X-Message-Number: 24057
Date: Thu, 6 May 2004 20:54:46 -0400
From: Thomas Donaldson <>
Subject: CryoNet #24047 - #24053

Further for Mike Perry:

My calculations in the my last message on the number of possible
connections we could form in our brains were VERY approximate and
could easily be an overestimate. What we really want to find is
the number of possible connections between neurons which are shorter
than a given length L. Clearly we can't simply divide up the brain
into pieces of size L^3, because we must take account of the point
that not every neuron will be at the center of such a piece, and
hence not every neuron --- in fact virtually all of them - 1, will
have connections outside our little L^3 cubes. Nor can we do such
a calculation for small cubes around every neuron: that will give
us lots of duplicate connections. And to make the problem even worse,
we can't really represent neurons as single points. Some neurons
(most of them, but not all) have long axons, with a tree of connections
on one end of the axon, and a tree of dendrites spreading out from
their central cell body. So the best model of a neuron for these
calculations would be a LINE, with connections at each end.

I've been thinking about the best way to compute the number of
possible connections for a set of existing neurons. NEW neurons will
add to the problem, but for now I won't consider that --- though
it's clearly going to be important for understanding how brains 
work.

However it still seems clear to me that we will not get a count of
connections that grows like a polynomial as the number of neurons
increases. It will grow much faster. So I'm not retracting the basic
point of my previous message: growing new connections will turn out
to be vastly more efficient than any system which contains all 
possible connections and turns them on or off as change and learning
occur.

                   Best wishes and long long life for all,

                         Thomas Donaldson

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