A Mentalist Look at Gaussian Clock Arithmetic
The present paper takes as its starting point the most common metaphors used in natural language and the thought system behind it to approach the number sequence in a spatial and temporal context. The latter context being less dependent on completely external causal triggering, its cyclical perspective on number will be adopted as the cognitively more realistic option and presented in the well-known format of a Gaussian system of arithmetic commonly called clock arithmetic. The duodecimality that is typical of analog clocks will be argued to provide an optimal cognitive base, while a hexadic clock is argued to be the cognitive minimum. On the basis of naturalness considerations formulated in terms of degrees of symmetry, the geometrical patterns on multiplication clocks turn out to show relief and different degrees of symmetry and homogeneity depending on the choice of base. It is the homogeneity restriction, to be worked out below, which is the novelty on the mathematical side. On the basis of such considerations, base 10, the decimal system, can be shown to be a less symmetrical arrangement than base 12, notwithstanding its success thanks to the morphology of the human hands.