The vector algebra war: a historical perspective

TL;DR

This paper reviews the historical development of vector formalisms in science and argues that Clifford's multivectors offer the most comprehensive and unified approach for describing vectors in three-dimensional space.

Contribution

It provides a historical analysis and advocates for Clifford's multivectors as the most suitable formalism for a unified vector system in science.

Findings

Clifford's multivectors unify various vector formalisms.

Historical review of vector systems in science.

Multivectors best fulfill the goal of describing 3D vectors.

Abstract

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. 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 science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford's multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.