title: The power law of movement: an example of a behavioral illusion.
abstract: The curved movements produced by living organisms follow a power law where the velocity of movement is a power function of the degree of curvature through which the movement is made. The exponent of the power function is close to either 1/3 or 2/3 depending on how velocity and curvature are measured. This power law is thought to reflect biological and/or kinematic constraints on how organisms produce movements. The present paper shows that the power law is actually a statistical artifact that results from mistaking a correlational for a causal relationship between variables. The power law implies that curvature influences the velocity of movement. In fact, the power law is a mathematical consequence of the way that these variables are calculated. The appearance that curvature affects the velocity of movement is shown to be an example of a "behavioral illusion" that results from ignoring the purpose of behavior.
authors.affiliation: , 10459 Holman Ave., Los Angeles, 90024, CA, United States. rsmarken@gmail.com.
authors.forename: Richard S
authors.identifier: 0000-0003-4787-4891
authors.initials: RS
authors.lastname: Marken
authors.affiliation: Department of Psychology, Ohio State University Mansfield, Mansfield, Ohio, USA.
authors.forename: Dennis M
authors.initials: DM
authors.lastname: Shaffer
mesh_terms: D001696:Biomechanical Phenomena; D006801:Humans; D008962:Models, Theoretical; D009043:Motor Activity / Q000502:physiology*
keywords: Control theory; Movement control; Purposeful behavior