02/04 - Olivier Rioul
A mathematical analysis of Fitts' law
Fitts' law is a well-known empirical regularity which predicts the average movement time T it takes people, under time pressure, to reach a target of width W located at distance D with some pointer. This model has proven useful in several fields of applied psychology such as Human-Computer Interaction and Ergonomics. Whether Fitts' law is a logarithmic law or a power law has remained unclear so far: In two widely cited papers, Meyer & al. have claimed that the power model they derived from their celebrated stochastic optimized sub-movement theory encompasses the logarithmic model as a limiting case, when the number of submovements grows large. We review the Meyer & al. sub-movement theory and show that this claim is questionable mathematically. Our analysis reveals that the traditional theory implies in fact a quasi-logarithmic, rather than quasi-power model, the two models not being equivalent. Incidentally, the original logarithmic model was derived by Fitts (1954) in analogy with Shannon's information capacity formula (1948); we conclude this talk by discussing recent advances on a sub-movement model that justifies the information theoretic approach. At any rate, awareness that the two classes of candidate mathematical descriptions of Fitts' law are not equivalent should stimulate experimental research in the field.
Joint work with Yves Guiard (CNRS LTCI, France). This work was presented at the 2012 Meeting of the European Mathematical Psychology Group (see also , ).
Olivier Rioul (PhD, HDR) is professor at Telecom ParisTech and Ecole Polytechnique, France. His research interests  are in applied mathematics and include various, sometimes unconventional, applications of information theory such as in Bayesian dynamic estimation, hardware security, and experimental psychology. He has been teaching information theory at various French universities for almost twenty years. He has published a textbook  which has become a classical French reference in the field. A Brazilian edition of the book is scheduled to be published by Editora da Unicamp in the future.
 O. Rioul and Y. Guiard, "Power vs. logarithmic model of Fitts' law: A mathematical analysis," Math. Sci. hum. / Mathematics and Social Sciences, No. 199, 2012(3), p. 85-96.
 O. Rioul and Y. Guiard, "The power model of Fitts' law does not encompass the logarithmic model," Electronic Notes in Discrete Mathematics, Elsevier, Vol. 42, June 2013, pp. 65-72.
 O. Rioul, Théorie de l'Information et du Codage, Hermes Science, 2007.