Sameness; chimps

[From Bill Powers (920618)]

Martin Taylor (920619,19)]

OK, I think I see the "sameness" problem now. I had thought initially,
Martin, that there were 4 objects of one kind in the midst of n objects of
other kinds, and I didn't realize that _continuous_ tracking was required
(i.e., you can't break for lunch and then go back to noticing the 4
objects). I didn't realize that you were selecting 4 objects for tracking
out of many other objects OF THE SAME KIND. All this changes the nature of
the problem rather drastically.

As you describe the problem, some number of objects, indistinguishable from
each other except by position, is presented to the observer. One to four of
these objects are pointed out to the observer as individuals to be
followed. The objects then all begin to move about in some manner at some
speed, and when they stop you ask the observer to point out the original
one to four objects.

The question you ask, as I now understand it, is how the observer knows
that these are the "same" objects. And my answer is that he doesn't. There
is in fact no way to verify that they are -- that during the melee, one of
the non-indicated objects didn't suddenly swap places with a tracked one.
The initial condition is that there are no distinguishing characteristics
other than position. If this remains true throughout, it is true at the end
as well.

There is, of course, an hypothesis that they are the same individuals. But
if, at any point during the moving-about, one of the non-indicated
individuals momentarily coincided with an indicated one (dots or other
identical figures on a computer screen), no observer would be able to
differentiate them, even by position, at that moment. So the two
individuals that depart from that position afterward have lost their
distinct identities. The same result would occur if the two individuals
moved in smooth paths, or in paths with a discontinuous kink in them at the
point of coincidence. Only the hypothesis that they move continuously would
lead to choosing the one set of identities after the coincidence, and
rejecting the other. So the question is how that could be done.

The problem you state breaks down into two questions: first, how does a
person keep track of SINGLE individual in a set of identical moving
objects, and second, given that the first question is answered, how can
more than one such process occur in the brain at the same time?

If the objects are all alike, then clearly their "identity" in terms of
their classification at the beginning, before movement starts, is
irrelevant. The objects would all be classified alike. They would,
furthermore, all have the same configuration, the same sensations, the same
intensities. They would all be showing the same transitions (none). One
might initially define them in terms of spatial relationships, but as soon
as the objects began milling about, all initial relationships would be
destroyed. If the motions were random, no hypothesis about a distinguishing
relationship (such as "the top center object" or "the object between two
others just to the left and right of it") would be borne out. Only the
hypothesis of continuity of path could possibly distinguish any object from
another if their paths led to a momentary coincidence. But if the objects
moved in curves that met at a tangent, continuity of first derivatives
would no longer suffice to distinguish them; if the period of coincidence
included a brief straight-line segment, no number of derivatives would
suffice. Identity would be lost, and any further identification of the
original object would be only a guess.

Following a given object successfully, then, requires that no two objects
ever coincide in a way that renders all hypotheses about their
characteristics irrelevant. In practical terms it probably means that the
objects must never coincide at all for any discernible length of time.

For a single object, we are left, then, with simple x-y spatial tracking. A
gate of finite size must be placed about the image of the object (neural
image), small enough that normally only a single object occupies it.
Movements of the object within this gate are detected, and the position of
the gate is controlled to keep the object at the center. The control
parameters of the gate are such as to be able to follow changes in the
direction and velocity of the object. Whatever object is in the gate at the
end of a period of continuous tracking is understood to be the "same"
object that was there initially (although, under the conditions you state,
there is no way to verify this). If tracking is interrupted for some time,
all indication of identify is lost.

To distinguish objects that momentarily coincide, in the absence of any
distinguishing features in the images of the objects, certain assumptions
must be built into the tracking circuitry. For example, it may be that
objects never move in a curve with less than a certain radius (no true
right-angle movements, instantaneous reversals, etc.). The bandwidth of the
tracking system would then be limited so that an object that too-suddenly
changes direction passes out of the control range. Thus if two objects
crossed paths and both appeared in the tracking gate, the average position
would suddenly depart from the smooth path being followed, but the tracking
gate would not be able to follow immediately this sudden change of
direction. The gate would be momentarily disturbed, but not enough to "lose
track" of the object originally being followed; as the other object passed
out of the tracking range, the tracking gate would quickly center on the
original object again, its "momentum" having carried it more or less in the
original direction for a while during the disturbance. This "momentum", of
course, is the result of the deliberate restriction on the speed with which
the gate can change its vector velocity. [Pat Williams, when you get back
on the net: note the relevance of this to your problem of changing bit-maps
to line drawings].

If the second object remained within the gate for too long a time, the
tracking system, which can work only in terms of centroids, would be unable
to pick the right object when the two (or more) objects diverge again. So
the size of the gate matters as much as the dynamic characteristics of the
gate movements. The more likely it is that two objects can occupy a given
size of gate area, the smaller the gate must be to retain a good
probability of following the "same" object. If the gate is too small,
however, tracking even one object would become difficult.

The gate would be entirely neural in nature. It would correspond to
focussing attention on a particular small but movable area in the visual
map of the outside world.

Now: the second problem, which is "how many gates of this kind can be
maintained at the same time?" Apparently, the answer is three, or sometimes
four. But I would think that this would depend on the characteristics of
motion and the density of objects in x and y. If the motions entailed
abrupt and arbitrary changes in direction, and the field of view were
densely-enough occupied, tracking even one individual correctly would
become unlikely. So there are many parameters in this situation. The
apparent limit of four objects could be simply a matter of probabilities:
the more objects that are being tracked, the greater the probability that
at least one tracking-gate system would encompass two objects and make a
mistake. I would set the limit at four only if three objects could ALWAYS
be tracked without error and five objects could NEVER be tracked without
error.

This long treatise, of course, is simply an exercise in modeling. A gated
tracking system is a model of one way (the only way I can think of that
would work) to follow a single object moving among identical-appearing
objects. This model introduces certain parameters of the situation:
characteristics of the tracking circuitry, which we guess at, and certain
characteristics of the experimental situation that become relevant under
that model. The model can be tested by seeing whether it predicts tracking
success and failure under conditions where the model would succeed or fail;
the model can be trimmed up by varying the experimental conditions to see
whether predicted effects occur, such as effects of object coincidences and
near-coincidences. In fact, it seems to me that it would be possible to
measure the size of the gate and the parameters of the gate position
control system in this way -- provided that the results continued to be
consistent with the model.

Under this model, "identity" is irrelevant, in the sense of one object
having any unique distinguishing characteristic at any level of perception.
And even "continuity" is, under certain conditions of near-coincidence in
space, problematical.

···

-------------------------------------------------------------------
Bruce Nevin (920419.1348) --

Sorry to be obtuse and to seem rejecting (or perhaps I should interchange
"to be" and "seem"). But you got my true reaction, which was that this mode
of description isn't very useful, even as a point at which to start
guessing at controlled variables:

    The alpha male is sitting bolt upright, jaw set, staring confidently
    into middle distance. The hair on his head, shoulders and back is
    standing on end, which gives him an even more imposing aspect.
    Before him crouches a subordinate, in a bow so deep that his gaze
    must be fixed on the few tufts of grass directly before him.

This observation, whether made of chimpanzees or humans, puts more
imagination than observation into the picture. "Upright" is one thing;
"bolt upright" is another, implying an imagined way of getting into that
position. "Jaw set" is completely imaginary unless you can feel the efforts
(if any) involved in holding the jaw in that position. "Staring" is OK, but
"confidently?" "Into the MIDDLE distance?" Those observations tell us a lot
about the observer but nothing (verifiable) about the observed. Hair does
stand on end, in certain places, but in a human being it is not a
particularly striking effect. Whether it creates an imposing aspect depends
entirely on how much you feel imposed upon by it. A "crouching" figure I
can imagine, but calling this a "bow" is certainly going too far. And
"subordination" is surely an interpretation, as is one's guess as to what
part of the ground is being gazed at, and what it is within the field of
view to which the crouching figure's attention is turned. My own guess is
that this subordinate is focussing on a imagined scene of catching this
threatening son-of-a-bitch alone with his back turned.

The colorful descriptions by Sagan and Drayan are meant to convey a
message: that chimpanzees behave just like human beings in certain basic
social respects. To make the message stronger, they use a lot of imagery
deliberately designed to evoke familiar perceptions in the (human)
listener. But in doing so, they bring in a great deal that isn't actually
observed. Even worse, they reify subjective impressions, even when
referring to human beings, making it appear that these impressions
correspond to something objective in the world outside the observer (and
incidentally attempting to qualify themselves as unbiased objective
observers by the use of these biased and subjective descriptions).

I think this kind of rhetoric is all but useless as a way of understanding
behavior. It's all on the surface -- literally, it's superficial. All it
does is describe, and the description is so strongly biased by underlying
concepts of cause and effect that it unconsciously pushes those concepts on
us. This way of describing nature focusses entirely on actions, outputs,
side-effects. It scarcely touches on what such actions accomplish -- or
even whether the effects noticed have anything to do with what the actors
are trying to accomplish.

If control theory teaches us anything, it's that actions and outputs and
side-effects thereof are only an indirect indication of what is actually
going on. We see what the actors are doing to their bodies and the world
around them, but we don't see what perceptions are important to those
actors, or what states of those perceptions the actors are trying to
achieve. We see, under the old way of thinking, that all these actions are
causing certain effects in the situation. What we don't realize is that the
effects are what are causing, calling for, the actions.

The "perks" of the alpha male are simply what the alpha male, and probably
any other male, wants. What are those things? Should we take it for granted
that some abstract condition called "dominance" is an end in itself, or
that it even has objective existence? Is dominance something sought, or is
it simply a side effect of being the strongest control system in a conflict
situation? Are the marks of submission effects of the dominance, or are
they simply all that is left to do by way of control when alternative modes
of action have been defeated by superior force? Do "perks" entail
obligations, or is it that when one set of goals has been accomplished,
others come to the fore?
----------------------------------------------------------------
(to everybody)

I've ranted for years to the CSG that if we want to have a revolution, we
must revolt. We can't just go on using the same old customary modes of
observation, description, and explanation if we want to find the
significance of the first new concept of human nature since Descartes. If
people are going to try to make a smooth transition into control theory,
preserving everything they had thought important up to that point and
simply adding a few new interpretations, where convenient and supportive of
former beliefs, we are going to get exactly nowhere. Control theory gives
us the chance to tear all of our old ideas down to their components and put
them back together into a new structure of understanding. There is a great
reluctance even in the smartest people I know, many of whom are on this
net, to give up on the old approach and really try out the new one.
Everyone has something (and for different people, different things) that is
too valuable or true to give up or rethink. Everyone has past
accomplishments that they don't want to analyze too deeply in terms of
control theory, lest a flaw be found. That's just controlling for being
right, and is quite natural.

But anyone who wants to be a control theorist has to start trying out
things that seem unnatural, doubting what seems right, giving up what seems
valuable. We have to have faith that by such acts of internal destruction,
we will arrive at something closer to the truth, and salvage what is really
worth salvaging, when the reconstruction, under new management, begins.
God, I really sound like a mindless revolutionary. But this is the way it
has to be. Otherwise we're just fooling around and trying to impress each
other for our own entertainment.
-----------------------------------------------------------------
Best to all,

Bill P.

[Martin Taylor 920622]
(Bill Powers 920618 ?)

Yesterday was the first day of summer. Temperature maximum in Toronto 10.8C
(about 51F), breaking the previous record for coldest maximum by 4 degress C.
Has Mount Pinatubo overcome the global warming?

Bill addresses the problem of tracking multiple "same" objects, but I think he
still sidesteps the issue Bruce brought up initially, that I was trying to
buttress with my introduction of the tracking study. First, on the tracking:

The problem you state breaks down into two questions: first, how does a
person keep track of SINGLE individual in a set of identical moving
objects, and second, given that the first question is answered, how can
more than one such process occur in the brain at the same time?

Bill points out that in principle one can only the objects if the targets
maintain differences from the distractors in at least one of position,
velocity and acceleration. That's quite true, and experimentally verified.
But even after two have been confused, the observer can still track about
four (depending, I think, as Bill says, on the motion statistics of the
ensemble). One of the four may be, from the experimenter's viewpoint, wrong,
but the observer sees the one that best fits whatever tracking method is
used by the ECSs that are employed. To be brief, I think Bill's analysis of
these two questions is more or less correct. But...

As I see it, the key problem is more like: third, how does the brain identify
that there exists N objects of a certain kind rather than one strong exemplar
of the kind. I've forgotten how Bruce originally put it, but perhaps I can
paraphrase. If there is an ECS controlling for the perception of an X, it
should satisfy its reference if an X is in its input. What distinguishes
thes existence of exactly three Xs in its input from the existence of one X.
Bruce asked if there might be a multiplicity of ECSs controlling for an X,
which would solve the problem if each was controlling for "an X THERE" rather
than just for an X. If THERE were some kind of an internally generated
reference (like a memory--a novel construct at this point, which I am not
going to stand behind), then the discovery of an X could lock THERE to the
place where the X happened to be, and would permit tracking. But how could
any other ECS controlling for the perception of an X know that the first one
was "taken?" I think there is a real problem here, and none of Bill's proposals
to date seem to solve it.

Please note that I am neither expecting nor demanding that Bill solve every
problem of PCT. Noting his comments on leadership, I hope that other people
(perhaps including myself) can solve them. But problems such as this one are
fairly central, I think, and must be solved within the "natural" hierarchic
structure if HPCT is to be taken seriously as the instantiation of PCT that
corresponds to real living beings. The basic statement of PCT, that behaviour
is all and only the control of perception, seems incontrovertible. How that
fact is developed into structure is not. HPCT seems a very sensible proposal,
but there may well be other equally sensible instantiations, and not all
living things necessarily use the same instantiation.

We accept as a working hypothesis that the perceptual control structure is
layered. Bill said in some posting shortly after I joined this group that
whenever he had thought of a level-jumping control, it turned out not to be
(appropriate/correct/necessary/simple?). Maybe so. In the neural network
business, multilayer perceptrons often work well, but there are other
architectures that are more appropriate for complex problems, including
specifically gated modular architectures in which smallish modules solve
sub-problems, and gating structures determine which subnetworks present their
solutions to higher modules. Perhaps control nets might work better on complex
problems if conflicts can be resolved by gating structures that permits some
modules but not others to exercise control? There are multitudes of possible
architectures, and we may not be constructed to use the most obvious one.

Simplicity is to be preserved where possible in science, and HPCT is a simple
structure. If it can solve problems as basic to perception as "there's an
X and there's another" or "I see a lot of Xs among the Ys" without the
introduction of new structures or concepts, so much the better. At present
I don't see the answer.

Martin

[From Bill Powers (920618)]

Martin Taylor (920619,19)]

OK, I think I see the "sameness" problem now. I had thought initially,
Martin, that there were 4 objects of one kind in the midst of n objects of
other kinds, and I didn't realize that _continuous_ tracking was required
(i.e., you can't break for lunch and then go back to noticing the 4
objects). I didn't realize that you were selecting 4 objects for tracking
out of many other objects OF THE SAME KIND. All this changes the nature of
the problem rather drastically.

As you describe the problem, some number of objects, indistinguishable from
each other except by position, is presented to the observer. One to four of
these objects are pointed out to the observer as individuals to be
followed. The objects then all begin to move about in some manner at some
speed, and when they stop you ask the observer to point out the original
one to four objects.

The question you ask, as I now understand it, is how the observer knows
that these are the "same" objects. And my answer is that he doesn't. There
is in fact no way to verify that they are -- that during the melee, one of
the non-indicated objects didn't suddenly swap places with a tracked one.
The initial condition is that there are no distinguishing characteristics
other than position. If this remains true throughout, it is true at the end
as well.

There is, of course, an hypothesis that they are the same individuals. But
if, at any point during the moving-about, one of the non-indicated
individuals momentarily coincided with an indicated one (dots or other
identical figures on a computer screen), no observer would be able to
differentiate them, even by position, at that moment. So the two
individuals that depart from that position afterward have lost their
distinct identities. The same result would occur if the two individuals
moved in smooth paths, or in paths with a discontinuous kink in them at the
point of coincidence. Only the hypothesis that they move continuously would
lead to choosing the one set of identities after the coincidence, and
rejecting the other. So the question is how that could be done.

The problem you state breaks down into two questions: first, how does a
person keep track of SINGLE individual in a set of identical moving
objects, and second, given that the first question is answered, how can
more than one such process occur in the brain at the same time?

If the objects are all alike, then clearly their "identity" in terms of
their classification at the beginning, before movement starts, is
irrelevant. The objects would all be classified alike. They would,
furthermore, all have the same configuration, the same sensations, the same
intensities. They would all be showing the same transitions (none). One
might initially define them in terms of spatial relationships, but as soon
as the objects began milling about, all initial relationships would be
destroyed. If the motions were random, no hypothesis about a distinguishing
relationship (such as "the top center object" or "the object between two
others just to the left and right of it") would be borne out. Only the
hypothesis of continuity of path could possibly distinguish any object from
another if their paths led to a momentary coincidence. But if the objects
moved in curves that met at a tangent, continuity of first derivatives
would no longer suffice to distinguish them; if the period of coincidence
included a brief straight-line segment, no number of derivatives would
suffice. Identity would be lost, and any further identification of the
original object would be only a guess.

Following a given object successfully, then, requires that no two objects
ever coincide in a way that renders all hypotheses about their
characteristics irrelevant. In practical terms it probably means that the
objects must never coincide at all for any discernible length of time.

For a single object, we are left, then, with simple x-y spatial tracking. A
gate of finite size must be placed about the image of the object (neural
image), small enough that normally only a single object occupies it.
Movements of the object within this gate are detected, and the position of
the gate is controlled to keep the object at the center. The control
parameters of the gate are such as to be able to follow changes in the
direction and velocity of the object. Whatever object is in the gate at the
end of a period of continuous tracking is understood to be the "same"
object that was there initially (although, under the conditions you state,
there is no way to verify this). If tracking is interrupted for some time,
all indication of identify is lost.

To distinguish objects that momentarily coincide, in the absence of any
distinguishing features in the images of the objects, certain assumptions
must be built into the tracking circuitry. For example, it may be that
objects never move in a curve with less than a certain radius (no true
right-angle movements, instantaneous reversals, etc.). The bandwidth of the
tracking system would then be limited so that an object that too-suddenly
changes direction passes out of the control range. Thus if two objects
crossed paths and both appeared in the tracking gate, the average position
would suddenly depart from the smooth path being followed, but the tracking
gate would not be able to follow immediately this sudden change of
direction. The gate would be momentarily disturbed, but not enough to "lose
track" of the object originally being followed; as the other object passed
out of the tracking range, the tracking gate would quickly center on the
original object again, its "momentum" having carried it more or less in the
original direction for a while during the disturbance. This "momentum", of
course, is the result of the deliberate restriction on the speed with which
the gate can change its vector velocity. [Pat Williams, when you get back
on the net: note the relevance of this to your problem of changing bit-maps
to line drawings].

If the second object remained within the gate for too long a time, the
tracking system, which can work only in terms of centroids, would be unable
to pick the right object when the two (or more) objects diverge again. So
the size of the gate matters as much as the dynamic characteristics of the
gate movements. The more likely it is that two objects can occupy a given
size of gate area, the smaller the gate must be to retain a good
probability of following the "same" object. If the gate is too small,
however, tracking even one object would become difficult.

The gate would be entirely neural in nature. It would correspond to
focussing attention on a particular small but movable area in the visual
map of the outside world.

Now: the second problem, which is "how many gates of this kind can be
maintained at the same time?" Apparently, the answer is three, or sometimes
four. But I would think that this would depend on the characteristics of
motion and the density of objects in x and y. If the motions entailed
abrupt and arbitrary changes in direction, and the field of view were
densely-enough occupied, tracking even one individual correctly would
become unlikely. So there are many parameters in this situation. The
apparent limit of four objects could be simply a matter of probabilities:
the more objects that are being tracked, the greater the probability that
at least one tracking-gate system would encompass two objects and make a
mistake. I would set the limit at four only if three objects could ALWAYS
be tracked without error and five objects could NEVER be tracked without
error.

This long treatise, of course, is simply an exercise in modeling. A gated
tracking system is a model of one way (the only way I can think of that
would work) to follow a single object moving among identical-appearing
objects. This model introduces certain parameters of the situation:
characteristics of the tracking circuitry, which we guess at, and certain
characteristics of the experimental situation that become relevant under
that model. The model can be tested by seeing whether it predicts tracking
success and failure under conditions where the model would succeed or fail;
the model can be trimmed up by varying the experimental conditions to see
whether predicted effects occur, such as effects of object coincidences and
near-coincidences. In fact, it seems to me that it would be possible to
measure the size of the gate and the parameters of the gate position
control system in this way -- provided that the results continued to be
consistent with the model.

Under this model, "identity" is irrelevant, in the sense of one object
having any unique distinguishing characteristic at any level of perception.
And even "continuity" is, under certain conditions of near-coincidence in
space, problematical.

···

-------------------------------------------------------------------
Bruce Nevin (920419.1348) --

Sorry to be obtuse and to seem rejecting (or perhaps I should interchange
"to be" and "seem"). But you got my true reaction, which was that this mode
of description isn't very useful, even as a point at which to start
guessing at controlled variables:

    The alpha male is sitting bolt upright, jaw set, staring confidently
    into middle distance. The hair on his head, shoulders and back is
    standing on end, which gives him an even more imposing aspect.
    Before him crouches a subordinate, in a bow so deep that his gaze
    must be fixed on the few tufts of grass directly before him.

This observation, whether made of chimpanzees or humans, puts more
imagination than observation into the picture. "Upright" is one thing;
"bolt upright" is another, implying an imagined way of getting into that
position. "Jaw set" is completely imaginary unless you can feel the efforts
(if any) involved in holding the jaw in that position. "Staring" is OK, but
"confidently?" "Into the MIDDLE distance?" Those observations tell us a lot
about the observer but nothing (verifiable) about the observed. Hair does
stand on end, in certain places, but in a human being it is not a
particularly striking effect. Whether it creates an imposing aspect depends
entirely on how much you feel imposed upon by it. A "crouching" figure I
can imagine, but calling this a "bow" is certainly going too far. And
"subordination" is surely an interpretation, as is one's guess as to what
part of the ground is being gazed at, and what it is within the field of
view to which the crouching figure's attention is turned. My own guess is
that this subordinate is focussing on a imagined scene of catching this
threatening son-of-a-bitch alone with his back turned.

The colorful descriptions by Sagan and Drayan are meant to convey a
message: that chimpanzees behave just like human beings in certain basic
social respects. To make the message stronger, they use a lot of imagery
deliberately designed to evoke familiar perceptions in the (human)
listener. But in doing so, they bring in a great deal that isn't actually
observed. Even worse, they reify subjective impressions, even when
referring to human beings, making it appear that these impressions
correspond to something objective in the world outside the observer (and
incidentally attempting to qualify themselves as unbiased objective
observers by the use of these biased and subjective descriptions).

I think this kind of rhetoric is all but useless as a way of understanding
behavior. It's all on the surface -- literally, it's superficial. All it
does is describe, and the description is so strongly biased by underlying
concepts of cause and effect that it unconsciously pushes those concepts on
us. This way of describing nature focusses entirely on actions, outputs,
side-effects. It scarcely touches on what such actions accomplish -- or
even whether the effects noticed have anything to do with what the actors
are trying to accomplish.

If control theory teaches us anything, it's that actions and outputs and
side-effects thereof are only an indirect indication of what is actually
going on. We see what the actors are doing to their bodies and the world
around them, but we don't see what perceptions are important to those
actors, or what states of those perceptions the actors are trying to
achieve. We see, under the old way of thinking, that all these actions are
causing certain effects in the situation. What we don't realize is that the
effects are what are causing, calling for, the actions.

The "perks" of the alpha male are simply what the alpha male, and probably
any other male, wants. What are those things? Should we take it for granted
that some abstract condition called "dominance" is an end in itself, or
that it even has objective existence? Is dominance something sought, or is
it simply a side effect of being the strongest control system in a conflict
situation? Are the marks of submission effects of the dominance, or are
they simply all that is left to do by way of control when alternative modes
of action have been defeated by superior force? Do "perks" entail
obligations, or is it that when one set of goals has been accomplished,
others come to the fore?
----------------------------------------------------------------
(to everybody)

I've ranted for years to the CSG that if we want to have a revolution, we
must revolt. We can't just go on using the same old customary modes of
observation, description, and explanation if we want to find the
significance of the first new concept of human nature since Descartes. If
people are going to try to make a smooth transition into control theory,
preserving everything they had thought important up to that point and
simply adding a few new interpretations, where convenient and supportive of
former beliefs, we are going to get exactly nowhere. Control theory gives
us the chance to tear all of our old ideas down to their components and put
them back together into a new structure of understanding. There is a great
reluctance even in the smartest people I know, many of whom are on this
net, to give up on the old approach and really try out the new one.
Everyone has something (and for different people, different things) that is
too valuable or true to give up or rethink. Everyone has past
accomplishments that they don't want to analyze too deeply in terms of
control theory, lest a flaw be found. That's just controlling for being
right, and is quite natural.

But anyone who wants to be a control theorist has to start trying out
things that seem unnatural, doubting what seems right, giving up what seems
valuable. We have to have faith that by such acts of internal destruction,
we will arrive at something closer to the truth, and salvage what is really
worth salvaging, when the reconstruction, under new management, begins.
God, I really sound like a mindless revolutionary. But this is the way it
has to be. Otherwise we're just fooling around and trying to impress each
other for our own entertainment.
-----------------------------------------------------------------
Best to all,

Bill P.