What the Neocortex Does

Harry Erwin herwin at gmu.edu
Fri Aug 4 10:13:04 EST 2000


Kevin K. <KK at _._> wrote:

> Harry Erwin wrote:
> > 
> > Kevin K. <KK at _._> wrote:
> > 
> > > Harry Erwin wrote:
> > >
> > > > On the other hand, it has some
> > > > relevance to Church's thesis, since I haven't been able to identify the
> > > > mechanism of a Turing machine (or any of the alternatives) in the
> > > > anatomy 8).
> > >
> > > You're not going to find a Turing machine in the nervous system of a
> > > bat. A Turing machine is an infinite object. Any biological system of
> > > nerves with binary states is a finite automata, and thus can be
> > > simulated by a Turing machine. Therefore, you will never find something
> > > a bat can do which a TM cannot do, and Church's thesis is unaffected.
> > >
> > > Kevin K.
> > 
> > Ah, but neurons do not have binary states.
> 
> I was under the impression that they do, i.e. firing or not firing.

I'd suggest experimenting with a model of a biological neuron (say using
GENESIS)--they're much more complex than that. The firing/not firing
dichotomy plays a role in long-range signalling, but the timing of the
action potentials is more important than their simple presence/absence.
Locally, there is a good deal of important intercellular and
intracellular signalling that may never generate an action potential.
For example, the only action potentials found in the retina are
associated with sending the final results of retinal processing to the
neocortex.

> 
> > In fact, to define the state
> > of a neuron, you have to treat it as a continuous extended object.
> 
> That doesn't prove anything. The same can be said about the logic gates on
> chip. Such gates are in a condition of continuous flux due to thermal
> fluctuations, noise, varying distributions of electrons etc. But these
> variations have no effect on the behavior of the chip as a computational
> device.

See above.

> 
> > It
> > gets worse when you're dealing with a collection of neurons, because you
> > now need to keep track not only of the internal states of the neurons
> > but also the glial cells. So we're not dealing with a finite automaton.
> 
> So you are saying that, in principle, the function of a bat brain cannot
> be simulated by a digital computer, no matter how advanced? I find that
> very extravagant.

Why not? There are systems that cannot be simulated by a digital
computer, no matter how advanced. Try modeling something that
incorporates turbulance. All you need to get into this situation are
significant non-linear multi-scale interactions so that decreasing the
scale of the time/space mesh does not result in convergence. (That's
also why the field of dynamic programming is said to consist of
'jillions of special cases.')

-- 
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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