Physicist Steven Weinberg writes about Steven Wolfram’s A New Kind of Science in the New York Review of Books.
Mostly he writes about why particle physics is better than other kinds of science: “although these free-floating theories are interesting and important, they are not truly fundamental, because they may or may not apply to a given system; to justify applying one of these theories in a given context you have to be able to deduce the axioms of the theory in that context from the really fundamental laws of nature.”
Weinberg disclaims this opinion, but he repeats it often enough that it’s clear which side of the flamewar he’s on. Weinberg thinks science should offer one fundamental theory of the world. He is not interested in the idea that there might be different levels of organization in the universe, so that the algorithm that modeled plant growth, say, was different than the algorithm that modeled competition among species in an ecosystem.
In fact Weinberg doesn’t seem convinced by the idea of modeling. “Take snowflakes. Wolfram has found cellular automata in which each step corresponds to the gain or loss of water molecules on the circumference of a growing snowflake. After adding a few hundred molecules some of these automata produce patterns that do look like real snowflakes. The trouble is that real snowflakes don’t contain a few hundred water molecules, but more than a thousand billion billion molecules. If Wolfram knows what pattern his cellular automaton would produce if it ran long enough to add that many water molecules, he does not say so.”
The whole trouble with complex systems is that they are programs that you need to run fully, with identical initial conditions, to get the exact result. If a model can be used regularly to make predictions about a real-world system — even if the model doesn’t duplicate the system — it seems to me that model is worth something.
The most interesting thing Weinberg says that Wolfram should do but doesn’t, is to offer a definition and measure for complexity. A very clever, erudite and witty person named Cosma Shalizi claims to have done this in his doctoral dissertation. Which I have not read yet, and my undergrad-level math may not be sufficient to understand.