[Martin Taylor 960621 15:30]
Chris Cherpas (960621.0946 PT)
I've been lurking in on the most recent information theory
discussion and find interesting Martin's statement that the
level in the control hierarchy is (or can be) related to bandwidth.
When you are thinking about that, keep two things in mind--well, at least
two.
Firstly, even though the job of control can be seen (through information-
theory spectacles) as being to reduce the bandwidth of the effect of the
outer-world disturbances more and more as one goes up the hierarchy,
nevertheless, each higher ECU takes input from several lower-level
perceptual signals. The bandwidth of outer-world disturbance effects
from all these different inputs is greater than that of any single
input, and can be as great as the sum of the bandwidths of the individuals
if they are orthogonal. It's not JUST a question of slowing the data
rates into any particular ECU at a higher level, though it does imply
that the overall information rates slow as one goes up the levels. That's
the nature of control.
Secondly, it seems not unreasonable to suppose that the processing ability
of a neuron is much the same no matter where it is in the hierarchy. If
ECUs at different levels have similar complexities (which may well be false,
but it's a baseline assumption), then the control bandwidth at different
levels may actually be fairly similar, just distributed differently over
time, lower levels having more uniform rates than higher levels, which
might be more impulsive. I don't know of any theory that says that this
kind of redistribution over time is required to happen, though. It's just
something to keep in mind as a possibility. More on this, below.
While the 11 levels are often intuitively
appealing, I keep looking for variables that would constrain
what the next level to develop in a developing organism
would be (or better, what it _must_ be if that's possible).
I can't imagine that there's any "must be" about it. I am guessing that
the acquisition of a new level is a serendipitous event based on the
fortuitous coming together of different functional operations to form
a perception whose control helps to stabilize intrinsic variables.
Functions of functions is the result of building hierarchies. What those
will do cannot be determined a_priori, in most cases.
But you can put some constraints on what _may_ happen. The new level will
combine data from the level below, and will do it in a way different from
combining the sensory inputs of the level below. If it did not, it would
be a member of the level below. The perceptual signals at the new levels
are going to be of a different _kind_ than those of the pre-existing levels.
Now, this will be so even if the combining function in the new level is the
same as the combining function at the lower level, if the perceptual
functions of the pre-existing levels are non-linear (as are most neural
functions). I think, here, of the profound difference in kind between the
outer-world correlates of the signals at the different levels of a multi-layer
perceptron.
The overall constraint on a new level is that the total information rate
of the perceptual signals in it will be lower than the total information
rate of the perceptual signals in the level below. If it were not so, the
new level would not be controlling. (Don't forget that the information rate
of the combination of two non-orthogonal signals is less than the sum of
the two individual rates).
Now, it seems likely that there are more different useful perceptions to
control as one goes up the levels--at least up quite a few levels. If this
is the case, and the processing capability of each ECU is much the same at
all levels, and yet the overall bandwidth of effects from the outer world
is being reduced as we go up the levels, don't we have a situation ripe
for conflict? Yes, we do, and that is where we get into the issues of
multiplexing. The higher one goes in the hierarchy (up to a point, probably),
the more the different ECUs rely on the same lower-level units for their
inputs and to receive their reference signals. There has to be multiplexing,
at least of the outputs, in such a way that one does not get muscle-level
conflicts between trying to perceive oneself picking up the toast and
picking up the coffee. The muscle outputs are devoted first to one purpose
and then to the other.
What this means is that the information bandwidth of higher-level units
is likely to be more impulsively distributed over time than is that of
lower-level units. The higher-level information rate is expressed in
more separated, but more complex chunks, whereas the lower-level rates
(numerically perhaps similar) are expressed in a distributed, but relatively
simpler temporal organization.
The implication here is that there exists some way of multiplexing the
control of different perceptions at higher levels. We know from first-hand
observation that this is so. We do not know, within PCT, exactly how it
is accomplished. Are there controlled perceptions of switches that
redirect the outputs of high-level ECUs to different low-level ones or
to nowhere? Are there controlled perceptions of the gains of different
high-level ECUs that turn some off and others on? What are the mechanisms?
We don't know, but there must be some.
Another implication is that there is an ever-increasing tendency as we go
up the levels for ECUs to act more as switched control units than as
continuous ones. The underlying signals may be continuous, but the error
signals may have periods of slow increase followed by rapid, impulsive
decrease, rather than looking like random noise. Interrupted random walks
may be a more appropriate metaphor a the higher levels.
Enough waffle. Sorry, but if someone is really interested, I enjoy
waffles (with maple syrup).
Martin
