In 3d spacetime, the double cover of the Lorentz group is SL(2,R), the group of 2×2 actual matrices with determinant 1. In this dimension, we will take a spinor to be a pair of actual numbers. 2×2 hermitian matrix. If you're a fancy mathematical physicist you already know that the house of 2×2 hermitian matrices is the same as 4d Minkowski spacetime, with the matrices of determinant zero corresponding to the lightlike vectors, so you're executed! Since Pythagoras had a strong fondness for quantity concept, if he were alive as we speak he might want 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", namely pairs of integers

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