Order for Free

By Stuart Kauffman, here. Excerpt:

What kinds of complex systems can evolve by accumulation of successive useful variations? Does selection by itself achieve complex systems able to adapt? Are there lawful properties characterizing such complex systems? The overall answer may be that complex systems constructed so that they're on the boundary between order and chaos are those best able to adapt by mutation and selection.

Chaos is a subset of complexity. It's an analysis of the behavior of continuous dynamical systems — like hydrodynamic systems, or the weather — or discrete systems that show recurrences of features and high sensitivity to initial conditions, such that very small changes in the initial conditions can lead a system to behave in very different ways. A good example of this is the so called butterfly effect: the idea is that a butterfly in Rio can change the weather in Chicago. An infinitesimal change in initial conditions leads to divergent pathways in the evolution of the system. Those pathways are called trajectories. The enormous puzzle is the following: in order for life to have evolved, it can't possibly be the case that trajectories are always diverging. Biological systems can't work if divergence is all that's going on. You have to ask what kinds of complex systems can accumulate useful variation.

We've discovered the fact that in the evolution of life very complex systems can have convergent flow and not divergent flow. Divergent flow is sensitivity to initial conditions. Convergent flow means that even different starting places that are far apart come closer together. That's the fundamental principle of homeostasis, or stability to perturbation, and it's a natural feature of many complex systems. We haven't known that until now. That's what I found out twenty-five years ago, looking at what are now called Kauffman models — random networks exhibiting what I call "order for free."