At a recent dinner, joined by a small coterie of postdocs, Arkani-Hamed drew a pentagram on a napkin. The pentagram, like the amplituhedron, is defined by a finite set of lines crossing at a finite number of points. Arkani-Hamed darkened nine points in the configuration and explained that the first eight of these dots can be placed on a grid. But no matter how fine the grid, the ninth dot always falls between grid points; it is forced to correspond to an irrational number. There is a mathematical proof, Arkani-Hamed observed, that all algebraic numbers can be derived from configurations of a finite whole number of intersecting points and lines. And with that, he expressed a final conjecture, at the end of a long, cerebral day, before everyone else went home to bed and Arkani-Hamed headed to the airport: Everything — irrational numbers, along with particle interactions and the correlations between stars — ultimately arises from possible combinatorial arrangements of whole numbers: 1, 2, 3 and so on. They exist, he said, and so must everything else.
Credit : Béatrice de Géa