The Geometric Product

Whenever we attempt to learn something completely new, all sorts of mental barriers are raised, especially if the subject matter appears foreign or irrational. This often happens when we learn a new language and wonder why its syntax differs from our own native language. Mathematics is a minefield for such experiences, and as we explore the world of GA, don’t be surprised if you feel uncomfortable or bewildered by its structure and ideas.

if this is the first time you have studied GA this chapter will be both challenging and exciting. It will be challenging not because it is difficult, but because there is so much to remember as the algebra unfolds. For example, some elements of the algebra commute, whilst others anticommute. Some functions are symmetric, whilst others are antisymmetric. Certain conditions arise with orthogonal elements, and others arise with parallel elements, and there is a sense of being overwhelmed by a world of axioms, rules and special conditions. It will be exciting as GA is extremely rich in new concepts that will draw you into its strange world of symbol manipulation that correspond with the world of space.