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From: bradley@think.COM (Bradley Kuszmaul)
Newsgroups: sci.math
Subject: Re: Analog models of computation
Message-ID: <6540@think.COM>
Date: Tue, 21-Oct-86 11:28:25 EDT
Article-I.D.: think.6540
Posted: Tue Oct 21 11:28:25 1986
Date-Received: Wed, 22-Oct-86 04:26:12 EDT
References: <3529@columbia.UUCP> <6528@think.COM> <3542@columbia.UUCP>
Reply-To: bradley@godot.think.com.UUCP (Bradley Kuszmaul)
Distribution: net
Organization: Thinking Machines, Cambridge, MA
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In article <3542@columbia.UUCP> zdenek@heathcliff.columbia.edu.UUCP (Zdenek Radouch) writes:
>In article <6528@think.COM> bradley@godot.think.com.UUCP (Bradley Kuszmaul) writes:
>[me]  As I said, his method might not be practical, but it's elegant and
>    much faster.
>
>>
>>If it is not practical, then how can it be faster.
>
>There is no relationship between "practical" and "fast". One of the synonyms
>of practical is USEFUL.
>You have climbed a tree and want to get back to the ground level. You can:
>	1. Jump.
>	2. Climb down the tree.
>Method (1) is always faster than (2), but it might not be always practical.

Like I said, I never feel very good about algorithms which run very
fast but give the wrong answer (in this case, broken limbs).  In this
case,  I believe your analogy does nothing to deny my point, since my
point was that if an algorithm is not practical, how can it be fast.
There are several ways for an algorithm to be impractical:
 (1) Too expensive to implement (in which case it never runs and is
     very slow indeed),
 (2) Gives incorrect answers (in which case who cares how fast it is),
 (3) others?....

>>I also have the belief, with no proof, that there are no analog
>>machines which will do better than digital machines, because whatever
>>analog machine you build, I can build a digital machine with about the
>>same hardware cost, and the digital machine will be able to simulate
>>the analog machines behavior ......
>
>	Don't rely on your feelings or believes. In this case you are orders of
>magnitude off. Your environment is ANALOG. All the machines that deal with it
>have to be at least partially (front and back end) analog.

I am not sure what the point of demonstrating that "everything is
analog" is.  Showing that everything is analog merely proves that you
can't do better than the best analog machine.  It does not prove that
you CAN do better than a digital machine.

There may be some question as to what I mean by "can't do better".  I
admitted that I might have to pay a polylogarithmic penalty to
simulate your arbitrary analog machine with my general purpose digital
machine, and if you think things like constant factors are important
then the digital machine will sometimes lose (constant factors, are of
course, just a special case of polylogarithmic penalties).  Sure, as
an engineer, there are always special cases where an analog machine
can do better, but those special cases in the real world seem to be
becoming more scarce.

As an example, consider the clothes washing machine.    The machine
that was in my parents house when I was a child had an analog
controller, and it worked for a long time.  (Lasted twenty years).
Today, most washing machines are controlled by a microprocessor.  Now,
admittedly, it would be pretty silly to go to all the trouble of
inventing transistors, and building the VLSI technoglogy and factories
to build microprocessors just to control washing machines, but once we
have the microprocessors, it becomes cheaper to use them than to build
an analog control system.  (In fact the microprocessors might do a
better job or a worse job, depnding on the software.  I know that in
my  audio turntable, the extra smarts of a microprocessor is great:
It won't set the read head (I guess you'd call that the cartridge?)
unless it has some evidence that a record is actually on the platter,
the rotational speed is controlled by the processor and the specs are
something like 0.001% variation in the rotational speed (which at
least impressed my dad, who supposedly understands the technology for
building turntables with analog controllers).  Of course, these
examples are really getting of the track, since they are not really
"computing" per se, but are performing a control task.

It is true that it is hard to simulate a capacitor for as cheap as a
capictor costs, but it is much cheaper to build a simulator (in
software) to simulate arbitrary circuits, and then feed a description
of the circuit to the computer than it is to actually build the thing
out of hardware to simulate it.  Of course, the hardware may still
turn out to be cheaper and faster, especially if you are going to mass
produce it, and use it for something in the critical path of a very
high speed computation (e.g. for signal processing at 1GHz).

>It is easy to say "Hey, I've got a workstation on my desk; I can simulate
>EVERYTHING." You probably can. But if you say "Here's the problem, what's the
>best machine to solve it?" that's another story.

I never did really understand how to use general purpose computers
anyway.  Why would anyone want them?  All I need is text editing. :-)

>	My point is that the mathematics is a tool that was designed by us
>in order to simplify our lifes when dealing with the environment. It wasn't
>here before we got here. The analog machines were!

I'm really getting random here:  There are certain philosphies of
mathematics which state that the math was here before us.  The job of
the mathematician is to discover it.

Speaking of random... What was the original posting?
 -Brad