Complex numbers are just 2d numbers and they are mapped on a 2d plane, yeah. They are just a 2d vector. Callling them imaginary numbers is silly in the first place, 2+i is just the vector (2,1), all we mean here are the two numbers are orthogonal, i.e they are destinguished by some independent factor. The imaginary component is no more imaginary than the real component.
I mean what problems does physics solve not with just complex number but with even more complex vectors? Problems of...space-time.
Aliens in a SF book. What do you imagine? I see some kind of physical entity having geometric compomnents in some kind of space.
Context free grammers are represented by...trees where one side of a spatial relationship maps to one idea and the other to another. What is context? Things surrounding something, where something is.
Come up with any idea, it can be represented in space and time.
