Why You Should Care about Sphere-Packing

Never underestimate the value of woo

Photo by Terry Vlisidis on Unsplash

Unpacking sphere-packing

People must wonder why I spend so much time and energy writing about sphere-packing. What is the point? Why should anyone care about how balls fit together?

For my answer to make any sense, we need to go back to around 4000 BC when clay tokens of specific shapes were used for record-keeping. There were six basic shapes used: sphere, cone, disc, cylinder, tetrahedron, and obloid.¹

The obloid tokens represented jars of oil. Cylinders were animals. Cones, discs, and spheres were different measures of grain. A cone was the smallest measure of grain. The sphere was a larger measure, while the disk represented the largest measure of grain. The tetrahedron represented one day's work from one man.²

Tokens from Tepe Gawra, present-day Iraq, ca. 4000 BC. Courtesy the University Museum, the University of Pennsylvania, Philadelphia.

This is called a concrete counting system. If you were counting workdays you need to do it in tetrahedrons. Nothing was written down because writing things down hadn’t been invented yet. Mathematical operations were performed with the tokens by physically adding and subtracting and moving them from one account to…