# visual encoding

[From Rick Marken (2000.02.14.1300)]

Bruce Nevin (2000.02.13.2037)--

"Encoding" is a metaphor that implies discrete bits of
information.

Martin Taylor (20000214 09:42) --

Is that your point (Rick and Bill?).

I don't think so. I think encoding is a real process, not a
metaphor; and it can be applied to discrete or analog data.

Here the distinction I'm trying to make. Take (for simplicity)
a 16 bit digital array, analogous to the retinal array:

0100000101000010

I think of encoding as a process that maps an input array
like this into an encoded version of the array, like this
10 bit string:

0000100010

If you know the input array is going to consist mainly of
certain patterns (like the 8 bit ASCII letter codes) then
you can _encode_ 8 bit patterns of the input array into
a 5 bit code (enough bits to identify the 26 possible 8
bit patterns plus some codes indicating non-letter ASCII
strings) and reduce the amount of data you send to 62% of
that in the original array. Of course, the destination has
to know your coding scheme so that it can decode the ten
bits you sent (0000100010) into the original 16 bit message
(0100000101000010).

Neither the encoding nor the decoding is a perceptual
process from my point of view; the result of the encoding
is just the input in a new form; the result of the decoding
is the original input.

I think of a perception as a function that maps some _aspect_
of the input array into an output whose value indicates the
state of that aspect of the input. One aspect of the input
array that could be perceived is the ASCII letter code found
in the first 8 bits of the input array. A perceptual function
would transform this 8 bit string into a number (possibly a
five bit binary number like the encoding scheme above) whose
value indicates the ASCII state of the first 8 bits of the
input array (1-26, say, with a value of 27 meaning a non-letter
ASCII state of the array).

I wouldn't call this 5 bit output of the perceptual function
a _coded_ representation of the input array because it's not
going to be _decoded_; it's just what it is; a value. In PCT,
that value _is_ a perception. If that value is the controlled
input to a control system then it's that value (and, as a side
effect, the input bit string to which it corresponds) that is
controlled.

I think this distinction, between a value that functions as
a code and a value that functions as a perceptual variable, is
important to understand. It could be just a verbal problem; I
think the word "code" is sometimes used to mean the same thing
as we, in PCT, mean by "represent". After all, the perceptual
signal is just blips in a neuron which represent ("code"), in
terms of firing rate, some aspect of the input to the system.
But I think it's best to try to avoid using "code" to mean
"represent" because I think it confuses the issue. "Code"
implies decoding; "represent" implies no decoding; you just
deal with (control) the representation (perception) as is.

I admit that the distinction is subtle; but I think it's very
important in terms of communicating (and using) PCT.

Best

Rick

···

---
Richard S. Marken Phone or Fax: 310 474-0313

[Martin Taylor 2000.02.15 09:53]

It seems that the word "encode" has different meanings to me, to
Bruce N. to Rick, and to Bill, so it just confuses any real issue if
the word is used.

In particular, Rick and Bill both seem to think that if one talks
about an "encoded" signal, then there must be an intent that the code
should later be inverted to reproduce the original. I have never
thought that the existence of a function or the execution of a
process involved the need for the inverse function to be applied or a
process to be executed to undo the work of the original process.

Rick describes precisely what I would say is prototypical encoding.

[From Rick Marken (2000.02.14.1300)]
I think of a perception as a function that maps some _aspect_
of the input array into an output whose value indicates the
state of that aspect of the input. One aspect of the input
array that could be perceived is the ASCII letter code found
in the first 8 bits of the input array. A perceptual function
would transform this 8 bit string into a number (possibly a
five bit binary number like the encoding scheme above) whose
value indicates the ASCII state of the first 8 bits of the
input array (1-26, say, with a value of 27 meaning a non-letter
ASCII state of the array).

Now Rick says that this is _not_ a coded representation...

I wouldn't call this 5 bit output of the perceptual function
a _coded_ representation of the input array because it's not
going to be _decoded_; it's just what it is; a value.

The code is just what it is, a _set of_ values--a set of perceptual
signals. Any one of them is an element of the code.

But I think it's best to try to avoid using "code" to mean
"represent" because I think it confuses the issue. "Code"
implies decoding; "represent" implies no decoding; you just
deal with (control) the representation (perception) as is.

I'll try to avoid using "code" and "encode" in future, but I can't
promise to succeed always. As I understand the words, they describe
_exactly_ what a set of feature detectors does to an input array--and
indeed, whether the brain "decodes" or not, decoding at least partly
possible, as has been shown by reconstituting the retinal image from
the neural impulses of cats.

The point here is clarity of communication. CSGnet gets into quite
enough unnecessary hassles based on undetected misunderstandings
about the use of words, without my adding another. So I'll try to
avoid words based on "code" although it will be hard to convey the
same concept when we are talking about arrays of perceptual signals
rather than one single perceptual signal. What other word is suitable
to describe it?

Martin

[From Rick Marken (2000.02.15.1100)]

Martin Taylor (2000.02.15 09:53) --

I'll try to avoid words based on "code"

Probably a good idea.

although it will be hard to convey the same concept when
we are talking about arrays of perceptual signals rather
than one single perceptual signal. What other word is
suitable to describe it?

How about "array of perceptual signals"? And why do we need
to talk about such arrays, anyway? Control systems control
perceptual signals, not arrays of perceptual signals.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[Martin Taylor 20000216 0106

How about "array of perceptual signals"? And why do we need
to talk about such arrays, anyway? Control systems control
perceptual signals, not arrays of perceptual signals.

One control unit controls one perceptual signal. One person controls
many arrays of perceptual signals. So we need to talk about them,
particularly when we are concerned with the interactions among
control systems.

Martin

[Bruce Nevin (2000.02.16.1042 EST)

Martin Taylor 20000216 0106 --

One control unit controls one perceptual signal. One person controls
many arrays of perceptual signals. So we need to talk about them,
particularly when we are concerned with the interactions among
control systems.

Rick's point, as I understand it: If an array of perceptual signals is
controlled, it is controlled by being combined into a single perceptual
signal at a higher level.

Martin's point, as I understand it, concerns the functions by which an
array of signals is combined into one signal. A PIF combines a number of
perceptual signals into one perceptual signal that is input to a
comparator. Another sort of input function (a RIF? Just joking.) combines a
number of error signals into one reference signal that is also input to a
comparator. Then there may be particular organizations of
cross-connections, like Martin's flip-flop notion.

from Rick's POV, if you want to talk about controlling the array, just talk
about controlling the one signal into which the array is combined, and
about how the combining functions weight the signals that they combine.

If an error signal is copied to more than one reference input function, you
have more than one control loop affecting one perception, without
necessarily incurring conflict, depending not only on relative gain, but
also on what other signals contribute to the reference and perceptual
inputs of those lower loops, how they are weighted, etc. Is this what you
are referring to, Martin?

Bruce Nevin

···

At 01:07 AM 02/16/2000 -0500, Martin Taylor wrote:

[Martin Taylor 2000.02.16 20:43]

[Bruce Nevin (2000.02.16.1042 EST)

Martin Taylor 20000216 0106 --
>
>One control unit controls one perceptual signal. One person controls
>many arrays of perceptual signals. So we need to talk about them,
>particularly when we are concerned with the interactions among
>control systems.

Rick's point, as I understand it: If an array of perceptual signals is
controlled, it is controlled by being combined into a single perceptual
signal at a higher level.

That would be wrong, if he did think that, which I doubt, since he
wrote his spreadsheet demo to demonstrate the contrary.

Martin's point, as I understand it, concerns the functions by which an
array of signals is combined into one signal.

Nope.

A PIF combines a number of
perceptual signals into one perceptual signal that is input to a
comparator. Another sort of input function (a RIF? Just joking.)
combines a number of error signals into one reference signal that is
also input to a comparator.Then there may be particular
organizations of
cross-connections, like Martin's flip-flop notion.

From Rick's POV, if you want to talk about controlling the array, just talk
about controlling the one signal into which the array is combined, and
about how the combining functions weight the signals that they combine.

If an error signal is copied to more than one reference input function, you
have more than one control loop affecting one perception, without
necessarily incurring conflict, depending not only on relative gain, but
also on what other signals contribute to the reference and perceptual
inputs of those lower loops, how they are weighted, etc. Is this what you
are referring to, Martin?

I'm afraid I can't be sure I understand any of that. It doesn't
correspond with my view of what a control hierarchy looks like, and
it has nothing to do with my comment that at any one time a person is
controlling more than one perception at any level. Have a look at
Rick's spreadsheet demo to see an example of this in simulation. You
will see an array of six perceptual signals at each of three levels
being controlled even though the control of each affects all the
others. They all interact.

In the real world, there are more, and the possibilities for the ways
they interact are manifold.

Now I have to try to make some sense of what you wrote: "Another sort of
input function (a RIF? Just joking.) combines a number of error
signals into one reference signal that is also input to a
comparator." I can make sense of this only if I substitute "output
signals" for "error signals." And if I do this, I don't understand
"Just joking" because there does have to be a "Reference Input
Function" of some kind. Bill has tended to assume that it is a simple
addition of all the outputs that converge on that reference input,
but the function doesn't have to be a simple adder, and in Rick's
spreadsheet demo it is a weighted addition. There are lots of other
possibilities. RIFs have not been studied in the way PIFs have been
studied, and I'm not sure how one would study them. But they can be
important, because they affect the ways in which the outputs of
higher level control units disturb the perceptions of other units at
the same level.

If an error signal is copied to more than one reference input function, you
have more than one control loop affecting one perception, without
necessarily incurring conflict, depending not only on relative gain, but
also on what other signals contribute to the reference and perceptual
inputs of those lower loops, how they are weighted, etc. Is this what you
are referring to, Martin?

That's the way multiple degrees of freedom are ordinarily controlled,
if I interpret this statement correctly--it's quite ambiguous. The
"classical" hierarchy has an array of inputs to an array of control
units at any one level. The array of perceptual signals from that
array of control units goes up as the inputs to an array of control
units at the next level above, and the array of outputs is
distributed to an array of reference inputs of control units at the
level below. I'm assuming that's what you are trying to say.

No, it's not what I was referring to, though it is part of what I was
referring to. What I intended people to recognize is that the world
is (and here I have to use the e-word) encoded into a large array of
perceptual signals. Those signals (or some of them) are controlled by
an array of control systems. And that is why I felt the need to
respond to Rick's "And why do we need to talk about such arrays,
anyway? Control systems control perceptual signals, not arrays of
perceptual signals."

Martin

···

At 01:07 AM 02/16/2000 -0500, Martin Taylor wrote:

[Bruce Nevin (2000.02.16.1042 EST)]

Martin Taylor 2000.02.16 20:43]

I'm afraid I can't be sure I understand any of that. It doesn't
correspond with my view of what a control hierarchy looks like

OK, I'm out to lunch, or out on a limb. But I guess I'm glad RIF seems a
viable term. (I was reluctant to introduce yet another.) And I thought the
error signal was the output from a comparator. Is there an output function
other than the effectors at the interface with the environment?

it has nothing to do with my comment that at any one time a person is
controlling more than one perception at any level.

Can one not control "more than one" without controlling "an array"? Doesn't
the latter imply control of a single complex thing?

What I intended ... is that the world
is (and here I have to use the e-word) encoded into a large array of
perceptual signals.

Why do you have to? Why is it not sufficient to say "the world is
represented by many perceptual signals"? "Encode" carries a lot of baggage.
What does "array" buy you? Is this a reference to the term in mathematics
and in programming? Is there some way of modelling an array that is
different from modelling a plurality?

Those signals (or some of them) are controlled by
an array of control systems. And that is why I felt the need to
respond to Rick's "And why do we need to talk about such arrays,
anyway? Control systems control perceptual signals, not arrays of
perceptual signals."

Each perceptual signal can branch upward to more than one PIF.
Each RIF can combine more than one output from above.
Each error output can branch to more than one RIF below.
(In each case: Sometimes? Usually? Always?)
Is there some kind of "modelling of arrays" that handles this complexity in
a better way than simply modelling numerous simple systems with complex
interconnections? That's all I see in Rick's spreadsheet. Matrices are used
as a programmatic expedient to calculate the weighted sum of values
representing lower-level perceptual signals. Analog computation by neurons
would not refer to a table or matrix off to the side. Am I failing to make
a proper inference?

This is my understanding of Rick's objection. But I may be out to lunch. Or
out on a limb. And I am willing to learn.

Bruce Nevin

···

At 09:04 PM 02/16/2000 -0500, Martin Taylor wrote:

[From Rick Marken (2000.02.1100)]

Bruce Nevin (2000.02.17.1341)--

The key to PCT semantics is always: what does it refer to
in an explicit working model?

Exactly! The meaning is in the model. One can call the
perceptual signal an "encoding" but the perceptual signal
is just what it is in the model -- the scalar output of a
perceptual function that varies in magnitude depending on
the value of the "argument" to the function.

But I do think it's worthwhile to correct people when they
seem to be getting the semantics wrong verbally. So I think
your efforts _were_ worthwhile. Martin did get the semantics
wrong when he talked about perception as data reduction
But Martin quickly corrected himself so I was happy to drop
it.

Best

Rick

···

---
Richard S. Marken Phone or Fax: 310 474-0313

[From Bill Powers (2000.02.17.1723 MST)]

Martin Taylor 2000.02.16 20:43--

Have a look at
Rick's spreadsheet demo to see an example of this in simulation. You
will see an array of six perceptual signals at each of three levels
being controlled even though the control of each affects all the
others. They all interact.

The "person" may be controlling an array, but that "person" is a construct
in the eye of the beholder. No control system in Rick's spreadsheet
controls an "array" of perceptions. Each control system controls only one
scalar variable.
An "array" is a perception at a level higher than the elements of the
array, and to have real existence each perception at this level must be the
scalar output of a perceptual input function that constructs a measure of
some aspect of the array. For example, the array could be perceived as a
"vector", or as a "matrix", or as a "transpose", or as the "determinant" of
a matrix, and so on. To some people, an "array" is just a bunch of numbers
on a piece of paper in any old arrangement. To others who know mathematics,
it is a more clearly defined perception. In other words, an array "is" the
perception to which you refer when you use the word "array."

I concur with Bruce Nevin's comment.

Best,

Bill P.

[Martin Taylor 2000.02.18 10:09]

[From Bill Powers (2000.02.17.1723 MST)]

Martin Taylor 2000.02.16 20:43--

>Have a look at
>Rick's spreadsheet demo to see an example of this in simulation. You
>will see an array of six perceptual signals at each of three levels
>being controlled even though the control of each affects all the
>others. They all interact.

The "person" may be controlling an array, but that "person" is a construct
in the eye of the beholder. No control system in Rick's spreadsheet
controls an "array" of perceptions. Each control system controls only one
scalar variable.

...

All of which was why I _originally_ ([Martin Taylor 20000216 0106)said:

One control unit controls one perceptual signal. One person controls
many arrays of perceptual signals. So we need to talk about them,
particularly when we are concerned with the interactions among
control systems.

That message was in answer to _Rick's_ proposal that we use the
phrase "arrays of perceptual signals" rather than my preferred "an
encoding", and specifically to his question about why we need any
term to discuss more than one perceptual signal at a time. So, to
_avoid_ controversy, I accepted his rather cumbersome synonym for "an
encoding" since some people seem to have a fixed idea that if one
process (encoding) is performed another quite independent process
(decoding) is necessarily implied. I haven't understood why people
have this idea, but since they do, I agreed to try not to use
"encoding."

Now you seem to be arguing that Rick's wording is also wrong. Fine. I
don't want to argue about the use of words again, again, and again.
I'll use whatever words you want, provided thay can convey the ideas
clearly to most readers. Just make a reasonable suggestion.

What words would you substitute for my "an encoding" or Rick's "array
of perceptual signals" when talking about the interactions among
control units?

I concur with Bruce Nevin's comment.

In what way? What have you said that adds to, or disagrees with, my
original message on the topic?

Are you perhaps disagreeing with the notion that control systems can
interact, as, for instance by disturbing each other's perceptions?
Or maybe you do agree that one control unit's actions can disturb
another's perceptions but you don't think it a proper topic for
actions of more than one control unit at a time?

Martin

[From Rick Marken (2000.02.18.0830)]

Martin Taylor (2000.02.18 10:09) --

some people seem to have a fixed idea that if one process
(encoding) is performed another quite independent process
(decoding) is necessarily implied. I haven't understood why
people have this idea

Let me try to explain.

I think data is _encoded_ so that it can be passed from a
source to a destination along a comm channel. The goal of the
encoding is either 1) to get that data across the channel
without being deciphered by a third party or 2) to get a
large amount of data across a small channel (winzip type
encoding) or 3) both 1) and 2). So the encoded version of
the data is not "of interest" to the destination; the
destination is interested in the data itself. So the encoded
version of the data must be decoded so that the destination
can recover the original data.

In a control system, data (sensory information) is not encoded;
it is _transformed_ by a perceptual function into a controllable
scalar variable. The control system doesn't have to decode this
variable to recover the original data; it just acts on the basis
of the difference between the magnitude of this scalar variable
(the perceptual variable) and a scalar reference variable.

Saying that the scalar (perceptual) variable controlled by
a control system is an _encoded_ version of the data at the
sensory surface seems very misleading to me. Suppose that the
sensory input data values are x and y and that the perceptual
function is p = x+y. You would apparently be willing to say
that the input data values (x and y) are encoded by the value
of p. I think this is misleading because a control system
deals with p as is -- there is no decoding. If the value
of p is 10 then it doesn't matter to the control system whether
this is the case because x is 5 and y is 5 or because x is 1
and y is 9. If p is 10 and the reference for p is 9 then p
(which simply represents the sum of x and y) is too large;
if the reference for p is 11 then p is too small. That's
all the control system has to know. p is not treated as
a coded value of x and y; p _is_ is the variable that
is controlled, as is.

Does this help?

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[From Bruce Nevin (2000.02.18.1155 EST)]

Martin Taylor 2000.02.18 10:09

I _originally_ ([Martin Taylor 20000216 0106)said:

One control unit controls one perceptual signal. One person controls
many arrays of perceptual signals. So we need to talk about them,
particularly when we are concerned with the interactions among
control systems.

That message was in answer to _Rick's_ proposal that we use the
phrase "arrays of perceptual signals" rather than my preferred "an
encoding", and specifically to his question about why we need any
term to discuss more than one perceptual signal at a time.

For clarity: Rick Marken (2000.02.15.1100) took the phrase "arrays of
(2000.02.15 09:53) in a context where there was no claim to *control* an array:

I'll try to avoid words based on "code"

Probably a good idea.

although it will be hard to convey the same concept when
we are talking about arrays of perceptual signals rather
than one single perceptual signal. What other word is
suitable to describe it?

How about "array of perceptual signals"? And why do we need
to talk about such arrays, anyway? Control systems control
perceptual signals, not arrays of perceptual signals.

The statement that we control arrays came in your rejoinder (Martin Taylor
20000216 0106):

One control unit controls one perceptual signal. One person controls
many arrays of perceptual signals. So we need to talk about them,
particularly when we are concerned with the interactions among
control systems.

I guess that this means "the many control systems that make up a person
control many perceptual signals, and these naturally fall into groups which
we may refer to as arrays." However, it sounds like it means that we
control row-and-column structures of two or more dimensions whose
constituent "cells" are perceptual signals. (Unless for you "array" means
"a series of statistical data arranged in classes in order of magnitude." I
don't know how to refer that concept to perceptual signals.)

I know that you have been looking for ways to talk about cross-connections
between elementary control systems. Does the notion of arrays help you with
that? If so, can you explain how it helps?

And how is an array connected to your notion of encoding? Are you proposing
that an array-structure of perceptual signals corresponds to ("encodes")
something in the world? How is this different from saying that a perceptual
signal constructed (in a PIF) from many lower-level signals represents
something in the world (an edge, configuration, etc.)?

to
_avoid_ controversy, I accepted his rather cumbersome synonym for "an
encoding"

Reading his reply (quoted above) I don't see that he offered a synonym for
"an encoding." He suggested an alternative way to talk about arrays of
perceptual signals without using the word "encoding": just talk about them
as arrays of perceptual signals. That was before you suggested that we
*control* arrays.

since some people seem to have a fixed idea that if one
process (encoding) is performed another quite independent process
(decoding) is necessarily implied. I haven't understood why people
have this idea, but since they do, I agreed to try not to use
"encoding."

"Encoding" is an information-theoretic term. As it has been borrowed by
psychology, I have seen the term "code" applied to sought-for changes in
brain structure that "code for" specific memories. In this case, a reversal
or "decoding" is assumed (memory recall). PCT does not have a good account
of how memories are constructed and recalled. And I have seen the term
"code" applied to the "chunking" of simpler perceptions such that the
"chunkings" are then perceived and recalled as objects. PCT has a good
account for how this is done in the perceptual hierarchy. A perceptual
signal constructed (in a PIF) from many lower-level signals represents
something in the world (an edge, configuration, etc.) Is this what you are
referring to as "encoding"?

If you propose to add an information-theoretic notion of encoding to what
is already in PCT, what is its purpose (e.g. is it to account for complex
cross-connections?), and how is it integrated into the present theory?

Bruce Nevin

···

At 10:09 AM 02/18/2000 -0500, Martin Taylor wrote:

[From Bruce Nevin (2000.02.18.1224)]

Rick Marken (2000.02.18.0830)

Suppose that the
sensory input data values are x and y and that the perceptual
function is p = x+y. [...] If the value
of p is 10 then it doesn't matter to the control system whether
this is the case because x is 5 and y is 5 or because x is 1
and y is 9. If p is 10 and the reference for p is 9 then p
(which simply represents the sum of x and y) is too large;
if the reference for p is 11 then p is too small. That's
all the control system has to know. p is not treated as
a coded value of x and y; p _is_ is the variable that
is controlled, as is.

One information-theoretic view is that information about the environment is
encoded for processing within the organism. There is a kind of decoding
associated with this notion.

The error output must be connected to lower levels in such a way that
effectors acting through the environment change the values of x and/or y to
reduce the value of p. Presumably, a copy of the error output becomes
reference input to one or more comparators receiving the value of x and/or
one or more comparators receiving the value of y. This transformation of p
back into x and y is analogous to decoding.

Since decoding is irrelevant to your concept of encoding, Martin, you must
not have some variant of this Lockean notion in mind.

Bruce Nevin

···

At 08:30 AM 02/18/2000 -0800, Richard Marken wrote:

[From Bruce Nevin (2000.02.18.1224)]

I said (2000.02.18.1224):

This transformation of p
back into x and y is analogous to decoding.

Not a transformation of p but of the difference between p and the reference
input r. Perhaps an error signal e at a given level is also considered a
signal of the same type as p and r at that level? But even if that is the
case, the transformation back to values of variables in the environment is
not analogous to decoding because e is a different signal.

Bruce Nevin

[From Rick Marken (2000.02.18.1015)]

Bruce Nevin (2000.02.18.1224)--

The error output must be connected to lower levels in
such a way that effectors acting through the environment
change the values of x and/or y to reduce the value of p.

All you need is one output, connected to both x and y, in
order to control x+y.

Presumably, a copy of the error output becomes reference
input to one or more comparators receiving the value of x
and/or one or more comparators receiving the value of y.

Not necessary. The single output of the system controlling
x+y can directly affect x+y. I just created a system that
controls x+y where x=dx+o and y = dy+o (dx and dy are
independent disturbances to x and y, respectively, and o
is the output of the x+y controlling system).

This transformation of p back into x and y is analogous
to decoding.

I don't see this. My system transforms r-p into o. The
environment transforms o into x+y (via the equations
above) and the sensory system transforms x+y into p,
the controlled perception. If I know, say, that p = 10
and o =.21, in what sense have I decoded p back into
x and y? x and y can still be any pair of values that
adds up to 10. Not a very impressive decoding of p.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[Martin Taylor 2000 02 19 12:49]

[From Rick Marken (2000.02.18.1015)]

Does the concept of "tar baby" come to mind?

Rick to Bruce Nevin (2000.02.18.1224)--

> The error output must be connected to lower levels in
> such a way that effectors acting through the environment
> change the values of x and/or y to reduce the value of p.

All you need is one output, connected to both x and y, in
order to control x+y.

> Presumably, a copy of the error output becomes reference
> input to one or more comparators receiving the value of x
> and/or one or more comparators receiving the value of y.

Not necessary. The single output of the system controlling
x+y can directly affect x+y. I just created a system that
controls x+y where x=dx+o and y = dy+o (dx and dy are
independent disturbances to x and y, respectively, and o
is the output of the x+y controlling system).

> This transformation of p back into x and y is analogous
> to decoding.

I don't see this. My system transforms r-p into o. The
environment transforms o into x+y (via the equations
above) and the sensory system transforms x+y into p,
the controlled perception. If I know, say, that p = 10
and o =.21, in what sense have I decoded p back into
x and y? x and y can still be any pair of values that
adds up to 10. Not a very impressive decoding of p.

I believe Rick and I have identical or almost identical views as to
how the hierarchy actually works. I'm not sure whether Bruce Nevin
does, or not. I eschewed (so far as possible) using the term
"encoding" to describe the transformation between one perceptual
level and the next, although in my understanding of the term,
encoding is _exactly_ what the set of perceptual transforms does.

I accepted Rick's term "array", but then Bruce gets concerned because
an array is a rectangular matrix. I'm tempted to go back to using
"encode" because it _is_ precise. All that is needed to make its
intent clear is to modify trivially Rick's other message
(2000.02.18.0830):

I think data is _encoded_ so that it can be passed from a
source to a destination along a comm channel. The goal of the
encoding is either 1) to get that data across the channel
without being deciphered by a third party or 2) to get a
large amount of data across a small channel (winzip type
encoding) or 3) both 1) and 2).

Agreed, but there is a (3) that needs to be stated, because it is the
important one.

(3) The destination can use the data only in the encoded form, the
original being ill-formed.

So the encoded version of
the data is not "of interest" to the destination;

That "So" is a total non-sequitur. It is an added assumption, not
of my (3).

the
destination is interested in the data itself. So the encoded
version of the data must be decoded so that the destination
can recover the original data.

I emphasize that "encoding" is often done precisely so that the
destination can see it in a form it can use, and the destination has
absolutely _no_ need to recover the original data.

I'd like to use a term that does not have excess baggage, as
apparently both "encode" and "array" do. I don't really like
"transform", but I could use it if it conveys the right notion to
more people. The reason I don't like "transform" is that it conveys
to me the notion that the original is totally recoverable (as in
Fourier transform<->inverse Fourier transform), whereas "encode"
seems to convey that impression to some other people although not to
me. Bill, Rick, Bruce N: would the tar baby's tar dissolve if we used
the word "transform" rather than "encode" or "array of perceptual
signals?"

Martin

[From Bill Powers (2000.02.21.1257 MST)]

Martin Taylor 2000 02 19 12:49--

Bill, Rick, Bruce N: would the tar baby's tar dissolve if we used
the word "transform" rather than "encode" or "array of perceptual
signals?"

I think the word we're looking for is "function." y = f(x1,x2,...xn). All
these other fancy words just bring in unwanted connotations, which are not
the same across beholders, add no useful meanings, and are the cause of all
these semantic problems.

Best,

Bill P.

[Martin Taylor 2000.02.21 23;34]

[From Bill Powers (2000.02.21.1257 MST)]

Martin Taylor 2000 02 19 12:49--

>Bill, Rick, Bruce N: would the tar baby's tar dissolve if we used
>the word "transform" rather than "encode" or "array of perceptual
>signals?"

I think the word we're looking for is "function." y = f(x1,x2,...xn).

That doesn't cut it. We want a word for y1 = f1(x1, x2,...xn), y2 =
f2(x1, x2,...xn), ... yk = fk(x1, x2, ...xn). The set f1,...fk is a
transform that encodes the vector x into the vector y. It's a set, or
array, or whatever, of functions. That's a transform, except that
there is no need for an inverse transform to exist. It's also an
encoding function.

All
these other fancy words just bring in unwanted connotations, which are not
the same across beholders, add no useful meanings, and are the cause of all
these semantic problems.

Agreed. But then so does "perception" when used in the presence of
the uninitiated. Also "control" and most of the other technical terms
of PCT. What I'm looking for is a word that minimizes those unwanted
connotations while conveying an accurate meaning. "Transform" has the
same unwanted connotation for me that "encode" does for you, but I'm
willing to live with it, since it at least describes an approximation
to what we are talking about--the relationship between the inputs to
one level of control systems and all the perceptions that they
produce.

Martin

[From Bruce Nevin (2000.02.22.0020 EST)]

If there is some set of functions that express how a large number of
control units interact, and how those interactions evolve over long periods
of reorganization, would they do so by referring to the group/set/array of
control systems as a unit? On that question hinges my sole difficulty
understanding what you meant by "array."

I have no problem with "transform," nor with recoverability of the
"original" form (a torqued term in a closed loop!). There is in principle
an inverse in any mapping, function, transformation, or encoding. The
inverse of the mapping from one level of the perceptual hierarchy to the
next is unavailable only as a practical matter, due to ambiguity:
typically, many alternative combinations of input values at the lower level
could have resulted in the given perceptual signal at the higher level.

Martin Taylor 2000 02 19 12:49 --

I accepted Rick's term "array"

This was not Rick's term, it was your term, which Rick merely quoted back
to you. See my (2000.02.18.1155 EST) for the references demonstrating this.

Rick Marken (2000.02.18.1015)--

the encoded version of the data is not "of interest" to the destination

I agree with you that this is not a conclusion that follows from Rick's
premisses. It is a statement of his starting assumption--the usual
assumption that when you encode something, the encoded state is transient.
In the communication-theoretic imagery of cognitive psychology, the encoded
form of the percept is an intermediate state inside the black box of neural
systems, and this inscrutible encoding as neural spike trains eventually
gets transformed to an intelligible form, either as awareness or as action.

This assumption appears to contradict yours. I think perhaps in fact it
does not. Your assumption, that the encoded form is what the destination
cares about and indeed is all that the destination can make use of, refers
to an intermediate destination within the black box. If this understanding

Except that inside the black box it's just a neural signal. You have to
take an observer's point of view outside the organism-plus-environment loop
to reach the conception that the signal is an encoding of lower-level
perceptions or of events in the environment. This point of view cannot be
attributed to any entity or function that is a destination of the signal
within the organism; the signal cannot sensibly be called an encoding from
the point of view of that destination.

What is your point of view? I think you are looking for systemic properties
of aggregates of simple control systems that make up a complex control
hierarchy. I think you take the point of view of an analyst of connection
structures that might occur in control hierarchies. Is that accurate? A
modeller takes the point of view of the organism being modelled, or of the
model. I think it is this difference in point of view that results in your
communication not being understood as you intend it. Is this possible? I
recall the difficulty around your concept of information in the error
signal (or maybe I haven't got that quite right). That was a concept that
could only make sense for an observer who was external to the
organism-plus-environment loop, yet omniscient of details internal to that
loop. That was a point of view that modellers declined to take, so the

"Encoding" could be a technical term with a special definition. If you use
it this way, it may be misconstrued by the many people like myself who are
not competent to deal with the issues of how large
numbers/sets/arrays/groups of control units interact, and how those
interactions evolve over long periods of reorganization. It might be easier
to avert these misunderstandings if you use "transformation", or "mapping",
or indeed "function," though these terms might require you to be more
explicit from a model-centered point of view.

Bruce Nevin

[From Bill Powers (2000.02.25.0752 MST)]

Martin Taylor 2000.02.21 23;34]--

That doesn't cut it. We want a word for y1 = f1(x1, x2,...xn), y2 =
f2(x1, x2,...xn), ... yk = fk(x1, x2, ...xn). The set f1,...fk is a
transform that encodes the vector x into the vector y. It's a set, or
array, or whatever, of functions. That's a transform, except that
there is no need for an inverse transform to exist. It's also an
encoding function.

Is there any reason to believe that such a transform is carried out by the
inherent properties of a human brain? If such a transform is to be part of
a brain model, it has to be carried out by that brain, not by an observer
working with pen and paper and using a learned mathematical system. It is
possible for a set of variables yn such as you describe to exist in the
brain without those variables and functions being inputs to another process
that creates a transform with them as input. The mere existence of a set of
variables means nothing in itself; something has to receive information
about them and subject them to some computing process before they can be
represented as any kind of coherent entity.

We've had this discussion before; the question then was whether the
existence of a set of perceptions at a given level constituted perception
of a vector. I think the same principle applies: a set of functions does
not imply perception of a transform unless the "transformness" itself is
reduced to a scalar variable. Until there is a higher level perception of
the set of functional equations you describe, the functions simply remain
separate functions having nothing to do with each other (even if an
external observer could see what they have to do with each other).

Perhaps what you're getting at is that in a two-level perceptual hierarchy,
the second level of perceptions could be called transforms of the inputs
two levels down, because the perceptions are functions of variables which
are themselves functions of still-lower perceptions. However, if that's all
you mean, the concept of "transform" is simply descriptive, meaning only
"function of function of...". This might introduce a new way of talking
about the hierarchy, but makes no difference in the actual structure.

And "encoding" still doesn't seem to mean anything we can't already talk