science

I can give you my impression and that of the people I spoke to about it. I’m coming from the perspective of a theoretical biologist who was heavily involved with computational models of complex systems - particularly ones with biological foundations. I worked with simulations ranging from molecular cell biology up to ecosystems.

I don’t want this to sound dismissive, but CA are cartoonishly simple versions of complex systems. Once you get past illustrating the idea that simple rules can give rise to complex behaviors, that they’re Turing complete, and that there are neat and interesting phenomena that can arise, I think you’re pretty much done. They’re not going to show you anything about the evolutionary dynamics that drive carcinogenesis. They’re not going to let you explore the chemistry that might have given rise to the origin of life. They’re not going to let you model how opinions and behaviors cascade on social networks.

Topics like emergence are core to complexity theory, but CA can only illustrate that it exists, and it does so in such an abstract way that it doesn’t really translate into an understanding of how emergence is grounded in real world systems.

Wolfram’s problem, in my opinion, is that he was largely disconnected from the complex adaptive systems community, and for some reason didn’t realize we had largely moved on. I don’t know anyone in the CAS community that thought his work was groundbreaking.

I do have to say that Robert Sapolsky seems to have found his work interesting, and I am very deeply interested in Sapolsky’s work. But he’s a neurobiologist, not a complexity scientist, and he doesn’t draw a concrete connection between Wolfram’s work and his own, other than the generic connection that complex systems can arise from simple rules. That’s something we’ve known since Conway and Lorenz.

My mind is open to counter arguments, but that was my impression and as far as I could tell, the same was true of my colleagues. I think that the general academic reception to his book bears this analysis out. It’s like if someone wrote a comprehensive book about all kinds of Prisoner’s Dilemma models long after we’ve moved on from PD to modeling more complex and accurate depictions of cooperative versus competing interactions. Students should absolutely study PD, and they should study CA. It’s just not something you want to hang your academic hat on at this point.

Mathematica, on the other hand, is pretty neat.