From: barr@barrs.org (Michael Barr) Subject: Re: analog vs. digital Date: 18 Nov 2001 08:37:53 -0800 Newsgroups: sci.physics,sci.math,comp.theory Summary: Ancient history: analogue computers batman@batcave.cave (Batman) wrote in message news:<3BF740E8.499A46AE@batcave.cave>... > Hi, > > Perhaps this question is not "well formed", but I'll ask anyway, if only > to see its "stupidity". Well, there are two parts actually: > > 1. Can an analog computer be programmed? > > 2. If not, doen't this mean the universe itself is fundamentally digital > in > nature, because we can actually program stuff in it? > > Now I'll stand back...way back :-) Thanks, > > Rajarshi No need to stand back, no one is going to bite your head off. Yes, analog computers can be programmed. First let me mention that if you see pictures of the Eniac, there were cables all over, so cables were used to program even early digital computers. Now digital computers are programmed using stored programs. The Babbage engine, which someone finally built in London a few years ago using, it was claimed, only technology available to Babbage, was analog computer programmed using punch cards, but the only programmable analog computer I ever used was programmed with cables. Also potentiometers, used to set certain constants. The computer was built in the late 40s and was designed to solve certainly very specialized systems of simultaneous ODEs of the form \dot x_i = f_i(x_1,...,x_n) where f_i was a sum of terms of the form c_{ij}x_j and c_{ijk}x_jx_k. That is every term was of degree 1 or 2. In practice, there could be no more than 7 variables and I doubt if there any f_i with more than three terms. The DEs were first made into equivalent integral equations and then each variable was assigned to one of the 7 integrators and the outputs of the integrators were cabled to the constant multipliers (pots) whose outputs were cabled to the multipliers and then to the adders whose outputs were fed back to the integrators. The whole thing operated at 5 kh and that meant that a solution appeared 5000 times a second. You viewed the output by hooking the output of an integrator to an oscilloscope which displayed one variable. You could then twiddle the knobs and see the graphs change. The machine had hundreds, if not thousands, of vacuum tubes and they were forever burning out or otherwise going bad and operating the machine was a continual fight against entropy. I was the main operator for about 2 years. As soon as Remington-Rand donated Penn an obsolete Univac I, the lab hired a bunch of programmers and switched to that. That was a trip too, since the Univac I had only 1000 memory locations (even if each one could hold 12 bytes, 6 bits each) and the program that resulted took up 80,000 words about half of which were overlay instructions to make sure that the right code was in the machine when it was needed. Those were the days. ============================================================================== From: "Tom Potter" Subject: Re: analog vs. digital Date: Sun, 18 Nov 2001 23:01:56 +0800 Newsgroups: sci.physics,sci.math,comp.theory In sci.math Batman wrote: > Perhaps this question is not "well formed", but I'll ask anyway, if only > to see its "stupidity". Well, there are two parts actually: > 1. Can an analog computer be programmed? Yes. The power of a computer is a function of its' accuracy and frequency product. The faster a computer can compute to a particular level of accuracy, the more powerful it is. Before about 1970, analog computers, which were called "differential analyzers" were more powerful than digital computers, so they were use to simulate (Compute) dynamic systems. Analog computers were based on high gain D.C. amplifiers. These amplifiers amplified D.C. (Zero frequency) and frequencies up to about 1000 hertz or so. The voltage output of a high gain D.C. amplifier is a function of the input resistance and the feedback resistance. (Of course, the total output voltage is limited by the power supply voltage, so computations were scaled with this in mind. ) voltage(out) = voltage(in) * resistance(feedback) / resistance(input) Voltage(in) would be your independent variable, and you could multiply by a constant by setting the feedback resistance by means of a variable resistance. If you wanted to multiply by a variable, you could have the variable drive a servo to adjust the value of the feedback resistance. The real beauty of an analog computer was that a capacitor could be used in the feedback path to allow one to integrate or differentiate. Analog computers problems were almost always set up to differentiate, rather than integrate, as this would eliminate the problem of small input offsets being integrated over a period of time, and saturating the amplifier. Trig, log, and other functions were simulated with "diode function generators". These devices shaped the output vs. the input characteristics, by back biasing the diodes and adjusting the "breakpoints" where the diodes went into conduction. An array of diodes could be used to accurately simulate almost any desired input vs. output function. Although I covered multiplication by constants and variables, and functions, I almost forgot to mention that addition and subtraction was accomplished by simply combining electrical currents at a "summing junction". In other words, you combined currents to get a voltage drop across a "summing" resistor. NASA used analog computers extensively, and I might point out, that you could use an analog computer with Newtonian physics to control a flight to the Moon or Mars. You don't need, extremely precise computers nor theories to do this. The only advantage of more precise computers and theories, would be to minimize the number of mid course corrections, and these are a function of technology (Burn accuracy, gyro accuracy, fuel consistency, etc.) more so than computation. In other words, even if you had a perfect theory and a perfect computer, you would end up making the same number of midcourse corrections -- Tom Potter http://home.earthlink.net/~tdp -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 90,000 Newsgroups - 16 Different Servers! =-----