Global order from local sources
Charles Radin · Bulletin of the American Mathematical Society · 1991
This article contains introductions to three open problems of significant research interest, taken from number theory, logic, and condensed matter physics. All three problems will be shown to have at their core special cases of one simplystated optimization problem. Our goal is to use the intuition gained from these three perspectives to direct attention to this common core, which constitutes, in fact, one problem of remarkable depth and importance. We will also show that some of the tools developed in the separate problems are of real value in the others. Since each of the three problems uses jargon peculiar to its field, we will give an informal introduction to each, together with all relevant definitions, in the following section. However it may be useful to include here a very brief description of each of them to give some idea of our eventual goal. Our first problem is "sphere packing", in which we consider arrangements of infinitely many unit diameter spheres, each sphere having a variable position in R