I don’t recall doing that intentionally. Perhaps what you are seeing is a side effect of my failure to see any criticism in your posts that explains why my argument does not hold.

Again, you are coming to conclusions about my intentions (what I care about) based only on my overt behavior. Actually, I care very much about the validity of my arguments and I am willing to change my mind if I am shown that my arguments are incorrect.

Actually, that paper was accepted for publication faster than almost any paper I’ve written, and in a journal where much of the power law research has been published.

The core of you claim was that there is a necessary mathematical relationship between velocity and curvature and the “true” correlation coefficient between them is exactly 1/3. It is actually just the same it you would claim that there is a mathematical relationship between the width and height of a rectangle and true correlation coefficient between them is 1. (i.e. all rectangles are in reality squares even if their width and height does not seem same.)

No wonder you think my argument is BS. Your description of my “claim” is almost completely incorrect.

I do “claim”, as did Maoz et al, that there is a mathematical relationship between velocity (V) and curvature (C), the linear version of which is as follows:

log V = - 1/3* log C + 1/3 * log A

where A is affine velocity. In this equation -1/3 is the *true coefficient* of the power relationship between C and V, NOT the true correlation.

What this equation shows is that when you do a regression between log C and log V to determine the coefficient of the power relationship between C and V, using the regression equation:

log V = log k + beta* log C

you are leaving out one of the variables, A, that is involved in the mathematical relationship between C and V.

What Moaz et al and Marken & Shaffer (2017) showed is that when you leave variable A out of the regression equation, the observed value of the coefficient, beta, will differ from its true value, -1/3, by an amount proportional to the covariance between log C and the omitted variable, log A. This covariance will be different for different movement patterns but, as Maoz et al note, it will generally be small. So in a simple regression where C is regressed on V, the observed value of beta will generally not differ much from -1/3.

This analysis is not at all the same as if we had claimed that “there is a mathematical relationship between the width and height of a rectangle”. The proper analogy is this:

Using simple regression analysis of the form:

log A = log k + beta * log H

where A is area and H is height, researchers have found that A is a linear function of H sine beta will be approximately 1. The Maoz et al come along and point out that there is a mathematical relationship between A and H that includes another variable, W (width), so that the true relationship between log A and log H is

log A = log H + log W

So the true coefficient of H is 1.0 exactly and it is only approximately 1.0 when log W is left out of the regression analysis. This is because the beta calculated for log H depends on the covariance of log H and the omitted variable, log W.

You have said that power law is a statistical artifact and that means that it is produced as a result of methods which do not fit to reality – which are arbitrary.

The choice of analysis methods has nothing to do with whether they fit reality. Rather, they are chosen as the means of getting results that are presumed to give the best reflection of what constitutes the reality on the other side of our senses. The results of the use a particular analysis are artefactual if those results were “forced” by the way the data was collected or selected for analysis. The power law is a statistical artifact because the data is included in the analysis only after filtering and only a subset (V, C) of the variables (V, C, and A) that are known to be mathematically related are included in the analysis.

Do not blame Maoz et al, they do not make such problematic inferences as you did.

I didn’t blame Maoz et al for anything. I praised their analysis.

Your analysis only shows that if you use your very arbitrary and against the rules method of adding the velocity and curvature twice to the correlation analysis then you get always close to 1/3 correlation.

OK, it looks like that’s your story and your stickin’ to it. But I would like to know where you think the power law fits into PCT. You know where I think it fits: It’s an example of an irrelevant side effect of controlling. Where do you think it fits in?