Vectors versus Quaternions

Abstract

As in recent numbers of NATURE my views on analysis have been quoted, and not very correctly, I ask for space to state them more explicitly. I see truth in the quaternion analysis and in the vector analysis; but I believe that neither the one nor the other, nor the two combined, contain the whole truth. The vector is an important idea, and the quaternion is an important idea, but there are in physical science many other important ideas which call for a more direct notation. To avoid any narrow hypothesis I denominated my first paper “Principles of the Algebra of Physics”; but in the notice which NATURE honoured it with it was printed as “Principles of the Algebra of Vectors.” The title I gave it indicates briefly my position. I have been looking at analysis from the point of view of the physicist, and one of my guiding ideas has been that the fundamental rules of analysis, instead of being assumed as so many arbitrary rules of operation, should be grounded on the fundamental laws of physics.