Sunday, June 17, 2012

The Edge of Chaos

We were talking about a Cambrian explosion of complexity a few posts ago. The larger point is how the economy evolves, not just chordates or arthropods.

It is not just that there may be some resemblances to natural evolution. It is that the economy actually does evolve if variation, selection and adaptation take place. Instead of the nineteenth century idea of evolution as blood-soaked competition, think of it as a means to search a space of possibilities.

One important point in Stuart Kauffman's book At Home in the Universe: The Search for the Laws of Self-Organization and Complexity is the right balance between stability and flexibility is critical for evolution. Too much rigid order, and an organism has no adaptability. Too much change, and it could collapse.

The wonderful possibility, to be held as a working hypothesis, bold but fragile, is that on many fronts, life evolves towards a regime that is poised between order and chaos. The evocative phrase that points to this working hypothesis is this: life exists at the edge of chaos. Borrowing a metaphor from physics, life may exist near a phase transition. ... Were such systems too deeply into the frozen ordered regime, they would be too rigid to coordinate the complex systems of genetic activities necessary for development. Were they too far into the gaseous state, they would not be orderly enough. Networks in the regime near the edge of chaos - the compromise between order and surprise - appear best able to coordinate complex activities and best able to evolve as well. (p26)

So evolutionary systems have a tendency to show the right degree of flexibility.

Fitness landscapes

Kauffman talks about biologists notion of a "fitness landscape", where

the peaks represent high fitness , and populations wander under the drives of mutation, selection and random drift across the landscape seeking peaks, but perhaps never achieving them. (p27)

So you can think of evolution as a search for the highest point on a landscape, when you can't easily see around you. Sometimes all you have to do is walk uphill. But sometimes you might be just on a foothill, and much higher peaks are on the other side of a deep valley. How would you find them? How would you avoid getting trapped on a small hill, instead of keeping up the search for distant ranges?

It tuns out there is much one can say about the best way to search such a landscape for the highest peaks:

We will find in this book that where we are talking about organisms or economies, surprisingly general laws govern adaptive processes on multipeaked fitness landscapes. These general laws may account for phenomena ranging from the burst of the Cambrian explosion in bio-evolution, where taxa fill in from the top down, to technological evolution, to technological evolution, where striking variations arise early and dwindle to minor improvements.

The edge of chaos theme also arises as a potential general law. In scaling the top of the fitness peaks, adapting populations that are too methodical and timid in their explorations are likely to get stuck in the foothills, thinking they have reached as high as they can go, but a search that is too wide-ranging is also likely to fail. The best exploration of an evolutionary space occurs at a kind of phase transition between order and disorder, when populations begin to melt off the local peaks they have become fixated on and flow along ridges towards distant regions of higher fitness. (p27)

We already looked at some of these ideas in Steven Johnson's book Where Good Ideas Come From: The Natural History of Innovation. Johnson calls it "liquid networks". You need to have the right degree of interaction in a system for it to adapt and evolve effectively. The great cities are often just that sort of liquid network.

Johnson also stresses another one of Kauffman's ideas: the adjacent possible. Much innovation happens by exploring the adjacent squares on the fitness landscape, with occasional leaps towards more distant parts of the landscape.


Finally, another crucial idea: in some circumstances complexity can feed on itself. A system can go from subcritical to supracritical. As Kauffman says:

The striking possibility is that the very diversity of molecules in the biosphere can cause its own explosion! The diversity feeds on itself, dirving itself forward. Cells interacting with each other and with the environment create new kinds of molecules that beget yet other molecules in a rush of creativity. This rush, which I will call supracritical behavior has its source in the same kind of phase transition to connected webs of catalyzed reactions that we found may have pushed molecules into living organizations in the first place. (p114)

But cells themselves must remain subcritical.

That we eat our meals rather than fusing with them marks, I believe, a profound fact. The biosphere itself is supracritical. Our cells are just subcritical. Were we to fuse with the salad, the molecular diversity this fusion would engender within our cells would unleash a cataclysmic supracritical explosion. The explosion of molecular novelty would soon be lethal to the unhappy cells harboring the explosion. (p125)

So what should we take from this, especially in the context of explaining the industrial revolution and Deirdre McCloskey's book? The right degree of "near-chaos", of liquidity is absolutely crucial to searching out the best ways to evolve on a fitness landscape. It is possible that small institutional changes or changes in values or ideas could produce that right degree of liquidity and launch the search process into overdrive.

It is possible that just the right mix occurred in England, just the right degree of liquidity to start the evolutionary search algorithm. The balance of order and disorder is very important. And it did not take long for the whole system to go supracritical.



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