Be Persistent and Evolve

If we think about the evolution of living things we generally start from the idea that evolution requires replicators, variation, and selection. But what if we loosened that up to the more everyday semantics of the word “evolution” when we talk about the evolution of galaxies or of societies or of crystals? Each changes, grows, contracts, and has some kind of persistence that is mediated by a range of internal and external forces. For crystals, the availability of heat and access to the necessary chemicals is key. For galaxies, elements and gravity and nuclear forces are paramount. In societies, technological invention and social revolution overlay the human replicators and their biological evolution. Should we make a leap and just declare that there is some kind of impetus or law to the universe such that when there are composable subsystems and composition constraints, there will be an exploration of the allowed state space for composition? Does this add to our understanding of the universe?

Wong, et. al. say exactly that in “On the roles of function and selection in evolving systems” in PNAS. The paper reminds me of the various efforts to explain genetic information growth given raw conceptions of entropy and, indeed, some of those papers appear in the cites. It was once considered an intriguing problem how organisms become increasingly complex in the face of, well, the grinding dissolution of entropy. It wasn’t really that hard for most scientists: Earth receives an enormous load of solar energy that supports the push of informational systems towards negentropy. But, to the earlier point about composability and constraints, the energy is in a proportion that supports the persistence of systems that are complex.… Read the rest

The Goldilocks Complexity Zone

FractalSince my time in the early 90s at Santa Fe Institute, I’ve been fascinated by the informational physics of complex systems. What are the requirements of an abstract system that is capable of complex behavior? How do our intuitions about complex behavior or form match up with mathematical approaches to describing complexity? For instance, we might consider a snowflake complex, but it is also regular in it’s structure, driven by an interaction between crystal growth and the surrounding air. The classic examples of coastlines and fractal self-symmetry also seem complex but are not capable of complex behavior.

So what is a good way of thinking about complexity? There is actually a good range of ideas about how to characterize complexity. Seth Lloyd rounds up many of them, here. The intuition that drives many of them is that complexity seems to be associated with distributions of relationships and objects that are somehow juxtapositioned between a single state and a uniformly random set of states. Complex things, be they living organisms or computers running algorithms, should exist in a Goldilocks zone when each part is examined and those parts are somehow summed up to a single measure.

We can easily construct a complexity measure that captures some of these intuitions. Let’s look at three strings of characters:

x = aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

y = menlqphsfyjubaoitwzrvcgxdkbwohqyxplerz

z = the fox met the hare and the fox saw the hare

Now we would likely all agree that y and z are more complex than x, and I suspect most would agree that y looks like gibberish compared with z. Of course, y could be a sequence of weirdly coded measurements or something, or encrypted such that the message appears random.… Read the rest