[From Bill Powers (940422.0600 MDT)]
Bob Clark (940421.2155) --
Perhaps you were not surprised, as I was, by the implications
of the poor, that is, discontinuous, control of the usual
residential thermostatic system.
...
The Observer describes idealized living systems in terms of
variables that are continuous in both space and time. The
Observer converts seeming discontinuities into continuous form
by changing scales -- of space and time or both. Anything else
rapidly becomes unmanageable!
Sometimes a re-interpretation, a change of scale, helps in making
sense of a system. A home thermostat keeps room temperature within a
few degrees of the reference setting, which is good enough for human
comfort. What makes this system feasible is the thermal inertia of
the furnace and house. Although the temperature in the furnace flame
switches abruptly from room temperature to several thousands of
degrees c, the effect on room air temperature is very gradual, the
time-constant of temperature change being on the order of an hour.
If you stretch the time scale accordingly, the thermostat contacts
are always rapidly opening and closing, the continuous variable
being the "smoothly" changing duty cycle. When the heat losses are
high, the system behaves like
11111110011111110011111100...
and when they are low, it behaves like
11000000011000000110000001100000...
where 1 means "on".
···
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More important, perhaps, is _where_ is the ability to "predict"
included in PCT? And _who_, or _what_ does the "predicting?"
Well, how do you go about making a prediction? In the simplest
method, you estimate a trend, and then you extrapolate it in
imagination. You say "If it keeps getting warmer this fast, I won't
need to take a coat with me at lunch-time." Put this way, prediction
is a cognitive process using logical or mathematics-like
calculations. Sometimes we actually convert the problem into symbols
and use the formal calculations we have learned, with pencil and
paper. At other times we use a hybrid of logic and analog thinking,
as when we imagine throwing a ball, and see "in the mind's eye"
where its trajectory will end relative to an aiming point. Then we
think, "I'd better move closer -- I can't hit it from here." That's
the logic part.
I think that to make cognitive predictions, which is what we usually
mean by the term prediction, we have to be able to perform some sort
of mental calculations which create a symbolic representation (in
present time) of the states of perceptions at a future time. We can
then compare these predicted perceptions with present-time reference
signals, and use the error to alter our ongoing behavior. That
changes the input to the prediction process, thus changing the state
of the predicted perceptions, reducing the error, and so on until
the predicted perceptions match the present-time reference levels
for them. If the reference signals refer to the state of the world
at a fixed time in the future, then as we approach that time the
length of the extrapolation gets shorter and shorter and errors in
the method of prediction make less and less difference, so we can
guide present behavior cognitively to achieve a particular state of
perception at a particular time.
Even a home thermostat, however, can carry out a process analogous
to cognitive predictions. Most thermostats have an adjustment
labelled "anticipation." What this adjustment does is make the
contacts move closer together if the furnace is off or move farther
apart (that is, reduce the contact pressure) if it is on. The effect
is to make the furnace think the temperature has changed farther
than it has, so the furnace turns off before the set-point is
reached, and on sooner than it otherwise would have as the
temperature falls. The same effect is seen in the spinal reflexes,
where the muscle-length signal is actually the sum of one signal
proportional to length, and a second one proportional to the rate of
change of length. The net effect is to introduce some degree of
damping into a system that would tend to oscillate (or oscillate
more) without it.
In control theory the general term for predictive or anticipatory
control is rate feedback. The benefit of rate feedback is to make
control tighter and prevent overshoots. The cost is that as the rate
feedback component is increased, the system responds more and more
to small fluctuations in the controlled variable. In a home
thermostat, using too much anticipation setting causes the system to
cycle on and off more frequently, adding to the noise level and
wearing out the components of the system. The best setting is the
one that keeps the room temperature from cycling over a range large
enough to bother the human occupants.
When human beings do too much anticipating, they can waste a lot of
energy correcting random fluctuations that will probably correct
themselves without any need for action. People who do this are quick
and nervous types to jump at unexpected sounds and in general
"overreact." They react more to the first derivative of error than
to the actual error, as stock traders react in panic to a drop in
the Dow-Jones averages of 10 points (out of 3600). When I was almost
ready for my first solo flight (soaring over the saber-toothed
tigers and mammoths), I took off on one turbulent day and was having
a heck of a time keeping the airplane level. My instructor,
definitely not a rate-feedback type, look at me and asked "Why are
you doing that?" After a moment I got it and relaxed. If one bump
tipped the airplane one way, chances were that the next one would
tip the the other way. All I really had to do was control the
average levelness of the wings. No point in trying to correct every
tiny tilt, Ernie said. This wasn't just turning down the loop gain;
it was turning down the anticipation that if I didn't act instantly,
the airplane would end up upside-down.
At the other end of the scale, there are people who try to regulate
their lives, or the fortunes of a business, by making elaborate
cognitive long-range predictions. This is mostly a waste of time.
Events that take such a long time to develop are better controlled
in real time on the basis of current error. The bandwidth is very
low, because such long times are involved, so there is no need to
try to guess what every disturbance is going to be. NASA probably
operates with the most successful long-range plans ever seen, with
every contingency covered at great expense -- yet still they have to
send control systems along to handle contingencies that nobody could
anticipate. All plans -- which are really based on predictions --
start to go wrong the instant they are put into effect, and control
systems are needed to give events the little nudges, and sometimes
the big ones, required to keep the process near the "predicted"
trajectory. We almost always have to cheat to make predictions come
true. Not always, but usually. Martin Taylor will probably have a
comment about why this is true.
---------------------------------
Incidentally, Bob, one reason I'm lukewarm about your DME (decision-
making entity) is that it seems to require cognitive functions that
are not actually spelled out -- the same ones I have tried to make
explicit with my more numerous levels. One of those functions is
making predictions, which I think requires some sort of
logical/mathematica/rule-driven computational capability. "Making
decisions" seems to me too broad a term to describe a level. Even
"making predictions" is too broad, because by this term we mean many
different kinds of process.
On the other hand, I'm not wholly against the concept of a DME. In
our current state of understanding, it's often prudent to make
coarser distinctions, as we do when we distinguish merely between
"higher-level" and "lower-level" control processes. If we take the
DME to represent a long-distance view of a collection of higher
functions, it may serve as a shorthand way of making crude
distinctions, as between "cognitive" and "motor" systems.
On the other hand, we have to guard against letting the modeling
process degenerate into an unprincipled taxonomy. There are
unnumerable ways of classifying perceptions, with different
approaches slicing the pie in different directions to create
artificial categories. This can seem to create an orderly view of
the whole system, but since there are many alternative orderly
views, there is nothing to indicate that one is better than any
other. Some other criteria for ordering must be introduced. I tried
to do this in my guesses about levels, where I added the requirement
that higher-level perceptions must be functions of lower-level ones,
and controlling a higher-level perception requires altering lower-
level ones. Before I settled on the particular levels presented, I
spent a lot of time looking for exceptions and counterexamples --
and even then, didn't deal with all of them to my satisfaction. At
least I have presented some detailed rationales for each level,
other than the mere fact that one can choose to view the world in
that way. The way you create categories of perceptions seems
arbitrary to me.
Nevertheless I don't want to make a big deal out of this. We're
still at the beginning of constructing a justifiable hierarchical
model. It's just too soon to stake very much on guessing correctly
how decades of research are going to turn out.
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Richard Thurman (940421.0900)--
It's great to hear that you're introducing PCT to a big research
outfit. I should think that people working with virtual realities
and simulations would think PCT is self-evident -- doesn't everyone
know that? When you see a guy with his head hidden in a huge wierd
helmet waving his arms around and turning this way and that as if
looking at things, how else could you explain this than by saying
that this person is controlling perceptions? I think you should get
these people to rename their laboratory as "The Center for Applied
Epistemology."
Too bad about no bombs. I guess we'll have to keep trying to do this
the hard way.
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Best to all,
Bill P.