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We describe the real tessarines or \split-complex numbers" anddescribe a novel instance where they arise in biomedical informat-ics. We use the split-complex numbers to give a mathematical def-inition of a Hyperbolic Dirac Network (HDN) | a hyperbolic ana-logue of a classical probabilistic graphical model that uses quantumphysics as an underlying heuristic.The methods of theoretical physics should be applicable to all those branches ofthought in which the essential features are expressible in numbers.| P. A. M. Dirac, Nobel Prize Banquet Speech 1933

Split-complex numbers and Dirac <i>bra-kets</i>