[From: Oded Maler (931203)]
Bill Powers (931202.0750 MST)
[A post with which I agree wholeheartedly (?) about Engineers,
Mathematicians (and psychologists which are neither)]
* The second
* aspect requires mathematical training, the more the better. This,
* unfortunately for me, requires not only the availability of good
* mathematical training, but the capacity to absorb it, which is
* not given to all of us in equal measure. I absorb mathematics a
* little better than the average person does, but compared to what
* others can do with mathematics, I am a Neanderthaler.
Me too (in fact the scale of math skills is multi-dimensional).
* Good system analysis requires both aspects. Great mathematicians
* often have lousy physical intuition. Great intuitionists often
* detest and distrust mathematics. But most of us are neither kind
* of greats, so our best bet is to find a balance within our
* capabilities.
Yes! And unlike others (no names) you do not make an ideology
out of your limitations.
In the rest of this post I want to share some trivial thoughts
I had last night on the difference between PCT and Control Theory
(the latter is used in the general sense of math and engineering,
that is, the theory of how to influence dynamical systems by
observing them and by applying some input to them).
The (simplified) world picture of Control is that of a plant ( = an
open dynamical system) with two input channels (one for disturbances,
one for control) and one output channel (observations of the state
of the system). The controller is another dynamical system plugged
into the plant, taking the observation on the plant as its input,
and its output signal enters the control channel of the plant.
A controller is good if for all/almost all/all-reasonable possible
disturbance, the trajectories of the plant state over time will
have such and such properties (e.g., temperature always around 22
degrees). An ECS in PCT, for example, is good if for all reasonable
disturbances, the CEV (which is a function of the plant's state
variables) is most of the time near its reference value.
Ususally Control systems are discussed and analyzed using "objective"
terminology (Boss reality). It is the state of the plant that is
"controlled for" although the observation function (perception)
is all that can serve as a basis for the control law. The reason is
that we design such systems to achieve something in Boss reality
(at least in the shared consensus about it), so the CEV,
height-of-airplane is what is imoprtant for the analysis, not
the "inner feeling" of the controlling computers and sensors.
In this type of control, what is important for us is what is
controlled, and it is generally the "principal aspects" of the
plant (this is a vague term, I'll try to explain). The state
variables of the airplane as a plant, include height, velocity,
etc., and they are what is controlled. The sensored are designed
that way, and the effector indeed affect these variables.
If however we extend the boundaries of the plant to include
not only the spatio-temporal neighborhood of the airplane
at a given moment, but include a much larger region including
changes in whether, light, etc., we will see that the controller
controls a tiny portion of the plant/world/environment, and moreover,
viewed from a global point of view, this part is not fixed but moves
along as the airplane advances. The part of the world that is
controlled is carried away by the moving controller via its sensors.
The analogy with resepect to a living control system in the world is
clear. Such a system is also a controller but the tiny part of the
world that it controls is not fixed (from Boss reality point of
view). However (coming back to the "why-how" issue from a couple
of weeks ago) at certain periods of time, the living control system
is also a traditional engineering control system whose actions
influence directly the objective state variables (if coffee is too
complicated, consider walking) and the analysis of how/why it succeeds
is important.
End of armchair comments.
--Oded