Eh? It’s you who has switched from calling it an irrelevant side effect, to a relevant side effect…
No, I have continued to call it an irrelevant side effect since the power law is clearly irrelevant to the process of movement production. Power law researchers have been studying the power law because they think it is relevant to movement production when it actually is not.
I did note that you could also consider it a relevant side effect since a side effect of the power law has been to deceive researchers into thinking it was relevant to understanding the process of movement production. So it is relevant to the controlling done by the researchers who have been studying the power law thinking it was relevant to understanding movement production.
I thought (hoped, actually) you were agreeing with my original post because you understood that the power law was an irrelevant side effect of the controlling involved in movement production but a relevant side effect with respect to the controlling done by the researchers studying the power law.
Is that what you were agreeing with?
Since you haven’t answered I’ll assume the answer is “no”. Which is too bad. I guess I’m still a minority of one.
Sorry, I’m a bit slow on the replies. I think the choice of the definition of ‘irrelevant’ in this example is about subjective priorities and I can therefore see both sides.
Of course you do. But I would be interested in why you think the definition of “irrelevant” (irrelevant side effects, I assume) is about subjective priorities. And why, therefore, it allows you to see both sides.
A lovely suspension bridge of words. Or NIGYYSOB spider web.
Priorities which are not subjective are presumably objective priorities. An evolutionary basis for the distinction is stated e.g.at Bill Powers (2004.05.23.2026 NMDT) in the thread called ‘Evangelical Control Theory’. Intersubjective agreement is widely regarded as another basis (discussion), at least when the agreeing parties are engaged in a science.
‘Priorities’ are a function of reference values for CVs and loop gain in their control; if you want a lot of perception p it’s a higher priority, and if you want it a lot, i.e. will make efforts to overcome strong disturbances, it’s a higher priority.
Seeing both sides meets F. Scott Fitzgerald’s “test of a first-rate intelligence … the ability to hold two opposed ideas in mind at the same time and still retain the ability to function.” It can be tolerance for cognitive dissonance while working out an internal conflict. It can occur while imagining perceptions from another’s point of view. That is a prerequisite for the Test for Controlled Variables (viz. the subject’s point of view alongside that of the experimenter).
In this exchange, perceptions of ‘movement scientists’ are imagined, with some evidential basis, but not tested.
I’m afraid this doesn’t help me understand why Warren said that the definition of “irrelevant side effects" is about subjective priorities.
The “evidential basis” for what I imagine to be the views of movement scientists (and hangers on like Eetu, Martin, Warren and you) is the extremely strong negative response to the disturbance of my analysis. You guys are definitely controlling for the power law not being an irrelevant side effect of control.
So if the ability to see both sides meets Fitzgerald’s test of a first-rate intelligence, movement scientists don’t pass the test any better than I do.
I doubt you have any evidence for that. All Eetu and I have ever been controlling for (I can’t speak for Warren) is the correct usage of standard mathematics. If your power-law theory had used correct mathematics, I doubt there would ever have been an issue.
Here is the evidence:
My mathematical analysis of the power law is exactly the same as that of Maoz et al. You have only used the “bad math” argument against me, not Maoz et al, which means that their math was not a disturbance to what you are controlling for.
The only difference between my analysis and that of Maoz et al was the conclusion. This is pretty strong evidence that what you really don’t like is my conclusion – that the power law is an irrelevant side effect of control – not my math – that log V = -1/3 log C + 1/3 log D, which is exactly the same as the Maoz math
So it’s pretty clear to me that you are controlling for the power law NOT being an irrelevant side effect of control. What you (and your acolytes) think it is is beyond me.
Could you send a link to the Maoz et al paper? I can’t find it in google scholar. I remember looking at it a while back and not thinking it relevant to the discussion, so I’d like to have another look at it.
I didn’t see a link or an attachment in your reply, Rick, but a search on Maoz in our Discourse interface turned up this Dropbox link to “Noise and the two-thirds power law” in an August 1 post of yours.
It was under “Here”
Grazie mille.
Ah! Reading too fast again. But no harm, and what’s a little redundancy among friends.
You should stick with PCT on this - find controlled variables. The phenomenon is that people slow down in curves in most “natural” movement (“natural” meaning not too slow or too fast). The phenomenon is VERY RELEVANT because any model that purports to explain movement needs to also slow down in curves just like the people do, or not slow down, just like the people do.
The relationship between speed and curvature is either controlled or not, so the procedure should be directly disturbing this relationship and looking for the response from the participants: if they maintain it stable, it might be controlled. If it is not controlled, go for the next hypothesis of what is controlled and repeat the procedure.
Learn the basics of PCT, do some experiments, build a model, then you can understand what is relevant and what is irrelevant.
In principle, if you disturb a side effect there will be no resistance to the disturbance, yes.
How to disturb the speed of movement along a curved path without disturbing control of movement and/or control of curving? I don’t see an obvious way to tease these apart.
That’s assuming that movement and curving are CVs and speed is not.
Or is speed controlled, subject to disturbance due to control of curvature?
Yeah, it is tricky, it took me a few years to get to the bottom of it.
If the relationship between speed and curvature is the controlled variable, then this relationship should stay the same even when you change the one of the variables. Curvature is a spatial variable, pure geometry. Take any random path, you can change the speed as you wish - only if you move VERY SLOWLY. You can draw the letter “O” very, very slowly with a constant speed of 1mm/s at all times. You can draw ANY shape at a constant speed of 1 mm/s.
In that case, the relationship is NO CORRELATION. Constant speed regardless of curvature. I think we can control that even with a direct disturbance like a weight on your hand. Maybe up to a pound or two of mass in the hand.
In the low ranges of speed, we could even go faster in curves and slower in flat parts. Imagine driving a car with 0.1 meter/s in the straight parts and like 1 meter/s in the curves parts. We can change the speed as we wish - even if there is wind, and slopes in the road.
If we are going faster, on average, we have to slow down in curves, and we cannot maintain the same curvature (the same geometric path) with the same relationship to speed as before. We have to slow down in curves to stay on the path. This is what happens in the “natural” movement.
One way to test for controlled variables is to guess at what they are and then put them in a model and see how well the model fits the data. I was able to demonstrate how this is done using object interception data collected by Dennis Shaffer and I described the results of that testing in this paper. The main result was that a model that controlled vertical optical velocity fit the data somewhat better than one that controlled vertical optical acceleration. I used this approach to testing for controlled variables to model movement behavior that follows the power law.
A control model that successfully fits curved movement data – including yours --will show the apparent “slowing down through curves” power relationship between velocity and curvature. I describe a control model that fits power-law-conforming movement data in the behavioral illusions paper. That model perfectly accounts for cursor movements and the mouse movements that produced them. In both cases, the movement appears to slow down through curves, although there was nothing in the model that was designed to produce that result. The apparent slowing down though curves is a side-effect of control that results from the mathematical relationship between velocity, curvature and affine velocity.
Actually, I did all those things. But thanks for the tip.
That was good! Also not a formal TCV, but ok. It did not explain why do people slow down in curves in other types of movement, like handwriting or drawing ellipses, where the power law was initially found.
Apparent slowing down? I had real slowing down in my experiments. Raw speed and curvature plots over time show an obvious correlation, not merely an apparent correlation.
If you had only “apparent” slowing down - that means you had a statistical artifact, and there was no need to make a model to explain the findings - the statistics explain it all.
If the slowing down was real, then the model might explain it as a side effect of controlling the cursor-target distance. But you had some VERY slow movements, didn’t you?
The cursor-target distance control model produces much bigger ellipses than people in the same task, so it does NOT account for behavior or the power law in this task.
