The Unified Theory of Numbers, the Arithmetic of Space-Time

Abstract

BMJC Biezanek

Imagine that you are walking into town making direct steps towards the centre of town. Then, you remember that you left your umbrella at home and it is going to rain soon. So, although you have already walked 1,267 steps towards town, you bite the bullet, stop, rotate through 180 degrees and start making direct steps back towards your home. However, with respect to walking directly into town, you are now taking inverse steps towards town. As Carl Friedrich Gauss pointed out in para #24 of his 2nd letter to the Royal Society in 1831, calling our numbers positive and negative is very silly, we should rather call them direct and inverse. So, perhaps there is no such number as minus one (take away one), but there really is such a number as inverse-one, the rotational-inverse of direct-one?

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