The Yale University physicist Willard Gibbs had pamphlets with the plus one square in his three-dimensional vector system.
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It was Alexander Macfarlane who promoted this concept in the 1890s as his Algebra of Physics, first through the American Association for the Advancement of Science in 1891, then through his 1894 book of five Papers in Space Analysis, and in a series of lectures at Lehigh University in 1900 (see Historical Review below).
Nevertheless, the Weinberg form is consistent with Hyperbolic quaternions, a forerunner of Minkowski space.
Quaternion | quaternion | Hyperbolic tree | "Quaternion Eagle", '''Coat of arms of the Holy Roman Empire | Hyperbolic quaternion | Hyperbolic partial differential equation |