{[Hans Blom, 960712]
Well, let me try again. I seem not able to make myself clear.
I kind of find myself in the same position as that Inuit, whose
language has an adequate vocabulary to discuss the different types
of snow, who has to explain things to a visiting, let's say,
Englishman whose (non-technical) language does not have those
concepts (no English around, I hope ;-). When the Inuit talks
about x-snow and y-snow, the Englishman says "oh yes, snow; I
know what you mean!"
That reminds me of that mathematician, who tries to explain the
concept Aleph-Null to a student. After a while, the student says
"oh, infinity; I know what you mean!", whereupon the exasperated
mathematician shouts "no, a special KIND of infinity!"
Is the Inuit smarter? Is the mathematician? No. They just live in
different environments where additional distinctions make sense.
If you have no use for different kinds of snow or infinity or noise
or whatever, stop reading now. In science -- if I may be so bold to
consider that my area of expertise -- distinctions are important.
The ancient Greeks thought, that a heavier body falls more rapidly
than a lighter body. No, it was not lack of experiments that prompted
this "knowledge"; a cannonball does reach the ground more rapidly
than a feather. Nowadays, you see the opposite. When a student tries
to explain Newton's law to his mother, he is embarrassed by her
counterexample of cannonball and feather. He'd rather not have
those embarrassing things that he full well knows exist, but which
he cannot explain (yet), being unfamiliar with Navier-Stokes,
Poiseuille, Bernoulli and what have you. Yet it was these people
who carefully teased two effects apart that each have a different
effect that contributes differentially.
Science is concerned with making ever finer distinctions. You don't
have to do that; you can keep your blindfolds on, or you can be just
not interested. That's fine with me. But then don't ask me to explain
to you theories that crucially depend on that distinction. If you
don't accept this, talk about Kalman Filters, for instance, will have
to stop.
But let me try to use "English" and see if I can make the distinction
clear nevertheless. You can consider this discussion as an informal
but useful definition of "disturbance". In the standard PCT diagram,
the "disturbance" enters at some point in the "world", but it is not
specified where:
···
------------
perception | | action
--<---| "world " |---<--- (0)
> >
------------
^
>
--------- disturbance
Now some theories -- amongst them Kalman Filtering theory -- make a
distinction WHERE the "disturbance" enters. In one extreme case, (1)
it enters where the action enters:
------------
perception | +|---<--- action
--<---| "world " | (1)
> +|---<--- disturbance
------------
In another extreme case (2), it enters where the EFFECT of the action
enters a particular perceptual apparatus:
------------
perception--- | | action
---<--|+|<-| "world " |---<--- (2)
--- | |
^ ------------
>
disturbance
Intermediate positions are possible as well, but let's not discuss
those.
Can we distinguish between the effects? Yes, very clearly. In (1), the
disturbance acts on the world and, in principle, its effect would be
noticeable by everyone. Something else or someone else acts on the
world, in addition to me. In (2), the disturbance is a private
affair, which affects one a single individual and cannot be perceived
by anyone else. And intermediate positions don't actually exist; they
will always act on some part of the world and would thus be perceiv-
able by others as well.
Do (1) and (2) "really" exist? Case (1) is debatable. Some say that
the word "disturbance" was invented by humans to hide their embarrass-
ment. And they point to diagram (1) and say "If you could perceive the
disturbance, you could include its complement into your action. You
just don't perceive right!" This position cannot be invalidated. But
we can excuse ourselves and say that we can't see everything or even
much at the same time.
Case (2) is debatable as well. Some will say "But I can be able to
know at least something about your perception, because it has a real
world correlate. Nerve impulses, EMGs, EEGs, etc. So, at least in
principle, nothing is truly private." And that position cannot be
invalidated either. But we can say that in practice we can come pretty
close if we deny others to poke around in us or glue electrodes on.
Where does that leave us? Back to figure (0)? No, the distinction
between (1) and (2) makes sense, although both are idealizations.
But we are used to that: all models are.
An engineering example of (1) and (2). In satellite tracking, the
satellite's position is not a nice circle or ellipse. It is influ-
enced by earth's varying gravity, which depends on whether the
satellite overflies mountains or valleys, and on whether heavy ores
or natural gas are to be be found underground. So its height varies,
but in principle anyone could observe those variations. This is case
(1).
To establish the satellite's position, I use a radar echo. Yes, my
equipment is kind of old-fashioned, and I know that a laser reflection
is much more accurate. But I have just the sensors that happen to be
available to me. Now my radar echo will give me a fluctuating reading
even if the satellite's position were a perfect circle. That is due
to atmospheric conditions and to imperfect processing in the recon-
struction of the satellite's height from the radar echo. This is case
(2). The information is private, at least only accessible to those who
observe my readouts. Nobody else would be able to get the same data,
not even if they had the same radar equipment as me. Their position
on earth would be different and thus their atmospheric conditions. The
processing noise of their equipment will differ as well.
So, is the distinction between (1) and (2) necessary? Yes. In case (1)
I might want to correct for height deviations from optimal. In case
(2) I might want to average a number of readings before I attempt to
do something.
In practice, we usually have a combination of (1) and (2). Yet the
distinction makes sense, because we can tease the two effects apart.
Effect (2) can be reduced by buying better equipment or by taking more
readings and processing them in some "intelligent" averaging way.
Do you want to go back to (or remain in) position (0)? Or do you think
that the distinction between (1) and (2) might be useful? What is your
vote?
Greetings,
Hans