Study of the James algebra yields a new type of imaginary number J, the logarithm of negative one. This imaginary is simpler than the conventional imaginary value i, the square root of negative one, in that J has a period of two rather than four. The imaginary i is constructed from two out-of-phase instances of J. J is the additive imaginary, while i is the multiplicative imaginary. The Image shows some primary characteristics of J. Two copies of J add together to yield zero, even though J itself is not equal to zero. J provides a definition of the logarithm of negative numbers. Similar to i which defines a forbidden square root, J defines a forbidden logarithm. The significant results involving J, together with many computational applications for J, are contained in the attached 2001 paper, The James Imaginary. As a caution, the material in this paper requires a study of the James Algebra first. The content presented on this page and on the James Algebra page is discussed in depth in Jeffrey James’ 1993 masters thesis from the University of Washington. The thesis, A Calculus of Number Based on Spatial Forms, is available online on the Laws of Form website
This page is under construction, July 2013.