What's a CEV?

[Martin Taylor 940825 18:30]

Avery Andrews 940826.1528

My view of the relationship is as follows. Each perceptual signal is
associated with an indefinitely large collection of `complex environmental
variables' (term due to Martin Taylor), which are all the circumstances
that the perceptual signal indicates veridically (Drestke 'type I'
intentionality). E.g. the CEV's associated with the visually observed
deflection of a meter-indicator might include the current flowing in
a particular wire, and the water-temperature in the reactor core, if
the sensor-system is working properly, and many other things besides.
The idea that each sensory signal indicates all of an indefinite range of
CEV's is supposed to disolve the question of `where perception starts'.

If I understand you correctly, this is quite a different concept from the
one I intended when I introduced the label "Complex Environmental Variable."

In any Elementary Control Unit (ECU-a term I have come to prefer to my
original "Elementary Control System") there is a Perceptual Input Function
(PIF) that produces a scalar value by acting on its inputs (the arguments
to the PIF function). That scalar value is the perceptual signal in the
ECU, and the inputs are, for the ECU, its sensory inputs. (The sensory
inputs are normally perceptual signals from lower-level ECUs).

In my view, the CEV is DEFINED by the Perceptual Input Function, and has
no other existence. The world has no preference for any function over
any other (Watanabe's Theorem of the Ugly Duckling said the same). The
scalar perceptual signal is the organism's best estimate of the current
state of the CEV. The CEV exists in the outer (real?) world, and is
not accessible to any outside observer whatever, since no other observer
can guarantee to have the same PIF in any of its ECUs as the one under
consideration. But for analysis, one can treat a control system as if
on could see inside it and measure its signals.

If the PIF is a function P(s1, s2,...sn), where s1, s2, ...sn are its
sensory inputs that are scalar perceptual signals of lower ECUs, then the
CEV is a function C(V1, V2, ...Vn), where the function C is identically
the same as P, and V1 ...Vn are the CEVs corresponding to the perceptual
functions that give rise to the perceptual signals s1, ... sn. At the
lowest, sensor level, s is the sensor output corresponding to the value V
of some physical quantity.

At this point, notation becomes a little trickier, but we can try
(subscripts and superscripts would make life easier).

I will use a notation like 1P for a first-level (lowest-level) perceptual
function, and 1Pk for the k'th of many such functions at that level.
In this notation, 0s1 represents the output of sensor number 1, which
is sensitive to physical variable 0V1.

So, 1P1,...,1Pn describes a set of first-level perceptual functions, or,
more completely, a first-level signal is 1s1 = 1P1(0s1,...0sn). Using this
notation, the k'th second level perceptual function is 2Pk(1s1,...1sn).
But the sensory inputs to such a second-level PIF are the perceptual
signals of first-level ECUs, so that the k'th second-level function can
be written out as

2sk = 2Pk(1P1(0s1....0sn), 1P2(0s1,...,0sn),...,1Pn(0s1,...,0sn)).

This signal, 2sk, is the organism's best representation of the current
value of one particular CEV, that is DEFINED by the function 2Pk (or
equivalently 2Ck). The "real" value of the CEV 2Ck is notated 2Vk. It
exists, in a sense, in the "real" world, but since nobody has access to
the "real" world, nobody can know its real value.

When we are dealing as analysts observing control systems that we know
precisely (perhaps having specified them algorithmically, for example), we
can determine the value of 2Vk as precisely as we want, within measurement
limits, though the organism that defined 2Ck cannot. The function
giving rise to 2Vk is 2Ck, which is the "real-world" counterpart of 2Pk,
and we assert that we know what 2Pk is. (With living organisms, we cannot
know it exactly, of course). Since as analysts we know 2Pk (=2Ck) and the
other relevant PIFs, we can find

2Vk = 2Ck (1C1(0V1,...0Vn), 1C2(0V1,...0Vn), ... 1Cn(0V1,...0Vn)).

The variables 0V are physically measurable variables for which we can
construct measuring instruments of any desired precision (limited by
physical constraints, of course), and that precision may be orders of
magnitude greater than the precision achieved by the organism's sensors.
Given the values of the measurable variables, and the functions nCm, the
"true" value kVq of any CEV kCq can in principle be determined. It is not
necessarily the same as the estimate provided by ksq, because of the
imprecision of the organism's sensors. But nevertheless, the existence
and nature of the CEV is determined ONLY by the perceptual functions
in the control hierarchy.

When a disturbance (or many disturbing variables) affect a CEV, it is
because it changes the values of the variables 0Vn. A change in the
value of a CEV at level N cannot be achieved while all the lower-level
CEVs whose values contribute to it remain undisturbed. But a CEV at
level N can remain unchanged even though ALL the contributing CEVs are
changed. One can see this by noting that

pVk = pCk(p-1V1,...,p-1Vn) is a scalar function of several arguments,

and an increase in the value of such a function due to a change in one
argument can usually be compensated by an opposite-effect change in another.
In PCT, this represents the statement "many ways to achieve one outcome."

In summary, a CEV is very precisely determined. It is defined by a
Perceptual Input Function, and has no other reality. The VALUE of a
CEV is estimated by the perceptual signal output from the defining PIF,
and when a CEV is defined by a real living organism it cannot otherwise
be measured. Its precise value must remain unknown. But conceptually,
if the defining PIF and all lower-level contributing PIFs are known,
then the value of the CEV could be measured to any desired precision,
since the CEV, though defined by the internal structure of the perceiving
organism, has its value in the real world outside the organism.

I hope this might clarify a concept I think to be quite useful, the one
I originally gave the label "Complex Environmental Variable." The foregoing
is more or less the reasoning behind the introduction of the term, to
distinguish what is happening in the real world from the signals in
the organism itself. There has, over time, been occasional confusion
between the notions that the CEV is defined by the PIF in the organism
and that it has a value that is in the outer world inaccessible to any
organism except through its sensor systems.

To complete the picture, I draw the standard old diagram of an ECU acting
in the world, with labels and showing how kPq defines the CEV kCq and
as a corollary the disturbance kDq:

                ^
                > >
               ksq----------------
                > >
       +++<++++kPq output
       + | |
    defines ^ |
       + (k-1sn) |
       + | | | |
       + | | | |
======V======^=^=^===============V==
       + | | | |
       + (k-1Vn) |
       + | |
       + kVq |
       + | |
       + ^ |
       +++>++++kCq-----<----------
       + |
       + ^
       + |
       ++>+disturbance effect kDq (external influences acting on 0V1...0Vn,
                                   defined by its effect on kCq)

We have not, so far as I know, discussed the definition of the disturbance
effect by the PIF, but since a disturbance is one only by virtue of its
effect on a CEV, it seems reasonable to claim that it is defined as a
consequence of the definition of the CEV. This way of looking at it makes
particularly clear that the ECU has no access to anything relating to the
distal causes of the disturbance. All that physically happens is that the
variables 0Vn change value, the PIF may or may not thereby produce a
varying output ksq, and an external set of measurements to calculate precisely
the value kVq may or may not change. Nothing in this provides any link
to any particular reason why ksq (in particular) may change, nor to any
way to identify what changes might have happened in 0Vn. The signal ksq
relates ONLY to the value kVq.

Martin