20th century science is a bizarre tapestry of insight, achievement, and doom. Something something about quantum, the computer, and the fusion/fission bombs. One of my favorites in the mosaic is Complexity Theory, the study of how nonlinear systems, often with incredibly simple constraints, and transition into spontaneously ordered states. It’s a relatively new field, burgeoning off the rep of some of the most ridiculously talented thinkers of the late 1900s through the Sante Fe Institute (SFI). I recently read Waldrop’s Complexity, a narrative exploring the establishment of the institute and all of the academic drama entailing through the 70s, 80s, and early 90s. One of the more notable aspects of the early innings of complexity theory is the applications to economics – Kenneth Arrow and Brian Arthur were at the forefront of complexity economics back then, working to turn the tide against neoclassical economic theory, which had been mired by rigid optimal mathematical formalizations and generally lacked empiricism. Complexity in economics makes immediate sense and is likely why it has been so immediately successful at stirring up the field – economies run on ever-evolving landscapes of beliefs and those drive behaviors and those drive new beliefs ad infinitum. Nature has a great essay on the subject here. You can also go find the books from the SFI symposium’s proceedings online, they’re a great way to keep up with the most engaging aspects of the field.
What really gets me going about complexity though, is how fundamental simple “agents” performing simple tasks could be to the structure of reality, from physics to the human mind. It got Von Neumann excited too. It’s in Deutsch’s Constructor Theory and it’s in Wolfram’s Physics Project. The recursiveness of Conway’s Game of Life is what sold me. Go read more about it, it’s absolutely beautiful to think it might be patterns like this all the way down.
Waldrop’s book has a great list of follow-up readings at the end of it, and I’m working my way through them. One of the best characters in the book is Stuart Kauffman, a boisterous and intellectually adventurous theoretical biologist known for his work on autocatalytic sets of polymers. Basically, he suggested that molecular reproduction could exist as a type of closed feedback loop, where the dynamics of order (read: self-organization) were inherently stable and abundant, not simply “selected for” in a Darwinian sense.
Kauffman’s recent paper, “What is Consciousness” (LINK) is great fun and builds on the ideals of complexity in true Kauffman adventurous spirit. In it, among other things, he argues most strongly that Artificial General Intelligence (AGI) based on Universal Turing Machines is impossible because the set of knowledge that AGI must draw from in order to pass a Turing test exists with “no deductive relation” – that is, without a syntactic list of properties and goals, a machine cannot deduce the uses that exist in the ontological space of all uses for a given object (he uses several examples, like a car engine being used to open a coconut). He gets a little quantum hand-wavy with it all, but I’ll forgive him for that. I’m sure he’s forgotten more than I’ll ever know. But I think the main point in his paper stands in solidarity with the tenets of complexity for something really striking: we are not computers, we are minds that explore. It might seem that we are evolved to be the universe’s most powerful agents of exploration and key to that is our incredible ability to somehow imagine experiences.
Complexity theory is one beast, but our minds are born of life’s complexity. The mind is seemingly a layer higher than complexity, pulling some abstractions from this layer and implementing them in the space of complexity in the physical world. From where are we possibly perceiving the experiences we have? From where does the first layer of automata even arise? Perhaps the whole thing is one beautiful closed loop, made “real” from purely logical abstractions (i.e. some fundamental truth makes everything else “real”). Perhaps the whole thing is just patterns in some inconceivably cosmic noise, anthropic principle style.
What I do know is that we seem to be built to explore and wield this complexity. With it what can we do?
To Be Determined 
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