of quantum mechanics wasn't a mystery anymore. In Arthur’s equations,
The result wasn't a number. It wasn't a vector. It was a —a directed segment of a plane. Geometric Algebra for Physicists
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. of quantum mechanics wasn't a mystery anymore
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. It was a —a directed segment of a plane
"Why," he whispered to the empty room, "does the universe need three different grammars to say one sentence?"
manifested physically as a bivector representing a plane of rotation. When he squared it, it naturally became -1negative 1 . The math wasn't "imaginary"; it was spatial.