Hello, Martin --
I'm trying to lay out a way to determine for any given model
whether the way its behaviour is computed is likely to mislead you
as to way the continuous model actually behaves. Looking at the
Nyquist rates, the numerical resolution of the computer, and the
compute-imposed delays is part of ensuring the credibility of the
results.
Do you agree that in my sloppy, seat-of-the-pants, blue-collar empirical
way I have already taken care of ways in which the model can mislead us?
One of the consequences of what I have been saying is that if your
setup allowed you to do it (which it doesn't unless you have access
to the deflection circuitry of your CRT), you could achieve the
same result with a lower sampling rate and a better filter. Since
you can't do that, going as fast as you can is the best thing to
do.
But if I used a lower sampling rate and a better filter, I would be
limited to using disturbances within the bandwidth implied by the
sampling rate. As it is, I can use disturbances with frequency content
up to 30 Hz and see what effect disturbances outside the control
bandwidth have (for example, steps as in some of the models Bruce and I
have been working with). I like my instruments to be usable up to their
maximum capability.
The brute-force solution is always to sample and compute more
often. It usually works. But when do you know that you are safe,
and could perhaps safely go a lot slower (or get your results a lot
quicker by sampling less often)? You could do it experimentally in
each situation, and by so doing you could eventually get a "gut
feel" for when you are safe (as I suppose you now have).
Your prejudices are showing. I found out experimentally that the method
of obtaining and analyzing data IS safe -- not that it OUGHT TO BE safe
according to theoretical analysis done under a host of approximations
needed to make the calculations possible, but that it IS safe. I did the
equivalent of running an overloaded truck out to the middle of the
bridge and seeing that the bridge did not collapse, which is worth
several tons of reassurrances from the design engineer that it is
perfectly safe. As to speed of getting results, we are sampling in real
time and the analysis of an experiment takes about 10 seconds. Not much
left to gain there.
Or you could analyze the situation and see whether anything
important is happening within less than, say, 5 or 10 samples. If
it is, worry and experiment. If nothing happens so fast, be happy
that your results are at least likely to be reasonably safe from
the sampling problem. Then if your model works like (or unlike)
the real human, you can do the appropriate thing, with some
assurance that what you are dealing with is psychological science,
not computer science.
What the hell do you think I've been doing for 20 years? Your
condescension is sometimes unbearable.
Your money order was received -- I hope you use it yourself, but if not,
thanks on behalf of the CSG. I hope you do come in case I feel another
urge to throttle you in person, but also because I enjoy your company.
Bill
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