[From Bill Powers (931207.0920 MST)]
Martin Raylor (931207.1750) --
Sounds to me as though the Ecological Information Systems people
are trying to construct some perceptual input functions.
···
--------------------------------------------------------------
Hans Blom (931207) --
My models don't do any
predicting (except, perhaps, for functions which you "could
see as predictions" if that's what you wanted to see). Maybe
I'm missing your point.
You may be. Your models do what I call a prediction as soon as
you introduce a "slowing factor" or some such, so that your
system contains formulae like
x [k] := f (x [k-1])
Perhaps we mean something different by "prediction." To me,
prediction implies computing the value that a variable will have
some time in the future. The slowing factor results in computing
a value that is a summation over past values, decreasingly
weighted by time into the past. To make this into a prediction, I
should think that you would have to look at derivatives of past
values, compute a present value of the derivatives, and then
extrapolate using those derivatives to some value that has not
yet occurred. My models don't do that; such extrapolations would
require many more computations, including keeping track of first
and second differences and more, fitting of curves to the
resulting data, and computing a new value for t = present time +
deltat.
A more suitable candidate for the label "prediction" would be a
perceptual signal that contains a first derivative component of
the signal representing the controlled variable. As the
controlled variable changes, the rate component makes the
perceptual signal appear as it will be some short time into the
future (in comparison to a proportional representation), and that
is the signal that is actually controlled. The output of the
system will begin to drop before the proportional component of
the perceptual signal actually reaches the reference level. This
introduces damping into the system.
Prediction is not necessary, but only if you continuously have
and process all the perceptual information that is needed as
feedback for all your simultaneous goals.
This conclusion is one of the drawbacks you face because of not
using a hierarchical model. By requiring control to work at a
single level, you lay the burden on your model of keeping track
of great numbers of variables -- not all of which, as you say,
are actually represented in perception.
In a hierarchical model like HPCT, there are many hundreds or
even thousands of lower-level control systems that automatically
make their perceptual variables match the reference signals they
are given by higher levels, resisting disturbances without
needing to know what is causing them. Without lower-level
control, the overall system would somehow have to be able to
detect or guess at those detailed disturbances and compensate for
them, because their effects would not be nullified, nor would
they be directly manifested in the single composite perception.
I contend that at all times most of that information
is missing and that we, moreover, would not have the means to
process all that information in real time.
Under your model, processing all that detailed information may be
necessary. It is far less necessary under HPCT, because any one
control system is responsible for controlling only one scalar
variable in a single dimension. This means that there are no
multidimensional disturbances, either: the only effect a
disturbance, however complex, can have on one of these elementary
control systems is to increase or decrease the perceptual signal,
and the only effect that the output has to have is to decrease or
increase the same perceptual signal. This greatly reduces the
computational load on higher levels of organization. Just imagine
how complex a control system for directing walking to the mailbox
would have to be if it also had to adjust for irregularities in
the ground over which it was walking. In a hierarchical system,
the system that controls the spatial relationship between the
body and the mailbox doesn't have to be concerned with walking
over irregular ground or in a wind; it needs only to specify
walking speed and direction, and the lower systems take care of
achieving those subgoals, automatically resisting the effects of
detailed disturbances.
Luckily, our goals need not be realized EXACTLY. We seem to be
quite robust against disturbances, and we create our world that
way. The lane in which I drive is much wider than necessary,
were I able to drive exactly in its middle. Here, control is
allowed to be uncertain and involve statistical variations.
The reason we are robust against disturbances is that we prevent
most of their effects from happening before they become
important. That is what the lower levels of control do; the
higher levels aren't even aware that the disturbances occurred. I
contend that you are greatly underestimating the effect of
natural disturbances that occur during most ordinary behaviors.
The reason is that you see no effects from these disturbances,
and the reason you see no effects, I contend, is that there are
many lower-level control systems acting which you do not
acknowledge.
The lane is not so wide that you can have a net steering error
over a 100 km trip.
Yet, on the Autobahn I assume -- thus far correctly -- that I
do not suddenly encounter a large pothole. Here I rely on
prediction in order to be able to drive at the speed that I do;
feedback would be too late. Am I missing your point?
You may be predicting that there will be no potholes, but all
that means is that you are controlling in a way that makes no
provision for potholes. It isn't the prediction that enables you
to drive the car. It would be very useful in sorting out what is
happening here if you were to consider hierarchical levels; one
level that selects the manner of driving on the basis of a
slowly-changing perception of the frequency of potholes on the
Autobahn, and at least one lower level that receives the
reference-signal specifying how to drive and actually carries out
the driving.
That is a matter of how you define control. In my view, control
is still control if it includes episodes of going ballistic.
Are YOU controlling your way to Paris on board your plane? Or
are you just part of the plane's cargo during that part of the
trip? What is the "correct" view?
In a single-level model this problem is very hard to solve. If
the entire system is "flying to Paris," then it's hard to see how
there can be any control while the pilot, instead of you, is
flying the airplane. In a hierarchical model, the only
"ballistic" aspect is the decision to board the airplane as a
means of getting to Paris. However, it's clear that lower levels
of control are still operating; you can still walk to the gate in
the terminal carrying your baggage, pick your ticket out of your
pocket, have a friendly word with the flight attendant, find your
seat, sit in it, get up occasionally to stretch your legs or find
a magazine, balance upright while you are doing so, do some final
corrections on the paper you're going to present, eat a snack and
have a drink, and get off the airplane when it lands. None of
those detailed control processes is "ballistic."
A better way to see the situation, available only from the point
of view of a hierarchical model, is that the highest level of
control involved is very slow. Only after you have found yourself
disembarking in LeHavre several times will you perceive that this
way of getting to Paris is not working as well as it might, so
you have some reason to pick another way of getting there, like
another airline, or a train, or a bus, or a car -- as a way of
gradually correcting the high-level error over a long series of
trips. In the meantime, your lower-level skills at packing your
bags, buying tickets, getting to the airport or bus station or
car rental agency, amusing yourself on the trip, and proceeding
to your destination at the end of the trip, go right on working
as usual. All that differs from one instance to the next is which
set of lower control systems is brought into action by giving
them nonzero reference signals. And the system doing this
selection never has to be concerned with how to bring about the
specified perceptual situation; the lower systems already know
how to do that.
Are you saying that ALL perception is imagined?
Basically, yes. As you may recall from my diagram, all control
is based on the internal map. Perceptions, in my view, are used
to tune that inner map on which control, in turn, is based.
So the tuning of the inner map is based on imagined perceptions?
I think we need a way to include present-time perceptions with
those generated by the internal model. The problem with using
model-assisted control ONLY is that the process of updating the
internal model has to be extremely rapid if the system is to be
able to counteract ongoing disturbances -- like recovering from a
stumble while you're walking. If the updating is very rapid,
however, you lose the advantage of the model, which is to bridge
gaps in the input stream. It's important for control that the
perceptual signals that represent the environment represent the
_present-time_ environment as nearly as possible. When you're
driving past the downwind side of a truck in a crosswind, you
have only a fraction of a second to correct the tendency of the
car to swerve into the truck when you enter its wind shadow, and
to avoid overcorrecting and veering into oncoming traffic.
Somehow this seems too rapid to be accounted for by updating a
model of the car, the truck, and the wind effects.
In a hierarchical control system, model-assisted control would be
confined to higher levels, with lower levels operating in present
time only. Because the variables with which higher systems are
concerned change more slowly, and because disturbances of many
kinds are taken care of immediately by lower levels, the concept
of model-assisted control becomes more feasible at the higher
levels.
In a PCT model, a perception is used in order to satisfy a
goal. Perceptions that have nothing to do with goals are simply
discarded as "noise". How can you have accurate perceptions as
long as you have goals? Sounds like Zen?
In a PCT model, action is varied in order to bring a perception
to a match with a goal, which is specified as a reference signal.
The reference signal is like a sample of the perceptual signal as
it is to be (Sollwert). The subject of the accuracy of
perceptions (i.e., how well they correspond to other measures of
the environmental situation) is irrelevant. If the perception is
accurate, repeated episodes of control will bring the external
situation into a repeatable state; if perception is inaccurate,
matching the perception to the reference signal will result in
bringing the external world to a different state each time.
If you're going to draw conclusions about the PCT model, you
should use the PCT model. In the PCT model, it is perception that
is controlled, and each control system controls only one kind of
perception. This is very different from the model you use, in
which a perception is a whole vector of signals all being
manipulated at once, and in which the emphasis is on controlling
the external counterpart of the perception. In the PCT model,
control is maximally detailed, one control system controlling
only one degree of freedom of the perceived world. Other
perceptions (other degrees of freedom) are irrelevant; they are
not "discarded as noise" by a control system, because the control
system doesn't even know they exist. One control system perceives
only one variable. It controls only one variable. It is
completely (or nearly) independent of other control systems
operating at the same level.
So far I don't see how "real true Boss Reality" even gets into
the picture. Is it assumed that the internal x[k] is a real
true representation of Boss Reality?
Assume that you have what control engineers call a "black box",
a system with an input and an output, and that it is your goal
to "get to know" the object. If the "black box" is a hi-fi
amplifier, you know how to do this: offer a test signal to the
input and measure the output. You can get to know the
amplifier's frequency transfer function, the amplifier's
distortion at different frequencies and at different power
output levels, its music and sine wave output power, and a lot
more, if you're really interested. But if you are forbidden
to open the box, you will not be able to know its schematic.
I trust that you are speaking of how the envuironment looks from
the standpoint of the control system. I agree that this is how
the organism must go about understanding its environment: the
environment, as Ernst von Glasersfeld said, is the black box, not
the observer. All the observer can know of the environment comes
from the signals generated by its sensors.
So constructing the model depends on observing perceptual inputs
from the external black box, and acting on the black box, and
constructing some internal model that is equivalent in terms of
inputs and outputs.
I agree that this is how our higher-level systems work, most
probably (after all, aren't we living examples of that process?).
However, the lower-level systems needn't work this way. In the
Little Man model, there is no model (in the control system
itself) of the external world -- of the arm's masses, moments of
inertia, laws of dynamics, etc. Instead the physical arm itself
becomes part of the control loop; the control system, simply
through negative feedback actions of simple kinds, generates the
required inverses without ever explicitly computing them.
This, however, makes no sense in terms of your model, which has
only one level.
-------------------------------
RE: comments on "notes from an observer."
Thank you for your judgment; it makes me feel absurdly happy when
people like what I write. I have read Pirsig, and also did some
translating, much like yours. I wrote to Pirsig once, but you can
imagine that it must have looked like another nut letter among
the avalanche of mail he must get. No reply, of course.
-------------------------------
Can Hans' model have a conflict?
No, it cannot. And neither can people, in a way. We CAN have
incompatible goals, however. We want to eat our cake and have
it. That is human, all too human.
But "incompatible goals" is what "conflict" MEANS in PCT. It's
exactly wanting to keep your piece of cake (meaning that you
mustn't eat it) and eat it too (meaning that you will no longer
have the piece of cake) that sets up a conflict: two independent
control systems simultaneously send opposing reference signals to
the same lower-level system (the one that is in charge of eating
cake). As a result, neither higher-level system can achieve its
goal. The solution is to reorganize: one higher-level goal could
be changed from "wanting to eat THIS piece of cake" to "wanting
to eat SOME piece of cake." Then one control system could save
THIS piece of cake while the other ate a DIFFERENT piece of cake.
End of conflict.
Can it know it has a conflict?
Sure, why not? But then it will consider the different goals'
priorities, do some machine arithmetic as to future outcome and
discard one goal or find a best compromise, very much the way
people -- or chess computers -- do.
But how can a single-level system perceive anything about its own
operation? Its perceptions are a model of the external world, not
of the system itself. This is another disadvantage of a single-
level model. Remember that in an organism, there is no engineer
standing by to fix internal problems like conflicts. If your
model can "consider" goals, it must be able to _perceive_ goals,
which implies a higher level of perception. The only way a system
can know of internal conflicts is to be able to perceive them.
Half an hour in the life of a hierarchical perceptual control
system, babe, that's really what it is. All you have to do is
pay attention.
That's really WHAT IT LOOKS LIKE, babe. It's all perception,
you know. Or can you REALLY calibrate against Boss Reality?
Semi-touche'. But you don't need a model to see that your actions
are making your perceptions be what you want them to be. To see
that, all you have to do is put your hand in front of your face
-- that is, create an action that brings about a visual image
that you selected beforehand. That's the phenomenon that we try
to explain with PCT.
I do not care much for a hierarchical model, for several
reasons. First, there are the things that McCulloch pointed to
and why he talked about "heterarchies": it just isn't always
true that if we prefer A to B and B to C, that it follows that
we prefer A to C.
That's the wrong kind of heterarchy: it's a logical heterarchy,
not a physical one. In fact, you could set up three control
systems which perceive relations among A, B, and C, and easily
end up with three perceptions: A>B, B>C, and C>A. Apples are
redder than oranges; oranges are sweeter than lemons; lemons are
prettier than apples. So I like apples better than oranges when
considering color, oranges better than lemons when considering
sweetness, and lemons better than apples when considering beauty.
This is what McCullouch (and others who took this paradox and ran
with it) overlooked. The supposed paradox can occur only when the
basis of comparison shifts (as it often does in real life, as
when comparing pairs of political candidates).
Third, the hierarchical level seems to be very much in the eye
of the beholder. Assume that it is my goal to live for the next
ten years. Then it must be one of my subgoals to keep my heart
beating. But now assume that it is my highest goal to keep my
heart beating for the next ten years. Then I must have the
subgoal of staying alive all that time, with all that it
implies: getting food, the money for it, a job, ad infinitum.
Which is the "higher" goal?
Again, wrong kind of hierarchy: verbal, not physical. I am
talking about a physical hierarchy, in which systems of one level
are given their reference signals by systems of higher levels,
thus becoming part of the higher-level output function. If you
trace the source of reference signals, it's no longer a matter of
the hierarchy being in the eye of the beholder. The hierarchical
relationship is whatever you find it to be. The higher goal is
the reference signal entering a control system whose outputs are
routed to the comparators of lower-level systems; that's what
establishes the higher-lower dimension.
The rate at which your heart beats is set by signals coming from
the hypothalamus. The heart system is an output function for
other systems, such as those concerned with maintaining blood
pressure and oxygenation. So the heart is hierarchically lower
than the system controlling blood pressure and oxygenation. It's
just a matter of circuit-tracing, not verbal tricks. When you
talk about keeping your heart beating in order to live long,
you're confusing levels and mixing verbalizations with processes.
Living long may be a verbal goal, but it can't be part of a
control process because there's no corresponding perception to
control. How do you perceive the length of time that you lived,
until the instant before it's too late? You can only imagine it.
And, at that same conscious level, how do you choose to keep your
heart beating, other than by refraining from actions that might
indirectly force it to stop (suicide)? Your heart beats not
because you want it to beat, but because it is operated by
control systems in your midbrain and brainstem, which are in turn
operated by higher systems.
Again, the advantage of a hierarchical system over a single-level
system. In a single-level system, you can't distinguish
intellectual goals from physiological ones.
That is why I prefer to talk about multiple
parallel/cooperating goals. Why not, after all? There is multi-
processing parallel computer hardware, and "concurrent
cooperating processes" is a buzzword in the software circuit.
Nice metaphors!
Why not? Because we can find clear hierarchical relationship the
anatomy of the behaving system. At each level there are clearly
many parallel systems (there are about 800 sets of control
systems concerned with controlling muscle tension and joint
angle, all operating at once). There's nothing in HPCT against
the idea of multiprocessing parallel computers; that's the very
heart of HPCT. We just say it also occurs at multiple levels of
organization.
But "cooperating goals" is something a bit different. For two
goals to "cooperate" they would have to be coordinated by
something (or else the result would just be a chance outcome of
the effects of different independent goals existing at the same
time). In order to be coordinated, there must be a coordinating
system. And right away you're into a hierarchy.
All connections at higher levels of the hierarchy can be seen
as paths going up from some goals and then down to others,
which transport information that keeps the low level goals
aligned and cooperating in simultaneously reaching all goals
despite disturbances in the outside world that no single
elementary control system can tackle. See how much you can read
into a PCT model? :->
Yes, but put on your glasses and get under a brighter light.
Where in the HPCT model are paths going up from some goals and
then down to others? How could this, by itself, possibly keep low
levels goals aligned and cooperating? What kind of disturbances
can't (and can) lower level systems handle? You're indulging in
arm-waving.
This cooperation works at the lowest levels as well. I take it
for established, for instance, that one of the functions of
the muscle spindle sensors is to keep the muscle's force
properly distributed over all motor units of that muscle (re
Guyton, one of the best modelers in physiology).
_Formerly_ one of the best modelers in physiology. If this is
what he says muscle spindles are for, he has just dropped several
places in the standings. The Little Man model actually expresses
the same relationships that have been known since the 1960s, and
is an implementation of a model by Houk from that decade (the
only actual implementation in a complete working model, I
believe). Guyton is looking at, I will concede, a possible effect
of having multiple stretch-control loops operating in a single
muscle, but to label this the most important effect is just a
mistake. The most important effect is to assure that the arm will
move as the alpha and gamma efferent reference signals specify,
the feedback strongly stabilizing the arm against dynamical
effects and disturbances. Have you seen the Little Man model
running? Have you looked at its test modes that show how the
various control loops work, and their effects on arm movements?
Have you studied the organization of this model so you understand
how it works? All you need is a reasonably fast PC compatible
(386 or 486 is best). I'll send you a copy of the model and the
writeup on request. Until you understand this model, you can't
claim to know anything about it. It has been pronounced by
several people the model of arm control most likely to be
correct. Does Guyton understand this model?
There is no need to compute
inverse kinematics or dynamics to produce the required driving
signals.
Predictive control can do without inverse kinematics as well.
In effect, it has a simulation running in parallel to the real
thing. Predictive control provides a prediction of where the
system would go if a certain control trajectory were applied.
Yes, but it's by far the hardest way to achieve the result using
feedback. You have to have an actual dynamical model and
kinematic model of the arm running inside the system. In the
little man, there is no need for an internal model. The arm is
its own model, if you please. Since there are feedback signals
that continually measure acceleration, velocity, and position,
modeling these same variables would be superfluous; the
information is always available from sensors.
As to "control trajectories," I begin to despair. There are just
so many differences between my approach and the standard one,
it's hard to get through two sentences without running into "new
problems" that are already handled. If you had studied the PCT
model and understood how it is applied, I wouldn't even have to
go into these matters.
Under the PCT approach, it is not necessary to specify all those
derivatives as well as positions to create a trajectory: in the
little man model, you just set a reference signal to a value and
the arm assumes the corresponding position, with a time constant
of about 0.1 sec. With position under such tight control,
"trajectories" can be created arbitrarily just by varying the
position reference signals. From there on up, there's no need to
consider dynamics; the lower systems have turned the dynamical
system into a simple fast proportional position servo. With the
higher systems controlling the right functions of joint angles,
there's no further need to consider kinematics, either. In a
hierarchical model, trajectories can be considered completely
separately from the dynamics of control. Trajectories can be
specified to follow any desired spatial or temporal forms, and
the lower-level systems will automatically create the required
torques at the joints. In the Little Man, you can make the
fingertip move in a circle around the target (stationary or
moving); this is done just by sending a sine and cosine wave as
reference positions to two of the visual control systems. The
control systems then create the required joint torques to produce
this result. Less than 100 lines of code are required to
accomplish this, including all of the control systems at all of
the levels (not counting visual ray-tracing and calculation of
the arm response to torques).
As I said, you could represent this entire hierarchical
control system, containing three systems at each of four
levels (counting the visual level), as a single overall
control system of the same form you use to represent all
control systems: a parallel vector processing model. It would,
however, be very complex.
Why would it be more complex? It DOES the same thing...
Hans, I'm going to strangle you if you keep this up. What do you
mean, it "DOES the same thing?" Do you mean that all possible
ways of doing the same thing involve system designs of equal
complexity? That's complete nonsense. Did you ever see a Rube
Goldberg drawing of a mousetrap, which starts off with the mouse
displacing a candle so its flame burns through a string that is
holding a bowling ball back from rolling down a ramp to compress
a bellows that starts a fan turning and unwinds a string
supporting a hammer which comes down on the mouse? Are all
mousetraps equally complex just because they do the same thing?
A hierarchical control system can do things very simply and
elegantly and with a minimum of computations, where a single
equivalent control system has to perform explicitly many
computations that are done in the hierarchical system without any
need for explicit computation. How would you write a program for
the circuits accomplishing visual control of a fingertip relative
to a moving target in three dimensions (given the visual
positions and a correct dynamical model of an arm and muscle that
supplies the torques), all in 100 lines of code? How about 1000?
How about 10,000?
If the only designs you have any experience with are the single-
level type, if you're never tried out the hierarchical concept
seriously, then you don't know what I'm talking about, do you?
Also, there
would be no indication of the clever tricks nature has found
for stabilizing the limb in a very simple way ...
That may be true, but you have to decide whether you want a
"performance model", i.e. a model that shows the same outward
behavior only, or a model that is as accurate a replication as
possible of the full human physiology. A "performance model"
of a hi-fi amplifier may have very different entrails. If you
want to accurately model the entrails as well, you ought to
study physiology. The problem is that we want both in our
models. All too human...
Well, I have studied physiology (and neuroanatomy) to a
reasonable extent, and I have used what I have found in the
Little Man model. I'm no expert, though. What I want is an
accurate performance model that uses circuits like the real ones.
In fact, at the lower three levels at least, I don't see
anything but a hierarchical model as being justifiable.
YOUR lower three levels, the choice of which forces you to
leave out the cooperation between muscle spindles in force
distribution, for instance. Are you sure that disregarding this
"detail" is allowed/has no effect?
Nothing forces me to leave out that detail, if it is real, but an
unwillingness to program all the parallel loops that actually
make up each reflex. It really doesn't make much difference
whether the forces are equally distributed in a muscle when one
is using a lumped model. I have access to measurements of the
overall force/tension relationship, which is all that matters for
moving an arm. The hierarchical aspects of the model would be
unaffected. I didn't propose that arrangement in a vacuum -- it
comes out of neurophysiology. The basic arrangement of feedback
loops, including signs of feedback, has been known for decades
and is not at all controversial. All that hasn't been done before
is to figure out what this arrangement accomplishes, and I think
I have done that to a good approximation.
In the HPCT model, this distinction is not really relevant,
because the only disturbances that matter are those that act
directly on the controlled variable, and all reference signals
are variable even if, for the moment, they may be constant.
Huh?
What's so hard about that? You can hold your hand in a fixed
position for five or ten minutes, or you can move it around. When
you're holding it still, the reference signal is constant. When
you're moving it, the reference signal is changing. In the HPCT
model, all reference signals are potentially variable, even
though some of them may be, for long periods of time, constant.
While it's interesting that a change in parameters might optimize
a control system differently for these different conditions, I
can't see this as a factor of major importance. If "tuning" can
improve performance a little, then some day we will put tuning
into the model. Right now it's really not the main problem.
If the
bed is seen about 5 steps away before the lights go out, and
you take 5 steps in the dark, you perceive yourself as near
the bed.
What do you mean by "perceive" in this context?
I mean "experience." Perceptions are signals in afferent
channels. The PCT model is constructed so that imagination places
recorded (or model-generated) information into the afferent
channels. From the level where this takes place on upward, the
systems work as they do with real (vs. imagined) perceptions.
When you characterize "walking" as open-loop, I don't think
you're really considering what is entailed in walking.
I did not characterize "walking" as open loop. What I
characterized as open loop is determining, while walking, my
position relative to an object without having sensory access to
that object. No feedback information, no feedback, yet I do
something. I call this non-feedback something "feed- forward".
Well, if walking isn't open-loop then it must be closed-loop.
Since you're using walking to accomplish some other goal, you
must be talking about a hierarchical system.
You keep saying "no feedback information" when several of us have
been pointing out that there is LOTS of feedback information
available in the dark. It just isn't visual. You can imagine
where the destination is in your perceptual map, or remember
where it last was, and you can update your current position using
kinesthetic and other real-time perceptions. So what's the big
problem?
Evolution does not stop; it does not have a GOAL, it is a
PROCESS.
Evolution -- change of genetic organization -- stops when the
species is organized to prevent selection pressures from acting
on it. It is quite possible that evolution has a direction; the
Cairnes et. al. experiments and the extensions on them reported
recently by Rick show that natural selection can be biased to
produce very quick results; E. coli has the ability to alter its
own mutation rate in a way systematically connected to selection
pressures. I have developed an argument showing how evolution
must select for increasing control over the local environment.
As to the nations doing "best", notice how culturally biased
and shortsighted that notion is.
What's culturally biased about noting that human populations
which reproduce with the most abandon end up dying of famine,
disease, war, and general misery? Are you saying there's a
cultural point of view somewhere in the world that sets up such
conditions as admirable? When a population manages to reproduce
itself into extinction, I think that's a fairly good indicator
that maximum rate of reproduction is not the ultimate criterion
of evolution.
What would a historian say about that a millennium from
now?
That they are all dead.
I don't
think we need to model optimal control, although the methods
of optimal control theory that apply to acquiring and
improving control probably will be part of the ultimate model.
Huh?
Some of the concepts of optimal control theory, such as various
methods for adapting a control system to the properties of its
environment, may (and do) play a part in our modeling effort.
However, I do not believe that we need to try to explain why
organisms are optimally organized, because I am quite sure that
they are not. There is certainly no evidence that they are.
Incidentally, in your model, what determines the setting of
the reference signal (the goal)?
In adaptive control models, there is always one "prewired"
goal, a variable that has to be minimized. This goal may be
composed of several sub- goals that have different weights.
Subgoals are most often expressed as errors squared, such as in
the expression (x [i] - xopt [i])^2, where x may be anything, a
direct perception, an internal variable of the model such as a
prediction, and sometimes a parameter that needs to be kept
within a range.
You didn't answer my question. You told me what the goals are,
but you didn't say what sets them. Who or what selects a certain
possible value of x[i] and says that it is the target xopt[i]
against which x[i] is to be compared?
... even if the prediction is in error for long times into the
future, as the critical event nears, the extrapolations become
shorter and shorter, so errors of prediction make less and
less difference. After the final prediction, control merges
into normal present-time control.
Errors of prediction apply to the whole flight path, not just
the final destination.
They don't apply to the part of the path you have already
traversed. Each new prediction starts from where you are (the new
appearance of the goal-position) so as you approach the
destination, the length of time over which you have to run the
model becomes shorter and shorter. If the model is good enough
for short times into the future, when you get close enough the
model will be accurate enough even without modification. You may
simply approach the destination along a slightly non-optimal
path. Optimizing the entire flight path is unnecessary, and
probably unachievable. How could you optimize to take the weather
into account?
Perhaps you're assuming that your relationship to the destination
is invisible, and your actual position is uncheckable, until you
have arrived. In that case, I would advise against taking the
trip.
Modeling this kind of control for human behavior would require
a lot of stipulations about perceptual functions that we don't
know how to model.
Be assured, we know how to model this -- in an autopilot. It is
not a matter of perceptual functions, but of maintaining,
adjusting and using an internal model.
I am not assured. How the heck can an internal model be
maintained and adjusted without perceptions? Or are you talking
about that engineer again, who is standing by with his
screwdriver to adjust the autopilot, using his own perceptions?
Martin Taylor says:
Rocks don't involve negative feedback systems (at the level of
_being_ rocks)
You say:
Let me nitpick a little with you. When I try to pull the rock
apart, the rock resists with equal force.
I would love to hear your defense of that being a control
process. What is the loop gain of this control system?
A colleague, an electromechanical engineer, caught me red-
handed reading my CSG mail. So I had to explain. Then he
replied: "So an electrical motor is a control system? I apply a
voltage to a small DC motor. That determines the number of
revolutions that will result. Then I try to disturb its
rotational speed by imposing a frictive load. The motor's back-
EMF now starts to deviate from the applied voltage. This
difference causes the motor to develop a lot more energy, which
fights the slowing down effect of the load. I see all
components of a control system there. Is a motor a control
system?"
Same question: what's the loop gain? Your colleague is just
blowing smoke. Let's see some calculations.
I was flabbergasted and did not have an answer. Do you?
Of course. It is not a control system. Its loop gain is less than
1. But I want to see YOU calculate it. I'm tired of returning
lobs.
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Best,
Bill P