The mathematical methods that have in the past dominated theoretical science do not help much with [the question of how simple programs behave]. But with a computer it is straightforward to start doing experiments to investigate programs, and then run them and see how they behave. [NKS, p. 23]
This might have seemed an inconsequential, introductory-type question to many readers. However, coming from a pure math background — I was just getting into toric varieties and other meaty topics in differential and algebraic geometry — I found it rather astonishing that one can model the diffusion equation with block CAs, and never know a thing about differential equations. Of course, that was just the beginning of my astonishment.
My undergraduate background is mathematical physics. I originally went into a mathematics graduate program rather than a theoretical physics program because I believed, as my electromagnetism prof Sidney Redner (a theorist himself) used to tell us — “You should learn your physics from physics books, and your math from math books.” Now, where does that leave a theorist? If one embarks on a theoretical program in quantum mechanics and string theory, one needs to know an awful lot of fairly advanced techniques in order give a meaningful answer the simplest questions. Such advanced techniques that certain mathematicians have been able to get a foothold in the field while traditionally trained physicists have struggled.
Theoretical physics has realized a decreased marginal return as they’ve increasingly built upon “standard” methodological practices (like algebraic techniques in quantum mechanics, and geometric techniques in general relativity). Yet there is the hint — not the promise, due to the computational difficulty, but the hint — that one could produce an ultimate model for the Universe [NKS, p. 465] with comparatively simple computational techniques. So simple, a high school student could, after some study, understand them with relative ease.
Is this what makes NKS techniques seem so alien and “impossible” to traditional theorists? That evolving simple programs, with mind-bogglingly simple rules, can result in modeling diffusion, or even the Universe itself? Is that why they’re willing to reject it outright, with almost a religious fervor, as if it were a piece of blasphemy that, while simply true, must not be entertained or else their whole institution, with all its traditions, could come tumbling down?