Martin,
My regime is as chaotic as anybody's and I haven't a clue. My regime is also
Quixotic, but that's another story. ---------
Let me try out an idea for explaining need for info theory. I don't know if it
helps or not. There are two variations of the same argument.
First try: Consider an extension of the degrees of freedom argument. The
environment has many more degrees of freedom than an organism has sensors to
observe. The organism therefore has to infer an estimate of the environment
from a sequence of samples. The samples are notoriously incomplete. Viewed by
the ECS, the sequence of samples is a sequence of symbols that must be dealt
with by information theory. The percept developed at an ECS is an estimate of
the environment and will always remain so because of the incomplete sampling.
PCT functions to drive that toward an optimal estimate, which means
controlling for corroborative samples.Two points about the current model:
(a) The environment is considered equal to the sensory sample taken. There
is no uncertainty about the environment and therefore no information to
be considered. Certainty is certainty. (b) View presented required
use of memory to look at sequence. The CSGL acknowledges memory, but
I don't see role of memory explored.
Second try: As viewed from inside an ECS, the current models don't
consider memory--at least as a ubiquitous part of the discussion. Once
memory is introduced, a sequence of perceptions emerges. If the sequence
is invariant, then there is no uncertainty. However, if the ECS
functions as advertized (gradient descent), the perception changes over
the time required to reach zero error. Now we have a memory problem.
If we consider the change as continuously differentiable, we create a
requirement for infinite memory capacity. Since that is not physically
possible, we are reduced to storing a sequence of perceptual samples and
(I guess) impose a smoothing function when the sequence is recalled.
But here again, we are looking at an incomplete sequence of symbols and
a need for information theory. But if your model only contains the
here and now (no memory), you have no need for information theory--
nor the ability to deal with it. So it seems to come back to
the inclusion of memory and how it's treated.
ยทยทยท
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Dunno if that helps.
Bill C.