  Part I: The geometric algebra of space is derived by extending the real
number system to include three mutually anticommuting square roots of plus one.
The resulting geometric algebra is isomorphic to the algebra of complex 2x2
matrices, also known as the Pauli algebra. The so-called spinor algebra of
C(2), the language of the quantum mechanics, is formulated in terms of the
idempotents and nilpotents of the geometric algebra of space, including its
beautiful representation on the Riemann sphere, and a new proof of the
Heisenberg uncertainty principle. In "Part II: Spacetime Algebra of Dirac
Spinors", the ideas are generalized to apply to 4-component Dirac spinors, and
their geometric interpretation in spacetime.
