[Martin Taylor 970629 14:00]
[From Bill Powers (960719.0733 MDT)]
Remember that
_which_ category is detected is given by the physical pathway in which the
category signal appears, whatever its size. It is not necessary that the
category level itself do the conversion from continuous to discrete values.
One disadvantage of the flip-flop (or Schmidt-trigger) proposal for the
category level is that there can be no output values but "present" or
"absent."
No, that's not correct. Only if there is extremely high loop gain _and_
if the lack of category A forces the perception of category B to go
positive will you see a limitation to saturation values. The flip-flop
arrangement will actually stabilize at a level that sets the loop gain
(including the effect of the sensory input) to unity.
A child's drawing either is an elephant or is not. You can't say,
"I see a pretty good elephant," or "If that's an elephant, it's just barely
an elephant -- so you'd better tell your kid to take up writing."
I'm not clear whether you are saying that we normally can't say these
things, or that the output of a flip-flop (Schmidt-trigger) circuit
cannot be interpreted as equivalent to these statements. Whichever you
intend, I'd argue that you are wrong--at least for the person and for
the flip-flop.
I think we must be talking about different arrangements in some way not
clear to me, because the objections you raise to the "grand flip-flop"
(GFF) don't seem to apply to the circuit I have in mind. The GFF can have
a "no category" output, if none of the input patterns sufficiently match
any of the category inputs. It can have graded outputs (above some critical
value, or below some other critical value, but not in an intermediate
range) for any particular category, and many different categories can
be output simultaneously--with more difficulty if two of them are
ordinarily not co-occurring so that they tend to be mutually exclusive.
I suspect that one difference in our mental pictures is that I take
all perceptual input functions as subject to saturation, meaning that
as the input level increases by delta-I, the output level increases by
an amount delta-O that is smaller, the larger the value of I. I suspect
you are thinking of a linear perceptual function up to some maximum
output value. Such functions will indeed lead to flip-flops that take
on only limiting values, but I don't think they are realistic for _any_
perceptual input function at any level of the hierarchy. Logarithmic
functions seem more common, but they could be artifacts of experimental
technique, I suppose, whether the experiments are psychophysical or
neurophysiological.
Since we can perceive categories to greater or lesser degrees, it seems to
me that thresholding (with or without hysteresis) is better deferred to the
perceptual functions that _receive_ category signals.
Again, I don't see this as either necessary or useful.
At the sequence
level, for example, all that counts is the ordering of category signals; it
would be appropriate to set a threshold at the input to the sequence level,
to determine what will be counted as an occurrance of a particular element
of the sequence.
That's a property of the sequence input, isn't it? And you really want
not a "yes-no" identifier of the sequence, but a measure of how well
the sequence is matched. It may not be appropriate to set a threshold
there, either. A sequence that fits, but of which the category members
have measures that could be interpreted (by the external analyst) as
"dubious" may be no "better" than a sequence that has clean category values
as its input but for which one or two of the categories are wrong. By
analogy, think of a word cleanly written in which a letter is changed
(making it a different word) as compared to a word written clumsily so
that the "right" letters are poorly rendered.
At the logic level, thresholding and mutual exclusivity is
required, because logical variables must have only two values, true or
false. It is a _logical_ requirement that an object not belong to two
mutually-exclusive categories at once.
Yes, and that's a property of our symbolic-logical perceptions. I don't
conceive of it as being a property of the category perceptions. It comes
later.
At the category level, conceived as
operating without hysteresis and in terms of continuous degrees of
membership, it is possible to perceive a banana in pajamas with a smile on
its face, participating of several categories that, logically, are mutually
exclusive.
I don't see why these are mutually exclusive. They are of different kinds,
and one could easily fit out a banana with pajamas and paint a smile on its
face. One would hope that the person for whom this apparition was
constructed would see the joke. These categories aren't _logically_ mutually
exclusive. They are just not often observed together. But if you make
some precursor logical statements such as "A banana is a fruit" "Fruit
do not wear clothes" "Fruit do not have faces", _then_ it becomes a
question at the logic level, whether the set of statements is logically
plausible.
A streamlined toaster does not offend at the category level, but
at the level of logic. A photograph of a unicorn can exist at the category
level, but not at the logic level.I understand and accept your examples of hysteresis; I am simply suggesting
that it need not occur at the category level itself.
Sure. It might occur at many levels. What I am speculating, though, is
that the hysteresis is a consequence of the category _process_, and that
process is independent of perceptual level. The speculation is that the
output connections from a perceptual function are not limited _solely_
to going to the "own" comparator and to the next higher-level perceptual
input function, but that they sometimes connect also to other same-level
perceptual input functions. All else falls out from this relaxation of
constraint. What this speculation implies is that there will _be_
categorization in perception, that it will exhibit hysteresis, and that
between category perceptions there will be association. It also implies
something else I haven't mentioned so far, which is that it takes more
time for the category perception to develop than it does for the sensory
data to arrive, since the category perception develops in part from the
recursive connections from other perceptual functions--IF the sensory
data are not clear, prototypical instances of the category in question.
If hysteresis happens at other levels, too, it would be by a different
mechanism. The category process, as I conceive it, determines categories,
no matter what perceptual level they connect with. The category "red",
the category "chair", and the category "democratic" all are categories,
in this view, and all can participate in any perceptions for which at
least part of the input is categorical.
It might, but to
determine that would require more than the experiments with and examples of
hysteresis that you mention.
As with everything else in HPCT, lots of experiments are required, with
ingenious people to think of them and with opportunities and resources
to carry them out.
Look, I'm not asserting that the GFF arrangement is a fact. Only that we
once simulated a trivial version and found it seems to do some of the
things claimed, and that easy analyses suggest that with sufficiently low
linkage weights a large system ought to develop the kind of mutuality
relationships (association and tendency to exclusion) that we do observe.
And that the GFF connections are what will occur if perceptual inputs
are allowed to be derived from other perceptual outputs at the same level
in conjunction with the inputs from lower levels.
You seem to be taking the opposite view, that hysteresis is something that
possibly might be observed in some experiments, and that might be explained
by an ad-hoc set of assumptions like putting in a Schmidt trigger or a
flip-flop or some other mechanism yet to be described. And that it's such
a minor observation that we shouldn't worry about thinking up mechanisms
to account for it. I say it's a generic observation that happens to agree
with what is to be expected if we make a minor relaxation in the rules
you have proposed for the interconnection of perceptual functions.
Your stated reason for the rules was that you couldn't see what might
happen if the interconnections were not strictly hierarchic. I suggest
the GFF proposal helps one to see what might happen. And what one sees
is that a slightly messy element of the HPCT hierarchy (the level-skipping
connections) is cleaned up, a specific mechanism is proposed for one
of the "levels" (each of which is supposed to have a mechanism, but for
which in most cases the mechanism is as yet unspecified), and that the
proposed mechanism exhibits some properties that seem to agree with
what is actually observed in some studies.
None of which says it is right.
Martin