Marken Richard S, Shaffer Dennis M
, 10459 Holman Ave., Los Angeles, 90024, CA, United States.
Department of Psychology, Ohio State University Mansfield, Mansfield, Ohio, USA.
Exp Brain Res. 2017 Jun;235(6):1835-1842. doi: 10.1007/s00221-017-4939-y. Epub 2017 Mar 15.
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.
生物体产生的曲线运动遵循幂律，即运动速度是运动所经过的曲率程度的幂函数。幂函数的指数接近1/3或2/3，这取决于速度和曲率的测量方式。人们认为这个幂律反映了生物体产生运动时的生物学和/或运动学限制。本文表明，幂律实际上是一种统计假象，它源于将变量之间的相关关系误认为因果关系。幂律意味着曲率会影响运动速度。事实上，幂律是这些变量计算方式的数学结果。曲率影响运动速度的表象被证明是一种“行为错觉”的例子，这种错觉是由于忽视行为目的而产生的。
