[Martin Taylor 960912 16:00]
Rick Marken (960912.1300)
if someone put forward an ineffective control loop with parameters
that made the model oscillate instead of track? Would that be enough to
eliminate PCT?
No. That would be a poor approach becuase we already know that a PCT model
will fit the data.
...
The MCT model is rejected by the polarity reversal results
because the behavior of the MCT model does not resemble the behavior of the
human controller in any way. Adjusting parameters of the MCT model doesn't
help; the problem is that there is _no_ exponential runaway in the MCT model
as there is in the human. The MCT model is organized so that such a runaway
doesn't occur.
Hans has already suggested that an MCT model with a realistic loop delay
might show such a runaway. You are asserting that because one possible model
fails to show it, therefore _all_ MCT models will fail to show it. That's
being unreasonable. If Hans can find an MCT model that does give an
exponential runaway of the right duration before control is reestablished,
MCT would again be on the same footing as PCT in this respect. PCT has
the advantage of having shown that behaviour already--but not using a
one-loop model. It took an additional loop and a switch added to the
simple control loop, if I remember correctly (which may well not be the
case).
How would you think about it if we were to propose eliminating PCT as an
approach
I've been asking you and others to work on setting up experiments to do just
that. Instead, it appears that you prefer to defend, sans data, theories
that have already been rejected by data.
To which I have to ask "which theories?" I haven't defended MCT except to
ask whether there exists a way to distinguish it from PCT, and to argue that
any criterion used to exclude it should be the same as the criterion used
to exclude PCT. Fair play is what I defend, not a particular theory.
What would stop the argument about the relative merits of MCT and PCT is
human experimental data that contradicts the PCT model, not a version of
the PCT model that contradicts experimental data.
I would have thought that you should apply the same criterion to both MCT
and PCT, and not "eliminate" MCT on the basis of "a version of the MCT model
that contradicts experimental data" unless you would be prepared to
eliminate PCT on the same grounds. And I can easily provide those grounds.
ยทยทยท
-------------------
Your phrase "to get the PCT model to fit the results" set me into a slightly
different train of thought. Not really a new one, though.
There can be qualitative as well as quantitative failures to fit results.
The _immediate_ reversal of the particular MCT model in conditions where
the human's immediate actions cause an exponential runaway--that's an
example of a qualitative failure.
That's how Tom and Bill eliminated the S-R and cognitive models of behavior.
It was really rather simple because neither of those models can deal with
the effects of imperceptible disturbances.
Yes, and the problems lead to qualitative failures to fit, where the error
increases exponentially over time rather than oscillating around zero or
some small value, as does the human performance and any PCT model. I don't
see how those qualitative failures can be eliminated by tweaking the models
based on S-R or outflow planning.
But if a PCT (or other) model does not fit the human's tracking behaviour
_exactly_ (not only a correlation of 1.00, but also the exact magnitude
of action), there is a _quantitative_ failure to fit. The only question
is how bad is this quantitative failure. If it is bad enough, then
there are subsidiary questions about whether there are characteristic
failure modes (and if there are, then one can start to talk about
qualitative failures).
I have never heard of a model fit at a correlation level of 1.00--RMS error
zero over the whole tracking period. I would be highly suspicious of
equipment failure if such a fit were to be reported. So, what we are
talking about is "getting the PCT model to fit" very (or fairly) well.
In analyzing the sleep study data, one way of "getting the PCT model to fit"
was to add a derivative (predictor) function in the perceptual side of the
control loop. Without that, we don't get the 0.99 correlations I've mentioned.
Now, it's clear that one must expect to get improved fits by adding a third
parameter (or a second stage loop appropriately configured). The question is
how much of an improvement signifies something that matters. And the answer
to that is something I don't know. I believe the enhanced fits, and the fact
that the best-fit gain and delay values become more plausible when the third
parameter is used, argue that the predictive component is likely to be
a part of the human model. Against that is the fact that the "gain" of the
best-fit predictive component varies wildly from track to track, so I'm not
betting the store on it.
---------------------
How would you think about it if we were to propose eliminating PCT as an
approach
I've been asking you and others to work on setting up experiments to do just
that.
I know you don't approve, but my main reason for faith in PCT is that it
seems to be required by the entropic constraints of the universe (read
"information theory" if you want a good laugh). The presentation of a model
that didn't fit the data from human tracking results would make me look for
a different model, not discard PCT. It would take something more than an
ill-fitting model to make me discard PCT as a correct theory, though I might
discard some specific manifestations of PCT.
Martin