Part 6

A little thought will reveal that even prior to computers there were two distinct types of calculating; those of measuring (analog) and of counting (digital). Unless we are statisticians, we encounter 2-1/2 men or 3-1/2 women about as frequently as we are positive that there is exactly 10 gallons of fuel in the gas tank. In fact, we generally use the singular verb with such a figure since the 10 gallons is actually an arbitrary measurement we have superimposed on a quantity of liquid. Counting and measuring, then, are different things.

Because of the basic differences in the analog and digital computers, each has its relative advantages and disadvantages with respect to certain kinds of problems. Let us consider each in more detail and learn which is better suited to particular tasks. Using alphabetical protocol, we take the analog first.

_The Analog Measuring Stick_

We have mentioned the slide rule, the speedometer, and other popular examples of analog computers. There are of course many more. One beautiful example occurs in nature, if we can accept a bit of folklore. The caterpillar is thought by some to predict the severity of the winter ahead by the width of the dark band about its body. Even if we do not believe this charming relationship exists, the principle is a fine illustration of simulation, or the modeling of a system. Certainly there are reverse examples in nature not subject to any speculation at all. The rings in the trunk of a tree are accurate pictures of the weather conditions that caused them.

These analogies in nature are particularly fitting, since the analog computer is at its best in representing a physical system. While we do not generally recognize such homely examples as computers, automatic record-changers, washing machines, electric watt-hour meters, and similar devices are true analogs. So of course is the clock, one of the earliest computers made use of by man.

While Babbage was working with his difference engine, another Englishman, Lord Kelvin, conceived a brilliant method of predicting the height of tides in various ports. He described his system of solving differential equations invented in 1876 in the _Proceedings of the Royal Society_. A working model of this “differential analyzer,” which put calculus on an automated basis, was built by Kelvin’s brother, James Thomson. Thomson used mechanical principles in producing this analog computer, whose parts were discs, balls, and cylinders.

[Illustration:

_Science Materials Center_

A simple analog computer designed to be assembled and used by teen-agers. Calculo performs multiplication and division within 5 per cent accuracy, and is a useful demonstration device. ]

Early electrical analogs of circuits built around 1920 in this country have been discussed briefly in the chapter on the computer’s past. The thing that sparked their development was an engineer’s question, “Why don’t we build a little _model_ of these circuits?” Solving problems in circuitry was almost like playing with toys, using the circuit analyzers, although the toys grew to sizable proportions with hundreds of components. Some of the direct-current analog type are still operating in Schenectady, New York, and at Purdue University.

A simple battery-powered electric analog gives us an excellent example of the principle of all analog machines. Using potentiometers, which vary the resistance of the circuit, we set in the problem. The answer is read out on a voltmeter. Quite simply, a known input passing through known resistances will result in a proportional voltage. All that remains is assigning values to the swing of the voltmeter needle, a process called “scaling.” For instance, we might let one volt represent 100 miles, or 50 pounds, or 90 degrees. Obviously, as soon as we have set in the problem, the answer is available on the voltmeter. It is this factor that gives the analog computer its great speed.

General Electric and Westinghouse were among those building the direct-current analyzer, and the later alternating-current network type which came along in the 1930’s. The mechanical analogs were by no means forgotten, even with the success of the new electrical machines. Dr. Vannevar Bush, famous for many other things as well, started work on his analog mechanical differential analyzer in 1927 at the Massachusetts Institute of Technology. Bush drew on the pioneering work of Kelvin and other Englishmen, improving the design so that he could do tenth-order calculations.

Following Bush’s lead, engineers at General Electric developed further refinements to the “Kelvin wheels,” using electrical torque amplifiers for greater accuracy. The complexity of these computers is indicated in the size of one built in the early 1940’s for the University of California. It was a giant, a hundred feet long and filled with thousands of parts. Not merely huge, it represented a significant stride ahead in that it could perform the operation of integration with respect to functions other than just time. Instead of being a “direct” analog, the new machine was an “indirect” analog, a model not of a physical thing but of the mathematics expressing it. Engineers realized that the mechanical beast, as they called it, represented something of a dinosaur in computer evolution and could not survive. Because of its size, it cost thousands of dollars merely to prepare a place for its installation. Besides, it was limited in the scope of its work.

During World War II, however, it was all we had, and beast or not, it worked around the clock solving engineering problems, ballistics equations, and the like. England did work in this field, and Meccano—counterpart of the Gilbert Erector Set firm in the United States—marketed a do-it-yourself differential analyzer. The Russians too built mechanical differential analyzers as early as 1940.

Electronics came to the rescue of the outsized mechanical analog computers during and after the war. Paced by firms like Reeves Instrument and Goodyear Aircraft, the electronic analog superseded the older mechanical type. There was of course a transitional period, and an example of this stage is the General Electric fire-control computer installed in the B-29. It embraced mechanical, electrical, and electronic parts to do just the sort of job ideally suited to the analog type of device: that of tracking a path through space and predicting the future position of a target so that the gunsight aims at the correct point in space for a hit.

Another military analog computer was the Q-5, used by the Signal Corps to locate enemy gun installations. From the track of a projectile on a radar screen, the Q-5 did some complicated mathematics to figure backwards and pinpoint the troublesome gun. There were industrial applications as well for the analog machine. In the 1950’s, General Electric built computers to solve simultaneous linear equations for the petroleum industry. To us ultimate users, gasoline poses only one big mathematical problem—paying for a tankful. Actually, the control operations involved in processing petroleum are terribly involved, and the special analog computer had to handle twelve equations with twelve unknown quantities simultaneously. This is the sort of problem that eats up man-years of human mathematical time; even a modern digital computer has tough and expensive going, but the analog does this work rapidly and economically.

Another interesting analog machine was called the Psychological Matrix Rotation Computer. This implemented an advanced technique called multiple-factor analysis, developed by Thurston of the University of Illinois for use in certain psychological work. Multiple-factor analysis is employed in making up the attribute tests used by industry and the military services for putting the right man in the right job. An excellent method, it was too time-consuming for anything but rough approximations until the analog computer was built for it. In effect, the computer worked in twelve dimensions, correlating traits and aptitudes. It was delivered to the Adjutant General’s Office and is still being used, so Army men who wonder how their background as baker qualifies them for the typing pool may have the Psychological Matrix Rotation Computer to thank.

In the early 1950’s, world tension prompted the building of another advanced analog computer, this one a jet engine simulator. Prior to its use, it took about four years to design, build, and test a new jet engine. Using the simulator, the time was pared to half that amount. It was a big computer, even though it was electronic. More than 6,000 vacuum tubes, 1,700 indicator lights, and 2,750 dials were hooked up with more than 25 miles of wire, using about 400,000 interconnections. All of this required quite a bit of electrical power, about what it would take to operate fifty kitchen ranges. But it performed in “real” time, and could keep tabs on an individual molecule of gas from the time it entered the jet intake until it was ejected out the afterburner!

Other analog computers were developed for utility companies to control the dispatching of power to various consumers in the most efficient manner. Again the principle was simply to build a model or analog of an actual physical system and use it to predict the outcome of operation of that system.

From our brief skim of the history of the analog computer we can recognize several things about this type of machine. Since the analog is a simulator in most cases, we would naturally expect it to be a special-purpose machine. In other words, if we had a hundred different kinds of problems, and had to build a model of each, we would end up with a hundred special-purpose computers. It follows too that the analog computer will often be a part of the system it serves, rather than a separate piece of equipment.

[Illustration:

_The Boeing Co._

Analog machine used as flight simulator for jet airliner; a means of testing before building. ]

There are general-purpose analog computers, of course, designed for solving a broad class of problems. They are usually separate units, instead of part of the system. We can further break down the general-purpose analog computer into two types; direct and indirect. A direct analog is exemplified in the tank gauge consisting of a float with a scale attached. An indirect analog, such as the General Electric monster built for the University of California mentioned earlier, can use one dependent variable, such as voltage, to represent all the variables of the prototype. Such an analog machine is useful in automatic control and automation processes.

Finally, we may subdivide our direct analog computer one further step into “discrete” analogs or “continuous” analogs. The term “discrete” is the quality we have ascribed to the digital computer, and a discrete analog is indicative of the overlap that occurs between the two types. Another example of this overlap is the representation of “continuous” quantities by the “step-function” method in a digital device. As we shall see when we discuss hybrid or analog-digital computers, such overlap is as beneficial as it is necessary.

[Illustration:

_General Motors Corp._

Large analog computer in rear controls car, subjecting driver to realistic bumps, pitches, and rolls, for working out suspension problems of car. ]

We are familiar now with mechanical, electromechanical, and fully electronic analogs. Early machines used rods of certain lengths, cams, gears, and levers. Fully electronic devices substitute resistors, capacitors, and inductances for these mechanical components, adding voltages instead of revolutions of shafts, and counting turns of wire in a potentiometer instead of teeth on a gear. Engineers and technicians use terms like “mixer,” “integrator,” and “rate component,” but we may consider the analog computer as composed of passive networks plus amplifiers where necessary to boost a faint signal.

Some consideration of what we have been discussing will give us an indication of the advantages of the analog computer over the digital type. First and most obvious, perhaps, is that of simplicity. A digital device for recording temperature could be built; but it would hardly improve on the simplicity of the ordinary thermometer. Speed is another desirable attribute of most analog computers. Since operation is parallel, with all parts of the problem being worked on at once, the answer is reached quickly. This is of particular importance in “on-line” application where the computer is being used to control, let us say, an automatic machining operation in a factory. Even in a high-speed electronic digital computer there is a finite lag due to the speed of electrons. This “slack” is not present in a direct analog and thus there is no loss of precious time that could mean the difference between a rejected and a perfect part from the lathe.

It follows from these very advantages that there are drawbacks too. The analog computer that automatically profiles a propeller blade in a metalworking machine cannot mix paint to specifications or control the speed of a subway train unless it is a very special kind of general-purpose analog that would most likely be the size of Grand Central Station and sell for a good part of the national debt. Most analogs have one particular job they are designed for; they are specialists with all the limitations that the word implies.

There is one other major disadvantage that our analog suffers by its very nature. We can tolerate the approximate answer 3.98 instead of 4, because most of us recognize the correct product of 2 times 2. But few production managers would want to use 398 rivets if it took 400 to do the job safely—neither would they want to use 402 and waste material. Put bluntly, the analog computer is less accurate than its digital cousin. It delivers answers not in discrete units, but approximations, depending on the accuracy of its own parts and its design. Calculo, an electrical-analog computer produced for science students, has an advertised accuracy of 5 per cent at a cost of about $20. The makers frankly call it an “estimator.” This is excellent for illustrating the principles of analog machines to interested youngsters, but the students could have mathematical accuracy of 100 per cent from a digital computer called the abacus at a cost of less than a dollar.

Greater accuracy in the analog computer is bought at the expense of costlier components. Up to accuracies of about 1 per cent error it is usually cheaper to build an analog device than a digital, assuming such a degree of accuracy is sufficient, of course. Analog accuracies ten times the 1 per cent figure are feasible, but beyond that point costs rise very sharply and the digital machine becomes increasingly attractive from a dollars and cents standpoint. Designers feel that accuracies within 0.01 per cent are pushing the barriers of practicality, and 0.001 per cent probably represents the ultimate achievable. Thus the digital computer has the decided edge in accuracy, if we make some realistic allowances. For example, the best digital machine when asked to divide 10 by 3 can never give an exact answer, but is bound to keep printing 3’s after the decimal point!

There are other differences between our two types of computers, among them being the less obvious fact that it is harder to make a self-checking analog computer than it is to build the same feature into the digital. However, the most important differences are those of accuracy and flexibility.

For these reasons, the digital computer today is in the ascendant, although the analog continues to have its place and many are in operation in a variety of chores. We have mentioned fire control and the B-29 gunsight computer in particular. This was a pioneer airborne computer, and proved that an analog could be built light enough for such applications. However, most fire-control computers are earthbound because of their size and complexity. A good example is the ballistic computer necessary for the guns on a battleship. In addition to the normal problem of figuring azimuth and elevation to place a shell on target, the gun aboard ship has the additional factors of pitch, roll, and yaw to contend with. These inputs happen to be ideal for analog insertion, and a properly designed computer makes corrections instantaneously as they are fed into it.

A fertile field for the analog computer from the start was that of industrial process control. Chemical plants, petroleum refineries, power generating stations, and some manufacturing processes lend themselves to control by analog computers. The simplicity and economy of the “modeling” principle, plus the instantaneous operation of the analog, made it suitable for “on-line” or “on-stream” applications.

The analog computer has been described as useful in the design of engines; it also helps design the aircraft in which these engines are used, and even simulates their flight. A logical extension of this use is the training of pilots in such flight simulators. One interesting analog simulator built by Goodyear Aircraft Corporation studied the reactions of a pilot to certain flight conditions and then was able to make these reactions itself so faithfully that the pilot was unaware that the computer and not his own brain was accomplishing the task.

The disciplines of geometry, calculus, differential equations, and other similar mathematics profit from the analog computer which is able to make a model of their curves and configurations and thus greatly speed calculations. Since the analog is so closely tied to the physical rather than the mental world, it cannot cope with discrete numbers, and formal logic is not its cup of tea.

Surely, progress has been made and improvements continue to be designed into modern analog computers. Repetitive operations can now be done automatically at high speed, and the computer even has a memory. High-speed analog storage permits the machine to make sequential calculations, a job once reserved for the digital computer. But even these advances cannot offset the basic limitations the analog computer is heir to.

Fewer analog machines are being built now, and many in existence do not enjoy the busy schedule of the digital machines. As the mountains of data pile up, created incidentally by computers in the first place, more computers are needed to handle and make sense of them. It is easier to interpret, store, and transmit digital information than analog; the digital computer therefore takes over this important task.

Even in control systems the digital machine is gaining popularity; its tremendous speed offsets its inherent cumbersomeness and its accuracy tips the scales more in its favor. These advantages will be more apparent as we discuss the digital machine on the next pages and explain the trend toward the hybrid machine, ever becoming more useful in the computer market place. Of course, there will always be a place for the pure analog—just as there has always been for any specialist, no matter what his field.

_The Digital Counter_

The digital computer was first on the scene and it appears now that it will outnumber and perhaps outlive its analog relative. A simple computer of this type is as old as man, though it is doubtful that it has been in use that long. Proof of this claim to its pioneering are the words _digit_ and _calculi_, for finger and pebbles, respectively. We counted “how many” before we measured “how large,” and the old Romans tallied on fingers until they ran out and then supplemented with pebbles.

Perhaps the first computations more complex than simple counting of wives or flocks came about when some wag found that he could ascertain the number of sheep by counting legs and dividing by four. When it was learned that the thing worked both ways and that the number of pickled pigs feet was four times the number of pigs processed, arithmetic was born. The important difference between analog and digital, of course, is that the latter is a means of counting, a dealing with discrete numbers rather than measuring.

This kind of computation was taxed sorely when such things as fractions and relationships like _pi_ came along, but even then man has managed to continue dealing with numbers themselves rather than quantity. Just as the slide rule is a handy symbol for the analog computer, the abacus serves us nicely to illustrate the digital type, and some schools make a practice of teaching simple arithmetic to youngsters in this manner.

Our chapter on the history of the computer touched on early efforts in the digital field, though no stress was laid on the distinction between types. We might review a bit, and pick out which of the mechanical calculating devices were actually digital. The first obviously was the abacus. It was also the only one for a long time. Having discovered the principle of analogy, man leaned in that direction for many centuries, and clocks, celestial simulators, and other devices were analog in nature. Purists point out that even the counting machines of Pascal and Leibnitz were analog computers, since they dealt with the turning of shafts and gears rather than the manipulation of digits. The same reasoning has caused some debate about Babbage’s great machines in the 1800’s, although they are generally considered a digital approach to problem-solving. Perhaps logicians had as much as anyone to do with the increasing popularity of the digital trend when they pointed out the advantages of a binary or two-valued system.

With the completion in 1946 by Eckert and Mauchly of the electronic marvel they dubbed ENIAC, the modern digital computer had arrived and the floodgates were opened for the thousands of descendants that have followed. For every analog computer now being built there are dozens or perhaps hundreds of digital types. Such popularity must be deserved, so let us examine the creature in an attempt to find the reason.

[Illustration:

Courtesy of the _National Science Foundation_

The computer family tree. Its remarkable growth began with government-supported research, continued in the universities; and the current generation was developed primarily in private industry. ]

We said that by its nature the analog device tended to be a special-purpose computer. The digital computer, perhaps because its basic operation is so childishly simple, is best suited for general-purpose work. It is simple, consisting essentially of switches that are either on or off. Yet Leibnitz found beauty in that simplicity, and even the explanation of the universe. Proper interconnection of sufficient on-off switches makes possible the most flexible of all computers—man’s brain. By the same token, man-made computers of the digital type can do a wider variety of jobs than can the analog which seemingly is more sophisticated.

A second great virtue of the digital machine is its accuracy. Even a trial machine of Babbage had a 5-place accuracy. This is an error of only one part in ten thousand, achievable in the analog at great expense. This was of course only a preliminary model, and the English inventor planned 20-place accuracy in his dream computer. Present electronic digital computers offer 10-place accuracy as commonplace, a precision impossible of achievement in the analog.

We pointed out in the discussion of analog computers that the complexity and expense of increased accuracy was in direct proportion to the degree of accuracy desired. Happily for the digital machine, the reverse is true in its case. Increasing accuracy from five to six figures requires a premium of one-fifth, or 20 per cent. But jumping from 10-place to 11-place precision costs us only 10 per cent, and from 20-place to 21-place drops to just 5 per cent.

Actually, such a high degree of accuracy is not necessary in most practical applications. For example, the multiplication of 10-digit numbers may yield a 20-digit answer. If we desired, we could increase the capability of our digital computer to twenty digits and give an accuracy of one part in 10 million trillion! However, we simply “round off” the last ten digits and leave the answer in ten figures, an accuracy no analog computer can match. The significant point is that the analog can never hope to compete with digital types for accuracy.