Abstract
Fundamental questions in physics can be asked anytime, anywhere. Often they arise at the interface of physics, mathematics, and philosophy – where scrapping conversation turns into testable hypothesis. This essay explores the idea that the primitive act of counting "1, 2, 3 ..." makes an implicit assumption that ultimately causes some of the challenges faced in quantum mechanics today. A hypothesis for what could be done differently is developed during a humorous, yet serious, conversation among a physics student, a math student, an ex-philosophy student, and a city councilor. Beginning with a physics student's ill-fated attempt at bargaining for a lower price, the essay touches upon beauty in numbers and nature; repetition, inversion, and algebraic closure in mathematics; and observability in quantum mechanics. A surprising property of the complex numbers will be shown to indicate incompleteness or inadequacy in regard to resolving certain questions in quantum mechanics. A new kind of number and arithmetic may be needed, and a proposal for such is sketched using the E8 lattice.
Jens Koeplinger