Self-Made Space

I was thinking about orthogonal vector spaces today. (why? who knows) Anyway, from any three vectors we can construct an orthogonal vector space (a right angled vector space if we are using unit vectors, called orthonormal, whatever). This is basically akin to saying we can take three vectors and construct a three-dimensional Cartesian Plane. So I was looking out at work today, taking three distinct moving objects (or two and the direction I was looking in as a third vector) and thinking about constructing spaces based off of these. It is kind of interesting, because we can create a frame of reference out of just about anything. Once my thought experiment lead to the creation of one vector space, I could take all the other motions at work and relate them back to the others. So separating mathematics from causality, I could understand the motion of person A, say, and understand it as linearly dependant on the space I just created. Then making the jump (mentally) from math to reality, I could think about as person as a marionette, controlled by motions of completely unrelated things. Sure, it all falls apart once the person deviates from straight line motion, but if you think about it, most people walk in a pretty straight line. And once they change direction, you can just make that a new linearly dependant vector and let the person keep their puppet status.

Needless to say, I was bored this afternoon at work.