[From Bill Powers (940831.0610 MDT)]
Martin Taylor (940830.1258) --
(writing to Avery)
The output of sensor Sk is a signal 0sk, which is some function of
environmental (physically measurable) variables 0V1...0Vn. That sensor
function is usually weighted heavily on just one physical variable,
0Vk, and we say for convenience that the sensor provides an intensity
estimate of the single physical variable.
You're getting out of synch with the hierarchy here. The _first-order
perceptual signal_ 1pk is a function of physically measurable variables
0V1..0Vn. The sensor is the input function of the first level (i.e., the
Golgi tendon receptor is the PIF of a tension control loop). The initial
"sensor signal" is a function of multiple input variables, just as at
all higher levels.
By speaking of a zero-order sensor signal that is an input to the first-
order PIF, you leave room for the first-level CEV to be a function of
the measurable level-zero physical variables, while the corresponding
first-level perceptual signal is a function of level-zero _sensor_
signals. This is what I mean by getting out of sync. You've skipped one
level on the signal side, so the CEV can be seen as something other than
the perceptual signal. This effect then propagates up the levels, so at
each level it seems that the CEV is a function of variables one level
lower than the perceptual signal. It can therefore have separate
conceptual existence.
If you do the numbering properly, however, you have
1pk = 1sk(0V1..0Vn) and
1Ck = 1Sk(0V1..0Vn) and
1sk == 1Sk
1Ck == 1pk
Note that both the first-level sensor signal and the first-level CEV are
functions of 0-level physical variables. We no longer have a sensor
signal that is at the same level as the physical variables, level 0. And
now, at all levels of the hierarchy, the CEV corresponding to each level
is identical to the perceptual signal. We are back in synch.
I can see now why you paused to note that the sensor signal generally
tended to represent just one of the physical variables. What you were
doing was setting up a sensor signal that was simply equivalent to one
of the environmental variables, so you could construct parallel
hierarchies, with the sensory hierarchy starting with sensor signals and
the CEV hierarchy starting with the physical variables, as if the sensor
signals and the physical variables were at the same level. In that way
you could maintain a conceptual distinction between the CEVs and the
corresponding perceptual signals.
But they are not at the same level: the sensor signals are the first
level of perceptual signals, and the sensors are the first level of
PIFs. Each sensor signal is a function of many physical quantities
(variables measurable at many positions in the local environment), so
the first level of CEV must also be expressed as the same function of
the same collection of physical quantities. It is the nature of the
physical receptor and its relationship to the local environment that
determines the function that expresses the dependence of the first level
of perceptual signal on the variables in a small region around each
receptor. And that determines what function must be used to define the
first level of CEV. The CEV can never be defined independently of the
perceptual signal, not even at the first level.
ยทยทยท
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Best,
Bill P.