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Since Pythagoras had a robust fondness for number principle, if he have been alive in the present day he would possibly wish to simplify issues even additional and consider SL(2,Z), the group of 2×2 integer matrices with determinant 1. This acts on "Pythagorean spinors", namely pairs of integers. 2×2 hermitian matrix. If you're a fancy mathematical physicist you already know that the space of 2×2 hermitian matrices is identical as 4d Minkowski spacetime, with the matrices of determinant zero corresponding to the lightlike vectors, so you are done! In 3d spacetime, the double cover of the Lorentz group is SL(2,R), the group of 2×2 real matrices with determinant 1. In this dimension, we can take a spinor to be a pair of actual numbers

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