COMPUTERS—THE MACHINES WE THINK WITH
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Computers—
THE MACHINES WE THINK WITH
D. S. HALACY, JR.
[Illustration]
HARPER & ROW, PUBLISHERS
NEW YORK, EVANSTON, AND LONDON
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COMPUTERS—THE MACHINES WE THINK WITH. _Copyright © 1962, by Daniel S.
Halacy, Jr. Printed in the United States of America. All rights in this
book are reserved. No part of the book may be used or reproduced in any
manner whatsoever without written permission except in the case of brief
quotations embodied in critical articles and reviews. For information
address Harper & Row, Publishers, Incorporated, 49 East 33rd Street, New
York 16, N.Y._
_Library of Congress catalog card number: 62-14564_
F-S
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Contents
1. Computers—The Machines We Think With 1
2. The Computer’s Past 18
3. How Computers Work 48
4. Computer Cousins—Analog and Digital 72
5. The Binary Boolean Bit 96
6. The Electronic Brain 121
7. Uncle Sam’s Computers 147
8. The Computer in Business and Industry 171
9. The Computer and Automation 201
10. The Academic Computer 219
11. The Road Ahead 251
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COMPUTERS—THE MACHINES WE THINK WITH
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1: Computers—The Machines
We Think With
While you are reading this sentence, an electronic computer is
performing 3 million mathematical operations! Before you read this page,
another computer could translate it and several others into a foreign
language. Electronic “brains” are taking over chores that include the
calculation of everything from automobile parking fees to zero hour for
space missile launchings.
Despite bitter winter weather, a recent conference on computers drew
some 4,000 delegates to Washington, D.C.; indicating the importance and
scope of the new industry. The 1962 domestic market for computers and
associated equipment is estimated at just under $3 billion, with more
than 150,000 people employed in manufacture, operation, and maintenance
of the machines.
In the short time since the first electronic computer made its
appearance, these thinking machines have made such fantastic strides in
so many different directions that most of us are unaware how much our
lives are already being affected by them. Banking, for example, employs
complex machines that process checks and handle accounts so much faster
than human bookkeepers that they do more than an hour’s work in less
than thirty seconds.
[Illustration:
_General Electric Co., Computer Dept._
Programmer at console of computer used in electronic processing of
bank checking accounts.
]
Our government is one of the largest users of computers and
“data-processing machines.” The census depends on such equipment, and it
played a part in the development of early mechanical types of computers
when Hollerith invented a punched-card system many years ago. In another
application, the post office uses letter readers that scan addresses and
sort mail at speeds faster than the human eye can keep up with. Many
magazines have put these electronic readers to work whizzing through
mailing lists.
[Illustration:
_General Electric Co., Computer Dept._
Numbers across bottom of check are printed in magnetic ink and can be
read by the computer.
]
In Sweden, writer Astrid Lindgren received additional royalties for one
year of 9,000 _kronor_ because of library loans. Since this was based on
850,000 total loans of her books from thousands of schools and
libraries, the bookkeeping was possible only with an electronic
computer.
Computers are beginning to take over control of factories, steel mills,
bakeries, chemical plants, and even the manufacture of ice cream. In
scientific research, computers are solving mathematical and logical
problems so complex that they would go forever unsolved if men had to do
the work. One of the largest computing systems yet designed,
incorporating half a million transistors and millions of other parts,
handles ticket reservations for the airlines. Others do flight planning
and air traffic control itself.
Gigantic computerized air defense systems like SAGE and NORAD help guard
us from enemy attack. When John Glenn made his space flight, giant
computers on the ground made the vital calculations to bring him safely
back. Tiny computers in space vehicles themselves have proved they can
survive the shocks of launching and the environment of space. These
airborne computers make possible the operation of Polaris, Atlas, and
Minuteman missiles. Such applications are indicative of the scope of
computer technology today; the ground-based machines are huge, taking up
rooms and even entire buildings while those tailored for missiles may
fit in the palm of the hand. One current military project is such an
airborne computer, the size of a pack of cigarettes yet able to perform
thousands of mathematical and logical operations a second.
Computers are a vital part of automation, and already they are running
production lines and railroads, making mechanical drawings and weather
predictions, and figuring statistics for insurance companies as well as
odds for gamblers. Electronic machines permit the blind to read a page
of ordinary type, and also control material patterns in knitting mills.
This last use is of particular interest since it represents almost a
full circle in computer science. Oddly, it was the loom that inspired
the first punched cards invented and used to good advantage by the
French designer Jacquard. These homely forerunners of stored information
sparked the science that now returns to control the mills.
Men very wisely are now letting computers design other computers, and in
one recent project a Bell Laboratories computer did a job in twenty-five
minutes that would have taken a human designer a month. Even more
challenging are the modern-day “robots” performing precision operations
in industrial plants. One such, called “Unimate,” is simply guided
through the mechanical operations one time, and can then handle the job
alone. “TransfeRobot 200” is already doing assembly-line work in dozens
of plants.
The hope has been expressed that computer extension of our brainpower by
a thousandfold would give our country a lead over potential enemies.
This is a rather vain hope, since the United States has no corner on the
computer market. There is worldwide interest in computers, and machines
are being built in Russia, England, France, Germany, Switzerland,
Holland, Sweden, Africa, Japan, and other countries. A remarkable
computer in Japan recognizes 8,000 colors and analyzes them instantly.
Computer translation from one language to another has been mentioned,
and work is even being done on machines that will permit us to speak
English into a phone in this country and have it come out French, or
whatever we will, overseas! Of course, computers have a terminology all
their own too; words like analog and digital, memory cores, clock rates,
and so on.
The broad application of computers has been called the “second
industrial revolution.” What the steam engine did for muscles, the
modern computer is beginning to do for our brains. In their slow climb
from caveman days, humans have encountered ever more problems; one of
the biggest of these problems eventually came to be merely how to solve
all the other problems.
At first man counted on his fingers, and then his toes. As the problems
grew in size, he used pebbles and sticks, and finally beads. These
became the abacus, a clever calculating device still in constant use in
many parts of the world. Only now, with the advent of low-cost
computers, are the Japanese turning from the _soroban_, their version of
the abacus.
The large-scale computers we are becoming familiar with are not really
as new as they seem. An Englishman named Babbage built what he called
a “difference engine” way back in 1831. This complex mechanical
computer cost a huge sum even by today’s standards, and although it
was never completed to Babbage’s satisfaction, it was the forerunner
and model for the successful large computers that began to appear a
hundred years later. In the meantime, of course, electronics has come
to the aid of the designer. Today, computer switches operate at
billionths-of-a-second speeds and thus make possible the rapid
handling of quantities of work like the 14 billion checks we
Americans wrote in 1961.
There are dozens of companies now in the computer manufacturing field,
producing a variety of machines ranging in price from less than a
hundred dollars total price to rental fees of $100,000 a month or more.
Even at these higher prices the big problem of some manufacturers is to
keep up with demand. A $1 billion market in 1960, the computer field is
predicted to climb to $5 billion by 1965, and after that it is anyone’s
guess. Thus far all expert predictions have proved extremely
conservative.
The path of computer progress is not always smooth. Recently a computer
which had been installed on a toll road to calculate charges was so
badly treated by motorists it had to be removed. Another unfortunate
occurrence happened on Wall Street. A clever man juggled the controls of
a large computer used in stock-market work and “made” himself a quarter
of a million dollars, though he ultimately landed in jail for his
illegal computer button pushing. Interestingly, there is one corrective
institution which already offers a course in computer engineering for
its inmates.
So great is the impact of computers that lawyers recently met for a
three-day conference on the legal aspects of the new machines. Points
taken up included: Can business records on magnetic tape or other
storage media be used as evidence? Can companies be charged with
mismanagement for not using computers in their business? How can
confidential material be handled satisfactorily on computers?
Along with computing machines a whole new technology is growing.
Universities and colleges—even high schools—are teaching courses in
computers. And the computer itself is getting into the teaching business
too. The “teaching machine” is one of the most challenging computer
developments to come along so far. These mechanical professors range
from simple “programmed” notebooks, such as the Book of Knowledge and
Encyclopedia Britannica are experimenting with, to complex computerized
systems such as that developed by U.S. Industries, Inc., for the Air
Force and others.
The computer as a teaching machine immediately raises the question of
intelligence, and whether or not the computer has any. Debate waxes hot
on this subject; but perhaps one authority was only half joking when he
said that the computer designer’s competition was a unit about the size
of a grapefruit, using only a tenth of a volt of electricity, with a
memory 10,000 times as extensive as any existing electronic computer.
This is a brief description of the human brain, of course.
When the first computers appeared, those like ENIAC and BINAC, fiction
writers and even some science writers had a field day turning the
machines into diabolical “brains.” Whether or not the computer really
thinks remains a controversial question. Some top scientists claim that
the computer will eventually be far smarter than its human builder;
equally reputable authorities are just as sure that no computer will
ever have an original thought in its head. Perhaps a safe middle road is
expressed with the title of this book; namely that the machine is simply
an extension of the human brain. A high-speed abacus or slide rule, if
you will; accurate and foolproof, but a moron nonetheless.
There are some interesting machine-brain parallels, of course. Besides
its ability to do mathematics, the computer can perform logical
reasoning and even make decisions. It can read and translate;
remembering is a basic part of its function. Scientists are now even
talking of making computers “dream” in an attempt to come up with new
ideas!
More similarities are being discovered or suggested. For instance, the
interconnections in a computer are being compared with, and even crudely
patterned after, the brain’s neurons. A new scientific discipline,
called “bionics,” concerns itself with such studies. Far from being a
one-way street, bionics works both ways so that engineers and biologists
alike benefit. In fact, some new courses being taught in universities
are designed to “bridge the gap between engineering and biology.”
At one time the only learning a computer had was “soldered in”; today
the machines are being “forced” to learn by the application of
punishment or reward as necessary. “Free” learning in computers of the
Perceptron class is being experimented with. These studies, and
statements like those of renowned scientist Linus Pauling that he
expects a “molecular theory” of learning in human beings to be
developed, are food for thought as we consider the parallels our
electronic machines share with us. Psychologists at the University of
London foresee computers not only training humans, but actually watching
over them and predicting imminent nervous breakdowns in their charges!
[Illustration:
_Cornell Aeronautical Laboratory_
Bank of “association” units in Mark I Perceptron, a machine that
“learns” from experience.
]
To demonstrate their skill many computers play games of tick-tack-toe,
checkers, chess, Nim, and the like. A simple electromechanical computer
designed for young people to build can be programmed to play
tick-tack-toe expertly. Checker- and chess-playing computers are more
sophisticated, many of them learning as they play and capable of an
occasional move classed as brilliant by expert human players. The IBM
704 computer has been programmed to inspect the results of its possible
decisions several moves ahead and to select the best choice. At the end
of the game it prints out the winner and thanks its opponent for the
game. Rated as polite, but only an indifferent player by experts, the
computer is much like the checker-playing dog whose master scoffed at
him for getting beaten three games out of five. Chess may well be an
ultimate challenge for any kind of brain, since the fastest computer in
operation today could not possibly work out all the possible moves in a
game during a human lifetime!
As evidenced in the science-fiction treatment early machines got, the
first computers were monsters at least in size. Pioneering design
efforts on machines with the capacity of the brain led to plans for
something roughly the size of the Pentagon, equipped with its own
Niagara for power and cooling, and a price tag the world couldn’t
afford. As often seems to happen when a need arises, though, new
developments have come along to offset the initial obstacles of size and
cost.
One such development was the transistor and other semiconductor devices.
Tiny and rugged, these components require little power. With the old
vacuum-tubes replaced, computers shrank immediately and dramatically. On
the heels of this micro-miniaturization have come new and even smaller
devices called “ferrite cores” and “cryotrons” using magnetism and
supercold temperatures instead of conventional electronic techniques.
As a result, an amazing number of parts can be packed into a tiny
volume. So-called “molecular electronics” now seems to be a possibility,
and designers of computers have a gleam in their eyes as they consider
progress being made toward matching the “packaging density” of the
brain. This human computer has an estimated 100 billion parts per cubic
foot!
We have talked of reading and translating. Some new computers can also
accept voice commands and speak themselves. Others furnish information
in typed or printed form, punched cards, or a display on a tube or
screen.
Like us, the computer can be frustrated by a task beyond its
capabilities. A wrong command can set its parts clicking rapidly but in
futile circles. Early computers, for example, could be panicked by the
order to divide a number by zero. The solution to that problem of course
is infinity, and the poor machine had a hard time trying to make such an
answer good.
[Illustration:
_Aeronutronic Division, Ford Motor Co._
This printed-circuit card contains more than 300 BIAX memory elements.
Multiples of such cards mounted in computers store large amounts of
information.
]
There are other, quainter stories like that of the pioneer General
Electric computer that simply could not function in the dark. All day
long it hummed efficiently, but problems left with it overnight came out
horribly botched for no reason that engineers could discover. At last it
was found that a light had to be left burning with the scary machine!
Neon bulbs in the computer were enough affected by light and darkness
that the delicate electronic balance of the machine had been upset.
Among the computer’s unusual talents is the ability to compose music.
Such music has been published and is of a quality to give rise to
thoughtful speculation that perhaps great composers are simply good
selectors of music. In other words, all the combinations of notes and
meter exist: the composer just picks the right ones. No less an
authority than Aaron Copland suggests that “we’ll get our new music by
feeding information into an electronic computer.” Not content with
merely writing music, some computers can even play a tune. At Christmas
time, carols are rendered by computers specially programmed for the
task. The result is not unlike a melody played on a pipe organ.
In an interesting switch of this musical ability on the part of the
machine, Russian engineers check the reliability of their computers by
having them memorize Mozart and Grieg. Each part of the complex machines
is assigned a definite musical value, and when the composition is
“played back” by the computer, the engineer can spot any defects
existing in its circuitry. Such computer maintenance would seem to be an
ideal field for the music lover.
In a playful mood, computers match pennies with visitors, explain their
inner workings as they whiz through complex mathematics, and are even
capable of what is called heuristic reasoning. This amounts to playing
hunches to reach short-cut solutions to otherwise unsolvable problems. A
Rand Corporation computer named JOHNNIAC demonstrated this recently. It
was given some basic axioms and asked to prove some theorems. JOHNNIAC
came up with the answers, and in one case produced a proof that was
simpler than that given in the text. As one scientist puts it, “If
computers don’t really think, they at least put on a pretty creditable
imitation of the real thing.”
Computers are here to stay; this has been established beyond doubt. The
only question remaining is how fast the predictions made by dreamers and
science-fiction writers—and now by sober scientists—will come to be a
reality. When we consider that in the few years since the 1953 crop of
computers, their capacity and speed has been increased more than
fiftyfold, and is expected to jump another thousandfold in two years,
these dreams begin to sound more and more plausible.
One quite probable use for computers is medical diagnosis and
prescription of treatment. Electronic equipment can already monitor an
ailing patient, and send an alarm when help is needed. We may one day
see computers with a built-in bedside manner aiding the family doctor.
The accomplished inroads of computing machines in business are as
nothing to what will eventually take place. Already computer
“game-playing” has extended to business management, and serious
executives participate to improve their administrative ability. We speak
of decision-making machines; business decisions are logical applications
for this ability. Computers have been given the job of evaluating
personnel and assigning salaries on a strictly logical basis. Perhaps
this is why in surveys questioning increased use of the machines, each
executive level in general tends to rate the machine’s ability just
below its own.
Other games played by the computer are war games, and computers like
SAGE are well known. This system not only monitors all air activity but
also makes decisions, assigns targets, and then even flies the
interceptor planes and guided missiles on their missions. Again in the
sky, the increase of commercial air traffic has perhaps reached the
limit of human ability to control it. Computers are beginning to take
over here too, planning flights and literally flying the planes.
Surface transport can also be computer-controlled. Railroads are
beginning to use the computer techniques, and automatic highways are
inevitable. Ships also benefit, and special systems coupled to radar can
predict courses and take corrective action when necessary.
Men seem to have temporarily given up trying to control the weather, but
using computers, meteorologists can take the huge mass of data from all
over the world and make predictions rapidly enough to be of use.
We have talked of the computer’s giant strides in banking. Its wide use
in stores is not far off. An English computer firm has designed an
automatic supermarket that assembles ordered items, prices them, and
delivers them to the check stand. At the same time it keeps a running
inventory, price record, and profit and loss statement, besides billing
the customer with periodic statements. The storekeeper will have only to
wash the windows and pay his electric power bill.
Even trading stamps may be superseded by computer techniques that keep
track of customer purchases and credit him with premiums as he earns
them. Credit cards have helped pioneer computer use in billing; it is
not farfetched to foresee the day when we are issued a lifetime,
all-inclusive credit card—perhaps with our birth certificate!—a card
with our thumbprint on it, that will buy our food, pay our rent and
utilities and other bills. A central computer system will balance our
expenses against deposits and from time to time let us know how we stand
financially.
As with many other important inventions, the computer and its technology
were spurred by war and are aided now by continuing threats of war. It
is therefore pleasant to think on the possibilities of a computer system
“programmed” for peace: a gigantic, worldwide system whose input
includes all recorded history of all nations, all economic and cultural
data, all weather information and other scientific knowledge. The output
of such a machine hopefully would be a “best plan” for all of us. Such a
computer would have no ax to grind and no selfish interests unless they
were fed into it.
Given all the facts, it would punch out for us a set of instructions
that would guarantee us the best life possible. This has long been a
dream of science writers. H. G. Wells was one of these, suggesting a
world clearinghouse of information in his book _World Brain_ written in
the thirties. In this country, scientist Vannevar Bush suggested a
similar computer called “Memex” which could store huge amounts of data
and answer questions put to it.
The huge amounts of information—books, articles, speeches, and records
of all sorts—are beginning to make it absolutely necessary for an
efficient information retrieval system. Many cases have been noted in
which much time and effort are spent on a project which has already been
completed but then has become lost in the welter of literature crammed
into libraries. The computer is a logical device for such work; in a
recent test such a machine scored 86 per cent in its efforts to locate
specific data on file. Trained workers rated only 38 per cent in the
same test!
[Illustration:
_The Boeing Co._
Engineers using computers to solve complex problems in aircraft
design.
]
The science of communication is advancing along with that of computers,
and can help make the dream of a worldwide “brain” come true. Computers
in distant cities are now linked by telephone lines or radio, and
high-speed techniques permit the transmission of many thousands of words
per _second_ across these “data links.” An interesting sidelight is the
fact that an ailing computer can be hooked by telephone line with a
repair center many miles away and its ailments diagnosed by remote
control. Communications satellites that are soon to be dotting the sky
like tiny moons may well play a big part in computing systems of the
future. Global weather prediction and worldwide coordination of trade
immediately come to mind.
While we envision such far-reaching applications, let’s not lose sight
of the possibilities for computer use closer to home—right in our homes,
as a matter of fact. Just as early inventors of mechanical power devices
did not foresee the day when electric drills and saws for hobbyist would
be commonplace and the gasoline engine would do such everyday chores as
cutting the grass in our yards, the makers of computers today cannot
predict how far the computer will go in this direction. Perhaps we may
one day buy a “Little Dandy Electro-Brain” and plug it into the wall
socket for solving many of the everyday problems we now often guess
wrong on.
[Illustration:
_Royal McBee Corp._
Students at Staples High School, Westport, Connecticut, attend a
summer session to learn the techniques of programming and operating
an electronic computer.
]
[Illustration:
_The Saturday Evening Post_
“Herbert’s been replaced by an electronic brain—one of the simpler
types.”
]
Some years ago a group of experts predicted that by 1967 the world
champion chess player would be an electronic computer. No one has yet
claimed that we would have a president of metal and wire, but some
interesting signposts are being put up. Computers are now used widely to
predict the result of elections. Computers count the votes, and some
have suggested that computers could make it possible for us to vote at
home. The government is investigating the effectiveness of a
decision-making computer as a stand-by aid for the President in this
complex age we are moving into. No man has the ability to weigh every
factor and to make decisions affecting the world. Perhaps a computer can
serve in an advisory capacity to a president or to a World Council;
perhaps—
It is comforting to remember that men will always tell the computer what
it is supposed to do. No computer will ever run the world any more than
the cotton gin or the steam engine or television runs the world. And in
an emergency, we can always pull out the wallplug, can’t we?
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“_History is but the unrolled scroll of prophecy._”
—James A. Garfield
2: The Computer’s Past
Although it seemed to burst upon us suddenly, the jet airplane can trace
its beginnings back through the fabric wings of the Wrights to the wax
wings of Icarus and Daedalus, and the steam aerophile of Hero in ancient
Greece. The same thing is true of the computer, the “thinking machine”
we are just now becoming uncomfortably aware of. No brash upstart, it
has a long and honorable history.
Naturalists tell us that man is not the only animal that counts. Birds,
particularly, also have an idea of numbers. Birds, incidentally, use
tools too. We seem to have done more with the discoveries than our
feathered friends; at least no one has yet observed a robin with a slide
rule or a snowy egret punching the controls of an electronic digital
computer. However, the very notion of mere birds being tool and number
users does give us an idea of the antiquity and lengthy heritage of the
computer.
The computer was inevitable when man first began to make his own
problems. When he lived as an animal, life was far simpler, and all he
had to worry about was finding game and plants to eat, and keeping from
being eaten or otherwise killed himself. But when he began to dabble in
agriculture and the raising of flocks, when he began to think
consciously and to reflect about things, man needed help.
First came the hand tools that made him more powerful, the spears and
bows and arrows and clubs that killed game and enemies. Then came the
tools to aid his waking brain. Some 25,000 years ago, man began to
count. This was no mean achievement, the dim, foggy dawning of the
concept of number, perhaps in the caves in Europe where the walls have
been found marked with realistic drawings of bison. Some budding
mathematical genius in a skin garment only slightly shaggier than his
mop of hair stared blinking at the drawings of two animals and then
dropped his gaze to his two hands. A crude, tentative connection jelled
in his inchoate gray matter and he shook his head as if it hurt. It was
enough to hurt, this discovery of “number,” and perhaps this particular
pioneer never again put two and two together. But others did; if not
that year, the next.
Armed with his grasp of numbers, man didn’t need to draw two mastodons,
or sheep, or whatever. Two pebbles would do, or two leaves or two
sticks. He could count his children on his fingers—we retain the
expression “a handful” to this day, though often our children are
another sort of handful. Of course, the caveman did not of a sudden do
sums and multiplications. When he began to write, perhaps 5,000 years
later, he had formed the concept of “one,” “two,” “several,” and “many.”
Besides counting his flock and his children, and the number of the
enemy, man had need for counting in another way. There were the seasons
of the year, and a farmer or breeder had to have a way of reckoning the
approach of new life. His calendar may well have been the first
mathematical device sophisticated enough to be called a computer.
It was natural that numbers be associated with sex. The calendar was
related to the seasons and the bearing of young. The number three, for
example, took on mystic and potent connotation, representing as it did
man’s genitals. Indeed, numbers themselves came quaintly to have sex.
One, three, and the other odd numbers were male; the symmetrical, even
numbers logically were female.
The notion that man used the decimal system because of his ten fingers
and toes is general, but it was some time before this refinement took
place. Some early peoples clung to a simpler system with a base of only
two; and interestingly a tribe of Australian aborigines counts today
thus: _enea_ (1), _petchaval_ (2), _enea petchaval_ (3), _petchaval
petchaval_ (4). Before we look down our noses at this naïve system, let
us consider that high-speed electronic computers use only two values, 1
and 0.
But slowly symbols evolved for more and more numbers, numbers that at
first were fingers, and then perhaps knots tied in a strip of hide. This
crude counting aid persists today, and cowboys sometimes keep rough
tallies of a herd by knotting a string for every five that pass. Somehow
numbers took on other meanings, like those that figure in courtship in
certain Nigerian tribes. In their language, the number six also means “I
love you.” If the African belle is of a mind when her boyfriend tenderly
murmurs the magic number, she replies in like tone, “Eight!”, which
means “I feel the same way!”
From the dawn of history there have apparently been two classes of us
human beings, the “haves” and the “have nots.” Nowadays we get bills or
statements from our creditors; in early days, when a slate or clay
tablet was the document, a forerunner of the carbon copy or duplicate
paper developed. Tallies were marked for the amount of the debt, the
clay tablet was broken across the marks, and creditor and debtor each
took half. No chance for cheating, since a broken half would fit only
the proper mate!
Numbers at first applied only to discrete, or distinctly separate,
things. The scratches on a calendar, the tallies signifying the count of
a flock; these were more easily reckoned. The idea of another kind of
number inspired the first clocks. Here was a monumental breakthrough in
mathematics. Nature provided the sunrise that clearly marked the
beginning of each day; man himself thought to break the day into
“hours,” or parts of the whole. Such a division led eventually to
measurement of size and weight. Now early man knew not only how many
goats he had, but how many “hands” high they were, and how many “stones”
they weighed. This further division ordained another kind of mechanical
computer man must someday contrive—the analog.
The first counting machines used were pebbles or sea shells. For the
Stone Age businessman to carry around a handful of rocks for all his
transactions was at times awkward, and big deals may well have gone
unconsummated for want of a stone. Then some genius hit on the idea of
stringing shells on a bit of reed or hide; or more probably the necklace
came first as adornment and the utilitarian spotted it after this style
note had been added. At any rate, the portable adding machine became
available and our early day accountant grew adroit at sliding the beads
back and forth on the string. From here it was only a small step, taken
perhaps as early as 3000 B.C., to the rigid counter known as the abacus.
The word “counter” is one we use in everyday conversation. We buy stock
over the counter; some deals are under the counter. We all know what the
counter itself is—that wide board that holds the cash register and
separates us from the shopkeeper. At one time the cash register _was_
the counter; actually the counting board had rods of beads like the
abacus, or at least grooves in which beads could be moved. The totting
up of a transaction was done on the “counter”; it is still there
although we have forgotten whence came its name.
The most successful computer used for the next 5,000 years, the portable
counter, or the abacus, is a masterpiece of simplicity and
effectiveness. Though only a frame with several rows of beads, it is
sophisticated enough that as late as 1947 Kiyoshi Matsuzake of the
Japanese Ministry of Communications, armed with the Japanese version—a
_soroban_, bested Private Tom Wood of the U. S. Army of Occupation
punching the keys of an up-to-the-minute electric calculating machine in
four of five problem categories! Only recently have Japanese banks gone
over to modern calculators, and shopkeepers there and in other lands
still conduct business by this rule of thumb and forefinger.
[Illustration:
The abacus, ancient mechanical computer, is still in use in many parts
of the world. Here is the Japanese version, the _soroban_, with
problem being set up.
]
The name abacus comes to us by way of the Greek _abax_, meaning “dust.”
Scholars infer that early sums were done schoolboy fashion in Greece
with a stylus on a dusty slate, and that the word was carried over to
the mechanical counter. The design has changed but little over the years
and all abacuses bear a resemblance. The major difference is the number
of beads on each row, determined by the mathematical base used in the
particular country. Some in India, for example, were set up to handle
pounds and shillings for use in shops. Others have a base of twelve. The
majority, however, use the decimal system. Each row has seven beads,
with a runner separating one or two beads from the others. Some systems
use two beads on the narrow side, some only one; this is a mathematical
consideration with political implications, incidentally: The Japanese
_soroban_ has the single-bead design; Korea’s _son pan_ uses two. When
Japan took over Korea the two-bead models were tabu, and went out of use
until the Koreans were later able to win their independence again.
About the only thing added to the ancient abacus in recent years is a
movable arrow for marking the decimal point. W. D. Loy patented such a
gadget in the United States. Today the abacus remains a useful device,
not only for business, but also for the teaching of mathematics to
youngsters, who can literally “grasp their numbers.” For that reason it
ought also to be helpful to the blind, and as a therapeutic aid for
manual dexterity. Apparently caught up in the trend toward smaller
computers, the abacus has been miniaturized to the extent that it can be
worn as earrings or on a key chain.
Even with mechanical counters, early mathematicians needed written
numbers. The caveman’s straight-line scratches gave way to
hieroglyphics, to the Sumerian cuneiform “wedges,” to Roman numerals,
and finally to Hindu and Arabic. Until the numbers, 1, 2, 3, 4, 5, 6, 7,
8, 9, and that most wonderful of all, 0 or zero, computations of any but
the simplest type were apt to be laborious and time-consuming. Even
though the Romans and Greeks had evolved a decimal system, their
numbering was complex. To count to 999 in Greek required not ten numbers
but twenty-seven. The Roman number for 888 was DCCCLXXXVIII. Multiplying
CCXVII times XXIX yielded an answer of MMMMMMCCXCIII, to be sure, but
not without some difficulty. It required an abacus to do any kind of
multiplication or division.
Indeed, it was perhaps from the abacus that the clue to Arabic
simplicity came. The Babylonians, antedating the Greeks, had
nevertheless gone them one better in arithmetic by using a “place”
system. In other words, the position of a number denoted its value. The
Babylonians simply left an empty space between cuneiform number symbols
to show an empty space in this positional system. Sometime prior to 300
B.C. a clever mathematician tired of losing track and punched a dot in
his clay tablet to fill the empty space and avoid possible error.
The abacus shows these empty spaces on its rows of beads, too, and
finally the Hindus combined their nine numerals with a “dot with a hole
in it” and gave the mathematical world the zero. In Hindu it was _sifr_,
corrupted to _zephirium_ in Latin, and gives us today both cipher and
zero. This enigma of nothingness would one day be used by Leibnitz to
prove that God made the world; it would later become half the input of
the electronic computer! Meantime, it was developed independently in
various other parts of the world; the ancient Mayans being one example.
Impressed as we may be by an electronic computer, it may take some
charity to recognize its forebears in the scratchings on a rock. To call
the calendar a computer, we must in honesty add a qualifying term like
“passive.” The same applies to the abacus despite its movable counters.
But time, which produced the simple calendar, also furnished the
incentive for the first “active” computers too. The hourglass is a
primitive example, as is the sundial. Both had an input, a power source,
and a readout. The clock interestingly ended up with not a decimal
scheme, but one with a base of twelve. Early astronomers began
conventionally bunching days into groups of ten, and located different
stars on the horizon to mark the passage of the ten days. It was but a
step from here to use these “decans,” as they were called, to further
divide each night itself into segments. It turned out that 12 decans did
the trick, and since symmetry was a virtue the daylight was similarly
divided by twelve, giving us a day of 24 hours rather than 10 or 20.
From the simple hourglass and the more complex water clocks, the Greeks
progressed to some truly remarkable celestial motion computers. One of
these, built almost a hundred years before the birth of Christ, was
recently found on the sea bottom off the Greek island of Antikythera. It
had been aboard a ship which sank, and its discovery came as a surprise
to scholars since history recorded no such complex devices for that era.
The salvaged Greek computer was designed for astronomical work, showing
locations of stars, predicting eclipses, and describing various cycles
of heavenly bodies. Composed of dozens of gears, shafts, slip rings, and
accurately inscribed plates, it was a computer in the best sense of the
word and was not exceeded technically for many centuries.
The Greek engineer Vitruvius made an interesting observation when he
said, “All machinery is generated by Nature and the revolution of the
universe guides and controls. Our fathers took precedents from
Nature—developed the comforts of life by their inventions. They rendered
some things more convenient by machines and their revolutions.”
Hindsight and language being what they are, today we can make a nice
play on the word “revolution” as applied to the machine. The Antikythera
computer was a prime example of what Vitruvius was talking about.
Astronomy was such a complicated business that it was far simpler to
make a model of the many motions rather than diagram them or try to
retain them in his mind.
There were, of course, some die-hard classicists who decried the use of
machines to do the work of pure reasoning. Archytas, who probably
invented the screw—or at least discovered its mechanical
principle—attempted to apply such mechanical devices to the solving of
geometrical problems. For this he was taken to task by purist Plato who
sought to preserve the distinct division between “mind” and “machine.”
Yet the syllogistic philosophers themselves, with their major premise,
minor premise, and conclusion, were unwittingly setting the stage for a
different kind of computer—the logic machine. Plato would be horrified
today to see crude decks of cards, or simple electromechanical
contrivances, solving problems of “reason” far faster than he could; in
fact, as fast as the conditions could be set into them!
------------------------------------------------------------------------
_The Mechanics of Reason_
Aristotle fathered the syllogism, or at least was first to investigate
it rigorously. He defined it as a formal argument in which the
conclusion follows logically from the premises. There are four common
statements of this type:
All S (for is P (for
subject) predicate)
No S (for subject) is P
Some S (for is P
subject)
Some S (for is not P
subject)
Thus, Aristotle might say “All men are mortal” or “No men are immortal”
as his subject. Adding an M (middle term), “Aristotle is a man,” as a
minor premise, he could logically go on and conclude “Aristotle, being a
man, is thus mortal.” Of course the syllogism unwisely used, as it often
is, can lead to some ridiculously silly answers. “All tables have four
legs. Two men have four legs. Thus, two men equal a table.”
Despite the weaknesses of the syllogism, nevertheless it led eventually
to the science of symbolic logic. The pathway was circuitous, even
devious at times, but slowly the idea of putting thought down as letters
or numbers to be logically manipulated to reach proper conclusions
gained force and credence. While the Greeks did not have the final say,
they did have words for the subject as they did for nearly everything
else.
Let us leave the subject of pure logic for a moment and talk of another
kind of computing machine, that of the mechanical doer of work. In the
_Iliad_, Homer has Hephaestus, the god of natural fire and metalworking,
construct twenty three-wheeled chariots which propel themselves to and
fro bringing back messages and instructions from the councils of the
gods. These early automatons boasted pure gold wheels, and handles of
“curious cunning.”
Man has apparently been a lazy cuss from the start and began straightway
to dream of mechanical servants to do his chores. In an age of magic and
fear of the supernatural his dreams were fraught with such machines that
turned into evil monsters. The Hebrew “golem” was made in the shape of
man, but without a soul, and often got out of hand. Literature has
perpetuated the idea of machines running amok, as the broom in “The
Sorcerer’s Apprentice,” but there have been benevolent machines too.
Tik-Tok, a latter-day windup man in _The Road to Oz_, could think and
talk and do many other things men could do. He was not alive, of course,
but he had the saving grace of always doing just what he “was wound up
to do.”
Having touched on the subject of mechanical men, let us now return to
mechanical logic. Since the Greeks, many men have traveled the road of
reason, but some stand out more brightly, more colorfully, than others.
Such a standout was the Spanish monk Ramón Lull. Lull was born in 1232.
A court page, he rose in influence, married young, and had two children,
but did not settle down to married domesticity. A wildly reckless
romantic, he was given to such stunts as galloping his horse into church
in pursuit of some lady who caught his eye. One such escapade led to a
remorseful re-examination of himself, and dramatic conversion to
Christianity.
He began to write books in conventional praise of Christ, but early in
his writings a preoccupation with numbers appears. His _Book of
Contemplation_, for example, actually contains five books for the five
wounds of the Saviour, and forty subdivisions for the days He spent in
the wilderness. There are 365 chapters for daily reading, plus one for
reading only in leap years! Each chapter has ten paragraphs, symbolizing
the ten commandments, and three parts to each chapter. These multiplied
give thirty, for the pieces of silver. Beside religious and mystical
connotations, geometric terms are also used, and one interesting device
is the symbolizing of words and even phrases by letters. This ties in
neatly with syllogism. A sample follows:
… diversity is shown in the demonstration that the D makes of the E and
the F and the G with the I and the K, therefore the H has certain
scientific knowledge of Thy holy and glorious Trinity.
This was only prologue to the _Ars Magna_, the “Great Art” of Ramón
Lull. In 1274, the devout pilgrim climbed Mount Palma in search of
divine help in his writings. The result was the first recorded attempt
to use diagrams to discover and to prove non-mathematical truths.
Specifically, Lull determined that he could construct mechanical devices
that would perform logic to prove the validity of God’s word. Where
force, in the shape of the Crusades, had failed, Lull was convinced that
logical argument would win over the infidels, and he devoted his life to
the task.
Renouncing his estate, including his wife and children, Lull devoted
himself thenceforth solely to his Great Art. As a result of dreams he
had on Mount Palma, the basis for this work was the assumption of simple
premises or principles that are unquestionable. Lull arranged these
premises on rotating concentric circles. The first of these wheels of
logic was called A, standing for God. Arranged about the circumference
of the wheel were sixteen other letters symbolizing attributes of God.
The outer wheel also contained these letters. Rotating them produced 240
two-term combinations telling many things about God and His good. Other
wheels prepared sermons, advised physicians and scientists, and even
tackled such stumpers as “Where does the flame go when the candle is put
out?”
[Illustration:
From the _Enciclopedia universal illustrada_,
Barcelona, 1923
Lull’s wheel.
]
Unfortunately for Lull, even divine help did not guarantee him success.
He was stoned to death by infidels in Bugia, Africa, at the age of
eighty-three. All his wheelspinning logic was to no avail in advancing
the cause of Christianity there, and most mathematicians since have
scoffed at his naïve devices as having no real merit. Far from accepting
the _Ars Magna_, most scholars have been “Lulled into a secure sense of
falsity,” finding it as specious as indiscriminate syllogism.