FW: What is a "hybrid" model?

[Fry, Robert L.]

>On Wed, 27 Mar 1996, Lev wrote:

>Ron,
>Please note that the question is not really tricky. The question simply
>suggests that there is no need to attach the term "hybrid" to the model,
>because the combination (hybrid model) is both "ugly" and is likely to
>lead almost all researchers involved in the wrong direction: there are
>really no "hybrid" mathematical structures, but rather "symbiotic
>structures", e.g. topological group, (although I would also hesitate to
>suggest this combination as a research direction).

>In other words, once we find the right model that captures the necessary
>"symbiosis" of the discrete and the continuous, we will give it the name
>that reflects its unique and fundamentally new features, which it MUST
>exhibit.

     I agree whole-heartedly with Ron.  The term "hybrid" is like
so many other concepts that we confuse with reality, is of our own making.
Like George Spencer-Brown said, "the world is like shifting sands
beneath our feet..." It is up to the observer to segment and name the world
throught he process of learning and distinction.

     Historical perspective often sheds light on what are perceived
as new problems, but in fact are perhaps forgotten ideas.  Joshea Willard
Gibbs (see Volume I of the collected works) developed thermodynamics
and thermostatics through classical and macroscopic means.  He then
(see Volume II of collected works) treated statistical mechanics.   Gibbs
called his statistical mechanical treatment an "analogy".   Myron
Tribus (another famous thermodynamicists now more famous for
his popularization of Jaynes MaxEnt Principle) has told me that Gibbs
could not show a one-to-one correspondence with what he knew
about classical thermodynamics (discrete and quantized, albeit
quantum principles had not yet been proposed) and statistical
mechanics because all his statisrical functions were continuous.

     Perhaps this bit of historical perspective provides direct
insight in discrete-continuous formulations of neural computation.  This is
my understanding.

     Bob Fry
     Johns Hopkins University/
     Applied Physics Laboratory