# Controlled variables vs. side-effects

**URL:** <http://discourse.iapct.org/t/controlled-variables-vs-side-effects/3050>\
**Category:** CSG1995\
**Created:** [May 27, 1995, 5:49pm UTC](http://discourse.iapct.org/t/controlled-variables-vs-side-effects/3050 "1995-05-27T17:49:36Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![William\_T\_Powers4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/977dab/32.png) [@William\_T\_Powers4](http://discourse.iapct.org/u/William_T_Powers4)\
**Post date:** [May 27, 1995, 5:49pm UTC](http://discourse.iapct.org/t/controlled-variables-vs-side-effects/3050/1 "1995-05-27T17:49:36Z")

</div>

[From Bill Powers (950527.0950 MDT)]

Just got back from seeing our daughter Barbara off in the start of the  
Iron Horse bike race, Durango to Silverton. The length is 45 miles, the  
total climb over two main passes is 5500 feet (the highest pass, Molas,  
is about 11,000 feet). Last year (her first, at age 35) she did it in  
4:20; this year she hopes for under 4:00. The pro winning time last year  
was 2:10. She should be about halfway right now, starting the four-mile  
climb to Coal Bank Pass (2500 foot climb to over 10,000 ft). Go Bara!

> **···**
>
> # ----------------------------------------------------------------------- Rick Marken, Bruce Abbott (continuing) --
> 
> # When you push on a control system, it pushes back.
> 
> ------------------------------  
> RE: trajectories vs. system organization
> 
> In a great deal of modern behavioral research, trajectories of movement  
> are examined in the hope of finding invariants that will reveal secrets  
> of behavior. This approach ties in with system models that compute  
> inverse kinematics and dynamics and use motor programs to produce  
> actions open-loop. These models assume that the path followed by a limb  
> or the whole body is specified in advance in terms of end-positions and  
> derivatives during the transition, so the path that is followed reflects  
> the computations that are going on inside the system.
> 
> It is this orientation that explains papers like
> 
> Atkeson, C. G. and Hollerback, J.M.(1985); Kinematic features of  
> unrestrained vertical arm movements. The Journal of Neuroscience \_5\_,  
> #9, 2318-2330.
> 
> In the described experiments, subjects move a hand in the vertical plane  
> at various prescribed speeds from a starting point to variously located  
> targets, and the positions are recorded as videos of the positions of  
> illuminated targets fastened to various parts of the arm and hand.
> 
> The authors constructed a tangential-velocity vs time profile of the  
> wrist movement for various speeds, directions, and distances of  
> movement. They normalized the profiles to a fixed magnitude, then to a  
> fixed duration, and found that the curves then had very nearly the same  
> shape. Using a "similarity" calculation, they quantified the measures of  
> similarity.
> 
> They were then able to compare these normalized tangential velocity  
> profiles across various directions and amounts of movement and show that  
> the treated profiles were very close to the same. They conclude:
> 
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Taken together, shape invariance for path and tangential velocity  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;profile indicates that subjects execute only one form of trajectory  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;between any two targets when not instructed to do otherwise. The  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;only changes in trajectory are simple scaling operations to  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;accomodate different speeds. Furthermore, subjects use the same  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;tangential velocity profile shape to make radically different  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;movements, even when the shapes of the paths are not the same in  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;extrinsic coordinates. Different subjects use the same tangential  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;velocity profile shape.
> 
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;... this would be consistent with a simplifying strategy for joint  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;torque formation by separation of gravity torques from dynamic  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;torques and a uniform scaling of the tangential velocity profile  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;... (p. 2325)
> 
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;... if the motor controller has the ability to fashion correct  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;torques for one movement, why does it not use this same ability for  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;all subsequent movements rather than utilize the dynamic scaling  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;properties? Among the possibilities we are considering, the first  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is a generalized motor tape where only one movement between points  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;must be known if the dynanmic components in equation 6 are stored  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;separately....A second possibility is a modification of tabular  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;approaches [ref] where the dimensionality and parameter adjustment  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;problem could be reduced by separate tables for the four components  
> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in equation 6. (p. 2326)
> 
> This paper was sent to me by Greg Williams as a source of data about  
> actual hand movements, for comparison with the hand movements generated  
> by Little Man v. 2, the version using actual arm dynamics for the  
> external part of the model. The model's hand movements were, as Greg  
> will attest, quite close to those shown in this paper, being slightly  
> curved lines connecting the end-points. Forward and reverse movements  
> followed somewhat different paths, and by adjustment of model parameters  
> this difference, too, could be reproduced.
> 
> What is interesting is that the fit between the Little Man and the real  
> data was found without considering tangential velocity profiles or doing  
> any scaling or normalization. In other words, the invariances noted by  
> the authors were simply side-effects of the operation of the control  
> systems of the arm interacting with the dynamics of the physical arm. In  
> the Little Man there is no trajectory planning, no storage of movement  
> parameters, no table-lookup facility, no computation of invariant  
> velocity profiles. The observed behavior is simply a reflection of the  
> organization of the control system and the physical plant.
> 
> The path which Atkeson, Hollerbach (and many others at MIT and  
> elsewhere) are treading is a blind alley, because no matter how  
> carefully the observations are made and the invariances are calculated,  
> there will be no hint of the control-system organization, the SIMPLE  
> control-system organization, that (I claim) is actually creating the  
> observed trajectories. No doubt a sufficiently complex trajectory-  
> control model, with just the right tables of coefficients and velocity  
> profiles, would ultimately be able to match the behavior. But this line  
> of investigation, with its underlying assumptions, will never lead to  
> the far simpler and anatomically correct PCT model.
> 
> In terms of the current discussion on the net, the observations made by  
> the authors were interesting as checks on the model, but were actually  
> irrelevant to what the control systems were doing. The control systems  
> (the first two levels of the Little Man model) controlled only three  
> kinds of variables that underlay the perceptual signals: angular  
> positions, angular velocities, and angular accelerations. They received  
> no information about wrist position in laboratory space. They contained  
> no provision for computing tangential velocities, or for computing  
> positions of points on the physical arm in space, or for computing  
> space-time invariants. The behavior of the control systems, in other  
> words, took place in a proprioceptive perceptual space that no outside  
> observer could see. In order to translate from this perceptual space  
> into variables that were observable, the computer program generated the  
> resulting arm positions and plotted them in a form suitable for visual  
> inspection. So a side-effect of the actual control process was presented  
> for comparison with a corresponding side-effect of the real control  
> process, as visible to an outside observer.
> 
> The approach of Atkeson and Hollerbach appears in many guises. We have  
> already talked about the apparent scaling and normalization of  
> trajectories seen when two hands move rapidly and simultaneously to  
> targets at different distances. In operant conditioning experiments, we  
> have seen how the control of reinforcement by behavior is obscured by  
> the fact that variations in behavior tend to stabilize reinforcement  
> rates, thus making reinforcement rate appear to be the independent  
> variable.
> 
> We have also seen a few -- a very few, so far -- studies in which the  
> PCT orientation was used, Srinivasan's being the most recent. What is  
> the difference? I think the difference is in whether the emphasis is on  
> seeing the behavior from the behaving systems's point of view, as best  
> we can imagine it, and seeing it strictly from the human observer's  
> point of view.
> 
> > From the human observer's point of view, it seems that we must account
> 
> for the detailed movements and physical interactions that are seen to  
> occur. This leads to trying to find invariances or striking mathematical  
> regularities of some sort in the observed behaviors. It leads to  
> imagining an internal system that is producing explicitly what we are  
> observing; if we observe a trajectory, there must be some generator that  
> is specifically calculating that trajectory.
> 
> But from the behaving system's point of view, we can consider only the  
> information that is available to the behaving system; we must look for  
> our explanations there. The trajectories of movement that result from  
> the system's operation are basically side-effects; they are not planned  
> and they are constant only in a constant environment. Furthermore, they  
> are unknown to the behaving system and play no part in the production of  
> behavior. We can deduce from the model of the behaving system what the  
> observable side-effects would be in a given environment, and so can  
> compare those side-effects with our external observations of the  
> behavior. But our explanation of the behavior is not based on those  
> side-effects.
> 
> Most important, when we simply describe behavior as a sequence of  
> physical happenings and relationships, we have no way of knowing whether  
> we are describing controlled variables or side-effects. When we see a  
> fly landing on a ceiling, it is perfectly possible that NOT A SINGLE  
> ASPECT OF WHAT WE SEE is perceived and controlled by the fly. When we  
> see the fly extending its legs just prior to landing, the fly may have  
> no perception of the configuration of its legs; to the fly, all that is  
> controlled may be two or three joint-angle signals, not even identified  
> by the fly as representing joint angle. When we see the wings stop  
> flapping, to the fly all that may be controlled is a sensation of  
> vibration. When we see the fly's body making a steep angle with the  
> surface, the fly may simply be experiencing a visual signal indicating,  
> as Rick guessed, a gradient of illumination or texture. Not one of the  
> variables we are observing may ever appear in the ultimate model of the  
> fly's internal organization, just as in the Little Man the actual arm  
> configuration and hand position never appear in the model of the first  
> two (kinesthetic) levels of control. Once we have the right model, we  
> can always compute how its operation will appear to an observer who is  
> focusing on various side-effects of the actions. But the model itself  
> says nothing about those appearances, and makes no use of them.  
> -----------------------------------------------------------------------  
> Best to all,
> 
> Bill P.