A book review appeared in Nature [(23 May 2002) 417, p. 381], under the faintly ironic heading “Science is a computer program”, of A New Kind of Science by Stephen Wolfram. I have to confess right away that I have not yet tried to read the 1200 pages of this opus! The book, it appears, is entirely devoted to explaining and exemplifying the use, on a computer, of cellular automata as a means of generating a wide range of complex patterns (such as, for instance, snowflakes). Wolfram, who is a mathematician/computer scientist of awesome reputation, claims, according to John Casti's review of his book, that “the phenomena we see in the world around us should be thought of as the running of myriad simple computer programs. And the best way to understand these processes is by modeling them on a computer, not by working out the implications of an idealized mathematical model stemming from a set of equations. That's it. That is the 'new' kind of science.” Wolfram has made a quick impact. His book is even discussed in Time (10 June 2002). It is the habit of computer simulators to claim much for their craft, but never as much as this. Most of them know that to carry conviction with the rest of us, the simulator must frequently compare his predictions with experimental evidence. Every successful simulation (one that is in accord with experimental observation) enhances our faith in the simulator's skill, and predisposes us to accept his predictions. But it seems that Wolfram's 1200 pages do not contain a single reference to the literature out there, something the reviewer describes as “bizarre”.
For balance, herewith examples of a couple of typical (but exceptionally convincing) simulations from the domain of materials. One is a paper by Kwai Chan, of the Southwest Research Institute in Texas, on the design of ductile Nb-Ti-Cr-Al solid-solution alloys [Metallurgical and Materials Transactions A (2001) 32, p. 2475]. The point here is that Cr is added to niobium aluminide to enhance oxidation resistance, but Cr also impairs ductility. To counteract this, Ti is added. The objective was to use a first-principle approach, based on physical theory, to compute the Peierls-Nabarro 'barrier energy' that impedes the passage of a dislocation through the lattice, and the surface energy, as a function of alloy composition. Theory also tells us that the relation between these two quantities governs ductility. So here a computer is used to make feasible immensely elaborate calculations, using merely the composition as input. Then, to test the approach, fracture toughness is plotted against Ti content, both according to the theory and also according to experiment, and the two agree pretty well. That is one form of computer-aided modeling as I think it should be done in our science.
Another example was presented a few days before I wrote this, during a meeting at the Royal Society in London on Nucleation Control, by Murugappan Muthukumar of the University of Massachusetts at Amherst. His paper on the modeling of nucleation in polymers, was devoted to the genesis of polymer crystals of the now familiar kind, in which long polymer chains fold forwards and backwards through the thickness of slender crystals. Using well-defined rules sequentially deployed, he showed (in the form of time-sequenced videos) nucleation at more than one point along a long chain, followed by the merging of the separate nuclei as they grow. To watch these animations was an almost artistic experience, as the two nascent crystallites wander about blindly (as the polymer chain between the crystallites bends and straightens) until they blunder into each other and merge. Muthukumar matches his simulated crystallites for thickness against those found by experiment. This is the indispensable step.
Returning for a moment to Wolfram's book, the reviewer points out that Wolfram does compare his model predictions to observation, in the sense that one of his modeled snowflake patterns matches one of the many that have been observed. But, the reviewer adds, this does not prove that Wolfram's path is the only one that would lead to this pattern. This objection is one to which computer simulators are always open. But if they base themselves on a proper analytical theory as starting point, it is that much less likely that their agreement with experiment is merely fortuitous.