The vector algebra war: a historical perspective
Abstract
There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' threevectors, Minkowski fourvectors, 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 threedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1509.00501
 Bibcode:
 2015arXiv150900501C
 Keywords:

 Physics  History and Philosophy of Physics
 EPrint:
 8 pages, 1 figure, 1 table