ONT Re: Differential Logic B -- Discussion
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DLOG B. Discussion Note 1
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HT = Hugh Trenchard
HT: Just throwing out a thought (as usual):
if one of the units, or logical variables
is stable, while the other is active, do we
see a "radiating tree" something like this:
active active active
\ | /
active--- \ stable /---active
/ | \
/ active \
active active
HT: I know you were probably going to answer that
question in the next episode, but I wanted to
see if I roughly understand the concept.
Hugh,
Consider the logical expression that I write
as "(x , y)" and graph in the following way:
x y
o---o
\ /
@
According to the story that we are imagining about the relationship
of the logical syntax to the state of a quasi-physical system, this
expresssion describes the set-up of a neural pool with two mutually
inhibitory units x and y when it finally reaches equilibrium, which
in the sort of model we are imagining can only be one of two ways:
(1) x is active and y is stable, or (2) x is stable and y is active.
I can't remember if I had this in mind at the time, but I know that
shortly after I wrote this up for my master's work I recognized that
there were models of competition processes that Grossberg and others
had considered that have this very sort of "winner take all" behavior
at equilibrium. However, there is a different twist here that I was
just about to get into.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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