[From Rick Marken (931021.0830)]
Martin Taylor (931020 18:30) --
Bill,
I don't see how you can say:
Rick, you have taken the words out of my mouth;
...
Politic, but not obviously self-consistent.
Yes, Bill and I have an agreement. I will not defect from his PCT
cell and start my own organization if he agrees with me about
something every so often. That's how PCT works. Bill and Tom and I
don't agree becuase we do experiments and test models that lead us
to the same conclusions; we agree in order to maintain appropriate
power relationships in CSG.
I said:
imagine that there is a perceptual function (probably
at the sensation level) that produces a perceptual signal that
is proportional to the sum of its two lower level perceptual
inputs, s1 and s2. So p = s1+s2. Now the p signal "categorizes"
its inputs in the sense that it puts out the SAME value for many
different combinations of s1 and s2.
Martin Taylor (931020 20:10:39) replies
What you are calling "categorization" is what I would call "measurement"
or "evaluation."
Whatever.
If the measurement is to determine in which bin (there's
that word) the perception p (= s1 + s2) fits, then the result is a
categorization. p is in Bin 136. It is not in Bin 135 or 137. Its
value may be 136.7317854....
But this is just another many to one mapping -- just what I described
in the paragraph above. The only difference between your description
of categorization and mine is in the particular TYPE of function
used. My function was a summation and the result was invariant with
respect to changes that left the sum unchanges. So, changing s1 and
s2 from 2 and 2 (respectively) to 1 and 3 preserves the sum; the
result (a perception in this case) categorizes the two inputs
(2,2 and 3,1) the same (4). Your function is the equivalent of the
rounding function (the INT function in many programming languages). It
takes only one input and produces a result that is the rounded value.
So your function maps all inputs between 135.5 and 136.499999 into the
integer 136. Again, a many to one mapping. So BOTH your function and
mine do a categorization. That's what I meant when I said (and Bill
agreed) that all perception is "categorical"; it is because all
perceptual functions (except, I suppose, the identity operator) do a
many to one mapping. This means that the output of these functions will
remain invariant (the same) with respect to certain transformations
of the inputs. So the output of the summation is 4 (invariant)
with respect to changes in the input from 2,2 to 3,1 to 4,0 to (if
you like fractions) 3.3, 0.7. The output of the rounding function
is 136, which is invariant with respect to changes in the input
from 135.63 to 136.4 to 135.92, etc.
The fact that perception is a PROCESS of categorization (in the
sense above) does not mean that category type perceptions occur
at all levels of perception. There is a difference between the
PROCESS of categorization and the PERCEPTION of a category (this
is what Bill Powers was talking about in his "politic" agreement
with me). That's why the term "category" can create confusion.
All perceptions are categorizations (the result of a process of
categorizing lower level perceptions) but NOT all perceptions are
perceptions of categories. The "bin" that you hear each time it
is spoken is an event perception that is a categorization of the
many different "bin"s that occurred each time (and differed in
terms of intensities, sensations, configurations and transitions
each time); but you hear the same event-- "bin" -- each time as
a result of the categorical nature of the percetual process.
The perception OF a category is a bit more subtle. When I look at
my bookshelf and see a particular object as a "book" (even if I
don't say the word to myself -- the word is NOT the category
perception; it is an event that is associated with the category
perception) then THAT is the category perception. It is a SILENT
perception -- no words involved -- that's why it's so subtle. But
it obviously exists as a perception because we can "label it"
with words. The perception of category (like all other perceptions)
IS the result of a categorization process -- but the result is a
perception of what we CALL (in PCT) a category.
That wasn't too impolitic, was it?
Best
Rick