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From: chandros@topaz.RUTGERS.EDU (Jonathan A. Chandross)
Newsgroups: sci.math,sci.physics
Subject: Analog models of computation
Message-ID: <6241@topaz.RUTGERS.EDU>
Date: Wed, 15-Oct-86 18:38:45 EDT
Article-I.D.: topaz.6241
Posted: Wed Oct 15 18:38:45 1986
Date-Received: Wed, 15-Oct-86 21:57:21 EDT
Organization: Rutgers Univ., New Brunswick, N.J.
Lines: 37
Keywords: String Art, Why it's bad
Xref: mnetor sci.math:3 sci.physics:9


/* Message-ID: <8195@watrose.UUCP> From: rpjday@watrose.UUCP (rpjday) */
##>  I am interested in collecting examples of problems in the area of
##>computation that are generally acknowledged to be reasonably to
##>obscenely difficult using the digital computer model, but which have
##>simple elegant solutions if one was allowed to construct some form
##>of "analog" computer.  
##>  As an example, the problem of finding the shortest path between two
##>points in a graph is easily solved if one is allowed to build a string
##>model of the graph, then pick it up by the source node, and measure the
##> distance straight down to the target node.  I'm sure everyone is familiar

The technique you are referring to is called "rubber banding."   While
workable for small problems, the method degrades quite substantially for
large(r) problems.  The problem of finding a shortest path for, say 1000
cities, will degrade to such an extent that one of the known heuristics,
running on a digital computer, will outperform the analog version, both
in accuracy and in time.

The main reason that analog computing no longer flourishes is a result
of 1) inaccuracy in calculations, and 2) difficulty in scaling models.

Hopfield and Tank have come up with some amazing results for neural
networks computing TSP (travelling salesmen problem).  But it is very
difficult to make the networks very large, and the component tolerence
is not terrific.  Fractional percent errors add up quickly.

However, the topic is extremely interesting.  People have built the
seive of Erasthostenes (badly mangled spelling) out of bicycle rims
and wire, and matrix multipliers out of (fundamentally) oatmeal boxes.

Perhaps the topic could be expanded to bizarre analog computation in
general??


Jonathan Chandross
allegra!topaz!chandross