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.
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Notes
While this is not a literal model of how the brain implements these control systems (it would surely require a hierarchy of such systems, for example), it is a useful description of the mechanism of control at the “computational level” (Marr 2010).
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Marken, R.S., Shaffer, D.M. The power law of movement: an example of a behavioral illusion. Exp Brain Res 235, 1835–1842 (2017). https://doi.org/10.1007/s00221-017-4939-y
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DOI: https://doi.org/10.1007/s00221-017-4939-y