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.

The idea that simple rules lead to incredibly complex behavior is not new and wolfram was not the first mathematician to realize it even if he wants to pretend he is.

I'm big into fractal geometry so I would say Mandelbrot was the first 20th century mathematician to really get that concept along side the founding chaos theorist but even their realizations about the fractal nature of the universe ride off shoulders of others work.

I guess for computational mathematicians, the fractal nature of the universe and the simple rules making complex systems is new and mind blowing, for me and everyone whos read through deep simplicity its old ideas recycled into a new branch of mathematics reworded in terms a computer scientist thinks in.

Its not that the ideas aren't important or mind blowing, they just aren't new and the academic community has had decades to digest them.

And before the academic community came along many eastern religions came to similar concluions about the nature of the universe a couple thousand years earlier thanks to some good old fashioned shrooms and pot, so these general ideas have also been floating around forever and academics weren't even the first to suggest them only the first to kind of prove them right with logic and experimental evidence.