Bill Powers wrote:
Hello, all --
Attached is the Vensim sketch for a 4-level model, starting with a
contractile element that generates a force, followed by a velocity control,
a position control, and finally a visual control of the distance between a
cursor and a target. Most of the equations are shown in red.The constants produced by Vensim's optimizer are
Maximum of simulations/optimizations found at:
*delay = 0.00333438
Refdist = 7.92461
Kv = 1.57547
Kr = 6.6916
Kx = 1.1044
Kd = 7.61076
J = 0.0215284
Simulations = 1658
Optimizations = 5
Payoff = -636.836The "payoff" is just a measure of goodness of fit. The RMS error between
the model's output and the real output from an experimental run is about
3.5 units, with the peak-to-peak range of movement being about 350 units.A most interesting result is that the transport lag is only 3 milliseconds.
I believe this is because a second- or third-order system produces a lag
that behaves a great deal like a transport lag, much more so than a
first-order lag (leaky integrator) does. The response to a step input is an
initial acceleration to a maximum upslope, the velocity starting at zero
and only gradually becoming positive. That looks a lot like a shift of the
response in time -- a "reaction time."Of course this probably means we will have to find some other way to
distinguish between transport lags and the double or triple integral type
of lag. Three milliseconds, I wager, is much too short for a loop involving
vision, although we must also consider that the traditional "200
millisecond" lag could well be an effect of multiple integrals in a
hierarchy of systems, and not really a true reaction time at all.Also, the value of J (the moment of inertia about the shoulder joint in
this case) is probably way too low. Using so many parameters for optimizing
is not a good idea; as many as possible ought to be determined by
measurement and not included in the optimization. I have yet to learn how
to do a sensitivity analysis with Vensim, but when I do we can find out
just what the error bars are for each parameter.I haven't heard from anyone yet about purchasing the Pro version of Vensim
or getting a break if no funds are available. Is anyone in this group
working with me, or are you all just smiling and nodding? You have to know
the joke about the comedian in the Chinese theater to get that one.
I'm happy doing my modeling in Excel, since I plan to stay on a Mac (as my
main computer) for some time. If Vensim runs on a Mac then I'd be happy to
get a copy but I don't like paying much for software. It just all seems very
complex and confusing at the moment. I am certainly following your modeling
with _great_ interest and I hope to see a draft of the paper on the
"Adaptation Illusion" very soon (to which I'll be happy to contribute; I'd
also be happy to make an excel version of your model (augmenting mine, I
suppose) so John can see how it works.
Best regards
Rick
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Richard S. Marken, Ph.D.
The RAND Corporation
PO Box 2138
1700 Main Street
Santa Monica, CA 90407-2138
Tel: 310-393-0411 x7971
Fax: 310-451-7018
E-mail: rmarken@rand.org