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From: postpischil@castor.dec.com (Always mount a scratch monkey.)
Newsgroups: sci.math
Subject: Re: Analog models of computation
Message-ID: <6033@decwrl.DEC.COM>
Date: Mon, 20-Oct-86 08:51:52 EDT
Article-I.D.: decwrl.6033
Posted: Mon Oct 20 08:51:52 1986
Date-Received: Tue, 21-Oct-86 23:44:51 EDT
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Organization: Digital Equipment Corporation
Lines: 44

David desJardins makes much ado about the time needed to construct an
analog model but never speaks of the time needed to construct the hardware
required for a digital model.  He speaks of spending many days building
"special-purpose hardware to solve the one particular problem", but we
only need to consider how many days it would require to build the
special-purpose digital hardare to solve the same particular problem to
see the true situation.
 
If he insists upon going into the real world and worrying about
construction time and accuracy, let's consider that the time required to
build anything grows exponentionally with accuracy or size, just because
of the uncertainties of the real world and the inevitability of human
error, and this includes digital computers.
 
> If you really think this is superior, let's have a race.  I will spend no
> more for the computer hardware than you spend on strings and beads, and
> achieve 1000x the accuracy in 1/1000 of the time. 
 
You will do it in 1/1000 of the time because the machines are already
built.
 
If dropped on an planet with the necessary resources but without tools or other
created materials, which could you build first, a digital computer that would
solve the shortest-path problem for a graph of 1000 vertices and 100,000 edges
or an analog computer? 
 
Let's also note that we do not need to build special-purpose hardware for
analog models any more than we need to build special-purpose hardware for
digital models.  Even the single model of one graph can be used to find
the shortest paths between ALL pairs of nodes in the graph without being
torn down and rebuilt.  David desJardins points out it would take linear
time for the model to fall in place when lifted by a node.  However, this
linear time solves 999 shortest-path problems for a 1000-node graph.
Additionally, we can imagine a constructed machine to turn out graphs and
other analog models.
 
So why don't we turn our focus to the elegance mathematics of the models
instead of their physics and engineering?  I know I enjoyed the information
in _Scientific American_, and I'd like to hear more.
 
 
				-- edp
				Eric Postpischil
				"Always mount a scratch monkey."