[Martin Taylor 2017.04.02.23.10]
I see Rick has offered a pretty good answer to one of your
questions. I won’t comment on that, but I’d like to take a different
approach.
[Andrew Willett 20170401. 20:26 ET]
…
To be simple: The Test often is done alongside formal
model-building.
Just a comment on the word "Test". We usually use the "Test"
(capital T) to refer to a specific experiment, but you preceded this
by talking about tracking studies. It’s true that tracking studies
are in principle representative of what any control is, and indeed
any behaviour, if you accept the tenet that all intentional
behaviour is the control of perception. But the Test is usually used
to refer to a particular kind of experiment in which an experimenter
tries to determine what perception someone is controlling.
My first questions concerns the mathematics. As I am not
well-versed in mathematics (4 years ago I did AP AB calculus),
I wanted a clarification. Tracking is usually isolated to 2
spatial dimensions with time (time and x-y space), but I
imagine that it could be expanded to include a 3rd dimension
(time, x, y, and z). Is this correct? Can only certain types
of mathematics be used with tracking studies?
I’m trying to understand whether (if yes or no and why )
there is a limitation to the formal modeling used in PCT for
the Test, especially the modeling used with human-model
studies (the tracking ones).
I could understand what you are asking in at least two ways. One is
about the mathematical toolbox that is applicable to tracking
studies, the other is about the possibilities of formal modelling.
They aren’t the same.
A mathematical toolbox is like any other toolbox. You get toolboxes
for tiny tots, toolboxes for teenagers, toolboxes for skilled
amateurs, and toolboxes for professionals, whether they be
carpenters, surgeons, or plumbers. The contents of the toolboxes at
any of these levels will be different for the different kinds of
tasks, but when you consider just “tools” the universe includes
surgeon’s scalpel, plumber’s wrench, and carpenter’s lathe. So when
you think of a mathematical toolbox, the same kind of distinction
applies. Some tools will usually be very useful to look at tracking
studies, some will seldom, if ever, be useful. Just as I can (just
about) imagine a surgeon using a hammer, I find it much easier to
imagine a carpenter using one. For looking at tracking studies, will
set theory be useful? Maybe at the higher hierarchic levels. Who
knows, I don’t think it’s been tried. Is calculus useful for
tracking studies, surely it is at lower levels where the variables
are continuous, but is it likely to be useful above the category
level where variables are discrete? Maybe not. Again, who knows.
If your question is about formal modelling, I have to guess what you
mean by “formal”. Is a software program a formal model? A lot of
pattern recognition approaches to perception use fuzzy logic. Does
that count as “formal”? The most popular model for tracking studies
is a software program, because calculus-based mathematical models
that are easy to solve tend not to represent system nonlinearities
very well, whereas they can be built into software models if
necessary. The saving grace is that when control is good, the
Behavioural Illusion obscures the internal processing that is being
modelled so that simple models are about as good as you can usefully
get, as I explained in the attachment to [Martin Taylor
2017.03.28.23.36].
The more I think about it, the more I am feeling that beyond a
certain hierarchical level (I am thinking the relationship
level since this is [as far as I am aware] the highest level
discussed in tracking tasks), mathematics may not accurately
model what’s going on. In other words, it becomes harder to
create a formal model to relate to an aspect of human behavior
that is abstract (e.g., controlling a principle-level
perception).
It depends on what you mean by "mathematics". "It becomes harder" is
presumably true, but you can’t tell for sure, because even at the
lowest levels it is very hard to model anything but a drastically
simplified version of what goes on inside the organism. Think, for
example if Bill’s “neural current”, which is a really drastic
simplification of the firing patterns of lots of neurons that in
some way change in ways that relate to changes in sensory inputs.
The neat thing is that the behaviour of simulations that don’t even
try to mimic individual neurons is remarkably similar to the
behaviour of organic controllers that (presumably) use the neuron
firing patterns. How one might simplify the issues that arise at
higher levels, which involve imagined perceptions along with
perceptions derived from current sensory input – that’s a question
nobody has addressed as far as I know. That doesn’t mean it’s not
open to mathematical investigation. Remember that Boole considered
his binary logic to be the “Laws of Thought”.
This brings me to my next question.
If this is so, I am going to propose that qualitative
description/methods have some worth.
Of course they do. They are simplifications that work to some
degree. The question is whether they have enough worth for serious
study, and on that I don’t care to comment. Personally, I do a lot
of qualitative analysis. In my mathematical toolbox is a tool I call
“envelope constraints”, that sometimes say that this or that is
physically unrealistic. For example, brain heating due to neural
firing provides a cooling constraint that presumably will have led
evolution to favour minimizing the computation that needs to be done
to produce an improvement in survivability. This constraint leads me
to argue qualitatively that mechanisms for improvement in control
quality, and reduction of side-effects and of internal conflict
should exist. Powers calls the mechanism “reorganization”.
For example, it may not be useful to reduce an
individual’s perception of “United States politics in relation
to Canadian politics” over the course of a heated discussion
to a mathematical formula (we lose some important rich
subjective details?). I think it is even less possible that
this formula could then somehow track this relationship in the
local environment (like computerized tracking studies or
chasing choppers) . Am I wrong?
I'd say you are probably wrong in principle, but right in practice.
Most of the time. Would a tracking poll on the several dimensions of
the difference between the two political regimes, done on
individuals rather than on aggregates, count for you as a track? The
individuals could be subject to different disturbances on the
different dimensions if you wanted to test whether they controlled
those perceptions. I doubt you would get much out of such a study,
but I’m wondering whether it would fit your criterion.
Many scientists, especially those in model-based
disciplines like physics and chemistry, might see less worth
in my claim that, at a certain point in the hierarchy, we can
no longer do the Test with formal models. My (short-lived at
this point) experience has been that some scientists
(excepting, at least, anthropologists) see qualitative
description as second to quantitative descriptions. Yet, I am
sure that at some point the mathematics becomes
overly-reductive. In other words, my rich experience of
considering those politics or caring about being an honest
person ought not to be relegated to a mathematical formula.
Any thoughts on this?
Yes. It depends again on what you mean by "mathematics" and "formal
models". See above. If mathematics in some case has “become overly
reductive”, quite probably the wrong tool has been used from the
toolbox. The surgeon used a laser when an infra-red lamp would have
been more better for the patient. But in general, the more precise
you can be, the better you can relate what you find to other areas
of your knowledge.
This is a bit of a long post. Nonetheless, I hope it sparks
some discussion.
It's a difficult topic. We will see.
Martin