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 Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=24057