These conclusions are contradicted by (Gottlieb 1996) (Gottlieb 2001) based on an analysis of peak velocity data. Their commentary (Jaric and Latash 2001) on (Gottlieb 2001), makes three arguments. Under Methodology, they argue that because of the way I performed my experiments, I cannot draw conclusions about the EP hypotheses. Under Statistics they argue that in any event, my data support the EP predictions better than they support my own. Under Logic they argue that since I only presented data on one of the four variables they had measured, their other findings are unchallenged and correct. Except as examples of chutzpa, those arguments are without merit. Had their commentary gone through any sort of knowledgeable review process, it is hard to imagine them surviving.

The effects of load expectation will depend upon how the central command is adapted when changes in external load are known. The two versions of the EP hypotheses offer at least three options. The original Feldman model did not change the central commands for different loads. It is this version that (Jaric et al. 1999) use when they say that load expectation will not affect peak velocity. A more recent version (St-Onge et al. 1997) suggests that the slope of the R command is reduced when a heavier load is expected. Such a change would seem to predict that an unexpectedly heavier load would be moved more quickly than it would have if the load were expected. That is because the surprised mover would use a more steeply rising R and therefore accelerate more quickly. Increasing the slope of R is how speed is intentionally increased. This prediction contradicts common experience and is so silly, it is unsurprising that it is not pursued by (Jaric et al. 1999). Changes in the slope of R also imply changes in the rate of rise of the agonist EMG. That is in conflict with published data on the effects of different loads (Gottlieb et al. 1989; Gottlieb 1996) that show that the rate of rise of the agonist burst is insensitive to the size of the load.

The Latash version of the EP hypothesis prolongs the rise of R (but does not change its slope) for larger expected loads. If an increased load is unexpected, these changes cannot be made and the movement may be slightly slower, although (Jaric et al. 1999) state that the predictions of the two EP hypotheses are "qualitatively similar" and Table 1 is equivocal.

The central commands for the torque control model change the duration of agonist excitation and the latency of the antagonist burst with the size of the load (Gottlieb et al. 1989) which, at a qualitative level, have the same effect as the changes proposed by Latash. At a quantitative level however, (Jaric et al. 1999) tell us that EP models predict small to negligible effects while the torque control model predicts substantial effects. Since the predictions based upon the EP hypotheses are made by one of their principal advocates, it would serve little purpose for me to quarrel with them.

So how big a change in peak velocity will errors in load expectation produce? How big is a dog? The second question is silly unless you have a particular dog in mind. The first question is just as silly unless one believes that all expectation errors produce kinematic effects of equal size. The effects of expectation error will depend on the size of the discrepancy between the actual and the expected load and on the actual load itself. So any answer to such a question is necessarily dependent upon either a specific situation or is computed from a data set. If the latter, we can discuss the mean effect, the confidence limits and the extreme values.

The Latash version predicts peak velocity with an unexpectedly high load will be lower than if the load was expected, and "the difference may be expected to be about 10%." This numerical value appears to be an act of pure imagination since its data source is unstated. I interpreted the number not as a mean but as an upper bound since they were equally happy with 0%. However, from the "statistical" analysis in (Jaric and Latash 2001), that assumption may be false.

The torque control model predicts a lower peak velocity, of "about 30%-50%" but that is not my prediction. Those numbers were chosen by (Jaric et al. 1999) from the largest effects on peak velocity of known changes in inertial load (Gottlieb et al. 1989). In that experiment, weights were added to the end of the manipulandum, the largest of which increased its moment of inertia by about a factor of ten. Hence such data have nothing to do with errors in expectation. However, had they looked at (Gottlieb 1996) where unexpected loads were applied by a torque motor, they would have found that within that data set, the largest expectation effect was to slow a movement by 38% or speed it up by 43%. So, 30%-50% is not an unreasonable description of the range of effects found in my experiments but it is an absurd characterization of their mean. It is not "about" 30-50% although it can be "as much as" that when the error in expectation is greatest. This is a rather important point when it comes to statistical hypothesis testing.

According to (Jaric and Latash 2001), I got larger effects than they did because my subjects "were likely to generate corrections at a rather short delay" whereas they are confident that their subjects did not. They correctly (if selectively) note that my heaviest loads extended movement times to 500 ms with peak velocity occurring around 250 ms. That is probably long enough for a central correction but not proof of one. But they ignore that for lightly loaded movements, peak velocity was reached in 90-150 ms, an interval that is too short to be changed by a sensory triggered central reaction. Speculation about a change in the central command in response to sensory feedback is easy, but there is no evidence of it and its reasonableness for the faster movements is doubtful.

And if a correction had occurred, what kind of a correction might it have been? I would expect that if an unexpectedly heavy load slowed a subject, he would "correct" by contracting the agonist muscle more strongly in order to speed up. However, according to (Jaric and Latash 2001), my subjects must have "corrected" for a heavier than expected load by slowing down even more and for a lighter than expected load by further speeding up since that is what our data show happened to the movements. It is not merely implausible, it is a remarkable proposition from an advocate of the stretch reflex based equilibrium point hypothesis.

(Jaric and Latash 2001) go on to suggest that "if one ignores the first point related to the methodological problems of Gottlieb's study, his data are better statistically compatible with the second [Latash’s about 10%] version of the equilibrium-point hypothesis than with torque-control predictions." This conclusion is based upon a curious statistical analysis. It is, in brief, that 17±9% includes +10% but not +30% while —19±5%, although it does not include —10%, also does not include —30%. This "analysis" appears to treat 10% and 30% as mean values so that statistical arguments about them can be made. But as we noted above, their 30% prediction is based upon the extreme values of a data set (not withstanding the fact that it is the wrong data set). The fact that 95% confidence limits do not include the extrema does not support the conclusion that "about 10%" is compatible with my data, and is also compatible with their own.

(Jaric and Latash 2001) originally found me wrong in only two predictions. I got distance and symmetry right. Now it appears I am wrong about three. They lament "Unfortunately, Gottlieb in his paper does not present findings on movement time and symmetry ratio." Their implication seems to be that since I did not quarrel with their predictions about movement time and symmetry, I accepted them. I do not. I have little doubt that movement time, which tends to vary inversely with peak velocity (as in their Table 1), would lead to the same conclusions. Were there some doubt about the peak velocity data, there might be a reason to repeat the analysis for movement time but there is none. I have never taken a position on symmetry for these experiments and see no reason why they are entitled to give me one, just so they can argue that it is wrong. Movement symmetry depends upon the nonlinear, time-varying viscoelastic properties of the muscle (Jaric et al. 1998). This is such a strong factor and we have such a poor quantitative characterization of those properties that symmetry cannot be a strong basis for arguments about control theories. In any event, if the EP hypotheses are incompatible with the peak velocity data, arguing that they are not wrong about everything will not save them.

I am also accused of misrepresenting figures in (Latash 1994), (Gottlieb 1994) and (Gottlieb 1996). Those figures were cited simply show that unexpected loads have a visibly larger effect on movement speed than do the same loads when expected. (Some comparisons must be made on graphs left-to-right rather than within a single graph.) And the signs of the effects are all consistent with the signs of the expectation errors. That is in contradiction to the 0% claim of (Jaric et al. 1999) which did not mention these papers, even thought they described similar experiments. The sizes of some of the effects are admittedly small but the unexpected load changes in them were also small. Both sets of experiments for the 1994 papers were done on the same apparatus in my lab. The subsequent experiments published in 1996 were done on an improved and more powerful apparatus.

As for the suggestion that more subjects with small load changes is the way to go (Jaric and Latash 2001), I predict that should this be done, they will succeed in finding that small expectation errors have small effects. Until they come up with better quantitative predictions than "about 10%," they will be able to draw any conclusion from this that they like.

In both of their papers, Jaric et. al. describe my torque control model as inconsistent. Considering the source, such vague and gratuitous criticism is like being called ugly by a frog.

I stand by my statistical analysis (Gottlieb 2001) and conclusions drawn therefrom; Unexpected changes in inertial load have larger effects upon peak movement velocity than are compatible with the EP hypotheses. One cannot prove a hypothesis by showing that it is right some of the time but one can falsify a hypothesis by showing that it is wrong some of the time. The predictions of the EP hypotheses about the effects of unexpected load on peak velocity are not mine, they are those of the theory's advocates. And they are unambiguously wrong.

They did agree to publish the URL to this document. It is an expanded version of the rejected reply.