Through the Looking Glass: What Computation Found There
Commenting about the fact that two matrices 1 and −1 in the two dimensional complex space correspond to the identity matrix 1 in the three-dimensional real space, Goldstein (1957) remarks that “such a paradoxical situation plays no havoc with our common sense” as the complex space is entirely a mathematical construction. Focusing on the notion of ‘observability’, this paper aims to entrust the complex space with physical and computational meaning. In the light of quaternions, the efficiency of the Grover search algorithm finds its source in that “paradoxical situation”.
Keywords: Observability, measurability, computability, imaginary units, quaternions, mirrors