[From Bill Powers (950124.0600 MST)]
Rick Marken (950123.1010) --
Writing to Bruce Abbott, you say
Given the close proximity of your question about estimates of
reference [target] values to your statement about needing these
values to reconstruct d, it seemed to me (and to Tom too,
apparently) that you thought you had to estimate the reference
[target] value (rather than just look it up in the program code) in
order to reconstruct d. That is, it seemed like you didn't
understand that c = h+[d]+t.
I think you're misconstruing Bruce's intentions (although perhaps Bruce
hasn't worked out all the details, either). He's looking at the problem
that faces his five professors who don't know what our program is and
have observations only of handle and cursor behavior, as well as
constant target position (but with no indication of how the person's
behavior is related to the target). This is also the problem _we_ have
in observing any behavior in the wild, where we don't know what
invisible disturbances are acting or what the person's intentions are.
In general, we have to find out HOW the handle is affecting the
supposedly controlled cursor (as you pointed out yesterday). In our
computer demos, we know how the handle affects the cursor, but from the
standpoint of the five professors this knowledge is not available unless
we tell them. Actually, the five professors ought to be knocking on
Bruce's door about now, either asking that very question or requesting
access to the experiment again.
In a natural situation there is no Bruce to ask, so we have to look at
the physical connection between the action and the controlled variable.
When we understand this, we can deduce from physical principles how the
cursor would move if the handle alone were acting on it. Then, once we
know that, we can deduce an equivalent disturbance acting through some
assumed linkage to the controlled variable. We can't deduce the actual
disturbance, of course -- there may be multiple disturbances, and the
connections from disturbing variables to the controlled variable may be
nonlinear or changing. The best we can do is to assume some single
equivalent disturbing variable having a standard linear effect on the
controlled variable.
In Bruce's set of numbers
(3 cursors) (handle)
325 323 302 17
There is no way to deduce the disturbance unless you know what the
effect of the handle alone should be. If we know that the handle alone
will produce a value of each cursor of 320 when h = 0 and there is no
other influence acting (as is the fact), we can immediately say that the
disturbance values are -22, -20, and +1. This assumes that there is a
single disturbance acting on each cursor, and that the effect of the
disturbance is multiplied by +1 and added to the position of the cursor
(as, in this case, we happen to know is true).
So you are right, Rick, in saying that knowledge of the reference level
isn't needed to determine the value of an equivalent disturbance, if the
nature of the link from handle to cursor is known for each cursor.
However, if the link from handle to cursor is not known, then we have to
find out what it is before we can deduce the disturbance. So I think
that in fairness, Bruce should tell the five professors that when handle
position is 0, the natural position of all three cursors would be 320
(or is it 319?) when nothing else is acting on the cursors.
···
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Proof that the reference signal does not affect the relationship among
h, c, and d, assuming a linear model:
---------------------------------------
steady-state system equations:
c = cursor; h = handle; r = ref signal;
p = perception; d = disturbance; G = output gain
p assumed equal to c
c = h + d (environment)
h = G*(r - p) = G*(r - c) (organism)
---------------------------------------
simultaneous solutions:
h = Gr - Gh - Gd
G
(1) h = ----- (r - d) (handle as function of r and d)
1 + G
c = Gr - Gc + d
G
(2) c = ----- (r + d/G) (cursor as function of r and d)
1 + G
From the first system equation, we see that d = c - h, or combining
(1) and (2):
(1+G)d = Gr + d - Gr + Gd
d + Gd = d + Gd
d = d, QED.
The reference signal drops out, showing that it has no effect on the
relationships in the environment.
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Bruce Abbott (9550123.2030 EST)--
The "maxx div 2" constant is simply a way to set up a zero-centered
coordinate system on the screen. Presumably the control phenomena will
be independent of where we set the zeros of our measurement scales --
whether at the left edge of the screen, as you do, or at the wall of the
room to the right of the screen, etc.. The zero-centered system simply
leads to the smallest numbers. We would need a lot more storage to hold
the numbers in a philadelphia-centered coordinate system (at least I
would).
Tom said:
No matter what relationship the person controls between cursor and
target, c - h = d. By definition, that's the state of affairs in the
world.
You replied:
This function is not a state of affairs in the world, but a convention
you guys use in your programs. It could be any function, even a
nonlinear one. This one just simplifies the analytic task.
We could have (and in the past, actually have) used nonlinear functions
to set up a different world. But as you say, it's easier to work with
linear phenomena, which are fairly common in the real world.
A point that seems to slip by too easily is that given the physical
relations among handle, controlled variable, and disturbance, you need
to know only two variables and the two functional relationships to
deduce the third variable. This has nothing to do with the organism or
with control. In the rubber-band experiment, the two rubber bands create
nonlinear relations among the variables. These physical relationships
exist independently of the organism. The ends of the rubber bands don't
have to be positioned by a control system; anything that positions them
determines where the knot will be. If you know where one end is, and
where the knot is, and that the rubber bands are identical, you can
deduce that the other end is the same distance from the knot on the
other side. Reference levels are irrelevant.
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I hope this gets us all talking about the same thing.
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Rick Marken (950123.2130) --
--it's fun to work on a primative computing device like the PC once
again. Reminds me of the good old days with my Commodore 64. 
Right. A PC is a simple device for complex creators of programs. A Mac
is a complicated device for simple users of programs.
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Hans Blom (950124)(?) --
It is frequently expressed in these here csg-circles that an
organism _is_ a control system. It is not. Or that organisms _have_
control systems, in contexts where we cannot meaningfully say so.
... Let us be clear about what a control _system_ is. It always
consists of two parts, an inside and an outside, so to say.
Let us be clear about who is saying what is what. You're not telling
anyone what a control system IS. You're telling us that you prefer your
definition. We use the term "control system" to mean the active agent as
opposed to the passive environment in which control takes place. I don't
think there's any ambiguity. Your suggested definition is no better --
how can you call the organism a "controller" independently of its
environment? The definition of "system" is fuzzy at best, depending on
the whim of the observer. The main thing is to be consistent.
One reason for my usage is that the same controlling organization is
normally applied to a great many different environments; we move around
in the world, unlike an industrial control system, with the external
part of the loop changing from moment to moment. At one moment we pick
up a pencil, in the next we pick up a wrench, and in the next we pick up
a length of pipe. Our control systems are set up so they can work in a
variety of environments without having to go through the slow process of
adaptation. This is one reason, I think, for the hierarchical control
arrangement.
It doesn't make sense to speak of "exquisite" adaptations when the whole
point of a control system is its insensitivity to changes in loads and
properties of the external part of the loop. True, there are limits to
what a control system with fixed parameters can accomplish, but they're
very broad. There is no need to reajust the control system that picks up
a coffee cup just because the cup may be full on one occasion and empty
on another. When we move something heavy, we simply take a little longer
to move it; we don't adapt ourselves so we can move it just as fast as
we move a light object. For higher-level purposes, the differences in
control dynamics at the lower levels simply don't make a difference.
Human adaptation takes place on a scale of weeks, months, and years. It
doesn't happen between the time I extend my hand toward my coffee cup
and the time I return my hand toward my mouth carrying the coffee cup.
Examples are easy to construct. Invert the sign of the
environment's transfer function and what was an excellent
controller is now an oscillator.
Yes, positive examples are always easy to construct. But negative
examples also abound. For example, if we reverse the external connection
in a tracking task, a runway movement starts, but about 0.4 sec later,
the internal sign is also reversed and control returns. The reversal
takes place in a fixed manner after a constant delay, so this is clearly
the operation of a higher-level control system operating in a fixed way.
Make the environment unresponsive (massive, sluggish), and control
is control no more.
Nonsense. I can pick up a loaded suitcase as easily as an empty one.
You're speaking as if control systems can work only in a single closely-
defined environment and fail as soon as there is any change.
A human may be an excellent controller on earth, he isn't in
Jupiter's immense or in an asteroid's negligable gravity.
You're letting your theory lead you to make up facts. One of the first
observations of astronauts in orbit was that all the difficulties in
moving around they had been led to expect (by S-R theorists) simply
didn't occur. They just moved a little more slowly, but had no
remarkable trouble with controlling things. Their main problem was
dizziness; it did take some time to get used to the new vestibular
signals. But ordinary control tasks worked just as well as they did on
earth. When the astronauts went to the Moon, they had been coached on
simple mechanisms of locomotion that might enable them to stay upright,
such as the "kangaroo hop." What happened was that Neil Armstrong got
off the landing pad and started walking around without any problem. At
one point they tried the kangaroo hop and reported that it worked just
fine (being nice to the psychologists), but they soon went back to
walking and trotting as usual.
Jupiter's gravity is about 2.5 g's at the surface, I believe. People
have been moving around in 2.5 g's for quite a while (test pilots, etc)
without collapsing or losing control.
Adaptation is the only possible strategy in all cases where the
characteristics of the environment change significantly.
Of course. But how much change is "significant?" I would agree that some
low level of adaptation is probably going on all the time, but it's not
essential until the local environment has changed by a rather large
amount.
Consider the range of feedback components that can be used with
operational amplifiers -- non-adapting amplifiers -- in analog
computing. You can go all the way from inductive through resistive to
capacitive feedback using the same high-gain amplifier with a fixed
dynamic design, and get accurate results all the way. Human systems are
similar: the same controlling mechanism can work perfectly well over a
WIDE range of feedback links. Not an infinite range, of course, but a
range that is wide enough that adaptation is seldom necessary.
Control can arise only as an _interaction_. And in this interaction
the controller usually has to adjust to the demands of the
environment -- except where the environment can be changed and
given different characteristics. But that is an entirely different
story.
What the controller has to adjust is its means of control, its actions.
But human control systems are not concerned with actions; they are
concerned with consequences of actions, outcomes. The human being is
autonomous in terms of selecting desired outcomes. Once the desired
outcome is selected, then of course the action required to produce it is
determined by the environment, and sometimes the properties of the
control process must change if the environmental properties change
enough. However, that is not the point of control. The point of control
is to make some perceived state of affairs match an internally specified
state. The environment determines primarily HOW we control, not WHAT we
control.
[Bill Powers (941227.0730 MST)]: All human beings set their own
goals;there is no mechanism by which any external agency can
directly determine the goals of an individual.
This is misleading at best. Goals are relative to the environment,
and without the "external agency" goals cannot even be defined.
The environment "affords" infinite possibilities for things to be
controlled, for goals. But it has no way of altering reference signals
in the brain. Reference signals are set by higher systems, and their
ultimate dependence on the environment is highly indirect and
historically ancient. In any given lifetime, the origins of goals are
inside the organism, not in its environment. Your soup does not tell you
what flavor to prefer, or how much salt, or what temperature.
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Best to all,
Bill P.