Fitts law, one of the rare quantitative relations in psychology, describes the time it takes for a human being to aim at and hit a target of a given size, starting from a given remote position. We provide here a new interpretation of this law, not invoking a discretization of space and time as in the original information theory representation of Fitts, but involving a simple restrained random walk on a continuum, in space and time. We not only predict that the pointing time is proportional to the logarithm of the starting distance relative to the target size (which is Fitts law), but also describe the complete probability of presence of the pointer in its route to destination. In particular, we quantify the pointer large time overlapping efficiency with the target from the comparison of a new length-scale intrinsic to the motion, with the target size.
La loi de Fitts, l’une des rares relations quantitatives en psychologie, décrit le temps nécessaire à un être humain pour viser et atteindre une cible d’une taille donnée, à partir d’une position éloignée donnée. Nous proposons ici une nouvelle interprétation de cette loi, qui ne fait pas appel à une discrétisation de l’espace et du temps comme dans la représentation originale de Fitts invoquant une théorie de l’information, mais qui implique une simple marche aléatoire restreinte sur un continuum, dans l’espace et dans le temps. Nous ne nous contentons pas de prédire que le temps de pointage est proportionnel au logarithme de la distance de départ par rapport à la taille de la cible (ce qui est la loi de Fitts), mais nous décrivons également probabilité de présence complète du pointeur sur son trajet jusqu’à la destination. En particulier, nous quantifions l’efficacité de la superposition du pointeur avec la cible à partir de la comparaison d’une nouvelle échelle de longueur intrinsèque au mouvement, avec la taille de la cible.
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Emmanuel Villermaux 1
CC-BY 4.0
@article{CRMECA_2024__352_G1_135_0,
author = {Emmanuel Villermaux},
title = {Fitts {Law} as a {Restrained} {Random} {Walk}},
journal = {Comptes Rendus. M\'ecanique},
pages = {135--142},
publisher = {Acad\'emie des sciences, Paris},
volume = {352},
year = {2024},
doi = {10.5802/crmeca.250},
language = {en},
}
Emmanuel Villermaux. Fitts Law as a Restrained Random Walk. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 135-142. doi : 10.5802/crmeca.250. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.250/
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