I had no idea this word could be used figuratively:
Oh, that's modern style. Old style and non-lining people prefer curves and slanted angles. BTW thanks for the word 'vectorsmith'.
I was thinking of the practice of drawing curves using the sort of methods described here:
If you are making a path and using your handles in 90º or 180º (orthogonal), make sure where you place the points. A misplaced point generally makes dirty curves...
Sounds like something a mathematician might say. An 'orthogonal' as something that has nothing in common with an argument makes perfect natural sense to maths majors. I sometimes catch myself using mathematical terminology figuratively in everyday situations, which is sometimes complicated by the fact that mathematicians use everyday words like 'normal', 'closed', and 'complex' in specialized meanings.
And "orthogonal" is used in Hilbert space too, so in Quantum Mechanics one can say, for example, that a position eigenstate of a particle is orthogonal to a momentum eigenstate of a particle (the integral of the product of the two wavefunctions is zero), which means that Heisenberg's uncertainty principle applies directly in its simplest form to those two observables.
From that usage, the figurative usage of "orthogonal" to mean independent or unrelated comes very naturally.
And of course the familiar Euclidean space, which forms the basis of our geometric intuitions, is just a special case of a Hilbert space.
And in art history, "orthogonals" is used for the lines that appear to be 90° to the surface of the picture (the diagonals in a perspective drawing, for example).