Information processing and Fechner's problem as a choice of arithmetic

TL;DR

This paper explores how Fechner's law and its extensions can be viewed as different forms of arithmetic, suggesting that sensation and stimulus worlds can be described by generalized mathematical calculus.

Contribution

It introduces a novel perspective that interprets Fechner's law as a choice of arithmetic, linking sensory perception to alternative mathematical frameworks.

Findings

Fechner's law corresponds to a specific arithmetic choice.

Generalized arithmetic can model various sensory phenomena.

The approach unifies stimulus and sensation descriptions through mathematical calculus.

Abstract

Fechner's law and its modern generalizations can be regarded as manifestations of alternative forms of arithmetic, coexisting at stimulus and sensation levels. The world of sensations may be thus described by a generalization of the standard mathematical calculus.