Complexity --- everybody loves it, especially:

  1. scientists, who by studying it can get big grants, set up new institutes, attend conferences in nice places, and see their names in print; and
  2. journalists, who can fill column-inches, generate illustrations that make pretty eye candy for their words, and see their bylines associated with something mysterious yet familiar to the general readership.

But setting aside (some of) the hype, it recently occurred to me that the cellular automata which appear to produce complex behavior are actually just unveiling (some of) the genuine complexity hidden in an underlying mathematical system. No magic to it --- all the bizarre patterns were already there, just hidden.

For instance, look at the famous one-dimensional cellular automata that produce spreading pyramids of colored patterns on the covers of popular science magazines every year or two. The edges of the designs are simple, like the edges of a classic Pascal's Triangle of numbers. Deeper inside the artwork there seems to be "complexity". But it's a false complexity, I speculate, corresponding simply to the multiple routes by which one can reach that point via a succession of left-turns right-turns --- precisely like all the various ways there are to partition the mathematical integers. (5 = 1+4 = 2+3 = 1+2+2 = ... = 1+1+1+1+1.) In other cases, maybe the underlying driver is related to primes vs. composite numbers and factorization issues.

Combinatorial interference patterns, one might term these pictures. They're strongly reminiscent of the sum-over-paths interference fringes that particles show as they propagate through spacetime in path-integral formulations of quantum mechanics ...

(see the pellucid Steven Weinberg discussion of Stephen Wolfram's book A New Kind of Science in v.49, n.16 (the 24 Oct 2002 issue) of the New York Review of Books at (tnx to NF for pointing it out to me) ... and see also NaturalProfligacy (20 Dec 1999), EpistemologicalEnginerooms (10 Aug 2000), DeadBeginnings (28 Sep 2002), MindChildren (17 Apr 2003), ...)

TopicScience - 2003-09-10

(correlates: DogTicket, Comments on EssentialKnowledge, WakeUpCall, ...)