Schroedinger thought the wave function ought to be real:pic.twitter.com/3w7h0uG5Mv
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What is SO(n)? Scott talks about how complex numbers ensure every linear transformation has a square root in the same number of dimensions, is that the important part?
The space of real orthogonal matrices with unit determinant. Perfectly good space to work in, with square roots, and could easily have been the type of space used for quantum computing (or, with some generalization, quantum mechanics).
