits." Large networks with thousands of members adapted best with less than ten connections per member. Some nets peaked at less than two connections on average per node! A massively parallel system did not need to be heavily connected in order to adapt. Minimal average connection, done widely, was enough.

Kauffman's second unexpected finding was that this low optimal value didn't seem to fluctuate much, no matter how many members comprised a specific network. In other words, as more members were added to the network, it didn't pay (in terms of systemwide adaptability) to increase the number of links to each node. To evolve most rapidly, add members but don't increase average link rates. This result confirmed what Craig Reynolds had found in his synthetic flocks: you could load a flock up with more and more members without having to reconfigure its structure.

Kauffman found that at the low end, with less than two connections per agent or organism, the whole system wasn't nimble enough to keep up with change. If the community of agents lacked sufficient internal communication, it could not solve a problem as a group. More exactly, they fell into isolated patches of cooperative feedback but didn't interact with each other.

At the ideal number of connections, the ideal amount of information flowed between agents, and the system as a whole found the optimal solutions consistently. If their environment was changing rapidly, this meant that the network remained stable -- persisting as a whole over time.

Kauffman's Law states that above a certain point, increasing the richness of connections between agents freezes adaptation. Nothing gets done because too many actions hinge on too many other contradictory actions. In the landscape metaphor, ultra-connectance produces ultra-ruggedness, making any move a likely fall off a peak of adaptation into a valley of nonadaptation. Another way of putting it, too many agents have a say in each other's work, and bureaucratic rigor mortis sets in. Adaptability conks out into grid-lock. For a contemporary culture primed to the virtues of connecting up, this low ceiling of connectivity comes as unexpected news.

We postmodern communication addicts might want to pay attention to this. In our networked society we are pumping up both the total number of people connected (in 1993, the global network of networks was expanding at the rate of 15 percent additional users per month!), and the number of people and places to whom each member is connected. Faxes, phones, direct junk mail, and large cross-referenced data bases in business and government in effect increase the number of links between each person. Neither expansion particularly increases the adaptability of our system (society) as a whole.