This paper reviews some basic principles of Quantum Mechanics, Quantum Computing, and Artificial Intelligence in terms of a specific unifying theme. This theme relates to the hyperbolic or split-complex imaginary numbers and their equivalent matrices, rediscovered by Dirac, and the underlying mathematics of the previously described Q-UEL language based on them. Hyperbolic imaginary numbers h have the property hh = +1: contrast the more familiar i such that ii = -1. Examples of analogous matrices include that for the Hadamard gate as used in quantum computing and the Pauli spin matrices, and all Hermitian matrices of interest in quantum computing can readily be derived from these. They also relate to Dirac dualization, spinor projectors of Quantum Field Theory, the non-wave-like part of quantum theory, collapse of the wave function, and a dualized form of classical probability theory that has advantages in automated reasoning for medicine.
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