Re: Neural netss (was Re: death of the mind.)

From: dan michaels (feedbackdroids_at_yahoo.com)
Date: 09/22/04 

Date: 22 Sep 2004 10:31:45 -0700

erayo@bilkent.edu.tr (Eray Ozkural exa) wrote in message news:<fa69ae35.0409171959.5ea498bf@posting.google.com>...

> d) "mathematics of continuous, complex systems" is *not* known. the
> stuff in physics is the mathematics of continuous, *simple* systems by
> any sensible measure of complexity! [ That's why the state-of-the-art
> *nonlinear* regression methods are algorithmic, and are not based on
> some outdated analog circuitry (that are *not* continuous anyway!) Why
> do we implement neural nets on discrete computers? Just because it's
> more practical? Think again! ]
>

> (d) rests on the mathematics of continuous, complex dynamical systems
> - for example portraying the behaviour of a cognitive system's
> state-variables in terms of a trajectory through a multi-dimensional
> phase space.

Hi Eray, let me give you an image to hold in your mind. First, forget
about all of the metaphysics being discussed on this forum. Think
about the question ... can the complexity of the brain completely
account for generation all of the behavioral output and processing of
all perceptual inputs, storage of memories, consciousness as we know
it, etc, without recourse to external entities [spirits, ephemeral
minds, cadres of homunculi, on and on]?

Now think about there being some 100 trillion synapses located in a
volume roughly the size of your own fist. This is literally a "sea" or
"cloud" of synapses not unlike the idea of a cloud of electrons in
some piece of matter. We're assuming of course that action at these
synapses is fundamental to all mental/brain/behavioral processes. Now,
if you could describe this mathematically, how would you go about
doing so?

Quantcast