It sure does shake up one’s paradigms, Lysander. But that’s essentially what Wolfram is trying to do with this book. As he puts it, he wants traditional mathematicians and scientists to “retrain their intuition.” He apparently believes that certain basic assumptions of the sciences are incorrect. A particularly famous one is the assumption that complex behavior must have complex causes. He repeatedly shows that this is untrue by modeling all kinds of systems, natural, physical, mathematical. And what he has discovered is that apparently random, extraordinarily complex behavior can be generated by the evolution of very simple rules. His piece de resistence is the Principle of Computational Equivalence, which holds that a fundamental unity exists across a vast range of systems and processes in nature and elsewhere; and that despite all their differences in detail, every system that is not obviously simple can be viewed as corresponding to a computation that is ultimately equivalent in its sophistication. Two important corollaries are universality and computational irreducibility. The presence of the latter ultimately means that there are limits to human knowledge and to human thinking itself that are quite likely impossible to overcome. Which sounds like something a philosopher might say, but it’s certainly not what we expect to hear from a scientist….
But then again, maybe he’s just been looking at computer screens too long: The systems he models are executed as computer graphics, whose behavior can be analyzed just by looking. He’s looked at millions of them over the past 20 years. It’s simply uncanny how often particular sorts of patterns can be seen in the evolution of widely disparate systems.
Anyhoot, there’s a lot of “food for thought” in this book. I'll be working through its implications for some time to come, I'm sure.