The Entropy of a Rapid Aimed Movement: Fitts’ Index of Difficulty versus Shannon’s Entropy

Abstract

A thought experiment is proposed that reveals a difference between Fitts’ index of difficulty and Shannon’s entropy, in the quantification of the information content of a series of rapid aimed movements. This implies that the contemporary Shannon formulation of the index of difficulty is similar to, but not identical to, entropy. Preliminary work is reported toward developing a model that resolves the problem. Starting from first principles (information theory), a formulation for the entropy of a Fitts’ law style rapid aimed movement is derived, that is similar in form to the traditional formulation. Empirical data from Fitts’ 1954 paper are analysed, demonstrating that the new model fits empirical data as well as the current standard approach. The novel formulation is promising because it accurately describes human movement data, while also being derived from first principles (using information theory), thus providing insight into the underlying cause of Fitts’ law.