[From Bruce Abbott (951112.1805 EST)]
If you plan to try the rubber-band puzzles for yourself, you should read
this post (and Rick's post to which it replys) after you're done.
Rick Marken (951112.1400 PST) --
Bruce Abbott (951111.1655 EST)
Bruce's answer.
The simple answer is that everyone will begin to pull so as to move the
other end of their band to a given position while resisting the
disturbances produced by the resultant forces produced by the pulling of
the other three participants.
My answer:
I think it's important to include the fact that all participants must have an
internal reference for perceiving the bands in a "square" (in a way that
is not inconsistent with reference perceptions of the other participants).
So the answer to the question "how do they make the bands a square" is "by
controlling their perceptions of the shape of the bands relative to their
references for a "square" shape.
Of course, that's where their reference for band end-position comes from. I
thought that was understood.
Bill's question:
what can one of the people do to make the square be some different size,
and still square?
Bruce's answer.
Just adjust her band tension and direction of pull.
My answer:
Yes. But I think it's important to note that this will change the shape
and/or orientation of the square only if none of the other three participants
is controlling for a square of a particular size and orientation. If some are,
then there is nothing one person can do to make the square a different size
or orientation (except to try to convince the others to change their
references).
My full answer:
Just adjust her band tension and direction of pull. Everyone else will follow,
attempting to restore the square shape in response to this disturbance.
I am assuming everyone else will attempt to preserve the square shape rather
than obstinately staying put. At the end of my answer to the previous
question I said:
The result will be a dynamic convergence of the corner-positions on some
position in which a square form appears. There may be some brief conflict
among the four control systems as to what the size of the square should be.
I am aware that conflict is implicit in this situation and yes, getting the
square to change size or orientation will require that the others only try
to preserve the shape and not the size or orientation of the square.
How can the experimenter prove that one knot is most likely under
control and the other most likely isn't?
Bruce's answer:
Pull in directions that would move a selected the knot off-target without
doing so to the other knot; observe whether the controller-person acts to
bring the selected knot back to target.
My answer:
Agree. I presume, however, you mean that part of the process of observing
"whether the controller-person acts to bring the selected knot back to
target" involves watching the hypothetical controlled knot to see if it
moves as expected. You can't just look at the controller's actions to
determine if those actions are protecting a particular variable from
disturbance; you must also monitor the hypothetical controlled variable.
How else are you going to determine that the knot is being brought back to
target? The only way is to look at the knot.
Bill's question:
can the experimenter find the answer by calculating the correlation of the
experimenter's hand movements with those of the controller?
Bruce's answer.
Yes.
My answer:
An emphatic "No!".
Yes, I screwed this one up, by not thinking it completely through. I could
see that, by controlling the selected knot, C's hand would have to mirror
the action of E's, yeilding a high correlation between the two motions. If
control were absent, the correlation would be low. But I forgot that C
would then be still be controlling -- controlling the position of the other
knot, yielding the same high correlation. What would differ would not be
the correlation but the ratio of E/C motion.
how could correlations be used to determine which knot is
under control?
Bruce's answer:
1. If the correlation between E's and C's hand movement is high, it's the
selected knot. If the correlation is low, it's the other one.
This answer and the previous one actually should count as one wrong answer,
because this is just the explanation I gave for saying "Yes" to the previous
one and is based on the same incomplete analysis.
Bill's question:
C and E are interacting as usual, but C is making the knot move in a
repetive SLOW sine wave laterally across the dot (at right angles to the
line of the rubber bands). What can E do that will bring C's hand to a
standstill while the knot continues to move side-to-side in a sine-wave
as before?
Bruce's answer:
E can begin to move her hand laterally (side to side) in phase with C's.
As E's input and C's on the position of the dot will be additive, the
E's excursions, the smaller C's will have to be to keep the knot moving
along the same path. E only needs to adjust the excursions until C does
not need to move at all to keep the knot moving in the same pattern.
My answer:
This is incorrect. Try it (everyone on the list should; they will be VERY
surprised)!
You could have predicted the result if you had looked at the situation
from a control rather than an S-R perspective. If E were actually able to
mimic C's actions precisely, C's sine wave actions would decrease, leading
to a decrease in E's sine actions, causaing a reduction in the sine wave
movements of the knot (the variable C is controlling ) resulting in an
increase in C's sine wave actions. Your analysis is wrong because you forgot
about the controlled variable (sine wave movements of the knot). You also
forgot that, if you use C's hand as the "stimulus" for your movements
that produce the desired effect on the knot, then if C's movements actually
did stop, your movement would stop to (because you are mimicing C) and
C would have to start moving her hand again. S-R does not produce control.
You have misconstued my answer. I'm not saying that E ought to mimic C
throughout, but only C's _initial_ behavior. If accurately done, this will
bring C's hand to a standstill. If not, E can then adjust her hand
excursions as necessary to accomplish this. If you compare what you said
below with what I said above, you will realize that we are saying the same
thing.
E can bring C's hand to a standstill by moving his hand back and forth as
necessary until E perceives that C's hand no longer moves; E can't know
the details of the back and forth actions required to control his percepion
of C's hand movements; as in all control, the detailed actions that control
a perception (C's hand mvoements in this case) are largely determined by
disturbances to the controlled variable (such as slight variations in C's
effects on the controlled variable), disturbances that are typically
unpredicatble and undetectable.
Yep, just what I said. Apparently, I _was_ looking at the situation from a
control perspective.
Pretty darn good. Your problems come mainly (I think) from clinging to
the S-R point of view.
Nope. Just from not thinking the problem through all the way (in the first
case) and not providing all the details you wanted (I was assuming that
short answers were desired) in the others. Frankin was right: haste makes
waste.
Regards,
Bruce