[from Gary Cziko 920824.0010]
Bill Powers 920822
Consider sensations versus configurations. A sensation is a weighted
sum of intensity signals. So the number of possible sensations is the
number of different and independent weighted sums. If there are nine
intensity signals, there can be nine independent sensation signals at
a given time. Let's suppose that these nine sensations are
discriminable tones of a scale. Clearly, only nine notes at a time can
behave as independent tones.
Perhaps I need to go back to _BCP_ again, but I don't quite understand
this. And I get especially nervous when I don't understand something which
you preface with "clearly."
With nine intensity signals, why does "nine independent sensations signals
at a given time" mean? Do you mean nine sensation signals at the same
time? With nine intensity signals ranging from zero to some maximum neural
frequency it seems to me that there would be a lot more than just nine
sensations possible just using weighted sums. Consider at all the colors
we perceive with only three (I think) intensity signals related to color.
What am I missing here?
Once I understand this, I may have other questions about the perceptual
hierarchy raised by your interesting post to Martin Taylor.--Gary
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[From Rick Marken (920824.0930)]
Gary Cziko (920824.0010) asks
With nine intensity signals, why does "nine independent sensations signals
at a given time" mean? Do you mean nine sensation signals at the same
time?
Yes; Nine linear combinations of nine variables can be INDEPENDENTLY and
simultaneously brought to nine different values. It's just basic linear
algebra -- you can solve, at most, N simultaneous linear equations when
you N variables (and, of course, N unknowns).
With nine intensity signals ranging from zero to some maximum neural
frequency it seems to me that there would be a lot more than just nine
sensations possible just using weighted sums.
Yes - there are an infinite number of ways of combining the nine inputs
linearly to produce sensation signals. But you can only control nine of
these linear combinations simultaneously (that's why there are only six
sensations in my excel spreadsheet -- because there only six intensities;
but you can still find sets of 6 linear combinations that are not orthogonal
(they are linearly dependent) so you don't really have 6 independently
controllable sensations. This is how you can have conflict at level N+1
even though there are plenty of available inputs at level N).
penni sibun says (re:Preston paper):
you saw the abstract. she started off w/ saying that behaviorism
and cognitivism are looking at different aspects of the same thing.
Well, memory is the first to go (luckily). When did I see the Preston
abstract? Is it in an earlier post. It does sound like she is saying what
I am saying (behaviorism and cognitivism are looking at different aspects
of the same thing -- but what is that thing, according to Preston?)
Best regards
Rick
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