
as constants. Sure, we've been duped before by illusory geometries-like Pythagorean intervals, ideal Euclidean properties, and Kepler's harmonics of planetary orbits-so it's natural to be leery of physics as geometry. Nevertheless, mapped schematically, mass, coupling constant, spin, angular momentum, and charge generate polyhedra. Take, for example, the plotted relations of quarks and leptons on a horizontal plane-displaced vertically proportional to their respective charges, they polarize the angular coordinates of an ideal cube! Think on that."
"As blood is the bride to iron-he be right! Pull the electrode, and we be hard thinking on that."
"Aye, and the void bites its tusks!"
The blue words vanished, and the air smelled all at once of boiled milk. I noticed that, beyond the drifting tufts of dandelion, the twilit sky was precise with stars. I felt the silence of the wind opening in me again, and then
darkness came on.
The fire-flower of numbers and words opened and closed around me time and again. And I found myself square-summing the real and imaginary parts of a field specifying spin states of particles, measuring angular momenta, and plotting straight lines in the Regge trajectory. "Abstract geometry defines matter," I heard myself say.
Then I performed conceptual rotations on the doublevalued quality of fermions-"You know, matter particles"-in an abstract superspace with anticommutators and revealed deep angular identity with the class of
bosons-"Force particles! Do you see what I'm saying? Geometry shows they are the self-same entity!"
I babbled about heterotic string theory and the summary familial group designated E8xE8, reflecting a generalization of crystal symmetries, a strictly abstract pattern produced by categorical requirements applying directly to the macroscopic and observable order of structures. "Euclidean geometries are staring out from nature's apparent chaos. Salts, viruses, seashells, pinecones, honeycombs, galaxies, and galactic sheets hundreds of light-years huge!
