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.
A third perhaps not as important advantage the digital machine has is
its compactness. We are speaking now of later computers, and not the
pioneer electromechanical giants, of course. The transistor and other
small semiconductor devices supplanted the larger tubes, and magnetic
cores took the place of cruder storage components. Now even more exotic
devices are quietly ousting these, as magnetic films and cryotrons begin
to be used in computers.
[Illustration:
_Science Materials Center_
BRAINIAC, another do-it-yourself computer. This digital machine is
here being programmed to solve a logic problem involving a will.
]