Mathematical Tractability of Neural Nets

[slehar@bucasb.bu.edu]

You say:

  "But even if you COULD pinpoint broca's area  with precision for any
  given individual, that would not nail down  for you ANY particularly
  linguistic domain."

Do you mean that if, for an English speaking subject, Brocca's area is
identified, located,   and  ablated,  that we  could  not predict  the
resulting deficits?  I don't know if we are  splitting hairs here, I'm
sure we both agree that the subject would become "Brocca's aphasic", a
well defined syndrome with specific characteristics.

True, those characteristics  are defined in somewhat  fuzzy terms, and
even so, our patient is not guaranteed to suffer all the components of
the defined  syndrome.    Indeed,  immediately after the  ablation the
subject would immediately begin to re-organize his functional areas to
compensate for the loss, and the resulting mapping will be changing in
time and very individualized.   Even  in "normals" it is  clear   that
every  individual  organizes his  / her brain  in their own fashon, so
that  the distribution of functionalities  is somewhat individualized.
I don't dispute any of these facts, and I'm not  entirely certain what
your criticism is.

I  suspect that you  misunderstand my original  contention.  I did not
mean to say that brain functionality is segmented into predictable and
well defined  spatial locations such  that  grammar, for  instance, is
performed exclusively in the grammar area, and nowhere else is grammer
performed.   Some functions   are  performed  in  more localized areas
(including grammar) while   other   functions  are performed  in  more
distributed areas (spatial  thinking, higher  cognition, ...).   These
functionalities  are  flexible  and     adaptive, and  even  localized
functions like grammar   are not fully localized, but   have fuzzy and
overlapping boundaries,    and   receive  influence  from beyond those
boundaries as well.   My point is,  that people who  work in the field
understand these things.  That neurologsts are beginning to understand
the fundamental  principles of brain  organization.   The very  points
that you were making reflect a new insight  into the ways of the brain
that was hard to find ten years ago.

In order to contradict my contention you would  have  to say "We don't
know anything about brain organization,  everything  is confused."  On
the contrary, it is clear that we are beginning to get a good grasp of
the global principles, even though those principles define a fuzzy and
ill defined    scheme.    My point   is  that  the  neuropsychological
understanding of the brain is  quite good  at a global level, where it
has  difficulties is at the  fine grained level.   How are the signals
propagated within the brain in  order  to  produce the  kind of global
organization that we  observe?   This, I say,   is the question to  be
adressed by neural modelers,  and my argument  was  that we should use
the findings and insights of neuropsychology to guide the direction of
research in neural networks.  

Stated another way, you yourself would  be critical of  a neural model
that   is  brittle,  inflexible,  too  clearly  defined and localized,
because you know that that is not the way it  works in  the brain.  My
point is simply that neural modelers should listen to  people like you
for  guidance as to  whether they are  on the  right  track.  That the
science  is ready for  a  coming  together of   the local mathematical
models  and the global   neuropsychological  ones.  Surely   you don't
disagree with that?

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