Order/Disorder Dichotomies and the Structure of Matter

Conceptions of order and disorder date back to antiquity and colour modern understanding of the universe, matter, beauty in art, and social organization. Ancient notions of order and disorder are most precisely operationalized in modern physics where they provide quantitative metrics for the structural organization of matter. Here, we argue that ancient uncertainty- and symmetry-based concepts of disorder have contemporary echoes in physics in the form of entropy and Landau theory. Though many matter systems provide examples in which these two frameworks coincide, we show that recent results in the physics of soft, colloidal matter give a growing, systematically constructed set of discordant examples. The discord between uncertainty- and symmetry-based metrics of disorder we identify in physics casts doubt on the plausibility of drawing precise order--disorder dichotomies in other areas of thought where the concepts of order and disorder have been less precisely defined.