[Martin Taylor 960513 10:20]
Bill Powers (960511.1800 MDT)
Do I take it that "harmonics 6-20" means that the fundamental and the
first five harmonics are missing, so that the lowest actual frequency
presented is 960 Hz? Got to think about that one....Actually, if this input were passed through a nonlinear amplifier, there
would be frequency components in the output at the difference (as well
as sum) frequencies, and since there are 14 coherent contributors to the
160-Hz difference frequency, the output could actually contain a rather
strong 160-Hz component.
The kind of sound for which this explanation of pitch perception does not
hold is an artificially constructed one that never would occur in nature:
Take a harmonic complex, and add x Hz to each component, so that, say,
a 100 Hz base complex restricted to the harmonics 500, 600, ... 1000 is
replaced by a sound composed by adding together sinusoids of frequencies
512, 612, ... 1012. A lot of pitch perception work has been done on such
sounds in the last couple of decades.
This unnatural sound still has difference frequencies that are all harmonics
of 100 Hz, and if the ear were using the nonlinear difference frequencies,
that would be the pitch that is heard. But it isn't. This pitch that is
heard is higher by an amount proportional but not equal to the added number
of Hz (say the same as a 104 Hz harmonic complex, in this example--a number
I pulled out of a hat rather than from experiment).
I
recall an article from rather a long time ago in which an electrode
placed somewhere in the auditory nerve produced a signal that could be
amplified and heard on a loudspeaker as the sounds entering the ear. Is
this a popular-science myth?
No it's not. Event though the _rate_ of firing doesn't change with the
signal frequency, nevertheless, the _moment_ of most probable firing does.
Up to a significantly high frequency (Peter says about 8 kHz), if a nerve
fires, it will be at a moment phase-locked to a peak of the signal
waveform. The thing is, that the higher the frequency, the less probable
it is that any particular nerve will fire at any particular peak, so that
over a few milliseconds averaging period, roughly the same number of firings
will have occurred no matter what the frequency. Now, when you add up across
the whole auditory nerve, you have all these firings at the peaks of the
waveform summing together, making for a summed signal that is not unlike
the original waveform (since the phase locking is not exact). It's even
more like a signal that fires at the zero-crossings of the derivative
of the waveform (e.g. a first-order high-pass filter with a low cutoff
frequency). Of course, I've oversimplified terribly, but this is the basic
notion.
My point is that given any kit of fundamental
operations that you deem permissible, you can probably construct a model
that will do the right things.
Yes. "There are more things in Heaven and Earth, Horatio, than are dreamt
of in your philosophy." We have seen some really weird things in auditory
experiments. One of the weirdest involved an attempt to make an improved
stethoscope for cardiologists. The problem is that the most interesting
sounds for diagnosis are at very low frequencies, and cardiologists have
to train hard to hear them in a normal office. We thought that if we
transformed the instantaneous amplitude of the signal into instantaneous
frequency we might make it easier. Then, instead of hearing "whump-whump",
the cardiologist would hear "whooeeeooo--whooeeooo". (Our cardiologist
didn't like it, because he wanted to hear "nothing different, only better").
However, when we played speech through this transformation, we expected to
hear garbage. What we heard was perfectly intelligible speech, if a little
distorted. Quite unexpected.
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Where you and Martin Taylor seem to have a basic difference with me is
over the necessity of specifically representing these aspects of the
patterns as simple signals. I'm sure you don't disagree that doing so
would be possible. But I claim it is necessary in order to account for
the qualities of subjective experience.
I'm not arguing over the qualities of subjective experience. I'm arguing
over the performance of a control hierarchy that has developed to keep
intrinsic variables within their survival ranges. "Subjective experience"
to me has the qualities of an external analyst who is observing the actions
of such a hierarchy. Since PCT as such says nothing about the nature of
consciousness, an appeal to subjective experience seems to provide no
more than a guide to what might be going on in the thing observed. Just as
with the PIF and the external world, the perceptual function of the
Observer/analyst imposes a structure on the hierarchy observed.
If a person has to point to "green" on a spectrum,
control is easiest if there is a single signal for green that can be
specified.
What would "more green" and "less green" signify? Would "less green" mean
"less saturated same spectral peak", "spectral peak nearer _this_ value"
(a two-sided optimization problem), "less intensity in this spectral
region", or what?
Scalar control variables are easy to verbalize, and to discuss, but
I see no need at all for any perception discussed by the analyst to
exist as a separate scalar variable inside the control hierarchy
being analyzed.It's not the analyst I'm concerned with, but the higher systems that
will have to use the perception as a component of a higher-level
perception.
But it _is_ the analyst, if you are referring to "subjective experience"
as the criterion. For higher-level perception in the ordinary sense, you
are _always_ going to be taking inputs from several lower-level perceptual
signals; if you were not, the higher-level value would be only a transform
of the lower-level one, and would be redundant, with no loss to the system
if it were omitted. So what does it matter to a higher-level PIF if its
inputs come from a discrete or a (more robust) coarse-coded or distributed
lower-level representation.
It's when one labels or verbalizes the nature of a perception that it seems
probable that a single-valued scalar is entailed. And that is precisely
what the "generalized flip-flop" connection (usually) achieves at what
I call the "category interface" in the hierarchy.
No, "real" to the circuit. Suppose you have an R.F. signal in which
there are implicitly a carrier frequency and two sideband envelopes. In
the sideband envelopes (once they are isolated by tuned circuits and
heterodyning) there are, implictly, two audio signals. But before those
implicit audio signals can have the appropriate physical effects on the
rest of the circuits, one of them must be diode-detected and smoothed
and represented explicitly as a voltage varying at the audio frequency.
...
You give an example of a labelled single valued waveform that is required
for the function of the circuit. In such a case, it is natural that there
be a requirement for a single value to be constructed by the circuit. I
don't think the example has much to say about the operation of a control
hierarchy whose objective is to affect a complicated world in such a way
that a whole mess of intrinsic variables don't go out of whack.
I think that in the past few decades there has arisen a sort of
philosophical bias against the idea that there must be a perceiver of
perceptions.
I'm an agnostic on that issue.
This is entirely consistent with the idea that perceptions do not have
to be made explicit, as signals. The mere presence of a pattern of
firings is enough for the pattern to become a perception.
These two sentences sound to me to be orthogonal--unrelated to each other.
The label "a perception" is presumably used because there is some perception
to which it refers--and that perception defines a CEV, and therefore the
"real world" must be so constructed that the CEV has some reality. By using
the words "become a perception" you seem to intend to imply that something
in the real world exists, and is properly labelled "a perception." On the
other hand, the first sentence seems to refer to the effective functioning
of some apparatus that uses signals--the control hierarchy. No labellable
"perception" need exist for that purpose.
(I have a wording difficulty here, in that I accept each scalar perceptual
signal as the output of a single PIF in a network, and would use the word
"a perception" to refer to its value, yet this "perception" is not the
perceptual unity to which you refer, such as "green" or "house," or "good-
natured").
Only in this
way, where in effect the pattern is also the perception of the pattern,
can the Observer be done away with.
The hierarchy works equally well provided that the signals at the different
levels are sufficiently different to allow the necessary control actions to
control the perceptual signals. The Observer to whom you refer is what I
called the "external analyst" who is free to take any complex in the world
observed and to extract from it a single degree of freedom as a scalar value.
To see why it doesn't matter to a PIF in the hierarchy whether lower-level
perceptions are labellable, just think of the simplest form of PIF, a
weighted summation. If the inputs are labelled scalars, the exact same
sum can come as from any linear rotation in the space of the inputs, with
appropriately changed weights. The set of outputs of PIFs at level N is
totally unaffected by whether the inputs from level N-1 are discretely
labelled or are distributed across the whole set.
However, in a hierarchical model, we have a different non-metaphysical
observer, small-o, which is the set of all higher perceptual functions.
Right.
Now the idea of implicit patterns leads to a problem, because unless the
various attributes of the pattern are represented explicitly as signals,
there is no way to pass information about individual attributes to the
higher systems.
Who said there were no signals? We have the same view of the _structure_
of the hierarchy, and, I think, of its operation. The only difference of
opinion that I detect is whether an external observer could always take
one signal value and identify it with the value of something the observer
sees as a unitary "thing" in the outer world.
All that could be passed upward would be the pattern itself, unanalyzed.
If the operations of the PIFs are linear, that's all that is passed upward
in any case. There's no analysis in a linear rotation of a basis space, and
no value in having more levels than a single one that extracts (as scalar
signals) combinations that are useful to control.
But if you review Peter's recent post, you will see that he speaks of
doing explicit computations to extract from the pattern certain specific
attributes of it.
Back to my earlier message on which you comment: Peter's talking about a
design, and for the designer it is much easier to segregate the elements
of interest and deal with them individually than to partition them among
many different signal lines so that they overlap. My comment was to the
effect that one should not impose a designer's convenience _a priori_ on
the investigation of a system that has evolved for no convenience of an
external analyst or designer.
Now it becomes very simple to remember the pitch, to use a remembered
value as a reference signal, to compare a present pitch with the
reference pitch, and to generate an appropriate error signal. ...
... All this can be done with simple rate-coded signals.
Yes. Convenient, simple, but necessarily true as a representation of how
the hierarchy has evolved?
And since pitch is now represented by a single scalar number, a simple
signal can carry a copy of the pitch signal to higher systems, separated
from timbre and other attributes of the pattern, where it joins with
other inputs to higher perceptual functions.
I'm perfectly willing to believe that different attributes, as we label
them, are handled separately by the auditory (and visual and...) system.
I'm willing to believe that we have developed different labels for the
attributes that are agreed across people _because_ they are handled
separately. I'm not willing to _assert_ that they are, or to agree to an
assertion based on design simplicity, when a structure that is equally
simple _from the viewpoint of the structure_ will function equally well
in the job for which the structure evolved--survival to the point of
genetic propagation.
Even if you don't believe in an Observer, or see awareness as any
particular problem,...
It's a distinct problem--in both senses of the word. You've seen my take
on it many times, and I've seen yours and that of several other posters.
PCT _as such_ provides no definition of the function of the Observer, but it
provides a guide to what the Observer might be or might do.
There is no reason why these
output signals could not be rate-encoded, since each one represents the
final outcome of the kinds of computations that Peter proposes. And then
we would have what I think is required: one scalar signal per
perception, with the measure of that perception being representing by
firing frequency.Tell me what's wrong with that.
Nothing, until you assert it as what _must_ be.
It makes sense, and may be true. But it isn't the only possibility of
equivalent simplicity from the viewpoint of the evolution of the control
hierarchy.
Martin