He picked up a dusty, slim volume he’d found in a London bookstall: Die Ausdehnungslehre by Hermann Grassmann, a 19th-century schoolmaster ignored by his peers. Beside it lay the works of William Kingdon Clifford.
He looked at Maxwell’s Equations—those four beautiful but cumbersome pillars of electromagnetism. In the language of Geometric Algebra, they collapsed. The divergence, the curl, the time derivatives—they all merged into a single, elegant expression: Geometric Algebra for Physicists
To the outside world, Arthur was a success. He understood the language of the universe. But to Arthur, that language felt like a broken mosaic. To describe a rotating electron, he needed complex numbers. To describe its movement through space, he used vectors. To reconcile it with relativity, he turned to four-vectors and Pauli matrices. He picked up a dusty, slim volume he’d
As the sun dipped below the horizon, Arthur’s chalk began to fly. He realized that by simply adding these different types of objects together—scalars, vectors, and bivectors—he created a . This was the "Geometric Algebra" Clifford had dreamed of. Suddenly, the "imaginary" In the language of Geometric Algebra, they collapsed
Arthur began to draw. He didn’t start with a point or a line, but with an . He took two vectors,