[From Bill Powers (960517.1545 MDT)]
Peter Cariani (960517) --
The argument is heating up again, but I've decided that a little heat is
necessary before we can general some light. If you don't mind putting up
with it for a while longer, something may yet come of this.
Please listen. I have discussed several meanings of the word
"frequency" that are often confused and conflated: 1) the number of
events in a given time duration, i.e. a "rate", 2) the number of
regularly repeating events (however defined) in a given time, 3)
"frequency" as defined in terms of Fourier transforms operating on
infinitely long signals with infinitely long windows, 4)
"frequency" as defined in terms of short-term Fourier analysis.
Let's look at this question from the standpoint of basic mechanisms.
Receptors have the propery of generating impulses when physical stimuli
impinge on them. They generate a spike, after which they take some time
to recover. In effect, the time before the next spike is generated
depends on the "strength" of the stimulus, quite likely integrated over
at least the time since the last spike. In the absence of the normal
stimulus, the recovery curve rises toward some critical trigger point;
it may or may not spontaneously reach the trigger point and eventually
initiate another spike. The presence of a stimulus effectively lowers
the trigger point, so the recovery curve reaches it sooner and initiates
another spike sooner. Thus there is a relationship between the intensity
of the stimulus and the interval between spikes. I believe that this is
the basic picture of how physical stimuli are converted into spike
trains. I assume that you would agree with all this.
Obviously, whether one speaks of interval or reciprocal interval, the
time resolution of the signal as a measure of the value of stimulus
intensity depends on the spacing of the impulses in time and the rate at
which the stimulus value is changing. The signal representation of the
stimulus necessarily becomes worse as the stimulus variations become
faster. Furthermore, there can be no general definition of interval or
frequency, because whether the signal is a "good enough" representation
of the stimulus depends on what is done with the signal next. If the
signal enters a receiver that responds to it slowly, it is effectively
averaged over some time, and that time determines the rate of stimulus
variation that matters, and the definition of frequency or interval that
is appropriate. So there is no single "right" way to define either
frequency or interval.
The interval between spikes is inversely related to the stimulus
intensity, but it is natural (for me) to measure the signal in terms of
a variable that changes directly with, in the same direction as, the
stimulus intensity. In this way the measure of the signal goes to zero
(or some low minimum) when the stimulus goes to zero, and increases when
the stimulus increases. For varying stimulus intensities, the signal
will also vary, in the same directions. Questions of linearity and
dynamic response aside, the signal frequency can be considered a neural
analog of the stimulus intensity. Of course the mean interval between
spikes is also a measure of the stimulus intensity, but it is an inverse
measure, which for many purposes would be inconvenient.
This is my sole basis for preferring the frequency representation to the
interval representation. This is not to say that interval-based
calculations are not done by the nervous system -- that is, calculations
which are the simplest to describe by using the interval representation.
I said
The only basis for the distinction is which representation yields the
most tractable computations.
This is what is important here in terms of neural coding and also
in the system's ability to cope with noise and/or competing sounds.
The way WE describe the coding, and the computations WE find most
convenient in representing the system's functions, have nothing to do
with the system's ability to cope with noise or competing sounds. The
system deals in physical interactions involving jolts of
neurotransmitter, continuous intra-cellular chemical signalling
mechanisms, and a conversion of chemical effects into an effect on the
recovery of a relaxation oscillator from a previous firing. Those are
the mechanisms that determine how the system works, quite independently
of how we model them. No matter what model we use, the system will have
exactly the same ability to cope with noise or competing sounds. This
is, I am sure, as completely obvious to you as it is to me.
But this point tends to get lost when we talk about models that purport
to work like the real system. You propose a model in which the basic
veriable is an interval; I think we have agreed, in effect, that no
matter what model you propose, we could substitute 1/frequency for the
interval measures everywhere, and come up with an exactly equivalent
frequency-based model. We are not arguing about whether the real system
employs interval or frequency measures; the truth is that it doesn't
employ either one. We are only arguing about the best way to formulate a
model.
You yourself stuff every neural system you see into the standard
scalar control paradigm, and it's very hard to persuade you that
the system may be doing something different.
I take great pains not to do this. The very existence of a test for the
controlled variable is a way of always leaving the door open to a
different model. The test identifies variables that are being maintained
in stable states or patterns despite disturbances that tend to change
them, and it requires that specific input and output effects be
identified if we are to conclude that control is happening. This test
effectively defines what is meant by the word "control" in PCT. If the
test is passed in all its particulars, I feel confident in challenging
anyone to come up with a different explanation for it from the one
proposed in the basic PCT model. So far, no one has met that challenge.
What happens instead is that others claim that _something else is
happening_. If that's true, then of course the control model doesn't
apply. But the phenomena I talk about when defending the model are
specifically control phenomena, and unfortunately very few people who
talk about behavior have any idea that these phenomena even exist.
Furthermore, many of them speak of behavioral phenomena that do not in
fact exist -- for example phenomena that depend on a regular
relationship between actions and consequences of actions, which can
exist only in an imaginary disturbance-free world.
I'm prepared to perceive a great many things, and I'm prepared to
alter my beliefs if the evidence warrants it. Are you?
Of course.
Please listen. I said that my own concept of multiplexing signals
(and creating new ones) came from theoretical biology. I was
describing my own intellectual evolution, my own, mainly to tell
you that I didn't develop as an engineer, and that these ideas are
not just simple importations from electrical engineering (which is
what you were accusing me of).
Well, the word came from somewhere: it's not part of the normal
vocabulary of biology.
Before electronics, the idea was embedded in the mathematical
constructs of Fourier, and concurrent with the development of
electrical devices, it was inherent in the notion of multiple
frequencies comprising sound.
This is simply an example of a "foreign" term being picked up and
redefined. Multiplexing in its original sense had to do with
systematically combining separate streams of information into a single
signal, with a corresponding systematic demultiplexing operation at the
other end of the channel, to recreate the original streams. If you
aren't using this technical term that way, then you're just turning it
into an arbitrary noise. Sort of like saying "I got a lot of good
positive feedback in that meeting."
I was mistaken, by the way, in my previous post where I cited the
sending of radio signals over different frequencies as an example of
multiplexing. In fact, this effect is called "diversity," not
multiplexing. A better (i.e., valid) example of multiplexing is the
sending of multiple telephone conversations over a single phone line,
with each source being demultiplexed so it can reach its correct
destination.
Please listen. You have some baggage associated with the term
"multiplexing" that I don't have. I said that my use of the term
does not necessitate there being separate signals originally.
I repeat: in that case you're simply ignoring the technical background
of this term and co-opting it to mean something quite different.
When you say that sensory information is "combined in some way or
another," you are tacitly asserting that it was originally separated.
Please, listen. No, No, No! The information for loudness, pitch,
timbre, location is combined in the same channels. The same
channels carry this information, and (arguably) different aspects
of the neural spike trains in these channels encode each of these
stimulus properties.
All right. I will simply have to accept that when you use the technical
term "multiplexing," you are not using it in its established technical
sense.
But I still have a problem, because you are saying that aspects of a
single signal which _could_ be extracted by a suitable receiving
function necessarily have physical existence in the signal, and in the
stimulus. You are saying that there is a different aspect of the neural
spike train that encodes each specific stimulus property. I don't know
how else to read that. What could you mean by "channel" that would not
imply a specific kind of information carried in that channel? And when
you speak of "stimulus properties," how else can I read that except to
assume that you believe that stimuli have properties, in themselves? You
even enumerate them: "loudness, pitch, timbre, location."
Perhaps I need to say this: I view loudness, pitch, timbre, and location
as the outcome of applying human perceptual functions to stimulus
inputs. Since all human beings are constructed more or less the same
way, they all seem to perceive in approximately these same terms -- and
of course they interpret the world experienced by other organisms also
in the same terms. But a creature with a different organization of the
perceptual systems would not perceive sound in these terms; some other
set of invariants would be extracted, and sound would seem to involve
"channels" with different meanings. The physical stimulus would not
change; only its representation inside the observing system would
involve different dimensions. Despite your continuing to insist that you
don't see perception as an objective representation of the external
world, you still treat such measures as loudness, pitch, timbre, and
location as if they were fundamental properties of the stimulus. If this
is not what you mean, then your words are not conveying to me what you
do mean.
This is why I gave up, 40 years ago, on the idea that neural signals
could carry markers indicating what they mean: that somehow
information about "objects", for example, entered the nervous system
at the first level and was somehow preserved to be identified and
plucked out at a later stage of processing. This is not a viable view
of perception, in my opinion.
So tell us a more viable view, and how, in your opinion, these
perceptual problems are solved.
My take on this subject is simple: the "components" of neural signals
are the creations of the computing functions that receive the signals.
There is no unique set of components in a neural signal (or in a
stimulus).
The only viable view I have been able to come up with is that the
properties of the perceptual world are created by the neural functions
which receive one set of neural signals and generate others that are
functions of the input set. Each person experiences a world partitioned
as his perceptual functions partition it. The main criteria for
selecting a final way of perceiving, I think, are twofold: 1) the
perception should be subject to systematic effects by actions, so it can
be controlled, and/or 2), controlling perceptions defined in a given way
has results that do not lead to further reorganization of perception.
Of course since we are all human and share approximately similar
physical structures, and even some inherited organizations, we partition
our worlds in ways that are sufficiently similar to permit communication
(if not complete understanding). If I say I hear a "high pitch," you
will probably agree that you, too, hear a "high pitch." These judgements
might even agree with what a scientific instrument represents as a
numerical measure of frequency. But our internal neural representations
of pitch might still be quite different. This can't be resolved through
experiment, because we are all interpreting what the other says and does
through our own private ways of perceiving. I think there is an
irreducible minimum of ambiguity, and that not all differences in
internal representations of the world can be detected. I'm not even sure
that ANY of them can be detected.
···
------------------------
The set of all such sensory signals constitutes the only world that any
higher systems can experience.
Do you hold this view dogmatically, or could there be empirical
evidence that would change it? What sorts of evidence would cause
you to question this belief? I've mentioned the big problems with
these kinds of coding schemes for loudness and spectral shape --
how would you falsify your model?
I'm not sure what you're asking. Are you implying that the brain has
some way of knowing about the environment other than through the
behavior of its primary sensory signals? If so, I should think that the
burden of proof would be on you. My statement didn't rest on any one way
of encoding information.
In mechanoception and electroception, the receptors also follow
stimulus periodicities.
Of course, if the stimuli are periodic. But most stimuli, as we
understand them, are not periodic: they change with time, but not in
repetitive temporal patterns. Audition is unique in that the basic
phenomenon of sound is inherently periodic and it has periodic effects
on sensors. In all other modalities, you have to take special steps
(such as presenting moving gratings to the visual system) to create a
periodic input stimulus. In audition, there is no way NOT to present a
periodic stimulus.
-------------------------------
What if [a layer of computing functions] is just a "relay" layer?
What if it just looks at those aspects of the signal that are
relevant to its function, and passes the rest of the signal along?
That is possible. Actually, I include that as a special case in B:CP --
the "null transform" that simply passes the input signal to the output.
But I think that in general the output signals from a layer of
perceptual functions are not simply copies of the input signals; they
are _functions_ of the input signals that vary as many input signals
vary, but not as any one of them varies. Weighted summation is one
simple kind of function, where many lower-level signals are weighted and
added together to produce a signal that represents no one of them.
Signals representing line orientations are an example. But there's
nothing in principle to prevent some of the inputs to a given layer from
simply passing on upward to the next layer, even if their information is
also used in the partly-bypassed layer.
In this respect, I think that the basic differences in our proposals
have to do with the relative importance of the bypassing signals and the
signals that are passed upward from the outputs of nontrivial perceptual
functions. I see the basic organization as one in which most of the
perceptual inputs that reach a given layer are outputs of lower-level
perceptual functions and not just "relayed" copies of still lower-level
signals.
In your approach, you tacitly assume the reality of each aspect of
the auditory world that you, personally, experience.
Please, listen. I don't believe this at all (where do you get all
of this stuff?). It would be much more productive if you would
first check to see that the position that you disagree with is
really mine. ... Why don't you just ask me if that's what I mean?
It would be much simpler.
All right, I'm asking: what do you mean by saying
The information for loudness, pitch, timbre, location is combined
in the same channels. The same channels carry this information, and
(arguably) different aspects of the neural spike trains in these
channels encode each of these stimulus properties.
Doesn't this seem to assert the objective reality of "loudness, pitch,
timbre, location?" When you call them "stimulus properties," aren't you
asserting that they are properties of "the stimulus" -- i.e., the
physical situation outside the nervous system? If that isn't what you
mean, you are really going to have to walk me slowly through the way you
are using these terms. Perhaps you can get an inkling of how puzzling I
find the next statement, following statements that that above:
Please, listen. These properties DO NOT exist separately in the
environment. How many times do I need to repeat this?
You're going to have to explain to me how each stimulus property can be
"encoded" if the stimulus propery does not exist (separately or
otherwise) in the environment. To me "encoding" is an operation:
something comes in, and a code representing it comes out.
------------------------
The "analyses" of which you
speak correspond to what I call perceptual functions.
Except that you are not trying to explain how they could actually
work. Your explanation of how these perceptual systems operate
doesn't work (not that we have any adequate models for perception);
the barest outline of a model that you have proposed for audition
does not agree with the neural data.
Correct, I'm not making any serious effort to design perceptual
functions. But your judgment that my model "doesn't work" is surely not
based on any model I have presented. I haven't tried to model the
phenomena of which you've told me. I think you're basing your opinion on
rate-based models that others have proposed, and assuming that because
they haven't succeeded, I wouldn't succeed. That's an assumption that
you shouldn't bet much on; after all, I spent the past 45 years or so
not only working toward PCT, but designing all kinds of electronic
signal-handling systems, and I got pretty good at it, enough to make a
comfortable living. I think I could hold my own in any group of modelers
(although I would certainly not be one of the stars). And among modelers
who have no experience with designing and building working systems, I
might even be a moderately large frog in a smallish pond.
Hey, look at my PCT model for pitch control. There's a linear frequency-
detecting input function that receives sound from the environment, and
puts out a perceptual signal that I call "pitch." That gets compared
with a reference pitch, and the result is integrated to operate a pitch-
affecting mouse. This model reproduces human pitch-controlling behavior
with pretty good accuracy, even when the effect of the mouse on the
generated pitch is being continuously disturbed by a smoothed random
disturbance generated anew for each trial. That model certain "works."
If you now tell me that it wouldn't work, say, for a complex or very
loud pitch, my response would be to say "Oh, yeah?" and figure out what
the transfer function of the input device would have to be to MAKE it
work. Obviously my simple linear input function wouldn't do the job, so
I'd find one that would do the job. This doesn't mean that I would be
able to specify the structure of the input function at the level of
neural operations, but I sure as heck could specify it at the level of
what those neural operations have to DO. Of course you know this:
You can reply that at some level there are neurons or assemblies of
neurons that output specifically the signals you want to control,
but this is a postulation. This is fine, you can stick to the level
of black-box control theory, but then don't criticize those who are
searching for explanations of how the damn thing works.
Correct, and I respect that level of analysis. However, what you look
for in the nervous system is highly constrained by the kind of system
you think you're looking for. As you have described your system so far,
you don't provide any perceptual signal that I could use in my model,
except through some rather sketchily-defined and VERY complicated
computational processes that even you don't claim to represent how the
real system works. So don't put too much weight on a claim that you can
"explain how the damned thing works."
------------------------------
I'm tired of arguing over the semantics of words. Functionally a
percept is a distinction, a discrimination, the outcome of a
"measurement" operation. As such it exists as a particular sequence
of internal "states" amongst the set of possible sequences of
states.
Good, a percept is a distinction, a discrimination, the outcome of a
"measurement" operation. So in what physical form does this distinction,
discrimination or outcome appear in the system? You say it exists as a
particular "sequence of internal states." States of what? In what
physical form does a state exist? Could it be in the form of ... neural
signals?
If you're really talking about the nuts and bolts of how the nervous
system does these things, you can't just stop with a "functional"
description that leaves the most crucial question floating in some sort
of abstract conceptual space. In what form does a perception exist, that
it can be physically compared with a physical description of a reference
state, and so that the physical consequences of this physical comparison
can have a physical effect on the environment? I claim, dammit, that the
only physical form that makes any sense is that of a neural signal -- a
real neural signal consisting of a train of impulses, not some abstract
conceptual idea.
That's probably enough for now.
-----------------------------------------------------------------------
Bruce Gregory, Bruce Abbott --
Lovely posts, but you can see that I'm busy right at the moment.
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Best,
Bill P.