The vector algebra war: A historical perspective

There are a wide variety of different vector formalisms currently utilized in science. For example, Gibbs three-vectors, spacetime four-vectors, complex spinors for quantum mechanics, quaternions used for rigid body rotations and Clifford multivectors. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for the whole of science. This surprising situation exists today, despite the fact that one of the main goals of nineteenth century science was to correctly describe vectors and the algebra of three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines and requiring a very significant amount of time and effort in learning the different formalisms. We thus review historically the development of our various vector systems and conclude that the Clifford algebra multivector fulfills the goal of correctly describing vectorial quantities in three dimensions.

The entire paper can be read here.

H/T Math Update.

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