The second law of thermodynamics says disorder always increases. But life looks like an exception, since living things are ordered and create further order. Physicists usually explain this away: order here is balanced by extra disorder elsewhere. Philosopher Dorothea Olkowski doesn't dispute the law itself. Drawing on Ilya Prigogine's work, she argues that order is not a debt repaid elsewhere, but the natural result of open systems exchanging energy with their surroundings. The real question, she suggests, is not whether the second law is wrong, but whether its classical, closed-system version ever described the reality of life at all. Through natural selection, life's order overcomes reality's chaos.

Language, Logic, and the Limits of Formalization

I would argue that I have been working with the idea of complex systems since grad school, although I certainly would not have been aware of that term nor of the multitude of scientists, philosophers, and others who engaged with what became complexity theory. My first introduction to the term “science of complexity” came from the work of the mathematician John L. Casti in his book Complexification: Explaining a Paradoxical World Through the Science of Surprise. With Casti, we encounter the concepts of catastrophe, chaos, lawlessness, irreducibility, emergence, and surprise, but he begins with the simple question of whether our language accurately reflects reality.

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Chaos is the study of complex nonlinear dynamic systems. But if our subject is complexity, then why spend time explaining chaos?.

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When I say “desk,” I could be referring to the flat surface in the kitchen where I occasionally work, and when I say “counter,” I could be referring to an ad hoc table sitting in a corner or the app on my phone that keeps track of the number of steps I walk each day. The logical structure between language and the world is never as clear as we assume—and it’s not only ordinary language that suffers from this. If we look at the mathematical proof for 1 + 1 = 2 in Bertrand Russell and Alfred North Whitehead’s Principia Mathematica, we are always surprised that it takes up over 360 pages. And the light shining on that work dimmed when Kurt Gödel’s incompleteness theorem revealed that mathematical proofs cannot be both consistent and complete. These discrepancies become even more problematic when we are trying to make predictions about the future based on past states of the world—since this is the business of science by means of rule-following leading to formalization.

Dynamical Systems and Strange Attractors

One such set of rules is that of a dynamical system. If you’ve ever played “Treasure Hunt,” you know the rules of this game. Beginning from an “initial state,” players start at different locations and move from location to location on a trajectory guided by instructions or clues given at each location. The end point, where the winner finds a prize, is called an attractor and it governs the motion of the entire game. Fixed point attractors are definite domains of attraction, such as the point where the winner finds the prize. If the game’s creator were a bit devious, they might set up another attractor—a limit cycle—and send one or all the players in a fruitless round of movement retracing their steps over and over.