Charles Babbage and his accomplice,
Lady Lovelace, came very close to inventing the computer more than a
century before American engineers produced
ENIAC. The story
of the "Analytical Engine" is a tale of
two extraordinarily gifted and ill-fated British eccentrics whose
biographies might have been fabrications of Babbage's friend Charles
Dickens, if Dickens had been a science-fiction writer. Like many
contemporary software characters, these computer pioneers of the
Victorian age attracted as much attention with their unorthodox personal
lives as they did with their inventions.One of Babbage's biographies
is entitled Irascible Genius.. He was indeed a genius, to judge
by what he planned to achieve as well as what he did achieve. His
irascibility was notorious. Babbage was thoroughly British, stubbornly
eccentric, tenaciously visionary, sometimes scatterbrained, and quite
wealthy until he sank his fortune into his dream of building a
calculating engine.
Babbage invented the cowcatcher--that metal device on the front of
steam locomotives that sweeps errant cattle out of the way. He also
devised a means of analyzing entire industries, a method for studying
complex systems that became the foundation of the field of
operational research a hundred years later. When he applied his new
method of analysis to a study of the printing trade, his publishers were
so offended that they refused to accept any more of his books.
Undaunted, he applied his new method to the analysis of the postal
system of his day, and proved that the cost of accepting and assigning a
value to every piece of mail according to the distance it had to travel
was far more expensive than the cost of transporting it. The British
Post Office boosted its capabilities instantly and economically by
charging a flat rate, independent of the distance each piece had to
travel--the "penny post" that persists around the world to this day.
Babbage devised the first speedometer for railroads, and he published
the first comprehensive treatise on actuarial theory (thus helping to
create the insurance industry). He invented and solved ciphers and made
skeleton keys for "unpickable locks"--an interest in cryptanalysis that
he shared with later computer builders. He was the first to propose that
the weather of past years could be discovered by observing cycles of
tree rings. And he was passionate about more than a few crackpot ideas
that history has since proved to be nothing more than crackpot ideas.
His human relationships were as erratic as his intellectual
adventures, to judge from the number of lifelong public feuds Babbage
was known to have engaged in. Along with his running battles with the
Royal Societies, Babbage carried on a long polemic against organ-grinders
and street musicians. Babbage would write letters to editors about
street noise, and half the organ-grinders in London took to serenading
under Babbage's window when they were in their cups. One biographer, B.
V. Bowden, noted that "It was the tragedy of the man that, although his
imagination and vision were unbounded, his judgment by no means matched
them, and his impatience made him intolerant of those who failed to
sympathize with his projects."
Babbage dabbled in half a dozen
sciences and traveled with a portable laboratory. He was also a
supreme nit-picker, sharp-eyed and cranky, known to write outraged
letters to publishers of mathematical tables, upbraiding them for
obscure inaccuracies he had uncovered in the pursuit of his own
calculations. A mistake in navigational table, after all, was a matter
of life and death for a seafarer. And a mistake in a table of logarithms
could seriously impede the work of a great mind such as his own.
His nit-picking indirectly led Babbage to invent the ancestor of
today's computers. As a mathematician and astronomer of no small repute,
he resented the time he had to spend poring over logarithm tables,
culling all the errors he knew were being perpetuated upon him by "elderly
Cornish Clergymen, who lived on seven figure logarithms, did all their
work by hand, and were only too apt to make mistakes."
Babbage left a cranky memoir entitled Passages from the Life of a
Philosopher--a work described by computer pioneer Herman Goldstine
as "a set of papers ranging from the sublime to the ridiculous, from
profundities to nonsense in plain bad taste. Indeed much of Babbage's
career is of this sort. It is a wonder that he had as many good and
loyal friends when his behavior was so peculiar."
In Passages, Babbage noted this about the original inspiration
for his computing machines:
The earliest idea that I can trace in my own mind
of calculating arithmetical tables by machinery rose in this manner:
One evening I was sitting in the rooms of the Analytical society at
Cambridge, my head leaning forward on the table in a kind of dreamy
mood, with a Table of logarithms lying open before me. Another
member, coming into the room, and seeing me half asleep, called out,
"Well, Babbage, what are you dreaming about?" To which I replied, "I
am thinking that all these Tables (pointing to the logarithms) might
be calculated by machinery."
In 1822, Babbage triumphantly demonstrated at the Royal Astronomical
Society a small working model of a machine, consisting of cogs and
wheels and shafts. The device was capable of performing polynomial
equations by calculating successive differences between sets of numbers.
He was awarded the society's first gold medal for the paper that
accompanied the presentation.
In that paper, Babbage described his plans for a much more ambitious
"Difference Engine." In 1823, the British government awarded him the
first of many grants that were to continue sporadically and
controversially for years to come. Babbage hired a master machinist, set
up shop on his estate, and began to learn at first hand how far ahead of
his epoch's technological capabilities his dreams were running.
The Difference Engine commissioned by the British government was
quite a bit larger and more complex than the model demonstrated before
the Royal Astronomical Society. But the toolmaking art of the time was
not yet up to the level of precision demanded by Babbage's design. Work
continued for years, unsuccessfully. The triumphal demonstration at the
beginning of his enterprise looked as if it had been the high point of
Babbage's career, followed by stubborn and prolonged decline. The
British government finally gave up financing the scheme.
Babbage, never one to shy away from conflict with unbelievers over
one of his cherished ideas, feuded over the Difference Engine with the
government and with his contemporaries, many of whom began to make sport
of mad old Charley Babbage. While he was struggling to prove them all
wrong, he conceived an idea for an even more ambitious invention.
Babbage, already ridiculously deep in one visionary development project,
began to dream up another one. In 1833 he came up with something far
more complex than the device he had failed to build in years of
expensive effort.
If one could construct a machine for performing one kind of
calculation, Babbage reasoned, would it be possible to construct a
machine capable of performing any kind of calculation? Instead of
building many small machines to perform different kinds of calculation,
would it be possible to make the parts of one large machine
perform different tasks at different times, by changing the order in
which the parts interact?
Babbage had stumbled upon the idea of
a universal calculating machine, an idea that was to have
momentous consequences when Alan Turing--another brilliant, eccentric
British mathematician who was tragically ahead of his time--considered
it again in the 1930s. Babbage called his hypothetical master calculator
the "Analytical Engine." The same internal parts were to be made to
perform different calculations, through the use of different "patterns
of action" to reconfigure the order in which the parts were to move for
each calculation. A detailed plan was made, and redrawn, and redrawn
once again.
The central unit was the "mill," a calculating engine capable of
adding numbers to an accuracy of 50 decimal places, with speed and
reliability guaranteed to lay the Cornish clergymen calculators to rest.
Up to one thousand different 50-digit numbers could be stored for later
reference in the memory unit Babbage called the "store." To display the
result, Babbage designed the first automated typesetter.
Numbers could be put into the store from the mill or from the
punched-card input system Babbage adapted from French weaving machines.
In addition, cards could be used to enter numbers into the mill and
specify the calculations to be performed on the numbers as well. By
using the cards properly, the mill could be instructed to temporarily
place the results in the store, then return the stored numbers to the
mill for later procedures. The final component of the Analytical Engine
was a card-reading device that was, in effect, a control and
decision-making unit.
A working model was eventually built by Babbage's son. Babbage
himself never lived to see the Analytical Engine. Toward the end of his
life, a visitor found that Babbage had filled nearly all the rooms of
his large house with abandoned models of his engine. As soon as it
looked as if one means of constructing his device might actually
work--Babbage thought of a new and better way of doing it.
The four subassemblies of the Analytical Engine functioned very much
like analogous units in modern computing machinery. The mill was the
analog of the central processing unit of a digital computer and the
store was the memory device. Twentieth-century programmers would
recognize the printer as a standard output device. It was the input
device and the control unit, however, that made it possible to move
beyond calculation toward true computation.
The input portion of the Analytical
Engine was an important milestone in the history of programming.
Babbage borrowed the idea of punched-card programming from the French
inventor Jacquard, who had triggered a revolution on the textile
industry by inventing a mechanical method of weaving patterns in cloth.
The weaving machines used arrays of metal rods to automatically pull
threads into position. To create patterns, Jacquard's device interposed
a stiff card, with holes punched in it, between the rods and the
threads. The card was designed to block some of the rods from reaching
the thread on each pass; the holes in the card allowed only certain rods
to carry threads into the loom. Each time the shuttle was thrown, a new
card would appear in the path of the rods. Thus, once the directions for
specific woven patterns were translated into patterns of holes punched
into cards, and the cards were arranged in the proper order to present
to the card reading device, the cloth patterns could be preprogrammed
and the entire weaving process could be automated.
These cards struck Babbage as the key to automated calculation. Here
was a tangible means of controlling those frustratingly abstract
"patterns of action": Babbage put the step-by-step instructions for
complicated calculations into a coded series of holes punched into the
sets of cards that would change the way the mill worked at each step.
Arrange the correctly coded cards in the right way, and you've replaced
a platoon of elderly Cornish gentlemen. Change the cards, and you
replace an entire army of them.
During his crusade to build the devices that he saw in his mind's eye
but was somehow never able to materialize in wood and brass, Babbage met
a woman who was to become his companion, colleague, conspirator, and
defender. She saw immediately what Babbage intended to do with his
Analytical Engine, and she helped him construct the software for it. Her
work with Babbage and the essays she wrote about the possibilities of
the engine established Augusta Ada Byron, Countess of Lovelace, as a
patron saint if not a founding parent of the art and science of
programming.
Ada's father was none other than
Lord
Byron, the most scandalous character of his day. His separation from
Ada's mother was one of the most widely reported domestic episodes of
the era, and Ada never saw her father after she was one month old. Byron
wrote poignant passages about Ada in some of his poetry, and she asked
to be buried next to him--probably to spite her mother, who outlived
her. Ada's mother, portrayed by biographers as a vain and overbearing
Victorian figure, thought a daily dose of a laudanum-laced "tonic" would
be the perfect cure for her beautiful, outspoken daughter's
nonconforming behavior, and thus forced an addiction on her!
Ada exhibited her mathematical talents early in life. One of her
family's closest friends was
Augustus De Morgan, the famous British Logician. She was well
tutored, but always seemed to thirst for more knowledge than her tutors
could provide. Ada actively sought the perfect mentor, whom she thought
she found in a contemporary of her mother's--Charles Babbage.
Mrs. De Morgan was present at the historic occasion when the young
Ada Byron was first shown a working model of the Difference Engine,
during a demonstration Babbage held for Lady Byron's friends. In her
memoirs, Mrs. De Morgan remembered the effect the contraption had on
Augusta Ada: "While the rest of the party gazed at this beautiful
invention with the same sort of expression and feeling that some savages
are said to have shown on first seeing a looking glass or hearing a gun,
Miss Byron, young as she was, understood its working and saw the great
beauty of the invention."
Such parlor demonstrations of mechanical devices were in vogue among
the British upper classes during the Industrial Revolution. While her
elders tittered and gossiped and failed to understand the difference
between this calculator and the various water pumps they had observed at
other demonstrations, young Ada began to knowledgeably poke and probe
various parts of the mechanism, thus becoming the first computer whiz
kid.
Ada was one of the few to recognize that the Difference Engine was
altogether a different sort of device than the mechanical calculators of
the past. Whereas previous devices were
analog (performing calculation by means of measurement),
Babbage's was digital (performing calculation by means of
counting). More importantly, Babbage's design combined
arithmetic and logical functions. (Babbage eventually discovered the new
work on the "algebra of Logic" by De Morgan's friend George Boole--but,
by then, it was too late for Ada.)
Ada, who had been tutored by De Morgan, the foremost logician of his
time, had ideas of her own about the possibilities of what one might do
with such devices. Of Ada's gift for this new type of partially
mathematical, partially logical exercise, Babbage himself noted: "She
seems to understand it better than I do, and is far, far better at
explaining it."
At the age of nineteen, Ada married Lord King, Baron of Lovelace. Her
husband was also something of a mathematician, although his talents were
far inferior to those of his wife. The young countess Lovelace continued
her mathematical and computational partnership with Babbage, resolutely
supporting what she knew to be a solid idea, at a time when
less-foresighted members of the British establishment dismissed Babbage
as a crank.
Babbage toured the Continent in 1840, lecturing on the subject of the
device he never succeeded in building. In Italy, a certain Count
Menabrea in Italy took extensive notes at one of the lectures and
published them in Paris. Ada translated the notes from French to English
and composed an addendum which was more than twice as long as the text
she had translated. When Babbage read the material, he urged Ada to
publish her notes in their entirety.
Lady Lovelace's published notes are still understandable today and
are particularly meaningful to programmers, who can see how truly far
ahead of their contemporaries were the Analytical Engineers. Professor
B. H. Newman in the Mathematical Gazette has written that
her observations "show her to have fully
understood the principles of a programmed computer a century before its
time."
Ada was especially intrigued by the mathematical implications of the
punched pasteboard cards that were to be used to feed data and equations
to Babbage's devices. Ada's Essay, entitled "Observations on Mr.
Babbage's Analytical Engine," includes more than one prophetic passage,
unheeded by most of her contemporaries, but which have grown in
significance with the passage of a century:
The distinctive characteristic of the Analytical
Engine, and that which has rendered it possible to endow mechanism
with such extensive faculties as bid fair to make this engine the
extensive right hand of algebra, is the introduction into it of the
principle which Jacquard devised for regulating, by means of punched
cards, the most complicated patters in the fabrication of brocaded
stuffs. It is in this that the distinction between the two engines
lies. Nothing of the sort exists in the Difference Engine. We may
say most aptly that the Analytical Engine weaves algebraical
patterns just as the Jacquard loom weaves flowers and leaves. .
. .
The bounds of arithmetic were, however,
outstepped the moment the idea of applying cards had occurred; and
the Analytical Engine does not occupy common ground with mere
"calculating machines." It holds a position wholly its own; and the
considerations it suggests are most interesting in their nature. In
enabling mechanism to combine together general symbols, in
successions of unlimited variety and extent, a uniting link is
established between the operations of matter and the abstract mental
processes of the most abstract branch of mathematical
science. A new, a vast and a powerful language is developed for the
future use of analysis, in which to wield its truths so that these
may become of more speedy and accurate practical application for the
purposes of mankind than the means hitherto in our possession have
rendered possible. Thus not only the mental and the material, but
the theoretical and the practical in the mathematical world, are
brought into intimate connexion with each other. We are not aware of
its being on record that anything partaking of the nature of what is
so well designated the Analytical Engine has been hitherto
proposed, or even thought of, as a practical possibility, any more
than the idea of a thinking or a reasoning machine.
As a Mathematician, Ada was excited about the possibility of
automating laborious calculations. But she was far more interested in
the principles underlying the programming of these devices. Had she not
died so young, it is possible that Ada could have advanced the
nineteenth-century state of the art to the threshold of true
computation.
Even thought the Engine was yet to be built, Ada experimented with
writing sequences of instructions. She noted the value of several
particular tricks in this new art, tricks that are still essential to
modern computer languages--subroutines, loops and jumps.
If your object is to weave a complex calculation out of subcalculations,
some of which may be repeated many times, it is tedious to rewrite a
sequence of a dozen or a hundred instructions over and over, Why not
just store copies of often-used calculations, or subroutines, in a
"library" of procedures for later use? Then your program can "call" for
the subroutine from the library automatically, when your calculation
requires it. Such libraries of subprocedures are now a part of virtually
every high-level programming language.
Analytical Engines and digital computers are very good at doing
things over and over many times, very quickly. By inventing an
instruction that backs up the card-reading device to a specified
previous card, so that the sequence of instructions can be executed a
number of times, Ada created the
loop--perhaps the most fundamental procedure in every contemporary
programming language.
It was the conditional jump that brought Ada's gifts as a logician
into play. She came up with yet another instruction for manipulating the
card-reader, but instead of backing up and repeating a sequence of
cards, this instruction enabled the card-reader to jump to another card
in any part of the sequence, if
a specific condition was satisfied. The addition of that little "if" to
the formerly purely arithmetic list of operations meant that the program
could do more than calculate. In a primitive but potentially meaningful
way, the Engine could now make decisions.
She also noted that machines might someday be built with capabilities
far beyond those possible with Victorian era technology, and speculated
about the possibility of whether such machines could ever achieve
intelligence. Her argument against artificial intelligence, set forth in
her "Observations," was immortalized almost a century later by another
software prophet, Alan Turing, who dubbed her line of argument "Lady
Lovelace's Objection." It is an opinion that is still frequently heard
in debates about machine intelligence: "The Analytical Engine," Ada
wrote, "has no pretensions whatever to originate anything. It can do
whatever we know how to order it to perform."
It is not known how and when Ada
became involved in her clandestine and disastrous gambling ventures.
No evidence has ever been produced that Babbage had anything to do with
introducing Ada to what was to be her lifelong secret vice. For a time,
Lord Lovelace shared Ada's obsession, but after incurring significant
losses he stopped. She continued, clandestinely.
Babbage became deeply involved in Ada's gambling toward the end of
her life. For her part, Ada helped Babbage in more than one scheme to
raise money to construct the Analytical Engine. It was a curious mixture
of vice, high intellectual adventure, and bizarre entrepreneurship. They
built a tic-tac-toe machine, but gave up on it as a moneymaking venture
when an adviser assured them that P. T. Barnum's General Tom Thumb had
sewn up the market for traveling novelties. Ironically, although
Babbage's game-playing machines were commercial failures, his
theoretical approach created a foundation for the future science of game
theory, scooping even that twentieth-century genius John von Neumann by
about a hundred years.
It was Charley and Ada's attempt to develop an infallible system for
betting on the ponies that brought Ada to the sorry pass of twice
pawning her husband's family jewels, without his knowledge, to pay off
blackmailing bookies. At one point, Ada and Babbage--never one to turn
down a crazy scheme--used the existing small scale working model of the
Difference Engine to perform the calculations required by their complex
handicapping scheme. The calculations were based on sound approaches to
the theory of handicapping, but as the artificial intelligentsia were to
learn over a century later, even the best modeling programs have trouble
handling truly complex systems. They lost big. To make matters worse,
when she compounded her losses Ada had to turn to her mother, who was
not the most forgiving soul, to borrow the money to redeem the Lovelace
jewels before her husband could learn of their absence.
Ada died of cancer at the age of thirty-six. Babbage outlived her by
decades, but without Ada's advice, support, and sometimes stern
guidance, he was not able to complete his long-dreamed-of Analytical
Engine. Because the toolmaking art of his day was not up to the
tolerance demanded by his designs, Babbage pioneered the use of
diamond-tipped tools in precision-lathing. In order to systematize the
production of components for his Engine, he devised methods to
mass-manufacture interchangeable parts and wrote a classic treatise on
what has since become known as "mass production."
Babbage wrote books of varying degrees of coherence, made
breakthroughs in some sciences and failed in others, gave brilliant and
renowned dinner parties with guests like Charles Darwin, and seems to
have ended up totally embittered. Bowden noted that "Shortly before
Babbage died he told a friend that he could not remember a single
completely happy day in his life: 'He spoke as if he hated mankind in
general, Englishmen in particular, and the English Government and Organ
Grinders most of all.'"
While Ada Lovelace has been unofficially known to the inner circles
of programmers since the 1950s, when card-punched batch-processing was
not altogether different from Ada's kind of programming, she has been
relatively unknown outside those circles until recently. In the 1970s,
the U.S. Department of defense officially named its "superlanguage"
after her.
Although it came too late to assist in the original design of the
Analytical Engine, yet another discovery that was to later become
essential to the construction of computers was made by a contemporary of
Babbage and Lovelace. The creation of an algebra of symbolic logic was
the work of another mathematical prodigy and British individualist, but
one who worked and lived in a different world, far away from the parlors
of upper-class London.A seventeen-year-old Englishman by the name of
George Boole was struck by an
astonishing revelation while walking across a meadow one day in 1832.
The idea came so suddenly, and made such a deep impact on his life, that
it led Boole to make pioneering if obscure speculations about a
heretofore unsuspected human facility that he called "the unconscious."
Boole's contribution to human knowledge was not to be in the field of
psychology, however, but in a field of his own devising. As Bertrand
Russell remarked seventy years later,
Boole invented pure mathematics.
Although he had only recently begun to study mathematics, the teenage
George Boole suddenly saw a way to capture some of the power of human
reason in the form of an algebra. And Boole's equations actually worked
when they were applied to logical problems. But there was a problem, and
it wasn't in Boole's concept. The problem, at the time, was that nobody
cared. Partly because he was from the wrong social class, and partly
because most mathematicians of his time knew very little about logic,
Boole's eventual articulation of this insight didn't cause much
commotion when he published it. His revelation was largely ignored for
generations after his death.
When the different parts of computer technology converged
unexpectedly a hundred years later, electrical engineers needed
mathematical tools to make sense of the complicated machinery they were
inventing. The networks of switches they created were electrical
circuits whose behavior could be described and predicted by precise
equations. Because patterns of electrical pulses were now used to
enclose logical operations like "and," "or," and the all important "if,"
as well as the calculator's usual fare of "plus," "minus," "multiply,"
and "divide," there arose a need for equations to describe the logical
properties of computer circuits.
Ideally, the same set of mathematical tools would work for both
electrical and logical operations. The problem of the late 1930s was
that nobody knew of any mathematical operations that had the power to
describe both logical and electrical networks. Then the right kind of
mind looked in the right place. An exceptionably astute graduate student
at MIT named Claude Shannon, who later invented information theory,
found Boole's algebra to be exactly what the engineers were looking for.
Without Boole, a poverty-stricken, self-taught mathematics teacher
who was born the same year as Ada, the critical link between logic and
mathematics might never have been accomplished. While the Analytical
Engine was an inspiring attempt, it had remarkably little effect on the
later thinkers who created modern computers. Without Boolean algebra,
however, however, computer technology might never have progressed to the
electronic speeds where truly interesting computation becomes possible.
Boole was right about the importance of his vision, although he
wouldn't have known what to do with a vacuum tube or a switching circuit
if he saw one. Unlike Babbage, Boole was not an engineer. What Boole
discovered in that meadow and worked out on paper two decades later was
destined to become the mathematical
linchpin that coupled the logical abstractions of software with the
physical operations of electronic machines.
Between them, Babbage's and Boole's inspirations can be said to
characterize the two different kinds of
motivation that caused imaginatives over the centuries to try and
eventually to succeed in building a computer. On the one side are
scientists and engineers, who would always yearn for a device to take
care of tedious computations for them, freeing their thoughts for the
pursuit of more interesting questions. On the other side is the more
abstract desire of the mathematical mind to capture the essence of human
reason in a set of symbols.
Ada, who immediately understood Babbage's models when she saw them,
and who was tutored by De Morgan, the one man in the world best equipped
to understand Boole, was the first person to speculate at any length
about the operations of machines capable of performing logical as well
as numerical operations. Boole's work was not published until after Lady
Lovelace died. Had Ada lived but a few years longer, her powerful
intuitive grasp of the principles of programming would have been
immeasurably enhanced by the use of Boolean algebra.
Babbage and Lovelace were British aristocrats during the height of
the Empire. Despite the derision heaped on Babbage in some quarters for
his often-peculiar public behavior, he counted the Duke of Wellington,
Charles Dickens, and Prince Albert among his friends. Ada had access to
the best tutors, the finest laboratory equipment, and the latest books.
They were both granted the leisure to develop their ideas and the
privilege of making fools of themselves of the Royal Society, if they
desired.
Boole was the son of a petty shopkeeper, which wasn't the best route
to a good scientific education. At the age of sixteen, his family's
precarious financial situation obliged Boole to secure modest employment
as a schoolteacher. Faced with the task of teaching his students
something about mathematics, and by now thoroughly Lincolnesque in his
self-educating skills, Boole set out to learn mathematics. He soon
learned that it was the most cost-effective intellectual endeavor for a
man of his means, requiring no laboratory equipment and a fairly small
number of basic books. At seventeen he experienced the inspiration that
was to result in his later work, but he had much to learn about both
mathematics and logic before he was capable of presenting his discovery
to the world.
At the age of twenty he discovered something that the greatest
mathematicians of his time had missed--an algebraic theory of invariance
that was to become an indispensable tool for Einstein when he formulated
the theory of relativity. In 1849, after his long years as an
elementary-school teacher, Boole's mathematical publications brought him
an appointment as professor of mathematics at
Queen's College, Cork, Ireland. Five
years later, he published An investigation of the laws of thought, on
which are founded the Mathematical Theories of Logic and Probabilities.
Formal logic had been around since the time of the Greeks, most
widely known in the syllogistic form perfected by Aristotle, the
simplified version of which most people learn no more than: "All men are
mortal. Socrates is a man. Therefore Socrates is mortal." After
thousands of years in the same form, Aristotelian logic seemed doomed to
remain on the outer boundaries of the metaphysical, never to break
through into the more concretely specified realm of the mathematical,
because it was still just a matter of words. The next level of
symbolic precision was missing.
For over a thousand years, the only logic-based system that was
expressible in symbols rigorous and precise enough to be called
"mathematical" had been the geometry set down by Euclid. Just as Euclid
set down the basic statements and rules of geometry in axioms and
theorems about spatial figures, Boole set down the basics of logic in
algebraic symbols. This was no minor ambition. While knowledge of
geometry is a widely useful tool for getting around the world,
Boole was convinced that logic was the
key to human reason itself. He knew that he had found what every
metaphysician from Aristotle to Descartes had overlooked. In his first
chapter, Boole wrote:
1. The design of the following treatise is to
investigate the fundamental laws of those operations of the mind by
which reasoning is performed; to give expression to them in the
symbolic language of a Calculus, and upon this foundation to
establish a science of Logic and construct its method . . . to
collect from the various elements of truth brought to view in the
course of these inquiries some probable imitations concerning the
nature and constitution of the human mind. . . .
2. . . . To enable us to deduce correct
inferences from given premises is not the only object of logic . . .
these studies have also an interest of another kind, derived from
the light which they shed on the intellectual powers. They instruct
us concerning the mode in which language and number serve as
instrumental aids to the process of reasoning; they reveal to some
degree the connexion between different powers of our common
intellect; they set before us . . . the essential standards of truth
and correctness--standards not derived from without, but deeply
founded in the constitution of the human faculties . . . To unfold
the secret laws and relations of those high faculties of thought by
which all beyond the merely perceptive knowledge of the world and of
ourselves is attained or matured, is an object which does not stand
in need of commendation to a rational mind.
Although his discovery had profound consequences in both pure
mathematics and electrical engineering, the most important elements of
Boole's algebra of logic were simple in principle. He used the algebra
everybody learns in school as a starting point, made several small but
significant exceptions to the standard rules of algebraic combination,
and used his special version to precisely express the syllogisms of
classical logic.
The concept Boole used to connect the two heretofore different
thinking tools of logic and calculation was the idea of a mathematical
system in which there were only two quantities, which he called "the
Universe" and "Nothing" and denoted by the signs 1 and 0.
Although he didn't know it at the time,
Boole had invented a two-state system for quantifying logic that also
happened to be a perfect method for analyzing the logic of two-state
physical devices like electrical relays or vacuum tubes.
By using the symbols and operations specified, logical propositions
could be reduced to equations, and the syllogistic conclusions could be
computed according to ordinary algebraic rules. By applying purely
mathematical operations, anyone who knew Boolean algebra could discover
any conclusion that was logically contained in any set of specified
premises.
Because syllogistic logic so closely resembles the thought processes
of human reasoning, Boole was convinced that his algebra not only
demonstrated a valid equivalence between mathematics and logic, but also
represented a mathematical systemization of human thought. Since Boole's
time, science has learned that the human instrument of reason is far
more complicated, ambiguous, unpredictable, and powerful that the tools
of formal logic. But mathematicians have found that Boole's mathematical
logic is much more important to the foundation of their enterprise than
they first suspected. And the inventors of the first computers learned
that a simple system with only two values can weave very sophisticated
computations indeed.
The construction of a theoretical bridge between mathematics and
logic had been gloriously begun, but was far from completed by Boole's
work. It remained for later minds to discover that although it is
probably not true that the human mind resembles a machine, there is
still great power to be gained by thinking about machines that resemble
the operations of the mind.
Nineteenth-century technology simply wasn't precise enough, fast
enough, or powerful enough for ideas like those of Babbage, Lovelace,
and Boole to become practicalities. The basic science and the industrial
capabilities needed for making several of the most important components
of modern computers simply didn't exist. There were still important
problems that would have to be solved by the inventors rather than the
theorists.
The next important development in the history of computation, and the
last important contribution of the nineteenth century, had nothing to do
with calculating tables of logarithms or devising laws of thought. The
next thinker to advance the state of the art was
Herman Hollerith, a
nineteen-year-old employee of the United States Census Office. His role
would have no effect on the important theoretical foundations of
computing. Ultimately, his invention became obsolete. But his small
innovation eventually grew into the industry that later came to dominate
the commercial use of computer technology.
Hollerith made the first important American contribution to the
evolution of computation when his superior at the Census Office set him
on a scheme for automating the collection and tabulation of data. On his
superior's suggestion, he worked out a
system that used cards with holes punched in them to feed information
into an electrical counting system.
The 1890 census was the point in history where the processing of
data as well as the calculation of mathematical equations became the
object of automation. As it turned out, Hollerith was neither a
mathematician nor a logician, but a data processor. He was grappling,
not with numerical calculation, but with the complexity of collecting,
sorting, storing, and retrieving a large number of small items in a
collection of information. Hollerith and his colleagues were unwitting
forerunners of twentieth-century information workers, because their task
had to do with finding a mechanical method to keep track of what their
organization knew.
Hollerith was introduced to the task by his superior, John Shaw
Billings, who had been worrying about the rising tide of information
since 1870, when he was hired by the Census Office to develop new ways
to handle large amounts of information. Since he was in charge of the
collection and tabulation of data for the 1880 and 1890 census, Billings
was acutely aware that the growing population of the nation was
straining the ability of the government to conduct the constitutionally
mandated survey every ten years. In the foreseeable future, the flood of
information to be counted and sorted would take fifteen or twenty years
to tabulate!
Like the stories about the origins of other components of computers,
there is some controversy about the exact accreditation for the
invention of the punched-card system. One account by a man named
Willcox, who worked with both Billings and Hollerith in the census
office stated:
While the returns of the Tenth (1881) Census were
being tabulated at Washington, Billings was walking with a companion
through the office in which hundreds of clerks were engaged in
laboriously transferring items of information from the schedules to
the record sheets by the slow and heartbreaking method of hand
tallying. As they were watching the clerks he said to his companion,
'There ought to be some mechanical way of doing this job, on the
principle of the Jacquard loom, whereby holes in a card can regulate
the pattern to be woven.' The seed fell on good ground. His
companion was a talented young engineer in the office who first
convinced himself that the idea was practicable and then that
Billings had no desire to claim or use it.
The "talented young engineer," of course, was Hollerith, who wrote
this version in 1919:
One Sunday evening at Dr. Billings' tea table, he
had said to me that there ought to be a machine for doing the purely
mechanical work of tabulating population and similar statistics. We
talked the matter over and I remember . . . he thought of using
cards with the description of the individual shown by notches
punched in the edge of the card. . . .After studying the problem I
went back to Dr. Billings and said that I thought I could work out a
solution for the problem and asked him if he would go in with me.
The Doctor said that he was not interested any further than to see
some solution of the problem worked out.
The system Hollerith put together used holes punched in designated
locations on cardboard cards to represent the demographic
characteristics of each person interviewed. Like Jacquard's and
Babbage's cards, and the "player pianos" then in vogue, the holes in
Hollerith's cards were meant to allow the passage of mechanical
components. Hollerith used an electromechanical counter in which copper
brushes closed certain electrical circuits if a hole was encountered,
and did not close a circuit if a hole was not present.
An electrically activated mechanism increased the running count in
each category by one unit every time the circuit for that category was
closed. By adding sorting devices that distributed cards into various
bins, according to the patterns of holes and the kind of tabulation
desired, Hollerith not only created the
ability to keep up with large amounts of data, but created the ability
to ask new and more complicated questions about the data. The new
system was in place in time for the 1890 census.
Hollerith obtained a patent on the system that he had invented just
in time to save the nation from drowning in its own statistics. In
1882-83, he was an instructor in mechanical engineering at the
Massachusetts Institute of Technology, establishing the earliest link
between that institution and the development of computer science and
technology. In 1896, Hollerith set up the "Tabulating Machine Company"
to manufacture both the cards and the card-reading machines. In 1900,
Hollerith rented his equipment to the Census Bureau for the Twelfth
Census.
Some years later, Hollerith's
Tabulating Machine had become an institution known as "International
Business Machines," run by a fellow named Thomas Watson, Senior.
But there were two World Wars ahead, and several more thinkers--the most
extraordinary of them all--still to come before a manufacturer of
tabulating machines and punch cards would have anything to do with true
computers. The modern-day concerns of this company--selling machines to
keep track of the information that goes along with doing business--would
have to wait for some deadly serious business to be transacted.
The War Department, not the Census Office or a business machine
company, was the mother of the digital computer, and the midwives were
many--from Alan Turing's British team who needed a special kind of
computing device to crack the German code, to John von Neumann's
mathematicians at Los Alamos who were faced with the almost
insurmountable calculations involved in making the atomic bomb, to
Norbert Weiner's researchers who were inventing better and faster ways
to aim antiaircraft fire, to the project of the Army Ballistic Research
Laboratory that produced the Electronic Numerical Integrator and
Calculator (ENIAC).
It would be foolish to speculate about what computers might become in
the near future without realizing where they originated in the recent
past. The historical record is clear and indisputable on this point:
ballistics begat cybernetics. ENIAC, the first electronic digital
computer, was originally built in order to calculate ballistic firing
tables. When ENIAC's inventors later designed the first miniature
computer, it was the BINAC, a device small enough to fit in the nose
cone of an ICBM and smart enough to navigate by the position of the
stars.
Although the first electronic digital computer was constructed in
order to produce more accurate weapons, the technology would not have
been possible without at least one important theoretical breakthrough
that had nothing to do with ballistics or bombs.
The theoretical origins of computation
are to be found, not in the search for more efficient weaponry, but in
the quest for more powerful and elegant symbol systems.
The first modern computer was not a machine. It wasn't even a
blueprint. The digital computer was
conceived as a symbol system--the first automatic symbol system
--not as a tool or a weapon. And the person who invented it was not
concerned with ballistics or calculation, but with the nature of thought
and the nature of machines.
