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From: desj@brahms (David desJardins)
Newsgroups: sci.math
Subject: Re: Analog models of computation
Message-ID: <38@cartan.Berkeley.EDU>
Date: Mon, 20-Oct-86 17:43:16 EDT
Article-I.D.: cartan.38
Posted: Mon Oct 20 17:43:16 1986
Date-Received: Tue, 21-Oct-86 06:52:43 EDT
References: <6033@decwrl.DEC.COM>
Sender: daemon@cartan.Berkeley.EDU
Reply-To: desj@brahms (David desJardins)
Organization: Math Dept. UC Berkeley
Lines: 43

In article <6033@decwrl.DEC.COM> postpischil@castor.dec.com writes:
>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.

   There is no question of "special-purpose digital hardware" here.  The
digital computer is only a refinement of the simple notion of a tool to aid
in mechanical computation.  I could also do the calculation with pencil and
paper (or an abacus!) in far less time than it would take to build the model
and with 1000x the accuracy.
   The issue is not one of the speed of digital vs. analog hardware.  The
simple fact is that even graphical problems which have elegant analog methods
for solution are inherently much more amenable to algorithmic, arithmetical
computation.

>> 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? 

   I would build an abacus.  I could most certainly achieve 1000x the
accuracy in 1/1000 of the time, even with no existing tools.  And at the
end I would have an immensely useful tool for arithmetic calculation, and
you would have a worthless net of strings and beads.

>So why don't we turn our focus to the elegance mathematics of the models
>instead of their physics and engineering?

   Because the mathematics is trivial?  (Which, BTW, is why I am going to
say no more about this in {net|sci}.math, unless hopelessly provoked.)

   -- David desJardins