Control and the Test

[From Bill Powers (960216.0500 MST)]

Martin Taylor 960215 16:45 --

     I admit to being confused as to the agreement between Bill's
     pointing out that one cannot do the Test for the controlled
     variable in this situation and your saying that one can solve the
     problem by doing the Test for the controlled variable, but I'll
     take your word for the fact that these statements are not
     contradictory. It's a religious fact that what Marken and Powers
     say cannot be in contradiction, by definition.

It would be better if you understood why they are not contradictory. You
proposed that a variable V was seen to change and then to return to its
former value. I said that without knowledge of the disturbing variables
on which V depends, it is impossible to do the Test. Rick said that if
the Test _is_ applied, the problem can be solved. These statements are
not contradictory. In order to do the Test, you would have to FIND other
variables that influence V, and manipulate them. In other words, as you
initially stated the problem you had insufficient information for
identifying a controlled variable. Rick recommended that you get this
information before making any statements about control (spontefaction or
perfaction).

Your failure to grasp (or express) this basic aspect of the test is
evident in your "walk-through" when you say

     Let's walk it through: (1) apply disturbance by pushing particle
     away from where it seems to "want" to be. Result: pass.

No. That is not how the Test is done. You do not push the particle away
from where it seems to want to be. That is introducing an arbitrary
change into the supposed controlled variable itself, which breaks the
control loop. What you do instead is to find one other variable on which
the state of the putative controlled variable depends, and change THAT
variable.

The problem here is contained in the phrase "push the particle away."
This phrase conflates the application of a disturbing variable (push on
the particle) and a _consequence_ of that application (the particle
moves away). What your way of putting it really says is "apply a
sufficient push to the particle that it moves to a new position." This
means that _you_ are controlling the position of the particle, in
conflict with any other control system that may also be controlling the
position of the particle. If the particle does move to the position you
intended, you have simply applied a sufficient push to overpower any
control system that might exist.

To give you the benefit of the doubt, perhaps you actually understand
the Test but are simply being imprecise in describing it. If that is
true, then we need to consider a more precise way of stating it that
will remove the difficulty.

To be precise while using your own terms, we would say that you apply a
known amount of push to the particle, predicting the amount of movement
of the particle away from its apparent equilibrium position (or mean
dynamic behavior) that would be expected if there is no control. If the
particle moves exactly as predicted, there is no control of position, so
the test is FAILED.

If the particle moves less than predicted, this suggests but does not
prove that control is present; the failure to move might be due to the
fortuitious variation of some OTHER variable on which the position of
the particle depends -- for example, the moving particle may have
encountered a region of high friction, or it may have come up against an
obstacle.

So what you must now do is determine WHY the particle did not move as
much as expected: you have to track down the source of the opposing
push. For the test not to be failed again, you must identify the output
of some system that explains essentially all of the opposition, and show
that this output rises as the particle begins to move, opposing the
movement.

If that step is not failed, you can go to the final step, which is to
explain (as far as you can) how it is that the output of the system
varies when the particle moves. This means finding the path through
which the position of the particle affects the system which is producing
the counter-force. The most direct way to establish that you have
identified the path is to interrupt it and verify that the systematic
opposition disappears.

It is not always possible to complete the test. We may simply have
insufficient knowledge of the environment to identify the source of the
opposing push, or to find any paths by which the state of the controlled
variable can be known to the supposed control system. We may be unable
to predict the effect of a "push." In that case we simply have to
deliver the Scottish Verdict: not proven. We have to try to learn more
about how the environment works.

So what has been established when all phases of the Test have been
passed? We have shown that there is a physical system the output of
which, by itself, accounts for the failure of the applied disturbance to
have the effect predicted on the premise that there is no control
system. We have shown that the output of this system depends on
detection by that system of the state of the variable being affected. We
have shown, therefore, that there is a system that conforms to the
definition of a control system, or rather a spontefaction system (since
there are those who interpret "control" so it can include an open-loop
effect).

Behind all this there is a quantitative question: by how much must the
observed change in the particle's position fall short of the predicted
change in order for us to say that control exists? The extremes are easy
to identify. If the shortfall is only a small fraction, like 1%, of the
predicted change, we could say that technically this stage of the Test
has not been failed, but that practically speaking any control that
exists is serves no useful purpose. If the shortfall is 99%, so that
only 1% of the predicted change occurs, we can be quite confident that
this is a useful control system. But what if the shortfall is 80%, or
60%, or 40%? Then it's a judgment call. We have to consider the context,
and decide on other grounds whether this is a practically significant
control phenomenon.

You have raised another question, which is why the disturbance must be
sustained rather than transient. The answer is that the opposition to
the disturbance may require time to develop. If you apply the
disturbance and instantly remove it, you will never see the opposition
occurring while the disturbance is still present. The behavior you see
will not be equal and opposite to the disturbance. It will begin to
appear and then disappear again before it is fully developed, so you
will never get a simple picture of the relationship between disturbance
and action. Action will still be going on even after the disturbance has
been removed. So you will have to use a much more complex analysis to
show that if the disturbance HAD been sustained, the action would
eventually have come to oppose its effects.

···

-----------------------------------------------
As I read through later posts, I see that you maintain that your view of
the Test is the same as mine. Assuming that this is true, the difficulty
must lie in your way of expressing it, as outlined above ("pushing the
particle away..."). Also, you seem to be asking how the Test could be
performed when there is insufficient understanding of the situation to
permit predicting the effects of disturbances, etc.. I think I have
answered that: you can't apply the Test, so you can't know what kind of
system is involved. Rick assumes that we always understand the
environment so well that we can say what the effect of a given
disturbance would be without control. I'm not willing to go that far. If
I say to Rick, "You're a stupid jerk," I don't know whether this is a
disturbance, or what the effect would be if there were no control system
involved. So I can't really do the Test that way.
------------------------------------------------
In your example of moving the wastebasket and seeing if another person
moves it back where it was, you do not sustain the disturbance, so you
don't distinguish a control system from a stimulus-response system. It
is possible that the sight of the wastebasket moving from A to B causes
the person to move it by an amount equal to and opposite to the distance
from A to B. Since you do not apply any sustained force on the
wastebasket, you don't know whether the other person would exert an
opposing force and move the wastebasket back to point A anyway, or
whether the sustained force would result in moving the wastebasket to a
point other than A.

The Test is designed to detect purposive action, and distinguish it from
action that simply follows upon a prior cause, in some calibrated way.
If you want to investigate wastebasket-moving as a control -- perfaction
-- process, you have to devise means of ruling out non-control
explanations. For example, you might move the wastebasket by different
amounts and in different directions on successive trials. If the
movement of the wastebasket back toward point A is an open-loop process,
you might discover that no matter how you move it, the other person
moves it southwest by 10 feet. Then you realize that the only reason it
moved back to point A in the first trial was that you happened to move
it northeast by 10 feet. If you had moved it differently on the first
trial, the person would have moved it not "back", but to a position 10
feet southeast of wherever you left it.

In applying the Test, you have to keep thinking of alternative
explanations and devising disturbances to rule them out. Any alternative
explanation implies certain outcomes of experimental manipulations. You
can Test those implications, too, in the terms of the other explanation.
All that the Test amounts to is following out the logic of whatever
explanation is being offered. If you say that moving the wastebasket is
a stimulus-response process, you can Test this proposal by applying
disturbances and seeing if the response occurs as S-R logic predicts.
For example, if moving the wastebasket back to point A is an open-loop
response to the sight of the wastebasket in some other place, then
blocking the person's ability to see point A should have no effect on
the response. Applying a disturbance to the wastebasket as it is being
carried back toward point A should cause the wastebasket to end up in a
position other than point A. And so on.

Basically the Test is a multi-step attempt to disprove the hypothesis of
spontefaction. The theorist says, "I applied a wind force to this car
and it didn't move sideways. Therefore it must be under control by the
driver." The experimenter says, "Oh, yeah? Well I say that this car is
running on rails." That proposal disproven, the theorist says "The
driver turned the steering wheel to make the car stay in its lane around
the curve." The experimenter says "Oh, yeah? I happen to have measured
the wind force on the car, and it was sufficient by itself to make the
car go around the curve. That steering wheel isn't connected to the
front wheels." When it is established that the steering wheel IS
connected, the theorist says "The driver was controlling the way the
road looks in relation to the car." The experimenter says, "Oh, yeah? If
I paint over the windows, the car will stay in its lane anyhow." When
the car ends up in the ditch, and only then, the experimenter has to
give up and admit that the theorist might be right.

What the experimenter is always doing is saying "Oh, yeah?" and coming
up with some demonstration that the explanation is wrong, or that there
is another equally plausible explanation. If all attempts by the
experimenter fail, the theorist wins, for the time being. That's the
logic of the Test. Similar Tests can be devised for ANY theory. No
matter what the theorist says, the experimenter can look for ways to
test the implications of the theory. If all challenges fail, we have no
choice but to accept the theory -- at least until a more ingenious
experimenter finds a test that is failed.
----------------------------------
Incidentally, tensing a muscle does not, as Decartes believed, follow
from an increase in volume of the muscle as vital fluids pump it up. A
tensed muscle has LESS volume than a relaxed one. Now, you knew that,
didn't you?
-----------------------------------------------------------------------
Best,

Bill P.

[From Bill Powers (960220.1130 MST)]

Hans Blom, 960220 --

RE: epistemology

     Actually, my question was a bit broader than the measurement
     problem. In your example, my question would be how we can arrive at
     the concept of "relative humidity" unless it is somehow grounded in
     reality.

"Somehow" allows a lot of leeway. However, it is not necessary for a
perceptual variable to have any counterpart outside the controlling
system. I could build a control system, for example, which received the
clock time of day (T) and the Kelvin temperature (K) of a water bath,
and controlled [temperature minus time] by operating a heater in the
bath. There would be a brief glitch once a day when the clock went from
23.999 hours to 00.000 hours, but for the rest of the time the
perception could be maintained at any desired level that could be
achieved by varying the temperature of the water bath. Of course there
would be a finite range of control; not all reference values of T - K
could be reached.

You might ask why anyone would want to control T - K. The answer is the
same in any case: in order to control some other variable. I might build
such a device to achieve my goal of showing that perceptions can be
controlled even if they have no external counterparts.

Of course it is to the organism's advantage to control derived
perceptions that have some bearing on the organism's well-being. But
this is not the same as saying that such selected perceptions have one-
to-one counterparts in the physical world. The benefit of controlling a
made-up variable could be quite indirect. Isn't this the basis of
superstition?

···

-------------------------------------

RE: applying the test

     Say I create an extra flow in the fluid that introduces an extra
     force on the particle. In (discrete) simulations this, too, takes
     the form of picking up the particle and moving it somewhere else --
     just look at the formulas.

     [From your earlier post]

     In 1905 Einstein himself gave a theoretical foundation for Brownian
     motion by relating the particle's thermo-kinetic energy to the drag
     forces that arise due to its movement in the fluid (as had already
     been described by Stokes). Einstein provided us with the formula

          2 k.T
         d = ---------- . dt
              3.pi.eta.r
     where

        2
       d = the (average) square of the particle's displacement
         during a time dt; the direction of the displacement is random
       k = Boltzmann's constant
       T = absolute temperature
       pi = 3.14159...
       eta = the fluid's viscosity
       r = the particle's (average, effective) radius

The Einstein equation is not an equation of motion, but a solution of
such an equation. There is no place in an equation like this to
introduce another causal factor, such as a magnetic or gravitational
force on the particle. In fact, the equation can be true as stated only
if there are NO other forces acting. So we have to take a different
approach.

Your proposed control system makes r depend on d. You don't mention any
reference level for d, but I presume there is one in your simulation
(even if it's just zero). The reference level of d is defined for your
situation as that value of d at which there is no tendency to increase
or decrease r.

To introduce a disturbance, we would have to look at some of the other
variables on which d depends. In the above equation, we have only eta
and T as potential ways of introducing disturbances (we can't change
natural constants).

Suppose we choose T. If your system is a control system, then varying T
in the absence of your system would have a predictable effect on
displacement. With your system acting, the displacement should tend to
return to the undisturbed value, or to change less from the reference
value than it did when your system was not active.

So basically we want to see if the partial derivative of (d^2) with
respect to T is less when your control system is acting than when it is
not acting. And of course it is of interest to see _how much less_ the
effect is when control is present.

You could also vary the viscosity, eta, and use that in another Test.

When I suggested applying a disturbing force, I had not really looked at
the equations to see that there is no term corresponding to a force.

Can you try this with your simulation?
---------------------------------
I said

we have
(1) effect = f(cause)
In circular casuality, we have
(2) effect = f(cause,effect)

You said
     One of the first things that control engineering students learn is
     how to reduce expressions of form (2) into expressions of form (1).

I beg to differ: the first thing they have to learn is how to set up the
system equations. That is the stage where you come up with a type (1) or
a type (2) representation. Only then can you reduce equation (2) to its
simplest form. This does not mean that the physical systems are of the
same kind. Systems without feedback are physically different from
systems with feedback.

     Remember that a practical _passive_ LC-circuit can have a voltage
     gain of 100 or more, depending upon its "quality".

A voltage gain, but not a power gain. There is always a power loss in a
passive circuit. The electrical energy stored in the resonant circuit is
always less than the total energy that has entered it.

When we speak of loop gain in a control system, we should really refer
to power gain, not amplitude gain. The basic symptom of power gain is
the one-way effect we see in perception and also in action. On the input
side, a negligible amount of energy input is amplified to create a
signal, but injecting a signal at the same point does not cause an
equivalent reflected effect on the input energy process. At the output,
an energetically tiny signal produces a large output force, but pushing
on the output does not alter the signal (not backward via the muscle).
To maintain this assymetry of effect, in which action does NOT equal
reaction, it is necessary to draw on internal energy supplies. That is
where the power comes from in a system that shows power gain.

A step-up transformer seems to amplify the incoming AC signal, because
the output signal is larger than the input signal. However, the power in
the output signal is always less than the power in the input signal, and
loading the output will affect the input signal. In a transistor
amplifier that converts a low input voltage into a higher output
voltage, the power in the output signal can be thousands to millions of
times greater than the power in the input signal; the unaccounted-for
energy comes from the battery operating the transistor. Loading the
output -- even short-circuiting it -- will have only a neglible effect
on the input signal.

Equilibrium systems without internal power supplies always show an
energy balance; physical influences work in both directions, action and
reaction always being in balance. As I have pointed out before, when you
displace a marble in a bowl, the marble resists the push, but the energy
used to restore the marble to center when the push is removed is never
greater than the energy put into it by the push. The marble has no
internal store of energy on which to draw, so it can't be a control
system (or any other kind of active system). Its power gain is less than
1.
---------------------------------
     So to say that there is a "fundamental difference" between the two
     "types of causality" will not be appreciated by many control
     engineers.

Then they should go back to school. I think that any control engineer
who confuses systems with and without feedback is in big trouble.
--------------------------------------------------------------------
Best to all,

Bill P.