Arthur began to draw. He didn’t start with a point or a line, but with an . He took two vectors,

, and instead of forcing them into a "cross product" that spat out a third, artificial vector, he followed Clifford’s ghost. He multiplied them:

By dawn, Arthur looked at his chalkboard. It no longer looked like a battlefield of indices. It looked like a map. He realized that for a century, physicists had been like builders trying to describe a house using only the lengths of the boards, ignoring the angles at which they met. Geometric Algebra provided the angles.

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"

The year was 1964, and the corridors of Princeton were hushed, save for the rhythmic scratching of chalk against slate. Dr. Arthur Penhaligon sat slumped in his office, surrounded by the debris of modern physics: scattered tensors, sprawling matrices, and the jagged indices of differential forms.

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.