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

Abstract

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.

Advanced modeling of selection and steering data: beyond Fitts' law

“…This argumentation of MacKenzie is contested in Soukoreff et al (2011) because "the movement distance and target width are simply not equivalent to average power levels". In order to address this remark, it may be worthwhile to cite a paper (Smith, 1971) in which the information capacity of amplitude-constrained Gaussian channels has been determined.…”

“…This trend of comparing not only the task conditions but also other interaction conditions was adopted by several researchers in the HCI field, who use Fitts' law to compare input devices or interaction techniques with each other (Card et al, 1987;MacKenzie et al, 1991;Guiard et al, 1999;Balakrishnan, 2004;Isokoski, 2006). While the information-theoretical basis of Fitts' law has frequently been challenged (Plamondon and Alimi, 1997;Soukoreff et al, 2011), even leading to the statement that "currently no universally accepted explanation of Fitts' law exists" (Soukoreff and MacKenzie, 2004), the ability of Fitts' law to describe experimental data remains widely accepted and is seen by many as sufficient grounds for not considering alternative models. In this paper, we argue against this somewhat dogmatic stance by exploring alternative models and comparing them to the existing Fitts' model in a systematic way.…”

Contrasting contributions of movement onset and duration to self‐evaluation of sensorimotor timing performance

“…The stimulus was a white circle, whose size varied as a function of its distance from the starting point (radius 0.5, 1.5 or 2.5 cm). The size of the target was adjusted to account for the scaling of the spatial end‐point variability with movement amplitude (Fitts, 1954; Soukoreff et al, 2011). The sizes of the targets presented at 20 and 35 cm from the participant were scaled according to modified Fitts' formula, where index of difficulty equals the binary logarithm of one plus quotient of target distance and size.…”

Target Expansion Lens

“…1 defines the task's Index of Difficulty (ID). The ID measures in bits the information transmitted by the user to the system when pointing at a target [19]. [12,21] describes the optimization process of the sub-movements that constitute a pointing movement.…”