[From Bill Powers (931026.1230 MDT)]
Martin Taylor (931025.1505)--
Your post on the revisionist hierarchy is full of interesting
ideas. I think it needs some work but what doesn't?
Your way of converting back and forth among category perception
(mutually exclusive), association (positive feedback) and
independent perception (no feedback) is both ingenious and
workable. I particularly like the way in which this model allows
the logic level to select different modes of operation of
category perceptions by performing very simple operations on the
perceptual systems that are orthogonal to the dimensions of
perception.
As to the digital levels being "beside" the analog levels,
there's some merit in this. There has always been a problem in
the background, which I've mentioned once or twice, of explaining
how we manage to symbolize perceptions that are of a higher level
than the putative category level. In the standard HPCT model, the
category level input functions receive perceptual signals ONLY
from systems LOWER in the hierarchy. This is a glitch in the
model; it has kept me from flatly rejecting (as opposed to merely
being suspicious of) claims that the linguistic systems have a
separate existence. How come we can name a system concept
"democracy?" That really isn't possible under the current
organization of HPCT. Both you and Bruce Nevin have now shown
strong cases for treating linguistic systems (or at least symbol-
based systems) separately from the analog systems.
My only answer so far has been that the higher level controls for
a lower level's naming categories in such a way that the
resulting category and higher signals can be seen as an example
of the higher-order perception. This makes the naming of
perceptions higher than categories into an indirect closed-loop
process, very different from the direct naming that occurs at the
supposed category level. Maybe such a difference really does
exist. But maybe there's something wrong with the model.
At any rate, your suggestions bring up new possibilities that may
provide a new answer for this puzzle.
There is what seems to be one major problem with your suggestion,
and indirectly with Bruce's. If the categorization is done by
setting up lateral inhibition and enhancement at any lower
(analog) level, then it becomes impossible to control one of the
involved analog perceptions at the same time that it is being
categorized. Analog control requires continual smooth changes of
signals, not flip-flop operation. If categorizing implies
converting a lower perceptual level into a flip-flop
organization, I couldn't walk and say "I'm walking" at the same
time.
This problem is resolved if we simply take copies of the lower-
level analog signals and route them to a set of input functions
that are (potentially) cross-connected exactly as you describe.
The outputs of these input functions could then be cross-
connected to the inputs of other functions of the same kind, to
produce all the conditions you describe -- but without
interfering with smooth analog control of the perceptions in the
analog systems. One could control both hands smoothly, keeping
one hand "level with" the other in a smooth analog way, or "one
inch above" or "half an inch below," while the copies of the
perceptions were being interpreted as "left higher than right"
and vice versa in a flip-flop way, and raising either hand could
be associated with raising the other hand or "raising a hand" in
general.
These new input functions can be visualized as drawn to one side
of the analog hierarchy, with signals being received from all
levels of the analog systems and entering the new input
functions. Out of the input functions would come the signals
indicating individual categories, mutually-exclusive categories,
or associative categories, under logic control just as you
describe.
If you now seize the set of all these new input functions, and
rubber-band all the signals drawn from the analog hierarchy into
the categorizing functions, you can move these category
perceivers until they lie just above the highest analog level.
You will then have exactly the category level I envision, with
exactly the same input connections from all lower analog systems
-- and the analog systems will be able to continue controlling in
a smooth analog fashion at the same time that their perceptual
signals (copies of them) are leading to flip-flop category
perceptions of any of the three kinds.
However, your suggestion has introduced a new possibility.
Move all those new perceptual functions over to the right side,
rubber-banding all the input signal pathways, but now keeping all
the new functions at a vertical position just above the highest
analog level. And now draw another set of input functions, also
receiving signals from all the analog levels, located to the
left, at the same level as the categorizing functions. This new
set of input functions is a new ANALOG level, co-ordinal with the
digital category systems.
This enables us to draw what I have only intuited. Stacked above
the digital categorizing input functions are the digital levels
like sequencing, programs, and whatever of digital nature lies
still farther above. Stacked above the analog perceptions at the
left lie all the levels that represent experience in a smooth
continuous way at higher levels -- for example, at the program
level, perceptions of _quantitative functions of continuous
variables_.
This satisfies my sense that at all digital levels, there is also
an underlying (or now I would say beside-lying) continuum of
experience, so that even as we speak in terms of propositions and
digital functions, there are corresponding perceptions that are
present over a continuum of magnitudes. We perceive not only the
dichotomy "honest-dishonest" at the principle level, but at the
same time a continuum: honest, but just barely; or honest, but in
unreasonable excess. The qualitative and the quantitative are
always, it seems to me, mixed together at these higher levels.
Rather than posit two completely separate hierarchies at the
higher levels, I would prefer to merge the two branches and view
the digital and analog functions as extreme examples of functions
that can partake to varying degrees of the features of both.
"Fuzzy logic" would be an example of a hybrid process at the
program level, one combining the on-off dichotomies of digital
logic with continua of weightings typical of an analog process.
Piecewise continuous mathematical functions would have an analog
character between the points where a digital switch in conditions
occurs; a cusp or a pole or a catastrophe, or a switch from
regular oscillations to chaos, or a boundary condition that makes
a smooth function valid only in the interior.
Being strongly inclined to analog thinking, I have always been
uncomfortable with mathematical developments that are basically
analog in nature, but which include such "cheating" as Kronecker
deltas and such. Now I see that I was artificially dividing the
world of functions, where in fact real perceptions at this level
can include either extreme or blends of the two. In my digital
simulations of analog systems, I do this all the time -- but
without, until now, realizing its significance.
So your revisionist hierarchy has jogged my mind in a new
direction. Do you see anything useful there?
···
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Avery Andrews (931026.0851) --
I'll try your nu14 model today -- it's been sort of busy around
here.
I'm quite puzzled by the aim of Bill Powers' commentary on
Soechting et al in last years BBS. They were trying to show
that the brain computes a transformation from head-centered to
shoulder-centered coordinates (an idea that pleases me, since I
noticed in the course of the Cartesian Blues affair that this
might be a useful thing to do). They tried to do this with a
pointing task involving rather unusual conditions, and Bill
criticised them for having a wrong model of pointing. I find
this inappropriate, since they weren't trying to explain
pointing under ordinary conditions, but to use facts about
pointing under odd conditions to make a point.
I don't believe in using different models for different
conditions. If a model is any good, it applies under ALL
conditions, or offers a damned good reason for not applying (like
explaining that you can't point if your arms are cut off).
It's not the mapping per se that I objected to in the BBS
commentary, but its use in an open-loop model of pointing. I
didn't just say that their model was bad; I described some
obvious variations on their experiment that could tell us whether
the open-loop model was adequate, or whether a closed-loop model
was actually required. I predicted that their model would fail
under such tests. If it would, that would render all their
conclusions irrelevant, because they applied only to an open-loop
model.
Little Man v2 contains mapping, or at least a crude initial
attempt to include it. I don't have anything against the concept
of mapping from one coordinate system into another. Soechting et.
al. were far from the first to suggest it; see, for example, Paul
Churchland (Churchman?). But mapping is just part of a model, and
how you use it will depend on what the model is. If the model can
be shown to be wrong, then the effort to introduce mapping into
it is wasted.
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Bruce Nevin (931026.0935 EDT)
Bruce, thanks for the article by Keith Johnson et. al. on the
"Hyperspace Effect." I am very impressed by the quality of the
work described here; it is insightful experimental work without
any bs. It goes directly to the phenomenon instead of trying to
push some philosophical point of view. I really like this kind of
work. I learned a lot from it. Do you think that Keith Johnson
and colleagues might be interested in seeing what PCT might
contribute?
I saw at least one place where setting up the experiment as a
control experiment might sharpen up the data. It was in thinking
about how to do this that I got a pretty hot insight from the
paper; in a minute.
The experimental situation allowed participants to select the
first two formants of a sound indicated by a printed word on the
screen (which they had pronounced aloud). They did this by
clicking with a mouse on a two-dimensional display set up to turn
on preselected amplitudes of F1 and F2 (plus computed additions
of F3 and F4 and the driving waveform for realism). They then
heard a synthesized vowel generated from that pair of values.
They altered their selection until the vowel sounded "right" to
them -- either for the way they actually said it, or for how it
"should" be said.
This led to considerable scatter in the data over series of 10
repetitions of each task. The reason for the repetitions was to
make sure that the selected sound was actually close to what the
participants wanted to hear. But there is a different way to do
this, using the Test.
What was missing in this experiment was any disturbance. If the
mouse had been connected to vary the two formants more or less in
real time, but if the numbers representing x and y mouse
coordinates were being continuously and slowly disturbed, the
participants would have had to move the mouse continuously in
order to maintain the "right" sound. If they had maintained the
right sound for, say, one minute, a record of mouse positions
could be used to determine the reference-sound, the loop gain,
and the actual amount of random variation in the controlled
perception. Determination of the reference-sound would be very
accurate, because it would be determined from the whole run. The
evidence would become stronger if it could be shown that the
best-fit model entailed a constant reference signal and a
significantly high loop gain (indicating a clear perception of
differences). My hunch is that this would greatly reduce the
scatter in the observations.
If Keith Johnson et. al. want to try it this way, I'd be happy
for you to tell them about this idea, and to supply a modeling
program to do the analysis. Or if not, I think I would like to
try it myself, if I can learn to program my SoundBlaster in the
appropriate way. This sounds eminently doable. Martin Taylor has
sent me money toward purchase of the developers' kit, so I should
be able to try this pretty soon (after a current project reaches
a plateau).
Now the insight. I've been trying to think of how to construct a
perceptual function with scaling that would do some of the things
you report. This doesn't now seem very promising, because the
scatter in closely-spaced trials is so large -- it actually
encompasses a range of neighboring sounds even though isolated
vowels are being considered and the intent is to recreate the
same sound. There aren't even any contrast effects to blame.
As I thought of using the mouse to control the formants, I
realized that this is very much like using the articulators to
produce a sound by varying formants. Then I thought of the way I
sometimes will try to figure out a sound that someone made in
speech by whispering it or silently mouthing it, or even (if I'm
alone) saying it aloud. What I'm trying to do is figure out the
nearest sound I could make by using my mouth in a familiar-
seeming way.
Then it hit me: when I do that, I'm not so much trying to match
sound to sound as to find out how it feels when I'm making a
sound reasonably like the one I'm hearing. In other words, the
"likeness" that's critical isn't totally in the sound; it's
partly in the likeness of feeling. The feel of saying something
actually varies a lot more than the sound does. "ee" feels very
tight; "ih" is considerably looser. It may be that in the
kinesthetic signals representing HOW I make a sound, there is
information I can use in identifying the sound. This is a lot
like things you've been saying, maybe identical, but now it's
talking on some new meanings for me.
Anyway, this introduces a new dimension of control, which may
explain some phenomena like scaling without needing any scaling
procedure in the perceptual systems. Basically all it needs is
varying the loop gain in the articulator control systems, or the
speed with which one switches from one reference-configuration to
the next.
When I say "believe me" in a casual way, the first "ee" doesn't
get all the way up there for the simple reason that I don't
tighten up the articulators in the back as far as I would if I
were saying just "bee." It comes out more like "buhleeve me."
Either the loop gain has been lowered or the reference signal has
been switched before the control action is complete. I think the
loop gain has been lowered, because if I really pay attention I
can snap out a perfectly good "beeleeve me" at the same speed.
And lowering the loop gain means that I will fall short of
creating ALL the vowels that require extreme positions of the
articulators, except where it's easy. That will automatically
contract the vowel space around some neutral (zero-effort)
position.
If I'm hearing vowels being spoken in a contracted vowel space,
then according to my previous hypothesis I'd have to apply a
scaling-up function to all the vowel perceivers at once. But now,
if I'm using variations in loop gain, all I have to do is lower
the loop gain in my imagined speech until the imagined vowels
contract to fit the new contracted space; changing just this one
control parameter will then produce a fit over the whole space!
This still leaves the Johnson et. al. hyperarticulation
hypothesis intact: PHONETIC TARGETS ARE HYPERARTICULATED. But now
the emphasis shifts to the kinesthetic feel of making the
phonemes, which may even be the _primary_ means of
identification. If we say that the kinesthetic targets are those
of hyperarticulated speech, then falling short of those targets
is explained by control systems with a lowered loop gain, rather
than by a concerted shift in all acoustical targets. This just
sounds simpler to me.
Well, thanks much for the article. We'll see what comes out of
this.
As to the discreteness of phonemes, I think that AT THE LEVEL OF
SPEECH PRODUCTION AND RECOGNITION this is still a questionable
idea. It's very hard to separate our own conversion of phonemes
into categories for purposes of talking about them from the way
they are actually manipulated and recognized in ongoing speech.
The very facts we've been talking about, the more or less
continuous variations that we can produce and still recognize,
imply that we can hear a continuum of characteristic sounds, and
by paying attention can know that we are continuously varying
them even while we are categorizing them.
Enough for now.
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Joel Judd (private transmission) --
Fine, I'll look at it.
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Tom Bourbon (direct)
I'll try it out right away.
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Bruce Nevin --
You need a Mouse Systems driver. If you have Windows, there is
one included. I don't happen to have one! But I'll bet someone
else can supply it.......
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Best to all,
Bill P.