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From: desj@brahms (David desJardins)
Newsgroups: sci.math
Subject: Re: Analog models of computation
Message-ID: <23@cartan.Berkeley.EDU>
Date: Thu, 16-Oct-86 04:37:12 EDT
Article-I.D.: cartan.23
Posted: Thu Oct 16 04:37:12 1986
Date-Received: Thu, 16-Oct-86 22:11:20 EDT
References: <8194@watrose.UUCP> <6490@think.COM> <3504@columbia.UUCP>
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Reply-To: desj@brahms (David desJardins)
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Organization: Math Dept. UC Berkeley
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In article <3504@columbia.UUCP> zdenek@heathcliff.columbia.edu.UUCP (Zdenek Radouch) writes:
>Sorry, my friend, you totally missed the point. The author of the original
>posting brought up a very interesting idea, namely, that some problems can
>be solved more efficiently on machines that are NOT digital computers.
>He has chosen an example to illustrate, what he's looking for, and he
>certainly got his idea across.

   I'm afraid not.  Not to me anyway.  To me this example is a perfect illus-
tration of why analog computing is so spectacularly unsuccessful.  Be honest:
if you wanted to solve the shortest-path problem for a graph of 1000 vertices
and 100000 edges, would you prefer to use the analog or the digital method?
It seems obvious that the analog method is completely hopeless -- you could
spend many days building special-purpose hardware to solve the one particular
problem, or you could solve it in a few minutes (an hour at most, including
the time to write the code) on a desktop computer, with a general algorithm
that can be used to solve *all* shortest-path problems, not just a particular
one.

>   (1)	You didn't convince me, that it would be more efficient for ME
>	to use the computer insted of the strings.

   See above.  Would you really use the string model for 1000 vertices and
100000 edges??  I simply don't believe it.  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.

>   (2)	The machine has to grow only because YOU made it too small in the
>	first place.

   Nonsense.  Both the analog method and the algorithm require linear time
in the number of edges.  The analog method requires this much time to build
the model, or at least to adjust the string lengths to the specified para-
meters.

>His machine solves the problem in a time unit.

   Again, *nonsense*.  It takes at least one time unit per edge to adjust
the length of the string to the specified value.

   -- David desJardins