[Martin Taylor 940608 18:40]
Rick Marken (940608.1000)
Mea Culpa. On rereading, I was obviously doing at least some of what
I accused Bill of doing. All I can say is that I should try not to read
long postings in a hurry. I should leave them until I have time to digest
them properly before I respond (though that might be days or weeks away).
Anyway, I have to thank Rick for stepping on the problem before a possibly
continuing set of misconceptions could get out of hand.
I suspect one reason for my misreading was the following:
Bill Powers (940602.1520 MDT)
What bothers me is tacking an ad-hoc addition onto the model for
every new phenomenon, before trying to see whether the existing form
of the model already takes care of it.
I viewed the part quoted by Rick from Powers ((940601.2120):
This is far too much an argument from design for my taste. It gives
the alerting signals too much meaning in relation to a whole system
of perceptions that isn't even fully learned until the threshold of
adulthood.
as taking literally rather than metaphorically my reference to alerting
signals as "prespecified (by evolution or by the individual) indicators
that the moment holds the possibility of danger or opportunity." I read
into his posting what was not there--a structure in which literal "alerting
signals" on some kind of dedicated links affected some mechanism that
activated switches that changed which perceptions were at any moment
under control. Bill didn't say that, so I can only suppose that his
reference to an "ad-hoc addition" led me to interpret him as having said it.
Such a mechanism would be a baroque ad-hoc addition to PCT, but one that
might work. It is not what I had in mind at all, initially.
I did not want to get into a direct critique of the problems with Bill's
posting, in respect of degrees of freedom for perception and for output,
because of his imminent departure. To do so would not allow him to respond
properly.
···
===================
Me:
In the matter of alerting systems, PCT shows the necessity, not the
mechanism.
Rick:
This statement reveals, to me, the fundemental difference between my approach
to understanding nature and Martin's. I think Martin actually believes that a
theory (PCT) can show the "necessity" of an explanatory mechanism (the
alerting system). I believe that observation and test are what show the
necessity of an explanatory mechanism.
I'm not sure what you mean about a theory showing the necessity of an
explanatory mechanism. A thoery IS an explanatory mechanism, and as I
see it, a theory that showed the necessity of an explanatory mechanism
would do so only by demonstrating its own inadequacy in explaining some
phenomenon within its domain.
Yes, there are different approaches. I think I can say that my statement
could be rephrased more accurately as "If PCT is true, then necessarily
there must be an alerting system," or, "conditionally on PCT being true,
then it shows the necessity of alerting systems." I do not take PCT (or
any theory whatever) as being more than an approximation to a description
of nature. But since we can never know nature, a good theory is the best
description we can get, until a better theory shows up.
Observation and test provide only the perceptions that one is fitted
(trained, primed, evolved, has a theory...) to obtain. There is no such
thing as an atheoretic observation. So there is always a feedback process
akin to reorganization that links theories to the observations that test them.
In the case of alerting systems, the original observations are based on much
looser theories, hardly worth the name perhaps, but theories nevertheless.
There are observations such as that one's attention tends to be attracted
by changes in the visual periphery in patterns one cannot statically
discriminate, or that although one can focus one's auditory attention
nevertheless there are sounds that tend to redirect it, or that no matter
how engrossed one is in typing a response to CSG-L, a touch on the neck
will divert that attention when sound or sight of an intruder might not.
As one contemplates the various things that can serve as alerts or that
seldom do so, it becomes obvious (though perhaps not true) that the more
likely it is that a perception of the "alerting" kind will in fact draw
the attention, the more likely it is that dangerous things provide that
same kind of perception. This is a very old observation. There are
sensory systems that provide focal, usually "pattern" perception, and
sensory systems used by organisms to change the locus of attention. Some
have both functions.
Why does PCT show the need for some kind of attention-shifting system based
on events (I don't mean the event level) in perceptions not under control?
Why should those observations be expected, once one accepts the reality
of PCT? The argument is based on degrees of freedom (more correctly, on
informational analyses, but degrees of freedom is more straightforward).
There are only on the order of 10^2 joints and muscles for control of
soft parts like the face (a factor of 2 or 3 doesn't matter here). Most
of these joints can be moved only at a rate of around 1 Hz, though some
are a factor of 10 faster. But this is compensated by the face that many
groups of joints cannot be moved independently by most people. So we can
take the number of output degrees of freedom as being on the order of
10^2 per second, maximum, being very generous.
Now consider the input. There are some million optical nerve fibres to
each eye, 30,000 auditory nerve fibres, and I have no idea how many fibres
for the various skin sensations--lots. 10^6 is not a bad number for the
sensory inputs, and this is after enormous data reduction in the eye. There
are about 100 visual receptors for every nerve fibre, which takes care of
most of Bill's argument about the coherence of the world reducing the
degrees of freedom in the input. It does indeed, massively. But not
by 8 orders of magnitude.
Next, we have to consider the rates of the sensory inputs. Most of them
have bandwidths in the tens or hundreds of Hz. This gives a ballpark
figure of some 10^7 or 10^8 degrees of freedom per second for sensory input,
being somewhat niggardly. Potentially, each degree of freedom represents
a controllable perception AT EACH LEVEL OF THE HIERARCHY.
But, as Bill says, there is lots of redundancy in the input. The
information provided by the different fibres is not statistically
unrelated over the life of the individual. Some of this redundancy is
to provide robustness in the face of damage, and we might reduce the
degrees of freedom by one or two orders of magnitude for this, again
trying to minimize the sensory degrees of freedom. And we might be
able to reduce them even more; there might still be some pattern
redundancy in what we get from the world, even after the 99% reduction
within the retina, left in what is transmitted down the optic nerve.
Let's be REALLY generous and say that there are templates and pattern
recognition algorithms to deal with this kind of redundancy (based on
the way the world coheres), and that they get rid of 99% of what's left.
We still are left with some 10^5 or 10^6 potentially controllable
perceptual degrees of freedom per second. So let's be really extreme,
and say that thes templates get rid of all but 1/1000 of the original
sensory input. (One has to ask why evolution would provide us with it,
if all our systems were going to do was to get rid of it, but let that
pass.) That leaves 10^4 to 10^5, squeezing down by the most extreme
amounts.
Without PCT, one could say that any perceptual input stimulus could lead
to some response output. But when we are dealing with controlling
perceptions, this won't fly. The number of controllable degrees of freedom
depends on the bottleneck of (in this case) the output. We are stuck
with being unable to handle more than about 100 df/sec, and we have
available between 100 and 1000 times as many that we might need to control.
(I think the ratio is actually several orders of magnitude higher than
this, but it's enough to make the point).
Given that there is such a large excess of controllable perceptions over
perceptions being controlled, there MUST be some way that control is
shifted from one to another AS THE NEED ARISES. One kind of need comes
from changes in high-level reference signals, but dangers and opportunities
arise from unpredictable disturbances. The way they affect what is
controlled is called the alerting system. No mechanism is specified by
the analysis, but the necessity for an alerting system is, provided that
PCT's basic core statements are true.
===============================
Rick:
For me, it's phenomena first;
theories explain phenomena. For Martin, it seems to be theory first;
phenomena run at a distant second. All I can say is -- I think you're
missing a phenomenal world out there, Martin.
Is it clear now how PCT explains the phenomenon of alerting systems?
Martin