[Martin Taylor 950322 17:30]
Bill Powers (950322.0640 MST)
I think we may be getting somewhere. There's more, but different and
perhaps looser tangles to be sorted out, so here's another tease at the
comb.
I think the following is a key statement:
However, my only reason for introducing categories in the first place
was to provide a way to name things, so a symbol could be used to stand
for some collection of analog perceptions.
I don't see it that way, and perhaps this is why we talk a little at cross
purposes. What you call "category" I might call a mapping between category
perceptions. There's a category of a kind we might call "symbol" and
a category of a kind that corresponds to a perception based on something
in the outer world. The label "red" is not a colour. It's a word, and
is of a category distinct from the word "smooth," though of the same kind.
If the word is "red" it cannot be "smooth." But if a thing in the world
has a certain degree of redness, it might be of category /red/, and at
the same time it might have a low perceived degree of roughness and be
perceived as being of category /smooth/.
(I'm trying now to use // quotes in naming categories, "" quotes in naming
labels. But I may lose consistency, so bear with me).
The categories /red/ and /smooth/ don't conflict--they will not mutually
inhibit one another. The categories /"red"/ and /"smooth"/ do conflict,
at least as word perceptions. Categories /red/ and /yellow/ conflict,
as do categories /smooth/ and /rough/.
I now see why you made a comment earlier in a message I had intended
to respond to (so it was not lost in the disk crash):
Bill Powers (950309.0815 MST)
There is one possible solution to the category problem, which was called
"order reduction" in the 1960 paper by me, Clark, and MacFarland. I
think you may have mentioned this solution in passing quite some time
ago, but if so it has been lost.When you name something, such as "jump", you are linking a word-
perception to another perception, so either perception can evoke the
perception of the same category. After you have named a few other things
like "John" and "in" you can construct sequences like John jump in.But now you have three objects to play with, the three words.
I did not see then, but I see now, why you jumped from the notion of
category straight to the notion of word. You seem to treat the higher
logical operations as if they used the labels of categories as arguments,
rather than the category signals themselves. You don't accept that there
exists a kind of perception that I call "category," a perception that
has nothing to do with words, though much reinforced by verbal labelling.
(Sorry for the use of "reinforce." Here I mean the positive feedback
effect of mutual positive cross-links).
As you say, one can perceive all sorts of relationships among symbols, and
can control those perceptions by acting on the symbols. But those actions
do not directly affect the category perceptions to which the symbols
associate. At least not in the way I perceive a category.
Haven't you ever been in a situation where things you don't fully understand
are happening, but there are consistencies? Don't you say to yourself
"There's a 'one-of-those', and that was a 'one-of-the-other-things,' and
now here's a 'one-of-them-elses'...". You don't have labels, but you are
beginning to learn the categories. I do it with music, all the time. I
have very few labels for musical events--my musical training has been mainly
from listening and from sight-reading, not through words, and I don't have
words for most of my perceived categories.
When you identify category with label, you are really perceiving a mapping--
a relationship. It's like saying that if you are standing at 49deg+epsilon
North at a certain longitude, you are in Canada, but at 49deg-epsilon you
are in the USA. You need the categories /Canada/ and /USA/ before you can
make the mapping between the continuously variable location and the label.
ยทยทยท
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Back to your more recent message (Bill Powers (950322.0640 MST)):
Something is or is not a member of the category, and
if it is not, it is usually a member of a contrasting category.It may or may not be a member of a contrasting category -- but it will
not include ALL other categories.
True. But you ignored my distinction between "derived categories" and "natural
categories." I conceive only "natural categories" as being developed through
the mutual inhibition mechanism. "Derived categories" are logical functions
of natural categories, and have no necessary exclusionary properties that
are not based on their arguments.
If you think of the category "All things with
three legs" you can see that it includes a very large set of objects
with nothing in common but possessing three legs (a three-legged dog,
for instance). But this category does not exclude four-legged dogs or
other things like centipedes, and it is irrelevant to things with two or
fewer legs, like algebra.
If /three/ is a natural category, and /leg/ also (though I suspect it of
being a derived category, then "A thing with three legs" is a perception
/thing/ && /leg/ && /leg/ && /leg/ or something like that. It's a function
of categories, and therefor a derived category. Call it a perception at
the level of logical operations, if you like to define such a level.
For a perception to be irrelevant to another is to say either that it
does not enter as an argument to the other, or that its control does not
affect control of the other. There may be situations in which the category
"all things with three legs" is not irrelevant to some perception that
belongs to the category "algebraic" (a derived category based on the "or"
function).
I'm just making the claim that this is only one
kind of categorization.
That is also the claim I made in pointing up the distinction between
the natural and derived categories. My claim is that you can't do logic
without logical variables, whether they are soft or hard. And you can't
make logical variables without comparative relationships.
However...
You proposed elsewhere that a perceptual function A<B will produce a logical
variable when A and B are continuous variables, and so it will. That may
provide another kind of categorization, based on the relational level. I
hadn't included that kind initially. /Above/ and /below/ are mutually
exclusive, but they don't need to be perceived through a mutually
inhibitory connection. All the same, even there, it would be interesting
to do the experiment to see whether mutual inhibition exists (as would
be shown by a hysteresis effect). I think you could even try it in a
variant of the SD experiment, using the aboveness/belowness of some
aspect of the display as the "discriminating stimulus."
When you say that we are given a thing and must answer the question
"Which is it, X or Y?", you are implying that the perception must be
either X or Y: the question itself forces this choice. So from the point
of view of the asker of the question, the answer is found in a single
channel which can carry the message "X" or the message "Y", implying a
perceptual function that can deliver two different messages.
Could be. It is the asker, after all, whose reference signal needs the
input that a particular category exists, or which of several possibilities
might be the case.
If the "channel" is a higher-level system's perceptual function, then it
is that function that is deciding which category-signal to accept.
I don't see how it can decide which signal to accept--the signals arriving
at its PIF are what they are. What it CAN decide is that it needs one
of the choices--that there should BE a signal. Also, like any control
system, the output of the higher-level system might affect the world so that
the "right" category is perceived at its input, if its reference level
required that "right" category as an argument to its PIF.
I am having a problem with seeing every cross-connection as an example
of category perception. The reciprocal innervation in the spinal cord
brings opposing muscle systems into a single two-way control system, but
it's hard for me to see this as categorization.
I claimed (now apparently overstating the case) that all category perceptions
were based on the mutual inhibition mechanism acting among PIFs. I did not
claim that cross-links elsewhere had anything to do with categorization,
and I did not claim that all cross-links among PIFs involve categorization.
I think I described three different possibilities for the cross connections,
all of them among PIFs, and all leading to positive gain in the loop. If
there is one positive and one negative link, we have a negative feedback
loop, not under consideration at present.
Only one of those three connection possibilities leads to category perception.
The three were:
(1) Positive-positive high loop gain--leads to lockup, and perhaps exists in
pathological cases.
(2) Positive-positive low loop gain-- Association, but no lockup.
(3) Negative-negative variable gain--categorization when gain is high, not
when it is low.
On the output side, there seems hardly any point in either of the high-gain
cross-link connections, but at low gain, positive-positive seems to be
what is called "recruitment" and negative-negative might help with muscle
tone and therefore with gain control in opposed one-way systems. We've
spent some time discussing that in the past (Maybe output cross-inhibition
is useful at other levels of the hierarchy, but that's not something I've
thought about) (****Speculation Alert****could it relate to a mechanism
for shifting the locus of active control?).
I can see a lot of different ways to achieve
category-ness, but no way to pick one over another.
I can see fewer, at least with analogue values at the input to the relevant
PIF. They have been enumerated in this message: an arithmetic
relationship operation, and reciprocal inhibition. If you see others, it
would be very useful (for me, at least) if we could discuss them.
================
One of the big issues in non-classical AI is how discrete-logical operations
can be linked with analogue operations. I think there is a comparable issue
in hierarchic control, Rick's spreadsheet notwithstanding. It think the
mutual inhibition mechanism makes a clean and intelligible solution.
I have a problem with how the system doing the adjustments on
these cross-connections knows what it is doing -- it seems to me that it
would already have to know what a category is in order to tell whether
it is making the adjustment correctly. But this whole subject confuses
me; I'm not ready to understand it in any complex way.
I'm not clear what you think of when you say "know what a category is."
From the higher level, a category is a level on a signal line, just
like any other signal coming from a lower-level PIF to serve as sensory
input at a higher level. I don't see anything special about it. And
in the standard hierarchy, the higher level system doesn't "know" anything
about what its output does except for the effect that the output may
eventually have on the perceptual signal. What new difficulty do you
see here, when the output is affecting a gain rather than a reference
signal? You've discussed such connections before--or at least Tom has
and I think you have, in connection with adaptation.
Your proposal
suggests some immense complexities when you think of all the possible
combinations of cross-connections and strengths; I'm not up to grasping
them.
It's true, but then the same could be said about any network of connections
in which there is amplification. The standard hierarchy has its own
immense complexities. I go back to what you said in the previous
message,
There is one possible solution to the category problem, which was called
"order reduction" in the 1960 paper by me, Clark, and MacFarland.
An analogue signal potentially requires continuous control to maintain it
near its reference value. A category signal does not. It is a way of
reducing the degree of complexity of the controllable world. The information
rate in changes of category is less, often by orders of magnitude, than
that potentially involved in changes of the analogue variable to which the
category corresponds. Controlling categories without conflict is much
easier than controlling the corresponding analogue variables without
conflict. Consider /red/ and /smooth/. The perceived redness of a surface
will vary appreciably with changes in surface roughness, but the perceived
/red/ness usually will not change at all, so long as the surface stays
/smooth/, and can be labelled "red" and "smooth."
In other words, I think you had it right in 1960, if you drop the link to
the label of the category. Labels are associations--which I take to be
another use of the same mechanism, in positive-positive mode.
I think that your "immense complexities" actually are there, but are orders
of magnitude less complex than would be the case without the cross-connections.
Martin