Digital Arithmetic in Nature: Continuous-Digit RNS

It has been reported in the literature on computational neuroscience that a rat's uncanny ability to dash back to a home position in the absence of any visual clues (or in total darkness, for that matter) may stem from its distinctive method of position representation. More specifically, it is hypothesized that the rat uses a multimodular method akin to residue number system (RNS), but with continuous residues or digits, to encode position information. After a brief review of the evidence in support of this hypothesis, and how it relates to RNS, we discuss the properties of continuous-digit RNS, and derive results on the dynamic range, representational accuracy and factors affecting the choice of the moduli, which are themselves real numbers. We conclude with suggestions for further research on important open problems concerning the process of selection, or evolutionary refinement, of the set of moduli in such a representation.