SFI CSSS — Day 1

While it's doubtful that I'll keep up a diary of my experience at the Complex Systems Summer School, I'll at least give it a go starting out.

For our first lecture, the motivating question was: "What is complexity, and what is a complex system?" As someone training in computational mechanics, I have an answer in terms of the statistical complexity of the stochastic process underlying any complex system. But that definition is only useful if (1) we can write down a model of such a stochastic process or (2) we have enough data to infer the model. Beyond that, my best stab at a working definition was a system with many interacting parts where knowledge of how the parts behave in isolation is insufficient to describe the overall dynamics of the system. I don't want to throw in the word 'nonlinear' (that word gets thrown around way too much when 'linear' has a very technical definition) or stochastic or anything else.

Under this definition, the dynamics of the logistic map, \(x_{n+1} = r x_{n} (1 - x_{n})\), would not qualify as complex. For one thing, it's a first-order difference equation. For another thing, as \(r\) approaches 4, the behavior ultimately looks random. Randomness isn't 'complex' by any lay definition of complexity.

I'm getting off track. We watched a 15 minute video asking many researchers within the field of complex systems1 how they would define complexity. Refreshingly, they also had trouble coming up with a succinct answer to the question. I think I liked Cris Moore's answer the best: we shouldn't define complexity in terms of the system, but in terms of the question we're asking about the system. He makes this point again and again in his book The Nature of Computation (which I should really get around to studying in more detail).

We then got a whirlwind tour of standard tools from complex systems from Melanie Mitchell: genetic algorithms, cellular automata, and agent-based models. We wrapped up the day learning about arbortrons from Alfred Hubler, which are a scarily cool alternative to standard digital computers. Favorite quote from Hubler: "We will soon be to our machines as chickens are to us. Well, we treat chickens pretty well, don't we?" Uh...

Overall, the coolest part has definitely been meeting and interacting with so many great people. I had this same experience upon first entering graduate school, as compared to undergrad. Suddenly I was surrounded by people equally passionate about science and mathematics. Now, I'm surrounded by people passionate about topics even more specialized.

  1. One of the many nice things about this summer school: I don't have to put complex systems in quotes every time I mention it. That's something I've found myself doing back home in Maryland. Mostly because the field of complex systems isn't really a field. It's a hodgepodge of different results and tools that somehow got pulled under the same umbrella. For now, we don't have a unified theory of complex systems. That's not a bad thing, per se. But it is a thing.