Noise and the two-thirds power law

Uri Maoz*, Elon Portugaly, Tamar Flash, Yair Weiss

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

20 Scopus citations


The two-thirds power law, an empirical law stating an inverse non-linear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant of upper-limb movement. It has also been shown to exist in eyemotion, locomotion and was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed either to smoothness in hand- or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis of signal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying the power-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operating on the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.

Original languageAmerican English
Title of host publicationAdvances in Neural Information Processing Systems 18 - Proceedings of the 2005 Conference
Number of pages8
StatePublished - 2005
Event2005 Annual Conference on Neural Information Processing Systems, NIPS 2005 - Vancouver, BC, Canada
Duration: 5 Dec 20058 Dec 2005

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference2005 Annual Conference on Neural Information Processing Systems, NIPS 2005
CityVancouver, BC


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