What the Neocortex Does
Harry Erwin
herwin at gmu.edu
Sat Aug 5 11:56:16 EST 2000
Kevin K. <KK at _._> wrote:
> Gary Forbis wrote:
> >
> > "Kevin K." <KK at _._> wrote in message news:3989AC71.7969B1CA at _._...
> > >
> > >
> > > Harry Erwin wrote:
> > >
> > > > You're missing my point. Symbols are signs. They belong to a countable
> > > > set. Wind-tunnel models can vary continuously (or discontinuously). That
> > > > matters--there are some applications (for example in hydraulic analysis)
> > > > where symbolic modeling encounters an intractable problem, but analog
> > > > modeling works fine.
> > >
> > > Intractability is a an issue relating to computational efficiency --
> > > i.e. the time or space required to perform the calculation. It has no
> > > bearing on Church's thesis. A Turing machine can be written to solve the
> > > hydraulic problem to any desired degree of accuracy because the TM has
> > > an infinite supply of time and space. It may take a while, but that's
> > > okay, because Church's thesis concerns computability in principle, not
> > > in practice.
> >
> > I hate "in principle" arguments applied to real objects.
>
> That's what this thread is about, in reverse. Mr. Erwin claimed that a
> real object (the bat brain) had some bearing on a longstanding
> mathematical principle (Church's thesis).
>
> BTW, do you hate it when "in principle" arguments like "the interior
> angles of triangle total 180 degrees" are applied to real triangles? ;-)
Well, I did spend a year learning to program a Turing machine when I was
working on that PhD in algebraic topology. I'm probably one of the few
people actually qualified to compare mathematical reasoning (what Turing
was trying to reduce to syntax) to computational processes in wet
networks.
--
Harry Erwin, PhD, <mailto:herwin at gmu.edu>,Computational Neuroscientist
(modeling bat behavior), Senior SW Analyst and Security Engineer, and
Adjunct Professor of Computer Science, GMU. Looking--CV available at:
<http://mason.gmu.edu/~herwin/CV.htm>
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