Your gut is right, both about the answer and about its proof (n+1 nonzero vectors, all at right angles to each other, always span an n+1-dimensional space). You should trust it more!
I think that my 40% confidence basis for the very specific claim is proper. Typically I am wrong about three times out of five when I reach beyond my knowledge to this degree.
I was hoping that there would be some property true of 11-dimensional space (or whatever the current physics math indicates the dimensionality of meatspace is) that allows an arbitrary number of fields to fit.
Your gut is right, both about the answer and about its proof (n+1 nonzero vectors, all at right angles to each other, always span an n+1-dimensional space). You should trust it more!
I think that my 40% confidence basis for the very specific claim is proper. Typically I am wrong about three times out of five when I reach beyond my knowledge to this degree.
I was hoping that there would be some property true of 11-dimensional space (or whatever the current physics math indicates the dimensionality of meatspace is) that allows an arbitrary number of fields to fit.