[From Bill Powers (951112.2200 MST)]
Bruce Abbott (951112.1240 EST) --
Just to keep the suspense from killing anyone, I'll admit that I
made some mistakes. What is interesting (to me anyway) is why.
I disagree with Rick Marken's explanation of why, and I don't care
whether you "cling to S-R viewpoints" or not. The object of these
puzzles is to provide practice in applying PCT to real behavior, which
is the only way to make it seem as natural as other ways of
understanding behavior (eventually, I hope, more so).
Did you send your answers direct to Rick and Gary? Or did I post my
reply to CSG-L instead of directly? Or did you send them to CSG-L and I
haven't seen the post yet? I'm a little confused; that is, a little more
than usual. I'll reply publicly.
You did make a few mistakes, but as you said this was due to not
thinking the problem all the way through. In most cases, simply being
told that the answer was wrong was enough for you to come up with the
right answer.
In the "square" puzzle, the "right" answer depended on what you assumed
about the other players. You introduced pertinent assumptions and
handled their implications correctly. Actually doing this experiment
would reveal some facts that aren't evident in the verbal description.
If you get four people to hold the loose rubber band ends and ask them
to "make a square" they will do so _immediately_ with no communication
or hestitation. During this process any one person can cause either a
large or a small square to be formed just by pulling more or less on one
corner. The others will automatically compensate to maintain the
squareness, showing little sign of controlling for size, position, or
orientation. When one person pulls on a corner, the immediate effect is
on the angle at that corner. An adequate model would be four control
systems each controlling for an angle of 90 degrees at the nearest
corner. Of course if you mention a target size, orientation, or location
of the square, then you will have much less ability to determine these
aspects of the square by manipulating just one corner.
In the two-knot puzzle, the controlled knot can be found by looking for
the knot whose position correlates least with either the Experimenter's
hand position or the Controller's hand position. The correlation between
E's hand position and C's hand position will be the same whichever knot
is controlled -- very high, and negative. It can't be used to find the
controlled variable.
While the controller is given only the choice of controlling one knot or
the other, proof of the nature of the most likely controlled variable
does not depend on knowing this. Observing the relationship between E
and C, you might hypothesize that C's hand is maintained twice as far
from the controlled knot as E's hand, or if the other knot is being
controlled, half as far. The position of the knot relative to the dot
would then be thought of as a side-effect of controlling that
relationship. The data would support this, as would the regression
coeffient relating E's hand position and C's.
However, if C closed her eyes, we would still find that C's hand is
twice as far from one knot as E's hand, and half as far from the other
knot as E's hand. This would remain true even if C's hand stopped
moving, or moved at random. This proves that the proposed relationship
between the hands and the knots is not under control. In fact, we would
realize that it is just an unchangeable property of the rubber bands.
We are led to this realization by the principle that if a proposed
variable continues to appear to be controlled despite the fact that it
can't be sensed, it is not actually the right controlled variable.
The only variable that is controlled when the eyes are open and
uncontrolled when they are closed is the relationship of one knot to the
dot. So that is the controlled variable.
In the three-party puzzle, you overlooked the fact that E was continuing
to apply disturbances, although I had explicitly said that E is always
applying disturbances (most people do overlook this, even Rick). If the
third party pulls toward C's hand, C's hand could actually move either
toward or away from the knot, depending on what E is doing at the same
time.
I didn't try the sine-wave puzzle until later. Although I had specified
that the sine wave should be slow, I didn't emphasize that enough. It
should take at least 10 seconds per cycle, and what's more, the
controller should pick a specific amplitude for its motions. When I
tried this with Mary, she was moving the knot too fast, and I was unable
to stabilize her hand -- we just went into mutual oscillations, an
unstable conflict.
If the controller has in mind a specific and very slow alternating
movement of the knot, the experimenter can simply pick a position for
the controller's hand and -- eventually -- keep it there, almost. As you
indicated, the experimenter can start by moving the same way as the
controller's hand, but this merely establishes the right sign for the
relationship. From then on, all the experimenter has to do is move
enough to counteract any movement of the controller's hand. From the
controller's point of view, less and less movement is necessary to
maintain the desired pattern of movement of the knot.
There is probably a better way to illustrate this point, but I thought
it was neat to show that the experimenter would end up doing all the
work in moving the knot for the controller, while the controller put out
less and less effort to achieve the desired result.
There's another way for the experimenter to think of this. Watch the
knot for a while without putting in any disturbances, and then use the
rubber band to "help" C move the knot in the same pattern.
···
-----------------------------
RE: state diagrams
I can visualize a mechanism that, say, fires three blasting caps in
sequence via a timer. If the first cap failed to fire, the timer
would continue anyway, triggering the second and then the third
cap.
Yes, I can too. Any timer, however, involves a variable that changes
slowly with time -- position of a pointer or cam, or charge on a
capacitor. There's an implicit choice point, as in a TOTE unit: the
trigger point. One action is called for if the timer has not reached the
trigger level, another if it has.
Another mechanism might trigger the first cap, then trigger the
second on receiving feedback (e.g., blast pressure-wave) that the
first had fired, etc.
This isn't really feedback; it's just a signal. If you let the last
event in one sequence become the first event in the next sequence,
you've simply created one long sequence. Naming subsequences is just an
arbitrary subdivision of the whole sequence.
In a program, all the linkages exist, but there are test points so that
the path through the program depends on the outcomes of tests which
can't be determined until the program runs. Implied are variable inputs
from sources outside the program. If these inputs have one set of values
when the program tests them against a criterion, the program branches
one way; if the values are different, it branches another way. When the
program is executed, there will be paths that may never be used. Whether
they are or not depends on the data inputs used in the tests and choice-
points.
The entire structure of a program can be comprehended, but the sequence
of operations it will carry out can't be predicted without knowing what
the data inputs are going to be at the times the choices are presented.
In a true sequence, there can be only one sequence of events once the
first element has occurred (barring physical distruptions).
Computer programs are pure sequences (strings of operations carried out
in a fixed order) embedded in a network of choice-points, which
determine (on the basis of variable data inputs) which sequence is to be
started next.
At least that's how I've broken these processes down.
-----------------------------------------------------------------------
Best,
Bill P.
