Comment I on “Simple measure for complexity”

We critique the measure of complexity introduced by Shiner, Davison, and Landsberg Phys. Rev. E 59, 1459 (1999). In particular, we point out that it is over universal, in the sense that it has the same dependence on disorder for structurally distinct systems. We then give counterexamples to the claim that complexity is synonymous with being out of equilibrium: equilibrium systems can be structurally complex and nonequilibrium systems can be structurally simple. We also correct a misinterpretation of a result given by two of the present authors J. P. Crutchfield and D. P. Feldman, Phys. Rev. E 55, R1239 (1997).