Jane M Fraser

What’s new?

In the 22 July 2020 issue of New Scientist, Anna Demming reports on uses of analog (British: analogue) computing in an article titled “Why old school technology could shape the future of digital computing.”

What does it mean?

If you want to find the shortest route from Los Angeles to Boston, you can program a computer to use the simplex algorithm to solve the linear programming formulation of the problem; the data are the distances between all possible intermediary cities. Or you can, as proposed in 1957 by George Minty (Operations Research 5, page 724),

“Build a string model of the travel network, where knots represent cities and string lengths represent distances (or costs). Seize the knot ‘Los Angeles’ in your left hand and the knot ‘Boston’ in your right and pull them apart. If the model becomes entangled, have an assistant untie and re-tie knots until the entanglement is resolved. Eventually one or more paths will stretch tight – they then are alternative shortest routes.”

The first method of solution is described as “digital,” because the computer computes the solution using numbers, or digits. The second is described as “analog” because it uses a physical analogy to find the solution.

In engineering, we use models – mathematical and physical – to describe the world. We analyze those models in order to elicit the implications of the models and then we interpret those results back to the real world system. Analysis has increasingly taken the form of computation using digital computers, starting with the abacus and continuing through supercomputers.

In my field of operations research, researchers have developed powerful methods to optimize systems, that is, to find a solution that minimizes cost or maximizes benefit. Scheduling, production planning, and network design, as examples, have all improved from our ability to express these situations as mathematical models and use computers to find the optimal (or at least a very good) solution.

In many fields of engineering, the models take the form of differential equations, that is, equations written in the language of calculus in which the change in one quantity depends on the level of another quantity. For example, the rate of movement of a mass attached at the end of a spring is a function of the distance the spring is extended or compressed. The rate at which tea cools depends on the difference in temperature between the tea and the surrounding temperature. The essence of engineering is the application of differential equations.

One strength of digital computers is that they are general purpose machines that can be programmed to solve many different problems. The string and knots used to solve the Los Angeles to Boston problem has to be rebuilt to solve the Paris to Moscow problem, and can only solve shortest path problems, while the digital computer, using the same program and algorithm, can solve the problem of any two cities, given the data of distances between intermediary cities. And that digital computer can be programmed to solve other problems.

But digital computing has drawbacks. Digital computing uses numbers, always truncated. Digital computation is an approximation because computers use 0 or 1 – and no numbers between 0 and 1 – to represent all numbers. You can approximate the numerical quantity pi as closely as you want in a computer, but it is still an approximation because pi is an infinite decimal that never repeats; digital computation truncates pi at some number of digits and numbers in digital computers are always truncated from the true number in the real world. The sound wave that varies continuously to produce the sensation of music in your ear and your head is represented very closely – but not exactly – by the digits in digital audio. The speedometer showing your car’s speed on a dial is a continuous (analog) representation of speed while the digital readout on newer cars is an approximation.

Differential equations are continuous but are represented as difference equations in the computer, that is, time varies in discrete jumps not continuously. With an appropriate computer, the loss in accuracy is negligible, but always there. Also, a digital computer, unless designed with multiple processors to allow parallel computation, does one computation as a time.

But since many engineering models use differential equations, and since some differential equations recur again and again in physical models, some analog computers can be general purpose. An analog computer mimics the physical system it is modeling. As a result, unlike the digital computer that must laboriously compute the trajectory at each tiny step in time, an analog computer continuously follows the path that is the analogy of the physical system being modeled. As stated in the New Scientist article: “Quantities like electric current, charge and capacitance are related by rates of change in their values. This means they fit differential equations, allowing electrical circuits to serve as analogues for all other systems governed by such mathematical expressions.” Computing with beams of light or radiation at other wavelengths can simulate other systems of interest, such as earthquakes and stock market behavior.  Other devices called memristors (resisters with memory) can simulate brain activity. Analog computing has problems of course, including laborious programming and lack of accuracy (for reasons different from digital computing).

What does it mean for you?

Maybe not much. If you are an audiophile, you may have a strong opinion about analog or digital music. My father, a telephony engineer, hated to talk on a cell phone because of its awful sound fidelity. Some photographers prefer using film over digital cameras. I know that a car’s digital display of 38.1 mph or even 38 mpg is actually enough information for me as a driver, but I find it easier to quickly read and interpret an analog dial display of speed. And I learned to tell time on a clock face, not a digital display. I can more easily tell if I am speeding or if I am late for an appointment by glancing at an analog display rather than digital display. And I am amused by the digital simulation of an analog clock face.

Computation has been so successful in improving our lives that we sometimes forget that nature does not compute. A tennis ball does not compute the arc to follow after it leaves the racket; a swallow does not fly by computing the necessary muscle movements; your brain does not think by computing with numbers.

It may make a difference to you in the future if analog or hybrid computation, because of its inherently parallel nature, makes feasible the rapid solution of problems now intractable on digital computers. At a minimum, the use of analog devices in some widespread applications may slow the pace of increased energy consumption by our many devices.

Where can you learn more?

For keeping up on trends in science and engineering, no magazine beats New Scientist. I have been reading this British magazine since 1970 when I spent part of my junior year at the University of Glasgow in Scotland.

An article at IEEE Spectrum by one of the researchers in this area, Yannis Tsividis, has more description of analog computing. Other useful articles are by Bernd Ulmann, Bill Shweber (the slide rule, which engineers used to put a human on the moon, is an analog device), and Lou Frenzel. Ulmann has a fascinating blog devoted to analog computing.