  Several fundamental results in physics are derived from the simple starting
point of two commuting orthogonal unit vectors. The combination of these unit
vectors leads to spherical harmonics and Schwinger's expression of the
second-quantized angular momentum states in terms of bosonic operators.
Commuting unit vectors can be turned into anticommuting ones by the restriction
to a single unit vector. This leads to Pauli spin matrices. By including
hyperbolic rotations, vectors can be given a finite norm and results from
special relativity and Dirac's equation are found. The assumption that the
change in four-momentum is due to the change in four-potential leads to the
electromagnetic field tensor and the Lorentz force. Mawell's equations are
obtained by viewing the four-potential as an harmonic oscillator driven by the
four-current. The Schr\"odinger equation is obtained from the nonrelativistic
limit of the four-momentum.
