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Since Pythagoras had a powerful fondness for number principle, if he had been alive right this moment he may wish to simplify issues even further and consider SL(2,Z), the group of 2×2 integer matrices with determinant 1. This acts on "Pythagorean spinors", specifically pairs of integers. 2×2 hermitian matrix. If you're a fancy mathematical physicist you know that the house of 2×2 hermitian matrices is similar as 4d Minkowski spacetime, with the matrices of determinant zero corresponding to the lightlike vectors, so you are performed! In 3d spacetime, the double cowl of the Lorentz group is SL(2,R), the group of 2×2 real matrices with determinant 1. On this dimension, we are able to take a spinor to be a pair of real numbers

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