What type of "graph paper" do I need to graph an arbitrary solution, Ψ, of the Dirac equation in 3+1 dimensional spacetime? Assume the "graph paper" has the minimum dimensions required to do the job. Would this work? At each point of spacetime we need a complex plane which takes care of the magnitude and phase of Ψ. The spinor part of Ψ is graphed on a pair of properly ruled three-spheres, S^3 (do we need to allow for the spin part of Ψ vary with spacetime?). So we need 4 dimensions for spacetime, 2 dimensions for the complex plane, 6 dimensions for the two three-spheres, 8 dimensions at each point in spacetime, so we need 12 dimensional graph paper? Or could we cheat and approximately graph an arbitrary solution of of the Dirac equation by having a set of 4 (or 3?) independent complex vectors at each point of spacetime? Thanks for any help! Edit, I think I may have made things more complicated then needed. I think I was told in a thread that a time varying phase times a spinor just moves a point in S^3 on some "orbit" in S^3 so that the above can be simplified a bit?