[From Rick Marken (2018.08.17.04:48)]

[From Erling Jorgensen (2018.08.15 2345 EDT)]

RM: The fact that the power law is an illusion can be determined without any

knowledge of statistics.

EJ:Â I like how you insert the word âfactâ? about what is indeed a proposal

still being contested.

RM: I said that this fact “can be determined”. That is a conditional phrase. And it is correct; you can (if you want to) determine that the power law is an illusion without any of the statistical analysis that I provided. The statistical analysis just shows why something close to a power relationship between curvature and velocity is so regularly found using regression analysis.

RM:Â Once you know that, you know that the power law is an unintended side

effect of this controlling.Â

EJ:Â Yes, once you have presumed it as a fact, then you have constructed a

âknowingâ that it must be an unintended side effect.

RM: I did not presume anything as a fact. The “that” in my statement above referred to this statement: . “All you have to know is that movement – the changing positions of the wrist as the arm moves, for example – is a controlled result of action”. In other words, what I said was: once you know that the changing position of the movement is a controlled variable you know that the power law is an unintended side effect of controlling this variable".Â

Â

EJ:Â But there is another way to go about it, the way Bill demonstrated with

his Little Man V2 model.Â He showed that a very simplified control model could

generate what appear to be sophisticated calculations, as a by-product, or

side effect, of the working of the model.

RM: As did we. Marken and Shaffer (2017) found that the movement trajectories produced by the object interception model – movement trajectories that were not created with the aim of producing a power law relationship between velocity and curvature --Â conformed to a power law that was equivalent to that found byÂ Zago et al. (2016) for the movements of fruit flies.

EJ:Â If you read the rest of my post and my previous one, you will know I am

aiming at that very thing.Â I believe I am doing it with a little less hubris.

RM: Hubris?!?!Â

Â

EJ: However, following Bill, any alternate model will still need to generate

behavior that is akin to power-law data, without specifically controlling for

that outcome.

RM: As I noted, we (Dennis and I) have already done that with our control model of object interception. AndÂ power law researchers have already done it with their open-loop model of movement (see Gribble and Ostry, 1996, Table I). It’s easy to use a model to produce movements that follow the power law; it’s a little more interesting toÂ produce such movements in a disturbance-prone environment, as we did in Marken & Shaffer (2018, Figure 1). But it would certainly be great if you would develop a model of movement control and see if it produces a power law as a side effect. (I’ll tell you in advance that it will always produce something close to a power law, the degree of deviation from the power law being proportional to the covariance between the curvature and affine velocity of the movement trajectory).

Best

Rick

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–

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you

have nothing left to take away.â?

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery