>>37
why does negative area imply negative dimension?
That just doesn't follow. Dimension is really defined, and this is very loose here, as the amount of information needed to signify the structure. Areas require two "linearly independant" elements to make any sense.
You ever do any linear algebra?
The complex plane has dimension two, surely you can agree to that?
The elements 1 and i are linearly indepedent and spanning.
The real number line has dimension one.
So surely the imaginary number line, by your same argument has dimension 1 as well.
The complex plane is merely a way to visualise algebra on ordered pairs of numbers with multiplication and addition defined in a certain way it doesn't "signify" anything in the real world. As I said before, if you want to do any even quasi-serious maths you need to stop trying to anchor stuff in experience and deal with the abstract.