Musean hypernumbers are an algebraic concept envisioned by Charles A. Musès (1919–2000) to form a complete, integrated, connected, and natural number system. Musès sketched certain fundamental types of hypernumbers and arranged them in ten "levels", each with its own associated arithmetic and geometry.
Mostly criticized for lack of mathematical rigor and unclear defining relations, Musean hypernumbers are often perceived as an unfounded mathematical speculation. This impression was not helped by Musès' outspoken confidence in applicability to fields far beyond what one might expect from a number system, including consciousness, religion, and metaphysics.
The term "M-algebra" was used by Musès for investigation into a subset of his hypernumber concept (the 16 dimensional conic sedenions and certain subalgebras thereof), which is at times confused with the Musean hypernumber level concept itself. The current article separates this well-understood "M-algebra" from the remaining controversial hypernumbers, and lists certain applications envisioned by the inventor.
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