Discussion of the speed-curvature Power Law

[rsmarken]

@bnhpct

It is suggested that future posts about it be entered into Discourse as replies to this topic.

Thanks for doing this Bruce. I’ll reply to Eetu’s post here.

@EetuP

RM: Side effects are behavioral illusions when, as in the case of the power law, they are thought to tell you something important about how behavior works.

You have been saying that [the power law] does not require explanation because a) the phenomenon is not really existing; or b) there is a mathematical explanation; or perhaps for some other reason.

I don’t believe that I have ever said that the power law is not an existing (real) phenomenon. It is, indeed, a real phenomenon. I just don’t think it is really a “law” since the observed exponent of the power relationship can vary so much around 1/3. And the observed fit to a power relationship can also vary considerably.

I do think the mathematical relationship between speed and curvature explains why we do (and often don’t) find a power relationship between these variables. But after re-reading what Powers said in his 1978 Psych Review paper about PCT being a paradigm shift that makes many old problems obsolete, I think it’s better to just stop looking for an explanation of the power “law” and start studying movement as a control phenomenon.

@EetuP

But measurements show very convincingly that the phenomenon is real, surprisingly regular, but not at all universal. Because it is not universal, no mathematical explanation can do. Your mathematical explanation is tautological saying that if there is 1/3 power law then there is 1/3 power law. But why there is sometimes other power law and sometimes none?

The mathematical explanation is really a statistical explanation based on an understanding of how multiple regression analysis works and it does explain why sometimes power relationships between speed and curvature and sometimes none. It’s all explained by omitted variable bias (OVB) analysis that we described in our first paper (and that Moaz et al described in theirs). When I have time tonight I will explain why this is the case and also show – by “showing my work” – why my math describing the power between speed, curvature and affine velocity isn’t wrong.

By the way, I am not at all interested in shutting you out of this conversation of this forum; I don’t think you (or any of my other opponents in this argument) are heretics. I just think you are wrong. Actually, I appreciate your efforts to try to convince me that you are right. It helps me improve my arguments. And, who knows, maybe you will eventually convince me that you are right.

Best, Rick