Control theory

[From Bill Powers (991121.0633)]

I'll be getting back to the Crowd model any day now. I've been working on a
method for sharpening optical images beyond their "theoretical limit of
resolution," also using feedback principles, for nearly a year (having
given up on it in the 1960s), and have just lately been able to demonstrate
that it works using digital images of the Moon taken with a telescope
stopped down to 28 mm aperture. I'm halfway through a paper (for our
Journal on PCT) on the principles of E. coli reorganization; so far I have
demonstrated that the analysis Martin Taylor's mathematician friend came up
with a few years ago, showing that the number of iterations needed goes up
very steeply with the number of variables, is wrong; it increases
approximately in proportion to the number of variables. I have checked it
by using the method to solve sets of simultaneous linear equations with 10
to 144 variables (the maximum I can handle in my computer with Turbo
Pascal). I am still working with Tim Carey, David Goldstein (I hope), and
the IAACT people on exploring the method of levels as a theory-based
counselling approach. This Winter I am planning a special trip to Brandeis
University to consult with Marc (Isaac) Kurtzer and his colleagues about
the Little Man model. And next Spring, I hope to get together with Richard
Kennaway in Boston to see where the bug model stands and plan where to go
next with it.

All this is very real stuff related in one way or another to the theory I
have been working on since 1953. In all these pursuits, a theoretical model
is used as the basis for deducing what will happen in certain
circumstances, and then I try to figure out how to see if the model is
really right. I do not use common-sense ideas I grew up with; I do not try
to defend opinions I have acquired during my life, or to defend things I
have done, or to get political positions across, or otherwise to intrude my
personal life and beliefs into the search for understanding -- the pursuit
I like to think of as science.

I said yesterday that I was disappointed with the reception of my comments
on RTP and other subjects. The reason for the disappointment is very
simple. Only one or two other people have approached the discussion as an
application of theory; instead, they have obviously been disturbed because
my attempts to apply theory have come up with conclusions that clash with
what they already believe, or have suggested that things they have done
(especially in relationship to children) have theoretical implications they
do not like. Instead of engaging in counter-arguments showing how my use of
the theory is wrong, or needs to be modified, they have indulged in
sneering, vituperation, appeals to "common sense", and other such means
that show a minimum of interest in control theory and a maximum desire to
preserve their existing beliefs and practices. I have no interest in being
part of such discussions. They bring out the worst in me and they have no
relation to my real interests. They certainly do not further the
development of our understanding of human nature.

Periodically, I swear off participating in anything not directly related to
the development and testing of theories; every time, I fall off the wagon
like a drunk who thinks that just one little drinkie can't hurt anything.
But I'm swearing off once again. I will not participate in discussions of
religion, politics, RTP, or anything else but the applications of control
theory to furthering our understanding of how people (or anything else)
works. I will not listen to any proposals that have not been tested at
least in simulation. I don't care whether this leaves me with 130 friends
on the net or 3. I am not going to throw my life's work away by defending
it against other people who have their own axes to grind and have no
intention of giving up anything they already believe. I don't have the time.

Best,

Bill P.

from [ Marc Abrams ( 991120.1102) ]

[From Bill Powers (991121.0633)]

Well I didn't have to wait long for my answer. You can make it 21 now Rick
You and Bill do deserve each other. A lurking we will go, a lurking we will
go ... :slight_smile:

See ya 'round folks

Marc

[Martin Taylor 991124 18:10

[From Bill Powers (991121.0633)]

I'm halfway through a paper (for our
Journal on PCT) on the principles of E. coli reorganization; so far I have
demonstrated that the analysis Martin Taylor's mathematician friend came up
with a few years ago, showing that the number of iterations needed goes up
very steeply with the number of variables, is wrong; it increases
approximately in proportion to the number of variables. I have checked it
by using the method to solve sets of simultaneous linear equations with 10
to 144 variables (the maximum I can handle in my computer with Turbo
Pascal).

That's fascinating. Could you detail the method so that I can check what
David did worng--or whether we are talking about the same thing? I think
I can still find his code (no guarantees). I know I can find the graphs
of the results, and I hope I can still interpret them.

Actually, David didn't do any analysis. He did a lot of simulations,
and the results I reported were the results of _executing_ what we thought
was the e-coli approach to a target in spaces of high dimension that
had no preferred direction (i.e. error was simply the Euclidean distance
from the target). If you also have done simulations that give a quite
different result, you and Dave can't be using the same e-coli mechanism.
Or else we are reporting different aspects of the results.

This is rather important when we talk about the theory of reorganization.
If it is true that the time to a solution goes up linearly with the number
of variables rather than as a power law or exponential (I forget what
David found), it has strong implications for the modularity of reorganized
hierarchies.

Martin

PS As you can see, I'm falling well behind in my CSG reading again. Sorry.