twilight of the idols

MartinT · November 6, 2011, 3:08pm

[Martin Taylor 2011.11.11.05.14.47]

[From Bill Powers (2011.11.05.1053 MST)]
  Martin Taylor 2011.11.11.04.23.04
–
        MT: Both you and Bill have never addressed the question at
issue.
Bill talks about the problem of consciousness, which is not
relevant to
my questions except insofar as we consciously perceive the
world as
constituted of unitary things, whereas we know (if you
believe the
neurophysiologists) that the different attributes of these
“unitary
things” are processed in different parts of the brain.
BP:I said something about this in my last post. But I think
there’s
a problem with attaching “unitary” to consciousness. The very
point I made was that consciousness, as an input function to some
unknown system, can do something that no PCT input function can
do:
examine a field of experience in which there are many different
perceptions. They do not look like one single – unitary – thing,
but
like many separate things.

I think we are talking at cross purposes. That's not too unusual,

but let’s try to align our language a little better before we get
into an unneccessary hassle while losing the substance of any real
differences in our thinking. The problem is to align our
understanding of to what each of us applies the work “unitary”. A
mixup in that can lead to a lot of confusion and conflict where
conflict need not exist.

When I talk about the conscious perception is of unitary objects and

attributes, I mean that consciously one sees that there is “a glass”
on “a table” when one consciously is aware at that level. One can
also be aware of “the left edge of the glass” and “the edge of the
shadow of the glass on the table”. Depending on what one is
conscious of at any one moment, those items are unitary. When you
see the glass, you ordinarily do not see it as a concatenation of
its left edge, its right edge, the reflection of the table from it,
the shadow it casts, and so forth. When you see the glass, that’s
what it is, a glass. That’s the unitary perception to which I refer.
In consciousness at one time, there are several such unitary
perceptions. They truly are perceived as separate, which is the
property I was thinking of when I called them unitary.

  There is only one unitary field of experience
encompassing all these things.

Would you really call the field of experience at any one moment

“unitary”? That doesn’t correspond to my experience, nor,
connotationally, to the word “field”. I would probably substitute
the word “unique” for “unitary”.

There is, of course, a tautological sense in which the totality of

your consciousness is all there is in consciousness, and is
therefore unitary in a Zen kind of way, but I don’t think that’s a
very valuable way to use the word “unitary”. You say: “The very
point I made was that consciousness, as an input function to some
unknown system, can do something that no PCT input function can do:
examine a field of experience in which there are many different
perceptions. They do not look like one single – unitary – thing,
but
like many separate things.”, and that is why I would not call
consciousness unitary. I think we see the world similarly, but use
words differently.

Be that as it may, what I am talking about is the perception of

these separate attributes of the perceived environment as singular
entities. And my question is whether these conscious perceptions of
individual entities necessarily demonstrates that the controlled
perceptions of them – as opposed to the conscious perceptions of
them – are singular scalar quantities.

  My basic conjecture about awareness is that we are aware only of
perceptual signals. Those signals are provided by the perceptual
input
functions in the hierarchy. Awareness can indeed receive some
number of
these signals at the same time, not just from one level but from
any of
them, bottom to top. The intensity of pain from a stubbed toe can
steal
attention away from pondering the nature of
God.

Fair enough. We have no differences here.

        MT: Thinking about this a little more, I realized that one
of the
precepts of PCT is that controlled perceptions have nothing
to do with
conscious perceptions, except insofar as we probably are
able to become
conscious of any perception we control. To me, this was a
liberating
realization, because it meant that it was quite conceivable
that what is
controlled may not be represented in the brain in the
unitary way we
perceive it.
BP: I draw exactly opposite conclusion from the same observations.
In order for a perception to be controlled, it must exist as a
single
signal entering a comparator along with a single reference signal.

OK. You assert that the answer to my question is "Yes, a controlled

perception MUST be a scalar quantity."

Good. That's a definite answer, at last. A step forward. You say

that the conscious perception must be a simple replica of the
controlled perception rather than being functionally dependent on
the controlled perception. Now I would like to know the grounds on
which you make this assertion. I would like to have either a
theoretical or a practical (experimental) reason that this answer is
correct. A simple assertion that it is so is not enough, without a
demonstration that all other suggested alternatives cannot work.

        MT: It seemed to me quite possible that "consciousness",
whatever it might be, might have the equivalent of
perceptual input
functions that were not part of the control hierarchy. These
inputs to
consciousness might themselves be responsible for the
apparent scalar
nature of the controlled perceptions, while what was
actually being
controlled might sometimes be a vector of elements that were
not composed
into a scalar within the control hierarchy.
BP: Again, exactly the opposite of what I conclude. Does that
special set of input functions somehow sense reality directly
rather than
through sensory neural signals?

Not as I imagined the connections.

  The inputs to consciousness remain
separate from each other, which is the only way we could
experience a
multiplicity of different perceptions at the same time.

That is another assertion, but I do know of the existence of

holograms, so I consider its validity open to doubt.

  The scalar nature
of controlled perceptions is the “ground truth” of perception;
only a single signal can be controlled relative to a single
reference
magnitude.

Why, please, must this single signal and its reference be scalar?

Why? How does using the phrase “ground truth of perception” improve
the logic of proof? For me, the “ground truth of perception” is that
actions through the environment can bring controlled perceptions to
their reference conditions, rather than any statement about how
those controlled perceptions are represented internally. It is
through the ability to control that we learn what is in the
environment and how it works, by way of reorganization. I wish I
knew of some proof or demonstration that the reorganization process
MUST lead to a hierarchy in which each environmental object and
attribute is represented by a single scalar variable, rather than
being distributed across many such variables (i.e., as a vector).

  I don't think of consciousness as "having"
perceptual input functions, but as “being” a set of perceptual
input functions. And what we are conscious of is specifically the
set of
scalar perceptual signals in the hierarchy, which are the inputs
to the
input functions we call
consciousness.

I know, and I knew, that this was your model. When I suggested a

different possibility I did not intend to assert that your model was
incorrect, only to open the possibility that the system might work
in a different way, and to ask if there is any theoretical or
experimental demonstration that it could not. Here you simply
reassert your model, properly qualified by “I think”. You don’t give
a reason why the alternative possibility must be wrong.

···

At this point in my responding I erased a very long set of direct

responses to the following segments of your message. So far as I can
see, the differences between us are not that I dispute your model,
but that I am open to other possibilities that you believe not to be
possible.

I want to know the basis for your belief.

To help you understand better the alternative possibility about

which I have been enquiring, I ask you to think in terms of a
metaphor or analogy that may be less of a metaphor than at first
appears. I ask you to think of a hologram. Considering the relation
between a hologram and the viewed image may make it easier to
imagine the possibility that the representation of environmental
objects and other attributes might be distributed across each level
of the perceptual control hierarchy, rather than being concentrated
into the magnitude of a single scalar value.

Without going into the mechanics of how a hologram works, the core

of the metaphor is that the hologram is a surface with texture on
the scale of the wavelength of light but otherwise (usually) flat.
Each tiny region larger than the scale of the wavelength of light
contains information that relates to the entire scene, and yet when
one looks at a hologram, one sees precise, clear, and individual
objects in a 3D space. The larger the hologram surface, the clearer
the objects. If part of the hologram surface is damaged or
destroyed, the view of some objects may be lost from any particular
viewpoint, but all objects can nevertheless be seen clearly from
other viewpoints. The hologram, as a representation of part of the
world, is robust against substantial damage.

What I am suggesting as a possibility (the possibility I have been

trying to get shot down) for the perceptual control hierarchy is
that any level of the control hierarchy might act similarly to the
surface of a hologram (not, of course, meaning that the elements are
sinusoidal components), and that each control unit at the next level
might be analogous to a viewer of the hologram instantiated at the
level below. Conscious perception, in contrast to elements of the
perceptual control hierarchy, would be a viewer that could look
freely at any part of any holographic level. Rather than control by
way of a particular element of the environment being lost entirely
if a particular scalar control unit is damaged, the control
hierarchy would be affected only slightly by such a loss.

One should not take this metaphor too literally. I very much doubt

that the entire surface of any hierarchic level would contain
information about the everything one could perceive. If the metaphor
has any validity, I would expect it to be very patchy, different
parts of any level being related to different aspects of the
environment. I offer the metaphor as only an aid to thinking about
the possibility that controlled perceptions are vectors – as are
the sets of light-wave-scale elements of the hologram surface that
produce clear objects when viewed. I offer it because my attempts to
describe in a direct way what I have been trying to ask about have
failed to get my question across.

I hope that introducing this metaphor will help us to get at least

some idea as to why perceptions that correspond to attributes of the
environment MUST be scalar, or at least to get some suggestions as
to how one would go about getting a theoretical proof or an
experimental demonstration that it is so. Please don’t take any of
this as arguing that it is not.

Martin

MartinT · November 6, 2011, 3:26pm

[Martin Taylor 2011.11.06.10.14]

[From Bill Powers (2011.11.05.1520 MDT)]

Martin Taylor 2011.11.05.13.24 --

MT: I'm not saying that the scalar-magnitude-only model for perceptual signals is inconsistent with the neurophysiological data. I'm just saying that it's a bit of an intellectual leap of faith to assert that it is consistent.

All that's needed in order to be consistent with neurophysiological data is to show that a neural signal can vary only in the dimension of magnitude because of the all-or-none nature of a neural impulse.

I agree. As I said in a further response to Rick, I misspoke.

Given that (almost) all impulses in any given axon have the same amplitude and shape, the only way for them to vary is in the rate at which they occur. The rate can vary rapidly or slowly, in regular or irregular patterns, but there is no other way for them to vary. Hence, neural signals are scalar -- one-dimensional.

If you like, you can then look for groups of signal pathways that carry signals at the same time and from the same general source to the same general destination, and call them vectors. Since you define vectors that way, they are vectors. That does not give them any new properties or any new relationships to external variables. Each signal is still the output of one neuron, and it terminates at synapses on one or more other neurons. The parallel pathways may carry similar information, as in the connection between a set of spinal motor neurons and a common muscle at the destination. Or they may carry different information from independent sources.

If the information carried by some axons in a vector is related to information carried in others, for example in the signals representing color from cones in the fovea, that information remains implicit until the related signals reach a perceptual input function. At that point, in the case of color signals, they can be computationally combined so the maximum perceptual signal (at the next level) is generated for a narrow range of magnitudes in the three color channels.

Color signals from each cone in the fovea obviously do not expand into a million or so signal pathways for different scalar color signals. Instead, the initial color signals are carried all the way to the back of the brain as a vector, where they reach synapses in the primary visual cortex V1 (don't be impressed, I'm using the Web). Color vision arises there, where the separate scalar intensity signals enter perceptual input functions that extract the color information as new signals. The details get murky there, but we clearly have the signals in one vector being combined to produce new scalar signals, which is what perceptual input functions in PCT are supposed to do. I don't see any evidence that color is seen before the signals synapse in the visual cortex. The mere existence of the three color signals does not provide the experience of color. They have to be neurally combined into signals of the next order.

It still seems unlikely to me that awareness can get anything out of a vector of perceptual signals that is not in the individual signals. It's the brain that has to do the extracting of different levels of perceptual signals. Of course if awareness is actually a kind of neural input function at a level we haven't identified yet, it could perform the construction of a new level of perception in the usual way. No spooky conjectures necessary. But that would make awareness even less understandable, with its ability to expand and contract its range and to select information from any level in the nervous system.

We seem to be lacking a very large chunk of vital information here.

I suspect (and hope) that you will agree that all the above is consistent with what I wrote in the longer response to you that I posted a few minutes ago.

I'm pleased you wrote "It seems unlikely to me" at the start of the last long paragraph, in place of the positive assertions in your previous message. Funnily, on the particular point -- whether awareness can get anything out of a vector of perceptual signals that is not in the individual signals -- I would have been less circumspect, and would have asserted that it would be impossible on information-theoretic grounds. All the information in any vector about something that influences its elements is contained in how its elements change when that "something" changes.

That's as close to a proof as I want to get. It's the level of proof that I am seeking in support of your assertions earlier that each controlled perception corresponding to an object or attribute of the environment is necessarily represented as a scalar quantity.

Martin

Bill_Powers1 · November 7, 2011, 9:01pm

[From Bill Powers (2011.11.07.1230 MDT);

Today would have been Mary’s 81st birthday.

Martin Taylor
2011.11.11.05.14.47

MT:When I talk about the conscious perception is of unitary objects
and attributes, I mean that consciously one sees that there is “a
glass” on “a table” when one consciously is aware at that
level. One can also be aware of “the left edge of the glass”
and “the edge of the shadow of the glass on the table”.
Depending on what one is conscious of at any one moment, those items are
unitary. When you see the glass, you ordinarily do not see it as a
concatenation of its left edge, its right edge, the reflection of the
table from it, the shadow it casts, and so forth. When you see the glass,
that’s what it is, a glass. That’s the unitary perception to which I
refer. In consciousness at one time, there are several such unitary
perceptions. They truly are perceived as separate, which is the property
I was thinking of when I called them unitary.

BP earlier:There is only one unitary field of experience encompassing
all these things.
MT: Would you really call the field of experience at any one moment
“unitary”? That doesn’t correspond to my experience, nor,
connotationally, to the word “field”. I would probably
substitute the word “unique” for
“unitary”.
BP: Yes, I would call the field unitary: there is only one field of
experience, with everything that I know of at a given time contained in
it. The contents change, but the field remains – it’s been called
“the theater of the
mind.”

MT: There is, of course, a tautological sense in which the totality
of your consciousness is all there is in consciousness, and is therefore
unitary in a Zen kind of way, but I don’t think that’s a very valuable
way to use the word “unitary”.

BP: Of course you don’t. If you did think it was a valuable way, you
would use it that way. To me, it simply means that there is one frame
within which all the changing details of experience exist. When I don’t
notice the frame, all I see are the details, but just pulling back a bit
I can realize that I’m viewing a screen on which, or a stage upon which,
experience is displayed, just as the literal screen I’m looking at now
shows images that change even as I
type.

MT: You say: “The very point I made was that
consciousness, as an input function to some unknown system, can do
something that no PCT input function can do: examine a field of
experience in which there are many different perceptions. They do
not look like one single – unitary – thing, but like many separate
things.”, and that is why I would not call consciousness unitary. I
think we see the world similarly, but use words
differently.

BP: I think what you call consciousness, then, is what I would call
“the content of consciousness,” the “many separate
things” we are conscious of. The “many separate things”
are different perceptions which can all exist in the same frame, but that
which is aware of the many separate things is unitary, and can notice the
frame or area in which the separate things appear. It’s like being aware
of the words printed on a page, as compared with being aware of the page
on which the printing
appears.

MT: Be that as it may, what I am talking about is the perception of
these separate attributes of the perceived environment as singular
entities. And my question is whether these conscious perceptions of
individual entities necessarily demonstrates that the controlled
perceptions of them – as opposed to the conscious perceptions of them –
are singular scalar quantities.

BP: Scalarness and vectorness are not things that are directly
experienced (except as ideas). I call a variable scalar if it has only
one dimension in which it can change. If you consider something like
position in three-dimensional space, there are three independent measures
(a vector, of course) that together add up to position. If it is possible
to change position in one direction without affecting the other
directions (however many there are), then it is a scalar variable that is
being altered. Considering that every vector has such independently
variable components, it’s clear that every vector is simply a list of
scalar quantities. The vector has no other existence, does
it?

MT: Thinking about this a little more, I realized that one of the
precepts of PCT is that controlled perceptions have nothing to do with
conscious perceptions, except insofar as we probably are able to become
conscious of any perception we control. To me, this was a liberating
realization, because it meant that it was quite conceivable that what is
controlled may not be represented in the brain in the unitary way we
perceive it.
BP: I draw exactly opposite conclusion from the same observations.
In order for a perception to be controlled, it must exist as a single
signal entering a comparator along with a single reference
signal.

OK. You assert that the answer to my question is “Yes, a controlled
perception MUST be a scalar quantity.”

Yes, I guess that does follow. But your statement that the PCT precept is
that

“controlled perceptions have nothing to do with conscious
perceptions” is incorrect. Conscious perceptions, I would say, are
perceptual signals in the hierarchy that are being observed by awareness;
unconscious perceptions are those that are not being observed that way,
though many of them could be observed if attention shifted. So perceptual
signals, which are scalar quantities, are behind all conscious
experience, though they also exist without coming to conscious
awareness.

MT: Good. That’s a definite answer, at last. A step forward. You say
that the conscious perception must be a simple replica of the controlled
perception rather than being functionally dependent on the controlled
perception. Now I would like to know the grounds on which you make this
assertion. I would like to have either a theoretical or a practical
(experimental) reason that this answer is correct. A simple assertion
that it is so is not enough, without a demonstration that all other
suggested alternatives cannot work.

I think the experimental reason is mainly that the same control process
can exist with and without awareness of the controlled perception. This
does not rule out simultaneous control of some function of the components
of a vector, but as soon I put it that way, the value of the function
becomes a higher-level perception and once again we have a scalar
quantity. Consider, for example, controlling the magnitude of the vector
without changing its direction. To control the magnitude in linear 3D
space, you first have to perceive the magnitude, which would be sqrt(x^2

y^2 + z^2). That is a scalar quantity: it can only increase or
decrease. If you control the direction of the vector, you have to control
each of the three components, and again each component is a scalar. A
function of the three components such as y/x is again a scalar, the
tangent of the angle in the x-y plane, and it can controlled over some
range by varying x, y or both.

Remember that you have to control the components of a vector, not just
issue outputs calculated to alter them in a specific way. Control in PCT
is defined as acting to oppose the effects of disturbances, implying that
if a variable is not controlled, there will be no opposition to
disturbances. That’s part of the test for the controlled variable.

Having said that, I see that it may be that the concept of controlling
vectors is simply a way of speaking about different levels of controlled
variable. The vector itself has existence only as a function of its
components. That is the same as saying that the value of that function is
a higher-order perception based on the
components.

MT: It seemed to me quite possible that “consciousness”,
whatever it might be, might have the equivalent of perceptual input
functions that were not part of the control hierarchy. These inputs to
consciousness might themselves be responsible for the apparent scalar
nature of the controlled perceptions, while what was actually being
controlled might sometimes be a vector of elements that were not composed
into a scalar within the control hierarchy.
BP: Again, exactly the opposite of what I conclude. Does that
special set of input functions somehow sense reality directly rather than
through sensory neural signals?

Not as I imagined the connections.

When you say there can be perceptual input functions that are not part of
the hierarchy, where do you find them? Don’t they come from the same
sensory endings that underly controlled and uncontrolled perceptions in
the
hierarchy?

BP earlier: The inputs to consciousness remain separate from each
other, which is the only way we could experience a multiplicity of
different perceptions at the same time.
MT: That is another assertion, but I do know of the existence of
holograms, so I consider its validity open to doubt.

BP: A optical hologram can be observed only after being scanned by laser
light with the reflected result then interacting with the unprocessed
laser light. The result is an image on the retina like that from a real
object. I know of no process in the brain that works or could work like
that. That does not mean there is no such process, but neither does it
mean it exists or could
exist.

BP earlier: The scalar nature of controlled perceptions is the
“ground truth” of perception; only a single signal can be
controlled relative to a single reference magnitude.
MT: Why, please, must this single signal and its reference be scalar?
Why? How does using the phrase “ground truth of perception”
improve the logic of proof? For me, the “ground truth of
perception” is that actions through the environment can bring
controlled perceptions to their reference conditions, rather than any
statement about how those controlled perceptions are represented
internally.

I think you must agree that all perceptions begin as neural signals
coming out of sensory receptors. Those, clearly, are scalar quantities,
whether they are treated in groups by an observer or by higher levels as
vectors. That’s what I mean by “ground truth.” To alter any
property of the vector or higher-order perception, it is necessary to
alter one or more of the scalar components of the vector. To alter any
scalar component in a disturbance-resistant way, the component must be
compared with a reference-magnitude and the error signal must be
converted to a disturbance-opposing action. If the actions are governed
by vector errors, they have to be based on some function of the
individual components of the vector error – scalars. I see no other way
of producing an error signal. No matter how you do it, you end up
controlling scalar variables.

MT: It is through the ability to control that we learn what is
in the environment and how it works, by way of reorganization. I wish I
knew of some proof or demonstration that the reorganization process MUST
lead to a hierarchy in which each environmental object and attribute is
represented by a single scalar variable, rather than being distributed
across many such variables (i.e., as a vector).
BP: I think you keep overlooking a fact to which you say you agree,
that the vector representation is simply the way an observer chooses to
represent the variables, and in no way introduces anything that is not
present in the scalar representation. To subtract a vector perceptual
signal from a vector reference signal, it is necessary to subtract the
appropriate scalar components of one from those of the other to obtain
the components of the error vector. How else could it be done? Can you
give an example that does not require the operations on the scalar
components?

I don’t think there is any such thing as a vector or matrix operation in
the physical world, unless it is simply a shorthand way of describing
some set of scalar operations. And I do think that this whole puzzle will
be solved if we simply switch to thinking in terms of levels of
perception and control instead of imbuing vectors with an ability to
interact directly, in some way independent of the way the components
interact.

That means that there is no difference between the scalar and vector
representations. The vector representation is simply a disguised version
of the scalar representation – disguised by all the rules of vector
algebra which, by remaining in the background, allow the actual physical
processes involved to be concealed.

Your post goes on, but it seems to me that the points just made cover the
subject of vectors and scalars, so I’ll rest my case there.

Best,

Bill P.

BUSINESS_GAVIN_HERMA · November 7, 2011, 9:18pm

(Gavin Ritz 2011.11.08.10.05NZT)

[From Bill Powers
(2011.11.07.1230 MDT);

Today would have been Mary’s 81st birthday.

Then I will wish you Happy birthday, Bill.

It’s good to be born in the second
part of the year. I know this because I think I was born right in the middle (exactly).
But my mother bless her thinking decided that it was better to be in the first part
rather than the second (only god knows what she was controlling). So she promptly
changed my birth date and made the doctor sign the birth certificate (probably much
to his chagrin, which made not one iota of influence on my mother). I never did
get the real date from her although she let slip on many occasions it was on
the 1 July but as I got so many renditions of this story, ( I don’t believe
any) I guess it could have been anywhere from the 30^th June to 7^th
July. So I simply celebrate it 7 times.

So then a toast to Mary seven times.

Kind regards

Gavin

PS. PCT must be correct it is the only
theory that explicitly explains my mother’s behavior, all other theories
fall totally flat.

Martin Taylor
2011.11.11.05.14.47 –

MT:When I talk about the
conscious perception is of unitary objects and attributes, I mean that
consciously one sees that there is “a glass” on “a table”
when one consciously is aware at that level. One can also be aware of “the
left edge of the glass” and “the edge of the shadow of the glass on
the table”. Depending on what one is conscious of at any one moment, those
items are unitary. When you see the glass, you ordinarily do not see it as a
concatenation of its left edge, its right edge, the reflection of the table
from it, the shadow it casts, and so forth. When you see the glass, that’s what
it is, a glass. That’s the unitary perception to which I refer. In
consciousness at one time, there are several such unitary perceptions. They
truly are perceived as separate, which is the property I was thinking of when I
called them unitary.

BP earlier:There is only
one unitary field of experience encompassing all these things.

MT: Would you really call
the field of experience at any one moment “unitary”? That doesn’t
correspond to my experience, nor, connotationally, to the word
“field”. I would probably substitute the word “unique” for
“unitary”.

BP: Yes, I would call the
field unitary: there is only one field of experience, with everything that I
know of at a given time contained in it. The contents change, but the field
remains – it’s been called “the theater of the mind.”

MT: There is, of course,
a tautological sense in which the totality of your consciousness is all there
is in consciousness, and is therefore unitary in a Zen kind of way, but I don’t
think that’s a very valuable way to use the word “unitary”.

BP: Of course you don’t. If you did think it was a valuable way, you would use
it that way. To me, it simply means that there is one frame within which all
the changing details of experience exist. When I don’t notice the frame, all I
see are the details, but just pulling back a bit I can realize that I’m viewing
a screen on which, or a stage upon which, experience is displayed, just as the
literal screen I’m looking at now shows images that change even as I type.

MT: You say:
“The very point I made was that consciousness, as an input function
to some unknown system, can do something that no PCT input function can do:
examine a field of experience in which there are many different perceptions. They do not look
like one single – unitary – thing, but like many separate things.”, and
that is why I would not call consciousness unitary. I think we see the world
similarly, but use words differently.

BP: I think what you call consciousness, then, is what I would call “the
content of consciousness,” the “many separate things” we are
conscious of. The “many separate things” are different perceptions
which can all exist in the same frame, but that which is aware of the many
separate things is unitary, and can notice the frame or area in which the separate
things appear. It’s like being aware of the words printed on a page, as
compared with being aware of the page on which the printing appears.

MT: Be that as it may,
what I am talking about is the perception of these separate attributes of the
perceived environment as singular entities. And my question is whether these
conscious perceptions of individual entities necessarily demonstrates
that the controlled perceptions of them – as opposed to the conscious
perceptions of them – are singular scalar quantities.

BP: Scalarness and vectorness are not things that are directly experienced
(except as ideas). I call a variable scalar if it has only one dimension in
which it can change. If you consider something like position in
three-dimensional space, there are three independent measures (a vector, of
course) that together add up to position. If it is possible to change position
in one direction without affecting the other directions (however many there
are), then it is a scalar variable that is being altered. Considering that
every vector has such independently variable components, it’s clear that every
vector is simply a list of scalar quantities. The vector has no other
existence, does it?

MT: Thinking about this a
little more, I realized that one of the precepts of PCT is that controlled
perceptions have nothing to do with conscious perceptions, except insofar as we
probably are able to become conscious of any perception we control. To me, this
was a liberating realization, because it meant that it was quite conceivable
that what is controlled may not be represented in the brain in the unitary way
we perceive it.

BP: I draw exactly
opposite conclusion from the same observations. In order for a perception to be
controlled, it must exist as a single signal entering a comparator along with a
single reference signal.

OK. You assert that the answer to my question is “Yes, a controlled
perception MUST be a scalar quantity.”

Yes, I guess that does follow. But your statement that the PCT precept is that

“controlled perceptions have nothing to do with conscious
perceptions” is incorrect. Conscious perceptions, I would say, are
perceptual signals in the hierarchy that are being observed by awareness;
unconscious perceptions are those that are not being observed that way, though
many of them could be observed if attention shifted. So perceptual signals,
which are scalar quantities, are behind all conscious experience, though they
also exist without coming to conscious awareness.

MT: Good. That’s a
definite answer, at last. A step forward. You say that the conscious perception
must be a simple replica of the controlled perception rather than being
functionally dependent on the controlled perception. Now I would like to know
the grounds on which you make this assertion. I would like to have either a
theoretical or a practical (experimental) reason that this answer is correct. A
simple assertion that it is so is not enough, without a demonstration that all
other suggested alternatives cannot work.

I think the experimental reason is mainly that the same control process can
exist with and without awareness of the controlled perception. This does not
rule out simultaneous control of some function of the components of a vector,
but as soon I put it that way, the value of the function becomes a higher-level
perception and once again we have a scalar quantity. Consider, for example,
controlling the magnitude of the vector without changing its direction. To
control the magnitude in linear 3D space, you first have to perceive the
magnitude, which would be sqrt(x^2 + y^2 + z^2). That is a scalar quantity: it
can only increase or decrease. If you control the direction of the vector, you
have to control each of the three components, and again each component is a
scalar. A function of the three components such as y/x is again a scalar, the
tangent of the angle in the x-y plane, and it can controlled over some range by
varying x, y or both.

Remember that you have to control the components of a vector, not just issue
outputs calculated to alter them in a specific way. Control in PCT is defined
as acting to oppose the effects of disturbances, implying that if a variable is
not controlled, there will be no opposition to disturbances. That’s part of the
test for the controlled variable.

Having said that, I see that it may be that the concept of controlling vectors
is simply a way of speaking about different levels of controlled variable. The
vector itself has existence only as a function of its components. That is the
same as saying that the value of that function is a higher-order perception
based on the components.

MT: It seemed to me quite
possible that “consciousness”, whatever it might be, might have the
equivalent of perceptual input functions that were not part of the control hierarchy.
These inputs to consciousness might themselves be responsible for the apparent
scalar nature of the controlled perceptions, while what was actually being
controlled might sometimes be a vector of elements that were not composed into
a scalar within the control hierarchy.

BP: Again, exactly the
opposite of what I conclude. Does that special set of input functions somehow
sense reality directly rather than through sensory neural signals?

Not as I imagined the connections.

When you say there can be perceptual input functions that are not part of the
hierarchy, where do you find them? Don’t they come from the same sensory
endings that underly controlled and uncontrolled perceptions in the hierarchy?

BP earlier: The inputs to
consciousness remain separate from each other, which is the only way we could
experience a multiplicity of different perceptions at the same time.

MT: That is another
assertion, but I do know of the existence of holograms, so I consider its
validity open to doubt.

BP: A optical hologram can be observed only after being scanned by laser light
with the reflected result then interacting with the unprocessed laser light.
The result is an image on the retina like that from a real object. I know of no
process in the brain that works or could work like that. That does not mean
there is no such process, but neither does it mean it exists or could exist.

BP earlier: The scalar
nature of controlled perceptions is the “ground truth” of perception;
only a single signal can be controlled relative to a single reference
magnitude.

MT: Why, please, must
this single signal and its reference be scalar? Why? How does using the phrase
“ground truth of perception” improve the logic of proof? For me, the
“ground truth of perception” is that actions through the environment
can bring controlled perceptions to their reference conditions, rather than any
statement about how those controlled perceptions are represented internally.

I think you must agree that all perceptions begin as neural signals coming out
of sensory receptors. Those, clearly, are scalar quantities, whether they are
treated in groups by an observer or by higher levels as vectors. That’s what I
mean by “ground truth.” To alter any property of the vector or
higher-order perception, it is necessary to alter one or more of the scalar
components of the vector. To alter any scalar component in a
disturbance-resistant way, the component must be compared with a
reference-magnitude and the error signal must be converted to a
disturbance-opposing action. If the actions are governed by vector errors, they
have to be based on some function of the individual components of the
vector error – scalars. I see no other way of producing an error signal. No
matter how you do it, you end up controlling scalar variables.

MT: It is through
the ability to control that we learn what is in the environment and how it
works, by way of reorganization. I wish I knew of some proof or demonstration
that the reorganization process MUST lead to a hierarchy in which each
environmental object and attribute is represented by a single scalar variable,
rather than being distributed across many such variables (i.e., as a vector).

BP: I think you keep
overlooking a fact to which you say you agree, that the vector representation
is simply the way an observer chooses to represent the variables, and in no way
introduces anything that is not present in the scalar representation. To
subtract a vector perceptual signal from a vector reference signal, it is
necessary to subtract the appropriate scalar components of one from those of
the other to obtain the components of the error vector. How else could it be
done? Can you give an example that does not require the operations on the
scalar components?

I don’t think there is any such thing as a vector or matrix operation in the
physical world, unless it is simply a shorthand way of describing some set of
scalar operations. And I do think that this whole puzzle will be solved if we
simply switch to thinking in terms of levels of perception and control instead
of imbuing vectors with an ability to interact directly, in some way
independent of the way the components interact.

That means that there is no difference between the scalar and vector
representations. The vector representation is simply a disguised version of the
scalar representation – disguised by all the rules of vector algebra which, by
remaining in the background, allow the actual physical processes involved to be
concealed.

Your post goes on, but it seems to me that the points just made cover the
subject of vectors and scalars, so I’ll rest my case there.

Best,

Bill P.

MartinT · November 8, 2011, 4:55pm

[Martin Taylor 2011.11.08.10.07]

[From Bill Powers (2011.11.07.1230 MDT);
  Today would have been Mary's 81st birthday.

I hope this memory is not too painful, and I am sorry that we have

an apparent disagreement on such a day.

          BP earlier: The scalar nature of controlled perceptions
is the
“ground truth” of perception; only a single signal can be
controlled relative to a single reference magnitude.
MT: Why, please, must this single signal and its reference
be scalar?
Why? How does using the phrase “ground truth of perception”
improve the logic of proof? For me, the “ground truth of
perception” is that actions through the environment can bring
controlled perceptions to their reference conditions, rather
than any
statement about how those controlled perceptions are
represented
internally.
  I think you must agree that all perceptions begin as neural
signals
coming out of sensory receptors. Those, clearly, are scalar
quantities,
whether they are treated in groups by an observer or by higher
levels as
vectors. That’s what I mean by “ground truth.”

I think we have no difference of opinion on the relation between

scalars and vectors, so I will forbear to comment on the bulk of
your message, which largely consists of trying to convince me that
it is a matter of analytical preference as to whether one looks at
the vector as a whole or at its elements individually – a statement
that I have never questioned.

I also have no problem with the "ground truth" that the sensory

receptors provide scalar quantities. The “ground truth” that I
question is whether it is necessarily true that the aspects of the
environment that we perceive as singular (I use that term in place
of “unitary”, since you wish to reserve “unitary” for a different
purpose) are represented as scalar quantities in a single place in
the hardware (of teh brain or of the model). They are not so
represented at the sensory periphery, and so far I have seen no
evidence from you that would bear on the issue other than a bald
assertion that what is consciously perceived as scalar is so because
the controlled perception is scalar. I’m not saying it isn’t. I just
want evidence that it is, and your simple assertion really isn’t
adequate as evidence.

  BP: When you say there can be perceptual
input functions that are not part of
the hierarchy, where do you find them? Don’t they come from the
same
sensory endings that underly controlled and uncontrolled
perceptions in
the
hierarchy?

My suggestion for an alternative possibility is that their inputs

are precisely the elements of the controlled perceptions in the
hierarchy.

          BP earlier: The inputs to consciousness remain separate
from each
other, which is the only way we could experience a
multiplicity of
different perceptions at the same time.
MT: That is another assertion, but I do know of the
existence of
holograms, so I consider its validity open to doubt.
  BP: A optical hologram can be observed only after being scanned by
laser
light with the reflected result then interacting with the
unprocessed
laser light. The result is an image on the retina like that from a
real
object. I know of no process in the brain that works or could work
like
that. That does not mean there is no such process, but neither
does it
mean it exists or could
exist.

The analogue to the scanning light was actually one of the things

that led me to the holographic analogy. (By the way, it doesn’t have
to be a laser. Sunlight or a light bulb both work quite effectively,
at least for some holograms.)

Whatever process it might be, it is no more complex than the process

by which a proposed scalar perceptual variable that corresponds to
some environmental attribute is created from elements derived in
widely separated brain regions. The only difference is that
consciousness can select different subsets of elements and create
consciously perceived patterns fairly freely, whereas the
corresponding scalar control system is fixed except when altered by
reorganization.

Perhaps it would help our mutual understanding if I come at the

question from a different angle, ignoring the question of
consciousness entirely, and considering only the control hierarchy
and reorganization. This approach might be amenable to experimental
investigation through modelling, and you may already have done the
experiment.

I expect it is obvious to you that what an observer/analyst sees as

a scalar variable need not be represented as a single variable
signal in the analyzed hardware. The value of the scalar variable
could equally refer to magnitude of a vector with many elements. The
observer/analyst could not tell the difference.

Reorganization depends only on the success of perceptual control in

keeping intrinsic variables in genetically determined appropriate
states. That’s a very general statement, and for my purposes it need
not be made more specific.The control hierarchy must be built in
part by genetic directives and in part by reorganization as a
consequence of attempts to control in the individual’s environment.

In order for a perceptual control action to influence an intrinsic

variable, the side-effects of that action must have a reasonably
consistent effect on the intrinsic variable. Typically, those
side-effects work through their influences on environmental
variables; the only hitherto proposed exception of which I am aware
is the intrinsic variable “control quality”, which is necessary if
the side-effects of action on intrinsic variables is to be
reasonably consistent.

The same question arises whether the control structure is

genetically determined or created through individual reorganization:

  Given that the sensory periphery provides many separated
scalar values corresponding to any single entity in the
environment, and that each of these values may be influenced by
states of more than one such entity, what is there about the
process of reorganization that guarantees there will exist some
control element for which the controlled perceptual signal is a
single scalar variable corresponding to the state of any single
entity? Is it necessarily the case that reorganization destroys
the distributed, hologram-like, nature of the initial sensory
representation of environmental entities?

This way of asking the question leads back to my original question:

Is there any theoretical or experimental evidence to suggest that
the controlled perceptual representation of any or all environmental
entities and attributes is a single scalar-valued signal in the
hardware? (I count multiple parallel paths for noise-reduction as
being a single scalar representation).

Martin

Bill_Powers1 · November 9, 2011, 6:14pm

[From Bill Powers (2011.11.09.1028 MDT)]

Martin Taylor 2011.11.08.10.07

···

–

The “ground truth” that I question is whether it is
necessarily true that the aspects of the environment that we perceive as
singular (I use that term in place of “unitary”, since you wish
to reserve “unitary” for a different purpose) are represented
as scalar quantities in a single place in the hardware (of the brain or
of the model). They are not so represented at the sensory periphery, and
so far I have seen no evidence from you that would bear on the issue
other than a bald assertion that what is consciously perceived as scalar
is so because the controlled perception is scalar. I’m not saying it
isn’t. I just want evidence that it is, and your simple assertion really
isn’t adequate as evidence.

Right. So why do I think it’s scalar? At the moment, the reason
seems mostly subjective. I think it’s because of the idea of a variable
– some one thing that can change. It’s because I can attach a single
number to any aspect of an experience; I can say how much of it there is.
How much distance, how much honesty, how much fairness, how much pain,
how much size, how much speed – even how much logic. There seems to be a
single thing varying in each case, a scale of something that runs from
zero to as much as possible. That “unitary” business you talk
about.
Since all these experiences are made up of multiple components which are
not of the same kind as the experience, clearly somehow all those
independently variable parts are being brought together to produce a
sense of how much of one thing there is. That idea naturally (to me)
calls up the notion of a function. The unitary experience is some
function of all those components. The value of the function has a
magnitude. That value is a variable, because it can vary as the arguments
of the function vary.
Whether that function is being computed all in one place in the brain, or
the computational machinery is not spatially contiguous, is relatively
unimportant. The 3-D geometry of the brain is not what determines its
organization. All that matters is what is connected to what via a signal
pathway, and what functions are performed when different signals arrive
in some common location. Of course it is likely that parts of the brain
that compute similar things will be spatially close to each other, since
that would seem to be helpful in constructing functions that make sense
instead of doing it completely at random. It makes sense to have levels
of perception and control that deal with variables constructed according
to some principle or theme such as sequence or shape – this makes it
possible, it seems to me, for different systems at the same level to deal
with different, but mutually consistent, aspects of the lower-order
world.
To approach this from a different angle: A principle I have used is that
implicit variables have no effects. The mere fact that two signals exist
does not imply that any function of them has physical significance,
because there is an infinity of different functions one could imagine,
leaving the probability that any one of them is meaningful at zero. For
any function of multiple signals to have any real effect, there must be a
physical function that computes a new variable that has real physical
existence. Only variables that actually exist as physical representations
can have physical effects.
This is why I treat vectors with skepticism, because there has to be
something more than mere coexistence to make a collection of different
variables have some unitary significance. What is required, as I see it,
is not that some observer be able to construct a proposed function of the
components of the vectors; what is required to give the vector any
reality is that the system being observed itself contain means of
converting the collection of variables into a new variable by means of
some computation. The eye of the beholder is not what gives a vector
significance, though the beholder may be convinced of the reality of the
observed pattern. In fact, the proposed variable may have quite real
existence in the observer, and indeed must if the observer is
perceiving it, according to this same argument. But it may not exist in
the observed system.

MT: This way of asking the question leads back to my original
question: Is there any theoretical or experimental evidence to suggest
that the controlled perceptual representation of any or all environmental
entities and attributes is a single scalar-valued signal in the hardware?
(I count multiple parallel paths for noise-reduction as being a single
scalar representation).
All I can do here is counter with another question. Can you imagine
any way in which a collection of independently generated variables can
lead to a perception of some unitary thing without first being
represented as signals, and then passing into a computing function that
generates some particular value?

Best,

Bill P.

rsmarken · November 11, 2011, 5:30pm

[From Rick Marken (2011.11.11.1111)]

It's not 11:11 but I just couldn't resist;-)

Bill Powers (2011.11.09.1028 MDT) to Martin Taylor 2011.11.08.10.07 --

MT: This way of asking the question leads back to my original question: Is
there any theoretical or experimental evidence to suggest that the
controlled perceptual representation of any or all environmental entities
and attributes is a single scalar-valued signal in the hardware? (I count
multiple parallel paths for noise-reduction as being a single scalar
representation).

BP: All I can do here is counter with another question. Can you imagine any way
in which a collection of independently generated variables can lead to a
perception of some unitary thing without first being represented as signals,
and then passing into a computing function that generates some particular
value?

That's basically been my question all along. I'm looking forward to
hearing what Martin has in mind.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

MartinT · November 12, 2011, 4:57am

[Martin Taylor 2011.11.11.23.02]

[From Bill Powers (2011.11.09.1028 MDT)]
  Martin Taylor 2011.11.08.10.07
–
        The "ground truth" that I question is whether it is
necessarily true that the aspects of the environment that we
perceive as
singular (I use that term in place of “unitary”, since you
wish
to reserve “unitary” for a different purpose) are
represented
as scalar quantities in a single place in the hardware (of
the brain or
of the model). They are not so represented at the sensory
periphery, and
so far I have seen no evidence from you that would bear on
the issue
other than a bald assertion that what is consciously
perceived as scalar
is so because the controlled perception is scalar. I’m not
saying it
isn’t. I just want evidence that it is, and your simple
assertion really
isn’t adequate as evidence.
  Right. So why *do* I think it's scalar? At the moment, the
reason
seems mostly subjective. …
        MT: This way of asking the question leads back to my
original
question: Is there any theoretical or experimental evidence
to suggest
that the controlled perceptual representation of any or all
environmental
entities and attributes is a single scalar-valued signal in
the hardware?
(I count multiple parallel paths for noise-reduction as
being a single
scalar representation).
All I can do here is counter with another question. Can you
imagine
any way in which a collection of independently generated variables
can
lead to a perception of some unitary thing without first
being
represented as signals, and then passing into a computing function
that
generates some particular value?

No.

The question is whether this function is necessarily a component of

the perceptual control hierarchy, or exists only as a process of
consciousness.

Let me repeat myself: Is it necessarily true that what is

consciously perceived as scalar is so perceived because the
corresponding controlled variable is itself a scalar?

Let me go back to my more recent attempt to get at the question by

asking about reorganization.

What we perceive as environmental attributes such as objects enter

our neural system as patterns distrubuted widely across different
pathways, and most of those pathways are influenced by several
different things we consciously perceive as distinct. This is
analogous to a holographic representation, in which each object is
represented in a widely distributed area of the hologram, and each
point of the hologram is influenced by many different objects. Since
I know of no real word to suit the case, I will call this
generalized form of hologram a “holoform”, meaning that the objects
represented are represented in a distributed way, and that most
elementthat contribute to the representation of an object are also
influenced by other objects. The contrasting term is “idioform”, in
which each element of the representation pertains to one and only
one object. A scalar is an extreme case of an idioform.

At the sensory periphery, the representation of the world is a

holoform. In consciousness it is a scalar. Either the holoform
representation slowly is converted into an idioform at successively
higher perceptual processing levels, or the transformation occurs at
exactly one place. Does reorganization (or genetic evolution) create
idioform representations from a holoform base structure for the
purpose of control at just one level, successively in the various
transitions from level to level, or is the idioform representation a
feeature only of consciousness?

When viewing a pictorial hologram, the objects become visible

because the structure of the representation creates interference
patterns in the reproduction light beam, Only when that beam exists
can the objects that are accurately represented in the hologram be
seen in their “idioform” character. This fact is one of the reasons
I have been asking my question, which can be rephrased in yet
another way: “Could the process of consciousness be an analogue to
the light beam that allows the objects represented in the hologram
to be seen.”

Using this wording, we come once again to the question of whether

any or all controlled perceptions (outside of consciousness) that
correspond to environmental attributes could be represented as
vectors at each level within the perceptual control hierarchy. And
for yet another rephrasing, is it possible that some or all of the
scalar controlled variables at any one level within the hierarchy
are influenced by several environmental attributes at that level? We
know that even in consciousness perceptions are often quite
context-dependent.

  BP: For
any function of multiple signals to have any real effect, there
must be a
physical function that computes a new variable that has real
physical
existence. Only variables that actually exist as physical
representations
can have physical effects.

What is a "real effect" in this context? Is it that control works in

the environment or that there is a conscious perception of a single
variable? And what do you mean by “real physical existence”. Is this
reality one perceived by the actor or one perceived by the analyst
when something the analyst perceives as an environmental attribute
is influenced by the actor?

  This is why I treat vectors with skepticism, because there has to
be
something more than mere coexistence to make a collection of
different
variables have some unitary significance. What is required, as I
see it,
is not that some observer be able to construct a proposed function
of the
components of the vectors; what is required to give the vector any
reality is that the system being observed itself contain
means of
converting the collection of variables into a new variable by
means of
some computation.

My view is a little different. It comes from the ability to control.

If varying the magnitude of a vector influences something
consciously seen to be a single attribute, then the vector has
unitary significance. We aren’t talking about imagination, here. We
are talking about testing in the environment. If someone perceives
the pattern of tealeaves in the bottom of a cup as a unitary
something and uses error created that perception in acting on the
world, does the action influence the world to reduce error
consistently. If “Yes”, then the pattern of tealeaves is of “unitary
significance”. If “No”, then it is not demonstrated to be of unitary
significance (but it not proven not to be).

I think control, not consciousness, is what matters here. My

question can be rephrased in yet another way: “Could our conscious
perception of the world mislead us about how our control machinery
is constructed?”

If it is possible that the perceptual control levels in the

hierarchy are holoform all the way up, then we have a subsequent
question: Is there a conceivable experimental test to see whether
they are holoform, idioform (the standard assumption of one scalar
controlled variable for one environmental attribute), or something
in between, without actually examining the hardware?

If it is not possible, then there must be some general theorem

relating to reorganization that would show how what is holoform in
the sensory periphery is translated into an idoform representation
before any control level of perception. How could we find such a
theorem?

Martin

MartinT · November 2, 2011, 7:20pm

[Martin Taylor 2011.11.01.22.15]

  [From Bill Powers (2011.11.01.1845 MDT)]




  Martin Taylor 2011.11.01.17.35 --
    MT to RM: You have one already -- your
three-level three unit excel spreadsheet. It’s a good example of
what I am talking about. The top-level reference is a pattern of
three values – a vector. The system controls a three-element
vector perception. There is no top-level scalar perception being
controlled through these three levels. What is controlled is a
pattern perception.
  BP: That's a vector only in the trivial sense of a list of
arbitrary magnitudes. The pattern is in your perceptual system,
not Rick’s spreadsheet. In the spreadsheet there are simply three
unrelated reference signals at the top level, any of which can be
set to any value regardless of the others. There is no “pattern”
unless you pick one and set those signals to match it, in which
case it is your pattern-controller at the top level.

I don't think you are getting the point. I'm not making it very

well, I know. I think that’s because I haven’t properly resolved the
question in my own mind. If I did, I might also have the answer.

Who is the "you" in your last sentence when the spreadsheet is

transposed into a biologically acting control hierarchy? Is it the
so-called “observer”, the conscious perception? That’s one aspect of
the fuzzy thinking lurking behind my question(s).

In respect of the spreadsheet, my notion is that a particular

pattern at the top level could in principle correspond to a state of
some one variable that could be represented by a function of the
existing top-level variables, in the way perceptual functions are
normally considered. If only certain kinds of relations among the
variables correspond to “interesting” environmental states (e.g.
“objects”), then the different patterns could perform the same
function in the control system as would a single higher level
controlled perception. But no such higher-level perception has in
fact been defined by any perceptual function, since there is no
control system above the top level. There is just a pattern, and as
you say, “There is no “pattern” unless you pick one and set those
signals to match it, in which case it is your pattern-controller at
the top level.”

Think about the creation of novel top-level controlled perceptions

in the maturing reorganization of the control hierarchy. Initially,
those perceptions don’t even exist, let alone form a component of a
control function. But patterns of perceptions controlled at certain
values do exist, and at some point such patterns may be subsumed
into a single controlled perception, allowing for coordinated
variation in the pattern of reference signals at what used to be the
top level.

The question I am wrestling with is whether there is _ever_ a

requirement that a consciously observed unidimensional variable must
exist as a single scalar variable at some point in the neural
system, or whether it can sometimes or always exist as a distributed
pattern of the outputs of the kinds of lower-level patterns that
gave you problems early in this thread – oriented line detectors,
retinal locations of edges, and so forth. And if this is true of the
highest-level patterns, why should it not be so for all the
perceptual levels.

Maybe the question isn't so much about the actual anastomatic

control hierarchy, but about the identification of individual
controlled perceptions as being individually related to consciously
perceived properties of the external environment.

[Anastomatic is the term Warren McCullough used to describe a neural

network in which the level-to-level connections were unidirentional
and many-to-many, as are both the perceptual and the output
connections in the HPCT hierarchy.]

    MT: My question is whether it is
necessary that such vector perceptions be controlled only by
way of their individual vector elements.
    I imagine you were taught in your perception classes about
integral and separable variables. Integral variables interact,
in the way that colour hue does, whereas separable variables
done, in the way that length and width don’t. Colour can be
described as a three-variable vector, but until Newton and his
successors started doing scientific experiments with colour,
nobody imagined that all colours could be described by three
numbers, and even now, there are many different three-number
sets that can be used to describe a colour. And when you have
done that, it won’t describe the perceived colour, which depends
greatly on context. What people would do when trying to control
colour would be to say “a little more pink…no, a bit of
beige… perhaps lighter and a bit bluer…”, which doesn’t
sound like they were controlling a scalar variable.
  BP: That's a good example. Could this be an example of the mapping
phenomenon that’s been bugging me? Is this happening in a “color
space” with three dimensions, the location in which is set by the
magnitudes of the three variable intensities? This is very much
like what happens in taste-space, too, with four variable
intensities of taste signals.
  The thing is that with color, you can construct any color by
adjusting the three intensities, …

We know that, but for thousands of years people have matched colours

without knowing it. It took careful experimentation to discover that
fact, whereas I don’t think the makers of stone tools ever had a
problem determining that an arrowhead had a pointy direction
different from the direction across the base or the direction of the
thickness of the flake. Those directions are clearly separable
perceptions, whereas the various possible directions in which
colours can be specified are not.

  ...and you can build a perceptual input function as a
weighted summation that will give a maximum signal for only one
combination of intensities (normalized to a constant sum). That
would be the current PCT way of representing the colors. There
would be one input function per color, which doesn’t sound very
practical, does it? This screen can show 16 million colors.

Maybe the screen can show 16 million colours, but how many can you

distinguish, pixel by pixel, patch by patch side-by-side or from one
part of the screen to another. I think the numbers under those
conditions range from teens to hundreds, rather than millions. But
even if millions happened to be correct, isn’t that rather trivial
when compared to the number of available neurons? And what matters
in real life isn’t the colour of a point, but a complicated mess of
colours at different retinal locations that change very rapidly as
one moves one’s eyes.

  However, I wrote a color-matching program for David Goldstein in a
different way, more like the mapping approach (not on purpose, I
was just following my nose without any deep thinking). As you move
the cursor from left to right in a square field, the red intensity
(of the whole square) decreases from maximum toward zero and the
green intensity increases from zero toward maximum; as you move
the cursor down from the top, the blue intensity increases from
zero to maximum. This seems to allow matching of any color I could
find, even purple and orange and brown (the mouse wheel controlled
the average brightness).
  This method creates a color by positioning a point in two
dimensions inside a square. The resulting three color signals exit
the retina and enter the midbrain, and after some magic occurs, we
see a unitary color: the whole square is one color. So do those
three signals somehow locate a point in a color space or volume in
a brain map? And how does that connect to the fact that we see one
uniform color over a square area instead of just one point? I
could have separated the color display, just showing a color patch
outside the square where the mouse pointer was being moved. That
might have lessened the confusion, but it doesn’t solve the
problem. How can the whole patch seem to be of one uniform color?
How would position on a color map get attached to a whole
geometric area?
  I know this is at a level of detail that doesn't interest you
much,

Actually it does interest me, insofar as it is an illustration of a

general issue, as you say in what follows…

  but it seems to me that there must be some principle
here that would be very useful to understand. It would be a new
way of generating perceptions, perhaps not as signals per se but
simply as some other aspect of neural activity – maybe “slow
potentials.” It could be that true vector algebra would be
appropriate, but I just don’t know enough to say. The difficulty
lies in how to get the “vector” to matter to the perceiving system
rather than just to an observer looking at the brain from outside.

Going back a couple of paragraphs, I'm not going to try to suggest

answers to your questions, but rather I want to add to the confusion
by asking about colour and brightness illusions. Under what
conditions will your square patch seem to not to be of a uniform
colour when it is? Under what conditions will it appear to be
uniform when it isn’t? How did Korean potters manage to make a
bright moon shine on a dark landscape when moon and landscape have
the same shade of grey glaze?

Here's a nice example provided by Bruce Gregory from the Journal of

Neuroscience. Look at the figure, and then cover the seam between
the upper and lower half with your finger and look again.

<img src="cid:part1.02060304.06030104@mmtaylor.net" alt="">

Is the colour uniform between the top and bottom half, or is it not?

We have to remember that real neurons may have thousands of inputs,

and may do complex timing-dependent operations on subsets of those
inputs. It may be too much, trying to speculate on one or two
globally applicable mechanisms for the detailed functions involved
in control. I don’t think there’s any issue (other than getting the
world to understand) about the reality of perceptual control at the
kind of level of detail we usually discuss. There are obvious
difficulties, as our history of interchanges has shown, about both
the testing of prediction in experiment, and the theoretical
implications of different assumptions.

So, rather than pursuing these delightful speculations, I would like

to return to my ill-defined question about whether it is necessary
to restrict consideration of control to the control of scalar
variables in individual control units.

Martin

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