Analog Vs. Digital Computing

Digital computers calculate by manipulating binary digits (bits; ones and zeroes). Because bits are so simple to handle they can be made easily to stand for almost anything; hence the general usefulness of digital computers. Bits can symbolize words, instructions, laws of logic or of physics, numerical measurements, recorded images and sounds--anything that can be written down. In using a digital computer to solve a mathematical equation, for example, certain bits inside the computer are arranged to symbolize the constants and variables in the equation and others are arranged to symbolize the mathematical rules for manipulating those constants and variables. When the computer runs, it applies the rules to the variables just as a person would, only faster.

There is another quite different way to solve an equation: instead of symbolizing an equation, one can set up an experiment in which certain physical quantities are analogous to that equation (that is, which behave like it). One sets up a carefully designed experiment, lets it run, and measures some result; this measurement gives the solution of the original equation. Since this kind of computation uses physical events that are analogous to (like) mathematical symbols and rules, it is called analog computing. For example, pouring three equal quantities of water into a tall tube and measuring the height of the resulting column would be an analog method of calculating that x + x + x = 3x.

In one sense all computers are analog computers. Digital computers merely employ more roundabout analogies: in them, voltages are made to behave like binary digits and binary digits are made to behave like higher-level mathematics. Analog computers skip the binary bottleneck, so to speak, and make voltages (or other phenomena) behave like mathematics directly. It is thus not too surprising that recent theoretical work by Hava Siegelmann and others has shown that some computational problems not solvable even by ideal digital machines should be solvable by ideal analog machines.

If analog computers are so smart, why do digital computers rule? The answer is that analog computers must be built for specific applications. Consider, for example, the computation of Fast Fourier transforms (FFTs). The calculation of FFTs is a computational task that requires on the order of N log₂N arithmetical operations for the transformation of N data points; that is, the more points to be FFT'd, the longer a digital computer must work on the problem. When the number of points involved is not too large or where time is not of the essence, digital machines compute FFTs adequately. Sometimes, however, the number of points involved is very large and time is of the essence. Such applications include the rapid processing of images. Optical analog computers can be purchased that compute the FFT of an image in as little time as it takes the image (in the form of light) to pass through a special lens. Such a device does its special job supremely well, but can do no other; a general-purpose digital computer can be programmed not only to compute FFTs but to play chess, spell-check documents, or tell time. Even "general purpose" analog computers, whose parts can be rearranged at electronic speeds under the control of a digital computer, are functionally limited compared to general-purpose digital computers.

Modern analog computers are mostly of three types: (1) differential analyzers, (2) neural nets, and (3) optical systems. An example of an optical system has already been given, so only differential analyzers and neural nets will be discussed below.

(1) In a differential analyzer voltages and currents are treated as analogs for the continuous variables of a differential equation. (Such equations are important because virtually all physical systems that vary continuously with time can be described by them.) By linking electronic building blocks that add, multiply, integrate, or otherwise manipulate continuously varying voltages and currents, almost any differential equation can be modeled by an analogous circuit. Circuit blocks are interconnected as the differential equation dictates, initial voltages are fixed, the circuit is set in motion, and the solution is observed. Many varieties of analog differential analyzer were built during the 20th century for solving equations in various fields of physics and engineering, but thanks to the increasing speed and cheapness of digital computers the differential analyzer has now largely fallen out of use.

(2) Analog neural nets are close kin of the differential analyzer. An analog neural net is also comprised of simple circuit blocks that handle continuously varying voltages or currents. The components of a neural net, however, unlike the specialized adders, integrators, and other building blocks of a differential analyzer, are all much alike. In this respect they are more like the neurons or individual nerve cells of a living nervous system. Furthermore, there are typically many more "neurons" in a neural net than there are circuit blocks in a differential analyzer. Finally, the signals inside a neural net do not represent the variables of any particular equation. It is rather the overall behavior of such a net--its ability to detect patterns, modify its own behavior ("learn"), or perform some other function--that is of interest. For the same reason that analog computers in general are rare, neural networks are still rarely used in real-world applications: they are inherently less flexible than digital computers.

Finally, a few words should be said about the meaning of "analog." A digital computer jumps from one state to another at every tick of its internal clock. Also, it represents all numbers as finite strings of digits, and so can only count by discrete jumps. In contrast, the physical phenomena exploited by analog computers--voltages, light intensities, and so forth--tend to vary smoothly. This difference (jumpy versus smooth) has, over the years, given the word "analog" a whole new meaning--"smoothly varying." Hence all smoothly varying electrical signals are called "analog"; a clock with smoothly rotating hands rather than numbers that change abruptly is said to be an "analog" clock. Strictly, however, a smoothly rotating pointer is no more or less like the passage of time--analogous to it--than a changing number. Both pointer and number are analogs, because both display visually something that is not inherently visual.