Monday, January 25, 2016

order for free?


edge |  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."

Complex systems have evolved which may have learned to balance divergence and convergence, so that they're poised between chaos and order. Chris Langton has made this point, too. It's precisely those systems that can simultaneously perform the most complex tasks and evolve, in the sense that they can accumulate successive useful variations. The very ability to adapt is itself, I believe, the consequence of evolution. You have to be a certain kind of complex system to adapt, and you have to be a certain kind of complex system to coevolve with other complex systems. We have to understand what it means for complex systems to come to know one another — in the sense that when complex systems coevolve, each sets the conditions of success for the others. I suspect that there are emergent laws about how such complex systems work, so that, in a global, Gaia- like way, complex coevolving systems mutually get themselves to the edge of chaos, where they're poised in a balanced state. It's a very pretty idea. It may be right, too.

My approach to the coevolution of complex systems is my order-for-free theory. If you have a hundred thousand genes and you know that genes turn one another on and off, then there's some kind of circuitry among the hundred thousand genes. Each gene has regulatory inputs from other genes that turn it on and off. This was the puzzle: What kind of a system could have a hundred thousand genes turning one another on and off, yet evolve by creating new genes, new logic, and new connections?

Suppose we don't know much about such circuitry. Suppose all we know are such things as the number of genes, the number of genes that regulate each gene, the connectivity of the system, and something about the kind of rules by which genes turn one another on and off. My question was the following: Can you get something good and biology-like to happen even in randomly built networks with some sort of statistical connectivity properties? It can't be the case that it has to be very precise in order to work — I hoped, I bet, I intuited, I believed, on no good grounds whatsoever — but the research program tried to figure out if that might be true. The impulse was to find order for free. As it happens, I found it. And it's profound.

One reason it's profound is that if the dynamical systems that underlie life were inherently chaotic, then for cells and organisms to work at all there'd have to be an extraordinary amount of selection to get things to behave with reliability and regularity. It's not clear that natural selection could ever have gotten started without some preexisting order. You have to have a certain amount of order to select for improved variants.