[From Rick Marken (970428.2300)]
Bill Powers (96042.1826 MST) --
Just a little addendum:]
Thank you.
Me:
ds is _not_ what I usually call d; d is an environmental variable;
Martin Taylor (970428 23:30) --
That's why you never add "d" to "o" in computing the influence on qi?
OK. I see your point. When I use d in the equation p = f(o + d) I am
assuming that ds = 1*d = d. So in this case d represents _both_ the
environmental variable (d) _and_ it's influence on the controlled
variable (ds). I'm sorry if this has caused you confusion but I don't
see how it is relevant to the discussion of information about the
disturbance in perception. If p = f(o+d) then there is no information
about d in p whether d is thought of as the disturbance variable (d)
itself or the influence of that variable (what you now call the
disturbance signal (ds)) . Given p, f() and o, an outside observer
can solve for d; but the control system itself, which knows only p,
cannot.
I think this discussion of disturbances is becoming an obtuse
mathematical exercise. It might be easier for everyone to understand
what's going on (and what's going on, believe it or not, is the
essense of PCT) if we make things very tangible.
On p. 172 of Living Control Systems, Bill Powers gives a nice
list of some of the variables that one controls when backing a
car out of the garage. In that table, Bill gives the name of each
behavior involved in backing the car out, the variable controlled
when performing each behavior, the means used to control each
variable and the reference state of each variable. What he doesn't
give are the disturbances that influence each variable. I'm going to
go through part of Bill's list and try to describe some of the
disturbances to each variables. The remainder of the table can be
done as an exercise by the eager student (I presume that everyone
has _at least_ one copy of LCS;-)).
The first behavior is "open door". The variable controlled is "angle
of door". The reference state of this variable is 80 degrees (relative
to the car frame, I presume). The means used to control this variable
are to "grasp and pull" the door. Some _disturbances_ to this variable
are 1) the mass of the door 2) the tilt of the road on which the car
is parked 3) the friction of the hinges. Note that these disturbances
are variables in the environment. The values of these variables are
different each time you open a car door; cars differ is the mass of
their doors; the same car is always parked at a slightly different tilt;
etc. Moreover, the influence that any one of these variables has on the
angle of the door depends on the state of the others. The effect of the
mass of the door depends on the tilt of the car, the effect of the tilt
of the car depends on the friction of the hinges.
So the "disturbing influence" (Martin's "disturbance signal") of
each disturbance variable is different on each occasion, as the the
value of the disturbance variable itself.
The disturbances that influence the angle of the door are essentially
invisible; you can't see the mass of the door, the tilt of the car
(unless it's pronounced) or the friction of the hinges. Moreover, you
can't see how all variables actually influence the angle of the door.
Nevertheless, you open car doors, over and over again, always exerting
just the right pull to get the door to the reference angle. This is
because you control the perception of door angle, continuously exerting
more or less pull, as necessary, to keep the door at the reference
angle.
The MCT approach to opening a door is to build a model of all the
variables (disturbances) that influence the result and a model of _how_
these variable influence this result. Since the values of
these variable and the way they influence the controlled variable
are different every time you open a door (bring the angle to 80 degrees)
you would have to rebuild the model every time you open
the door. To regularly perform even the simplest behaviors the
MCT model has to go through a set of implausibly complex
computations to produce a model of the world that is obsolete before it
is used.
Now let's quickly go through a few of the other behaviors. The next
behavior is "get in". The variable controlled is your relationship to
the seat. The reference state of this variable is "seated". The means
used to produce this results are "bend, sit, slide". Disturbances
include 1) angle of seat to back 2) distance from seat to top of door
3) distance from seat to dashboard 4) objects on seat, etc. Again,
all these distubances are variables; they can have different values
each time you try to sit in a car.
The next behavior is "shut door", which involves the same variables,
means and disturbances as those involved in opening the door -- all
that's different is the reference state for the controlled variable
(angle of door)-- 0 degrees rather than 80.
Next is "fasten seat belt". The variable controlled is the distance
between the fasteners. The reference state of this variable is zero
distance. The means used to produce this result is "push together".
Disturbances include 1) the initial location of each belt fastener
2) the tightness of the belts and 3) the size of your own tummy.
Again, all these variables have different values each time you
fasten seat belts (though some, like the tummy, might not be quite
as different each time).
I think it would be a good exercise to go through the rest of the
list on p. 172 and try to think of the disturbances that might
influence the controlled result -- in particular, try to think of
disturbance variables that might have different values each time
you try to bring the controlled variable to its reference state.
Also, try to think of disturbance variables whose values cannot
be sensed before one starts controlling the controlled variable.
PCT is a model of systems (like living organisms) that can
consistenty produce results like those in column 4 of Table 1
on p. 172 of LCS despite the fact that all these results are
influenced by _invisible_ disturbances that are different
on each occasion. That is, PCT is a model of systems that _control_.
Best
Rick