Finance, Mathematics, Software

Math is all about following your nose. Grassman had the notion that P² = 0, where P is a point, was how to detect intersections and somehow that idea generalized to higher dimensions. Don’t forget that in Grassmann’s time the of notion working in general n-dimensional space was a novelty. He ran into trouble when he tried to define a product that went beyond the dimension of the space. We’ll get back to that later.

Given points P and Q, what is Q – P? Note that Q – P is not equal to R(t) = (1 – t)P + tQ for any t. Since PQ(Q – P) = 0, it should be on the line determined by P and Q. In this sense, it has a direction. If Q – P = T – S, then T = S + (Q – P). In this sense, it has a magnitude. Differences of points are vectors.