[From Bill Powers (931027.1100 MDT)]
Bruce Nevin, Rick Marken (9310xx) --
Bruce:
The phonemic contrasts that a speaker and hearer of English
perceives partition the space. That is, the speaker/hearer
partitions the space. Rick, how could I have possibly intended
any meaning but that?
Rick:
The first sentence suggests (to me) that a characteristic of
the sound input, called a "contrast", determines the percept.
The second sentence suggests that something about the person
does it.
The argument/discussion that's been going on for months now over
"contrast" is extremely frustrating to all participants, because
it seems to each one that there is a clear and simple idea here,
clearly and simply described, that the other person just refuses
to see. Just when you are sure it must be straightened out this
time, something comes up that makes it plain that the gulf is as
deep as ever. There's obviously an important difference here, and
to discover what it is is probably also important.
I think that the problem may be in the approach to modeling
perceptual processes. Bruce, you are saying that IT IS AS THOUGH
the perceptual space has been partitioned, for example the space
represented by the two formants F1 and F2:
> p1 | p2 | p3 |
>-------|-------|-------|
> p4 | p5 | p6 |
F1 |-------|-------|-------|
> p7 | p8 | p9 |
>-------|-------|-------|
> p10 | p11 | p12 |
F2
When you draw the partitioning this way, it seems that you have
modeled perception: the world having dimensions F1 and F2 is
divided so that no matter where a point appears in this space, it
must be in one of the boxes labeled as a perception. Differences
that do not carry a point past a boundary are not rendered as
different perceptions. The boundaries are differently located in
different languages, and even in different dialects of the same
language. They also change according to the clarity of speech:
that is, the pattern of boundaries may expand and contract so
that a given point in this space can change categories depending
on where the boundaries are at the moment.
The problem here is that no matter how detailed you make this
representation, with scalings or without, it is still not a model
of a perceptual function. It is a description of what a
perceptual function must accomplish. In other words, by making
this description fit the phenomenon as generally as possible, you
have not produced a model; you have defined in a systematic way
the observations that require a model to explain them. A diagram
like the one above, with any amount of added detail required to
make it fit the facts, is a statement of the problem, not of the
solution. The problem is, "What kind of perceptual function(s)
would produce phenomena that fit this description?"
This is also the heart of the difficulties we have had over the
phenomenon of "social conventions." When we observe how language
or other social phenomena come into existence, we see that people
adjust their ways of speaking, dancing, or whatever to the ways
that are already established in their societies. We can see that
there are apparent influences acting on each person, tending to
bring that person's organization into congruence with other
people's organization, as evidenced in their actions.
To describe a social convention is to describe a phenomenon, not
to explain it. The appearance is that social conventions are
active things that have some sort of formative influence on
individuals. But when we try to model social conventions -- that
is, to propose an organization of matter and energy that could
produce this phenomenon -- we find that there is no organization
of matter and energy at the social level that could have such an
effect. The only active agencies involved are the individual
people; what exists in the spaces between them is only inanimate
nature, which influences people only through exchanges of forces
and sensory data. So our model has to explain social conventions
strictly in terms of the causal agents that actually exist, the
individuals. The explanation lies inside the individuals; the
explanation of their interactions also lies inside the
individuals. From the model embodying this explanation we could,
in principle, reconstruct the observation that "social
conventions" must come to exist: we could justify the metaphor,
but without confusing it with an explanation.
A physical model of sound-perception that will produce the above
partitioning would need some way of making one perceptual
response suppress all the others (as in Martin Taylor's
suggestions). That would create boundaries in a flip-flop way. It
would also need mechanisms for biasing the locations of the flip-
flop boundaries, based on some measurement of the locations of
many sounds in this space. A very complex perceptual model would
be needed.
When descriptions are used in place of models, tacit assumptions
are hidden in the metaphors that are used. Consider this diagram
of the perceptual space shown above:
>
> p
> *
F1 | *
···
p' *.
> * .
> * .*x
> * *
*------------------------
F2
Here we show just one perception, p. Now it is a vector with a
length and a direction. An arbitrary combination of F1 and F2 is
shown as a point x in this space at the end of another vector.
The periods are supposed to represent a line at right angles to
the vector p that passes through the point x. Where that line
intersects the vector p, we have another point p', which is the
projection of the vector x onto the vector p.
This diagram represents the same perceptual space using a
different set of tacit assumptions. The direction of the vector p
now represents a linear combination of F1 and F2: say, 2F1 + F2.
A perceptual function giving these weights to F1 and F2 will
produce a maximum signal p' when vector x is aligned with the
vector p. As the vector x rotates away from that direction,
maintaining the same length (F1^2 + F2^2 = constant), the
projection onto the vector p will become smaller: the magnitude
of the perceptual signal in the direction p then represents the
degree to which the vector x is an example of a perception in the
direction p.
A perceptual function which applies the weightings 2 and 1 to F1
and F2 will report ALL combinations of F1 and F2 as some degree
of the perception p. Another function with weightings 1 and 2
that defines another vector q will also report all combinations
of F1 and F2 as degrees of a perception q. A given arbitrary
point in this perception space will generally produce the most
perceptual signal when projected by weighted summation onto one
of the predefined vector directions. A set of perceptual
functions applying different weightings to F1 and F2 would result
in a set of perceptual signals which all could be nonzero, but
among which one would be the largest.
This, of course, does not give us any "partitioning" of the
space. It simply produces a set of perceptual signals in which
one of them will be the greatest. If the center of the vector
space is shifted to the "schwa" position (computationally easy),
then for the most familiar sounds it is most likely that only one
perceptual signal will be markedly greater than the others.
This set of perceptual signals enters higher-level input
functions. We have exhausted the processing that occurs at this
level. If any further phenomena remain to be explained, they will
be explained in terms of a model that receives a set of
perceptual signals in which one signal is larger than the others.
We are through with the F1-F2 space.
I'm not claiming that this second approach will solve the
problem, either. I'm just showing how the metaphor changes when
you approach the same phenomenon from a different angle, and how
a different metaphor requires a different physical model. The
choice of metaphor is more or less arbitrary; all that is
required is that it contain valid analogies with the observed
phenomenon. The choice of models is dictated by the choice of
metaphors.
There are other possible metaphors. I think it may be possible to
represent the vowels as points on a curve going through
perceptual space. The control system for producing vowels, which
after all can only produce one vowel at a time, would then run a
point along this curve, perhaps going from ee to oo in a single
swoop. Another control system, controlling along another curve,
might produce modifications at right angles to the first curve.
This would create a new two-dimensional space in which there
might be fewer problems of discrimination.
To decide among metaphors, we have to decide among the physical
models that they imply. The physical model underlying the first
diagram above would be all at one level and very complex. The
physical model underlying the second diagram is very simple at
the first level, but requires more processing at higher levels
which may or may not turn out to be simple as well. Simplicity is
a persuasive factor for modelers, but there is also the question
of anatomical correctness. The two models would imply different
kinds of neural computing functions. Even simplicity does not
take precedence over getting the physical structure right.
From time to time I detect a certain puzzlement in some posts
when I describe a possible organization of behavior, and then add
"but I don't know how to model that yet." Now I can, perhaps,
explain. What I mean is that I have a metaphor that looks
persuasive, but I don't know how to construct an actual device
(or a simulated one) that would behave in the ways that the
metaphor implies. You may have wondered why, when I talk about
scaling, I don't just say that that is my model of how constrasts
are generated. The reason is that scaling is the RESULT I want,
but I don't yet know how to bring it about within the strictures
of neural modeling. And I'm not sure that even if I DID think of
a way, the resulting model would behave like the real system.
Models, when you implement them, have a way of doing things you
didn't expect or want. When a properly-implemented model fails to
behave as the metaphor suggests, you have to look for a better
metaphor -- change the tacit assumptions.
I don't know if that gets us any closer to mutual understanding,
but it's a try.
----------------------------------------------------------------
Tom Bourbon (931026.1251)--
The Tao that can be named is not Tao. The categories of
"lower-level" perceptions that can be named are not categorical
lower-level perceptions.
Beautiful. Exactly. This whole post is a clear statement of the
category problem, and the general problem of projecting
inappropriate levels of perception onto lower-level perceptions.
This is even clearer with relationships. You can look at a
configuration, and see very clearly that it is created by
relationships among sensations. But the configuration level
doesn't perceive relationships; relationships don't exist at that
level, even though from a higher-level point of view you can see
relationships. What YOU can see is irrelevant to what the level
in question can see.
---------------------------------------------------------------
Best,
Bill P.