‘In the beginning, all is null’

Abstract

One pleasant early summer afternoon, I walked the couple of blocks down the hill frommy home in small-town South Dakota to the public library, and checked outMr g (Lightman, 2012) by physicist, novelist, essayist and poet Alan Lightman. I came home and read most of it in one sitting on the stone patio in my backyard, built by a previous homeowner who must’ve spent their summer afternoons in more productive activities than reading novels in the sunshine. In any case, I loved the book, a whimsical fable on the (literal) creation of (literally) something from (literally) nothing. Not long thereafter, inspired by themultiple choice theatre of the Oulipo and childhood memories of Choose-Your-Own-Adventure books, I was working on some mathematical multiple-choice poetry with a colleague. We’d been looking at several discrete, directed mathematical objects to structure the poetry we were writing. Mathematical details of this project can be found in (Wika & May, 2017), which includes a beautiful 80-in-1 labyrinth of a poem entitled ‘This Is Where You’ll Find Her’ by my collaborator Courtney Huse Wika. But othermathematical multiple-choice poemswere left on the cutting roomfloor. Submitted here is my poem ‘In the Beginning, All is Null,’ a Seuss-like bop (in my dreams), based on the Hasse diagram of a three-element set (Figure 1). Among other things, Hasse diagrams (Goodaire & Parmenter, 2006) can be used to display inclusion relationships among all the subsets of a given set. For the three-element set S = {x, y, z}, the Hasse diagram includes every element of the power set of S (meaning every subset of S), with arrows drawn from one set to another only when the second set covers the first. That is, an arrow only points from subset A to subset B if A ⊂ B and there is no subset C such that A ⊂ C ⊂ B. The arrows in the diagram are transitive in the sense that if there is any directed path of arrows from one set to another, regardless of the number of arrows it takes, the lower set is a subset of the upper set. Occasionally, Hasse diagrams are drawn without arrows; in this situation vertical alignment implies that the lower of adjacent sets is a subset of the upper. These diagrams are named for the Germanmathematician Helmut Hasse, whose activities during the rise of Nazi influence on German mathematics in the 1930s have been described as ‘ambiguous’ (Segal, 1980).