Magnitudes are intuitionally directionless (hence why norms and measures are nonnegative reals). Of course, you can extend notions suitably and make it work, bu

Magnitudes are intuitionally directionless (hence why norms and measures are nonnegative reals). Of course, you can extend notions suitably and make it work, but I really don't think that this is terribly intuitive. (Of course, different people will find different things intuitive.)