Models vs. perceptions

[From Bill Powers (950515.0750 MDT)]

Oded Maler (950515) --

     You see someone running at a visible point A from left to right,
     then disappears - what is the explanation of the fact that you will
     try to catch him at the next visible point B to the right?

     A -----> B
     <Obstacle>

There are at least three possibilities.

1. You have an internal model of the moving person which can run
independently of your perception of the moving person. Normally, your
eyes track the moving person using real-time perceptions. When the
perception is lost, you switch to tracking the output of the internal
world-model, an imagined moving object (this is the proposal Hans Blom
is offering).

2. When the person disappears, you know from experience that the person
is likely to reappear on the other side of the obstacle, so you cease to
track the person and you move your eyes to the point of previously
observed reappearance. When the person shows up, you switch back to
tracking.

3. Tracking consists of maintaining a relationship between the moving
person and the center of the visual field. The tracking control system
uses an integrating output function, and the output varies a reference
signal for eye-movement velocity so as to keep the target centered. When
vision is lost, the relationship control system is turned off, making
the error zero. The output integrator holds its output, maintaining a
constant reference signal for the eye velocity control system, so the
eyes continue to move at the same rate they moved when the perceptual
signal was lost. When (if) the person reappears, the relationship system
turns back on, and real tracking starts again.

1 and 3 are similar, except that the mechanism is different. In 1, there
has to be a world-model that can generate an imagined motion of the
person, leaving the control system to control as if the signal were
real. In 3, there is no imagination connection and no world-model; there
is only an integrating output function that maintains its output signal
until real-time tracking can start again.

2 uses neither a model of the person nor imagination: it relies on
sequence control, in which there is an expected sequence of
disappearance and reappearance at different places.

Which explanation should be used depends on how people actually behave
in this situation. A very young child seeing the person disappear will,
according to Piaget, simply turn its attention to something else, and
will be surprised if the person (or toy) appears again on the opposite
side of the obstacle. An older child will switch the visual focus to the
point where the person (or toy) had previously reappeared and wait for
it to show up (possibility 2).

I don't know if anyone has made the appropriate eye-movement
observations to see whether 1 and 3 actually apply to some or all people
-- whether the eyes ever continue to move at a constant rate while the
thing being observed is hidden behind the obstacle. We have to know what
really happens before we can try to explain it in terms of a model.

Tell me something: how do you know there are any real-world CEVs?
What's your proof? Come on, Oded, convince me!

     The existence of the real world is not one of my strongest
     convictions. There is however a sense of correlation between low-
     level signals and something physical happening on the boundary
     between my nervous system and the rest of the world.

But how do you know about the "something physical happening on the
boundary" unless it is already represented as a perceptual signal?

     So a low-level signal is a "model" of something. Now, that higher-
     level thing in my brain, responsible for my success in taking a
     train to Paris, is also a "model" of something, that unlike the
     lower-level one, is verified against perception in a much lower
     frequency.

I think we have to use the term "model" in a consistent way that
separates it from "perception." The way I use the word perception makes
the perception (a neural signal) a function of (hypothetical) physical
variables outside the nervous system. I use term "model," on the other
hand, to mean a structure, an organization of components, that
supposedly is functionally equivalent to another structure in terms of
the way it converts one kind of variable into others. So we have

                signals ---> MODEL ----> signal

corresponding to the hypothetical physical world organized as

        variables --> PHYSICAL STRUCTURE ---> variable

The model itself is like a mathematical function: it can be specified
without saying what the values of the input signals will be. It
corresponds to the _properties_ of a physical structure, which can also
be described without specifying what the input variables will be.

A perceptual function produces a perceptual signal given the states of
incoming physical stimuli (or lower-level signals). So we have

     input stimuli ---> PERCEPTUAL FUNCTION ---> perceptual signal

But the perceptual function is not a model of the external world,
because it does not correspond to any physical structure which converts
physical variables into other physical variables. What a perceptual
function does is to create a signal that is an analogue of some function
of physical stimuli or lower-level signals. It creates an "as-if"
situation: it is as if there were some entity in the external world
corresponding in magnitude to the magnitude of the perceptual signal.

An example is the relationship between a sensation signal and the
intensity signals from which it is drawn. If, as I propose, a sensation
signal is a weighted sum of many intensity signals, then a sensation
signal is the analog of something that apparently exists in the set of
intensity signals. If the sensation is warmth, and the intensity signals
come from individual temperature receptors over a region of the skin,
then the sensation signal has a magnitude that is analogous to a
generalized presence of warmth anywhere in the region where the
receptors are, as if there were a single quantity there which is the
same no matter what combination of temperature sensors is responding.

Obviously, what exists physically is simply a set of receptors that are
individually responding to locally elevated temperatures (I'm speaking
from the standpoint of the physics-model, of course). There is no single
quantity corresponding to "warmth." The weighted summation taking place
in the warmth-sensation perceptual function does not correspond to any
weighted summation taking place in the physical environment: nothing in
the environment is summing the individual temperatures, with or without
weightings. So the perceptual function is NOT a model of any physical
function outside the organism, nor does "warmth" correspond to any
single physical variable.

Now that you see where I'm coming from, perhaps you can see my problem
with your statement that the higher level thing responsible for your
success in taking a train to Paris "is verified against perception in a
much lower frequency." Higher perceptions can't be "verified" against
lower ones; they are simply functions of the lower ones. All you can
verify is that if you create certain lower-level perceptions by acting
on the world, the result will be a perception of being on the train to
Paris. But since "being on the train to Paris" is derived from lower-
level perceptions in the first place, all you have done is to show that
the same perceptual functions are still working the same way. The
question of true or false doesn't enter; it's a matter of definition,
not truth.

     The main insight of PCT is that everything works on subjective
     coordinate frame (the perceptions of the individual). "Model" and
     before it "information" seem to imply some direct magic
     correspondence with the real-world (and many people who talk about
     such things have not internalized this insight, or are working on
     engineering applications where the connection between the local
     coordinates and the real world is assumed).

You put it well. Hans Blom has pointed out that a world-model does not
have to be isomorphic with the external system that is being modeled.
That is a step in the right direction. However, the main point you bring
out is obscured, as you say, by the engineering situation in which
adaptive control is being worked out. In that situation, the engineer
knows everything about the system and about the environment (in terms of
a common physical model), and can judge whether a non-isomorphic model
results in "actually" controlling the external system in the desired
respects. In modeling human beings, this knowledge about the actual
state of the world is unavailable to the system being modeled, and to
the modeler as well. We have no objective way to verify that the "right
variable" is being maintained in the "right state."

This would be all right if it were not for this term "optimization." The
criteria for optimal behavior in engineering are external to the
controlling system: energy efficiency, speed, customer satisfaction, and
so forth. But in organisms, the criteria have to be completely internal:
the optimality of control has to be determined from effects on the
organism itself, without reference to objective criteria. The organism
will never know the actual organization of "the plant." All that can be
known has to be constructed from elementary intensity signals. "System
identification" is not possible in any objective sense.

···

---------------------------------------------------------------------
Wolfgang Zocher (950515.1330 MESZ) --

There are many on the net who will sympathize with your problem in
finding time to do research. You definitely are one of those who are
active PCT researchers. You will stand a better chance of being counted
when you are able to report some results.

I'll get around to commenting on that stuff you sent some time. This has
been much too busy a Spring, and it's not over yet. We're going to
Connecticut to see my father day after tomorrow, and right after we get
back we go on alert to travel to Boulder, Colorado where my elder
daughter is working herself up to producing a grandchild. Then comes a
brief space, after which we start getting ready for the CSG meeting July
19-23.

Greetings to Marion!
---------------------------------------------------------------------
Best to all,

Bill P.

[From: Oded Maler (950518)]

Bill Powers (950515.0750 MDT):

Oded Maler (950515) --

     You see someone running at a visible point A from left to right,
     then disappears - what is the explanation of the fact that you will
     try to catch him at the next visible point B to the right?

     A -----> B
     <Obstacle>

There are at least three possibilities.

1. You have an internal model of the moving person which can run
independently of your perception of the moving person. Normally, your
eyes track the moving person using real-time perceptions. When the
perception is lost, you switch to tracking the output of the internal
world-model, an imagined moving object (this is the proposal Hans Blom
is offering).

2. When the person disappears, you know from experience that the person
is likely to reappear on the other side of the obstacle, so you cease to
track the person and you move your eyes to the point of previously
observed reappearance. When the person shows up, you switch back to
tracking.

I think this can also be rephrased differently. At some level of the
hierarchy more abstract perception and "models" emerge, namely
automata (aka discrete- event systems, state transition diagrams,
etc.). These are involved in what you call sequence control. So
"knowing from ewperience" that the person would reappear in the other
side can be phrased as 1) having such a discrete model (= like your
(1) above); 2) having a good controller for such perceptions (your (3)
below) and 3) A more "conscious" (explicit if-the-else) knowledge.

3. Tracking consists of maintaining a relationship between the moving
person and the center of the visual field. The tracking control system
uses an integrating output function, and the output varies a reference
signal for eye-movement velocity so as to keep the target centered. When
vision is lost, the relationship control system is turned off, making
the error zero. The output integrator holds its output, maintaining a
constant reference signal for the eye velocity control system, so the
eyes continue to move at the same rate they moved when the perceptual
signal was lost. When (if) the person reappears, the relationship system
turns back on, and real tracking starts again.

1 and 3 are similar, except that the mechanism is different. In 1, there
has to be a world-model that can generate an imagined motion of the
person, leaving the control system to control as if the signal were
real. In 3, there is no imagination connection and no world-model; there
is only an integrating output function that maintains its output signal
until real-time tracking can start again.

2 uses neither a model of the person nor imagination: it relies on
sequence control, in which there is an expected sequence of
disappearance and reappearance at different places.

Which explanation should be used depends on how people actually behave
in this situation. A very young child seeing the person disappear will,
according to Piaget, simply turn its attention to something else, and
will be surprised if the person (or toy) appears again on the opposite
side of the obstacle. An older child will switch the visual focus to the
point where the person (or toy) had previously reappeared and wait for
it to show up (possibility 2).

A very good point.

I don't know if anyone has made the appropriate eye-movement
observations to see whether 1 and 3 actually apply to some or all people
-- whether the eyes ever continue to move at a constant rate while the
thing being observed is hidden behind the obstacle. We have to know what
really happens before we can try to explain it in terms of a model.

I'm sure there will be significant inter-personal differences. In some
people the dominant component will be the higher level sequence
control system while the others will move more "smoothly".

> Tell me something: how do you know there are any real-world CEVs?
>What's your proof? Come on, Oded, convince me!

     The existence of the real world is not one of my strongest
     convictions. There is however a sense of correlation between low-
     level signals and something physical happening on the boundary
     between my nervous system and the rest of the world.

But how do you know about the "something physical happening on the
boundary" unless it is already represented as a perceptual signal?

It depends on who I am. As an organism I know nothing at all. As a
theoretician these physical quantities are conceptual inventions as
are other constructs such as "perceptual signals" and others.

     So a low-level signal is a "model" of something. Now, that higher-
     level thing in my brain, responsible for my success in taking a
     train to Paris, is also a "model" of something, that unlike the
     lower-level one, is verified against perception in a much lower
     frequency.

I think we have to use the term "model" in a consistent way that
separates it from "perception." The way I use the word perception makes
the perception (a neural signal) a function of (hypothetical) physical
variables outside the nervous system. I use term "model," on the other
hand, to mean a structure, an organization of components, that
supposedly is functionally equivalent to another structure in terms of
the way it converts one kind of variable into others. So we have

                signals ---> MODEL ----> signal

corresponding to the hypothetical physical world organized as

        variables --> PHYSICAL STRUCTURE ---> variable

The model itself is like a mathematical function: it can be specified
without saying what the values of the input signals will be. It
corresponds to the _properties_ of a physical structure, which can also
be described without specifying what the input variables will be.

A perceptual function produces a perceptual signal given the states of
incoming physical stimuli (or lower-level signals). So we have

     input stimuli ---> PERCEPTUAL FUNCTION ---> perceptual signal

But the perceptual function is not a model of the external world,
because it does not correspond to any physical structure which converts
physical variables into other physical variables. What a perceptual
function does is to create a signal that is an analogue of some function
of physical stimuli or lower-level signals. It creates an "as-if"
situation: it is as if there were some entity in the external world
corresponding in magnitude to the magnitude of the perceptual signal.

An example is the relationship between a sensation signal and the
intensity signals from which it is drawn. If, as I propose, a sensation
signal is a weighted sum of many intensity signals, then a sensation
signal is the analog of something that apparently exists in the set of
intensity signals. If the sensation is warmth, and the intensity signals
come from individual temperature receptors over a region of the skin,
then the sensation signal has a magnitude that is analogous to a
generalized presence of warmth anywhere in the region where the
receptors are, as if there were a single quantity there which is the
same no matter what combination of temperature sensors is responding.

Obviously, what exists physically is simply a set of receptors that are
individually responding to locally elevated temperatures (I'm speaking
from the standpoint of the physics-model, of course). There is no single
quantity corresponding to "warmth." The weighted summation taking place
in the warmth-sensation perceptual function does not correspond to any
weighted summation taking place in the physical environment: nothing in
the environment is summing the individual temperatures, with or without
weightings. So the perceptual function is NOT a model of any physical
function outside the organism, nor does "warmth" correspond to any
single physical variable.

I don't have any problems with this description. You can view any
physical entity as a set of possible readings on a hypothetical
measurement instrument of any sort. This can be a simple scalar device
(which of course will not be scalr if you look at its structure more
closely), a weighted sum of those, or a complex function of readings
of an array of sensors distributed in time or space. (This could bring
us back to the argument about the "existence" of super-human entities
such as societies, people, cultures or ideas, but let's not).

Now that you see where I'm coming from, perhaps you can see my problem
with your statement that the higher level thing responsible for your
success in taking a train to Paris "is verified against perception in a
much lower frequency." Higher perceptions can't be "verified" against
lower ones; they are simply functions of the lower ones. All you can
verify is that if you create certain lower-level perceptions by acting
on the world, the result will be a perception of being on the train to
Paris. But since "being on the train to Paris" is derived from lower-
level perceptions in the first place, all you have done is to show that
the same perceptual functions are still working the same way. The
question of true or false doesn't enter; it's a matter of definition,
not truth.

Yes and no. I can mistakenly take the train to Chambery and for some
time believe wrongly that I'm on the train to Paris. However in order
to keep fooling me one has to close my eyes all the way, build a copy
of Gare de Lyon in instead of the railway station of Chambery, mimic
the special smell coming from the Metro and infinitely many other
perceptual illusions. It is tru that I can make errors in the other
direction, such as waking up in an anonymous hotel room (or MacDo) in
Paris not knowing where I am (this is more likely to happen to me in a
small american town or a French village in which I've never been) but
excluding pathological cases there is a certain objectivity in "being
in Paris".

     The main insight of PCT is that everything works on subjective
     coordinate frame (the perceptions of the individual). "Model" and
     before it "information" seem to imply some direct magic
     correspondence with the real-world (and many people who talk about
     such things have not internalized this insight, or are working on
     engineering applications where the connection between the local
     coordinates and the real world is assumed).

You put it well. Hans Blom has pointed out that a world-model does not
have to be isomorphic with the external system that is being modeled.
That is a step in the right direction. However, the main point you bring
out is obscured, as you say, by the engineering situation in which
adaptive control is being worked out. In that situation, the engineer
knows everything about the system and about the environment (in terms of
a common physical model), and can judge whether a non-isomorphic model
results in "actually" controlling the external system in the desired
respects. In modeling human beings, this knowledge about the actual
state of the world is unavailable to the system being modeled, and to
the modeler as well. We have no objective way to verify that the "right
variable" is being maintained in the "right state."

This would be all right if it were not for this term "optimization." The
criteria for optimal behavior in engineering are external to the
controlling system: energy efficiency, speed, customer satisfaction, and
so forth. But in organisms, the criteria have to be completely internal:
the optimality of control has to be determined from effects on the
organism itself, without reference to objective criteria. The organism
will never know the actual organization of "the plant." All that can be
known has to be constructed from elementary intensity signals. "System
identification" is not possible in any objective sense.

Yes. But this would cause a lot of misunderstanding with people doing
control (in the mathematical and engineering sense) and it restricts
the scope of scientific claims that can be made in the science of
living systems. In engineering/math control (in the wide sense, which
includes some branches of computer science) an objective model of the
environement is crucial. The controller need not have a full access to
all the variables, but what you show generally that a combination of a
certain controller with a certain environment behaves in a certain way
wrt to some objective (definable, speakable) criterion. Thus you can
say that under certain assumptions of probability distributions of
food, the expected performance of your E. Coli would be such as
such. Your E. Coli need not know about distributions or about the
performance critaria, but the model of the environment (in this case a
very crude probabilistic model) is necessary in order to say something
meaningful about this controller.

When you go higher you reach the realm of unspeakble perceptions,
namely perceptions that do not have a precise objective
description. Theoretically you could have modelled a class of
admissible moving points in 3D and show that for this class your
Little Man satisfies a certain objective performance criterion (e.g.,
the distance between finger and target will never exceed d for periods
longer than T). This is what will impress mathematicians/engineers.

Not having an objective performance criterion for the controller looks
indeed very strange. Each organism creates its own world of illusive
perceptions and somehow trying to satisfy subjective criteria in this
imagined world, the organism manages to survive for a while.

I think you (PCTers) should be aware of the importance of objective
description of performance in scientific and engineering discourse.
I understand that it cannot applied to living control systems, but
this should be made explicit, and the limitations of what can be said
by PCT (compared to physics statement such as "every object falling from
height x etc.") should be acknowledged.

--Oded