Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!caip!think!rutgers!seismo!columbia!heathcliff.columbia.edu!zdenek From: zdenek@heathcliff.columbia.edu (Zdenek Radouch) Newsgroups: sci.math Subject: Re: Analog models of computation Message-ID: <3542@columbia.UUCP> Date: Mon, 20-Oct-86 23:18:28 EDT Article-I.D.: columbia.3542 Posted: Mon Oct 20 23:18:28 1986 Date-Received: Wed, 22-Oct-86 04:01:26 EDT References: <3529@columbia.UUCP> <6528@think.COM> Sender: nobody@columbia.UUCP Reply-To: zdenek@heathcliff.columbia.edu.UUCP (Zdenek Radouch) Distribution: net Organization: Columbia University CS Department Lines: 55 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. >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. If by "no analog machine will do better than digital machine" you mean only machines that implement mathematics, you are still off. Yes, digital computers are easy to build because of the modularity of digital electronics, they're also flexible (as long as the software is flexible), but there's a problem. 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. 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! The sine wave wasn't just a curve somebody liked. It is derived from a circle, it describes a harmonic motion. To say that the digital computer is the best machine for playing with sine functions, is crude simplification. The time to discharge a capacitor C through resistor R from V1 to V2 is t = RC ln(V1/V2). You think you can build a digital hardware that's simpler? zdenek ------------------------------------------------------------------------- Men are four: He who knows and knows that he knows, he is wise - follow him; He who knows and knows not that he knows, he is asleep - wake him; He who knows not and knows that he knows not, he is simple - teach him; He who knows not and knows not that he knows not, he is a fool - shun him! zdenek@CS.COLUMBIA.EDU or ...!seismo!columbia!cs!zdenek Zdenek Radouch, 457 Computer Science, Columbia University, 500 West 120th St., New York, NY 10027