[From Bill Powers (930414.1300 MDT)]
I've finally obtained a book recommended by Avery Andrews:
Butterworth, B.; Language Production, Vol 1.; 1980, Academic
Press.
I had forgotten why I ordered it through interlibrary loan, so
when it came I browsed through it and found a number of places
where PCT could be applied. It wasn't until I got to page 398
that I came across a familiar-looking diagram, and then noticed
that the article was by Carol Fowler in conjunction with Rubin,
Remez, and Turvey, and realized what was up. The mass-spring
model strikes again, and we have another example for our
collection of misinterpretations and misstatements about control
theory.
If anyone has an internet address for Carol Fowler (didn't she
marry Turvey?) they might forward a copy of this to her. Every
word of it.
The control-system model comes up in connection with "immediate
readjustments" as when a person chewing on a bite-block is able
to pronounce natural vowels "within the range of variability for
normal vowel production." (p. 397)
On pp. 398-399, Fowler et. al. do a fairly decent job of
explaining how the control-system model works, even remarking
that the control systems involved must be kinesthetic rather than
auditory and that the driving signals to the muscles are provided
by feedback instead of being precalculated. But of course they do
this in order to set up control theory for the big fall.
This they do by introducing a hierarchical model. The model is
set up properly with three first-level systems and one of the
possible three second-level systems. The relationship between
lower-level perceptions and the higher-level perception is
correctly described, with a reference to BCP. It is correctly
noted that the error signal at the second level is the basis for
the reference signals going to the first level.
At this point the authors' understanding runs out. On p. 401 we
find
"Unfortunately, for any given error signal there are very many
possible combinations of values for r21, p11, p12, and p13 that
might yield that error, even if some boundaries are set on the
possible ranges of values that each might take on. The error
signal might be entirely due to an error of one of the first-
order systems, or it could be one of many combinations of errors
on the part of all three first-order systems. In summary,
unidimensional feedback must rarely be informative in a
hierarchical closed-loop system because, typically, there is a
one-to-one mapping between an error signal and the conditions
that may have provoked it."
"... In the absence of any well-defined, and possibly special-
purpose (Gel'fand and Tsetlin, 1962, 1971), search procedure, the
error-correcting process on n degrees of freedom would be
essentially random and temporally indefinite." (p. 401).
So with that bit of gobbledygook, the hierarchical control system
model is, with a minimum of regret, put aside. On to coordinative
structures!
The discussion certainly sounds authoritative, doesn't it? The
authors state, quite correctly, that many combinations of lower-
level signals could produce the same error signal, but having
said that they simply assume that for that reason, the system
couldn't possibly work. I agree that it would seem so, to a
person ignorant of control theory. The operation of control
systems, particularly multi-level control systems, seems to
bootstrap itself without any obvious justification, producing a
systematic control effect without, seemingly, enough
specification of conditions to permit that to happen. Such
puzzlement would be cleared up very quickly by seeing an actual
multi-level control system, or a model of one, working. But that
does not appear to be among the authors' experiences. I
particularly love their citation, which "proves" that
hierarchical control systems have to work essentially at random.
Like Rick Marken's three-level, six-system-per-level, spreadsheet
demos, perhaps?
Because of not understanding how this hierarchical model works,
the authors fail to see how it explains the very phenomenon that
led them to bring it up. If the second-level system perceives the
feature of kinesthetic articulation necessary to produce a
recognizeable vowel sound, then of course you would expect a
different combination of lower-level signals to be required to
create the same net effect at the second level with the bite-
block in place interfering with one of the first-level systems.
And this hierarchical system is just the ticket for doing that.
If one of the lower-level signals is interfered with, the error
signal that drives all three systems will change, altering the
reference settings for the other two first-level systems in
exactly the way required to make up the difference. The second-
level perceptual signal will be maintained at the specified
reference level even though all three lower-level perceptions
change. The second level system is not trying to maintain any
particular value of any of the first-order perceptual signals. It
is controlling a _function_ of all three signals. And this is not
just verbal speculation. We have demonstrated over and over how
this happens in working models. But we demonstrate, it seems, to
blind eyes and deaf ears.
Some of you folks out there in CSGnetland have complained about
the passion and fury that sometimes breaks out in the writings of
advocates of perceptual control theory. It's stuff like the above
that leads to Rick Marken using impolite terms like "dreck" and
"idiocy." One can stand criticism and even misunderstanding, but
when completely false conclusions are presented in a calm
authoritative tone that is bound to make readers think they are
listening to someone who knows what he or she is talking about,
it's very hard to avoid table-pounding oaths and name-calling.
It's a very helpless feeling to see one's work misrepresented,
and rejected on the basis of ignorance and sophistry --
particularly when one's attempts to publish a correct model are
consistently rejected because of reasoning of exactly the same
stupid kind. I think that a bit of fury is excusable.
Oh, the authors' explanation?
" ... for example, if P = kQ, then if P's value is frozen, Q
_must_ assume whatever value is necessary to keep invariant the
ratio k. ... The ability of speakers to generate acceptable vowel
qualities in the face of a fixed position of the mandible or
lips, can be accounted for in very much the same way."
In short, if something exists that can vary Q in just the right
way, the ratio k will be preserved. That something, according to
the authors, is an equation of constraint. And how does an
equation of constraint work?
"The constrained relationships among the components of the vocal
tract 'create' a vibratory system -- that is, a system with an
intrinsic goal which it attains from any starting point by virtue
of its dynamic configuration. When a bite block is introduced in
the system, it fixes the values of the variable for jaw position.
As we have indicated, under conditions in which the value of a
variable is fixed, the remaining variables assume values that
preserve the equation of constraint. So long as the requisite
values are attainable by the components of the vocal tract, the
effect of a bite block should be negligible." (p. 401).
Of course, if the remaining variables do NOT happen to change in
a way that satisfies the equation of constraint, the outcome will
NOT be the same as before. So what makes the other variables
change in just the required way? Why, the solution of the
equations of constraint!
That's a tight little logical circle. If the equations of
contraint are met, then the compensation will take place. If the
compensation takes place, the equations of constraint must have
brought it about.
The mass-spring model makes its appearance a little earlier. The
authors are unaware of its limitations, and do not mention that
exactly the same second-order differential equation will apply to
the behavior of an equivalent control system (except, of course,
for the constants like apparent mass and apparent spring
elasticity, which will be very different from the reality if we
plug in only the passive properties of muscles).
All this is quite typical of the problems we PCTers have had in
getting established behavioral scientists to learn what control
theory is about. We have not been met with open-minded and fair
skepticism. We have been met with attempts to preserve rival
views by any means, fair or foul, including misrepresenting what
control theory says and dismissing its capabilities without
understanding what they are.
Does anyone still wonder why I no longer try to publish in the
refereed literature of the behavioral sciences?
ยทยทยท
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Best to all,
Bill P.