E8 lattice (from Wikipedia)

It’s turning into an exciting week for spheres. In a tour de force of abstract thinking, mathematicians have finally proved how to best pack spheres in 24-dimensional space. We all know this problem in 3 dimensions: What’s the best way to stack oranges? In 1611, Johannes Kepler speculated that the pyramidal stacking used by grocers was the optimal arrangement, but it took until 1998 for that to be proved. Since then mathematicians have wondered about optimal sphere-packing in higher dimensions. They know the answer for 2 and 3 dimensions, but this is a hard problem to generalize. Some years ago it was speculated that in 8 dimensions the answer could be found in the structure of a glorious object known as the E8 lattice. Now Maryna Viazovska at Humboldt University in Berlin has proved this is optimal. By extending her work, Viazovska and a colleague were also able to deduce the answer for 24 dimensions, which involves one of E8’s cousins. Nobody knows why 8 and 24 dimensions are so elegant and special. 24 dimensional sphere-packing has applications in wireless communications, particularly involving spacecraft where signals are faint and noisy, so there is a link here to the cosmos itself. The IFF is delighted by these developments: in 2009, IFF director Margaret Wertheim wrote about E8 and its cousin “the monster symmetry group” in this article for Cabinet magazine.

In other rotund news, we draw readers attention to this video demonstration of hikaru dorodango, the ancient Japanese craft of making perfect spheres out of dirt. Here, artist Bruce Gardner shows how. Mud meets math, a meticulous fusion of the mundane and the sublime.

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