X-Message-Number: 15375
Date: Wed, 17 Jan 2001 23:25:06 -0500
From: Thomas Donaldson <>
Subject: more on brains and computers

To further comments about brains and neurons:

Given N neurons, the number of possible connections between them goes up
like N!. This is greater than exponential.

The fundamental issue here seems to be that of whether the neurons are
modified when they lose a connection or make a new one. The computational
(and all other abilities, which must not be forgotten though they are
too often forgotten) abilities of neurons depend on their connections.
These connections, according to the best evidence we now have, CHANGE
in many neurons. The suggestion behind such changes is that they are
themselves the formation of memory. If so, the connections of our brain
bear a very close relation to our particular memories... and thus our
ability to CHANGE our connections depends on the number  of possible
connections for each neuron, not a fixed number to a fixed set of other
neurons.

The above paragraph deserves a number of qualifications. As most people
who've done some reading about actual brains will know, many connections
seem to develop very early and remain fixed. Those involved with our
personal memories come last, and they are the ones which change constantly.
Basically this means that we cannot assume that ALL connections belong to
our memories. Sorry, but so far as I presently know, no one has counted
these enough for us to make some math formulas. Second, there is a 
theory of memories which would assume that all the connections remain
fixed, with memories changing due to changes in the connections
themselves. The problem with this theory is that synapses (connections
between neurons) have been found to change constantly. Yes, no doubt
this observation and others might have alternative explanations, but
they look weak to me and I'm hardly the most prominent person who would
say that they look weak.

It's what I understand about how brains work that makes me believe that
the math figure will come closer to N! than just to some power of N. 
Since we are talking empirical facts, all current theories may someday
be seen to be faulty. Still, even a little reading about brains will
suggest that they do not work like present-day computers, even parallel
ones, and that changes in connectivity (not to mention production of
new neurons!!!) make them at least quite different.

		Best wishes and long long life to all,

			Thomas Donaldson

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