Redeeming Charles Babbage's Mechanical Computer

A successful effort to build a working, three-ton
Babbage calculating engine suggests that history
has misjudged the pioneer of automatic computing

by Doron D. Swade

DORON D. SWADE is both an electronics engineer and a historian of
computing. He has been senior curator of the computing and control
section of the Science Museum in London since 1985 and has published
articles on curatorship and on the history of computing. He has
recently written two books: Charles Babbage and His Calculating
Engines, which accompanies the Babbage exhibition that Swade curated,
and, in collaboration with Jon Palfreman, The Dream Machine: Exploring
the Computer Age, a companion to the television series of the same
name. Swade led the project to construct a fullscale cabbage
calculating engine.

Charles Babbage is celebrated as the great ancestral figure in the history
of computing. The designs for his vast mechanical calculators rank among
the most startling intellectual achievements of the l9th century. Yet
Babbage failed in his efforts to realize those plans in physical form.
Histories of computing routinely assert that Babbage faltered primarily
because the demands of his devices lay beyond the capabilities of Victorian
mechanical engineering. Curiously, no contemporary evidence supports that
view.

In 1985 my colleagues and I at the Science Museum in London set out to
resolve or at least illuminate the question by building a full-size Babbage
computing engine based on his original designs. Our endeavor finally bore
fruit in November 1991, a month before the bicentenary of Babbage's birth.
At that time, the device-‹known as Difference Engine No. 2-‹flawlessly
performed its first major calculation. The success of our undertaking
affirmed that Babbage's failures were ones of practical accomplishment, not
of design.

Those failures have become inextricably associated with his creative
genius. Babbage, proud and principled, was famed for the vigor and sarcasm
of his public denunciations of the scientific establishment. The demise of
his engine project added a sense of injustice, bitterness and even despair
to his celebrated diatribes. Since then, he has acquired an image of
testiness and eccentricity; the first biography of Babbage, written by
Maboth Moseley and published in 1964, was titled Irascible Genius: A Life
of Charles Babbage, Inventor. Our work at the Science Museum emphasizes a
distinctly different side of Babbage: a meticulous inventor whose designs
were hugely ambitious but well within the realm of possibility.

Babbage's desire to mechanize calculation arose from the exasperation he
felt at the inaccuracies in printed mathematical tables. Scientists,
bankers, actuaries, navigators, engineers and the like relied on such
tables to perform calculations requiring accuracy to more than a few
figures. But the production of tables was tedious and prone to error at
each stage of preparation, from calculation to transcription to
typesetting. Dionysius Lardner, a well-known popularizer of science, wrote
in 1834 that a random selection of 40 volumes of mathematical tables
incorporated 3,700 acknowledged errata, some of which themselves contained
errors.

Babbage was both a connoisseur of tables and a fastidious analyst of tabular
errors. He traced clusters of errors common to different editions of
tables and deduced where pieces of loose type had been incorrectly replaced
after falling out. On one occasion, he collaborated with John Herschel,
the renowned British astronomer, to check two independently prepared sets
of calculations for astronomical tables; the two men were dismayed by the
numerous discrepancies. "I wish to God these calculations had been
executed by steam!" Babbage exclaimed in 1821.

Mechanical computers should, Babbage thought, offer a means to eliminate at
a stroke all the sources of mistakes in mathematical tables. He envisioned
a machine that not only would calculate flawlessly but would eradicate
transcription and typesetting errors by automatically impressing the
results of its calculations onto papier-mache strips or plates of soft
metal. A printed record could then be generated directly from those
plates, thereby eliminating every opportunity for the genesis of errors.

In 1822 Babbage built an experimental model intended to carry him toward
his goal. He called his mechanical calculator a "difference engine"
because it is based on a mathematical principle known as the method of
finite differences. The method permits one to determine successive values
of polynomial functions using only addition [see box on page 90].
Multiplication and division, which are far more difficult to mechanize, are
not necessary. Because the value of the function at each step is
calculated based on its predecessor, a correct final result imparts a high
degree of confidence that all previous values are also correct.

For economy of design, Babbage's difference engines use the decimal number
system rather than the binary system common to modern electronic computers.
Each digit in a multidigit number is represented by a toothed gear wheel,
or figure wheel, engraved with decimal numerals. The value of each digit
is represented by the angular rotation of the associated figure wheel. The
engine's control mechanism ensures that only whole-number values,
represented by discrete positions of the figure wheels, are valid. Babbage
boasted that his machines would produce the correct result or would jam but
that they would never deceive.

Babbage's most ambitious venture to construct a full-scale calculating
device was devoted to the ill-fated Difference Engine No. 1. His efforts
foundered in 1833 after a decade of design, development and component
manufacture, not to mention vast expense. The project collapsed after a
dispute between Babbage and his chief engineer, Joseph Clement, over
payment for relocating the machining works. Outwardly at least, technology
did not feature in the disagreement. The question that has remained
tantalizingly unresolved is whether the circumstances surrounding the
collapse of the project concealed the technical or logical impossibility of
Babbage's schemes.

Difference Engine No. 1 consists of a basic adding element, repeated many
times over in an arrangement that embodies the method of differences. The
size and complexity of the engine are monumental: the design calls for
roughly 25,000 parts; the assembled machine would measure eight feet high,
seven feet long and three feet deep; and it would weigh several tons. The
project, which was funded by the British government, was also enormously
expensive. When Clement's last bill was paid in 1834, the cost totaled
£17,470. For comparison, the steam locomotive John Bull, built in 1831,
cost all of £784.

Clement completed about 12,000 of the 25,000 parts required for Difference
Engine No. 1, most of which were later melted down as scrap. The British
government finally withdrew from the project in 1842, partly on the advice
of George Biddell Airy, Astronomer Royal, who pronounced Babbage's engine
"worthless." The failure to complete the difference engine was the central
trauma in Babbage's scientific life; it is a topic he returns to repeatedly
in his writings as though unable to reconcile himself to the dismal
outcome.

The years of work on Difference Engine No. I did produce one noteworthy,
tangible result. In 1832 Clement assembled a small section of the engine,
consisting of about 2,000 parts, as a demonstration piece. This finished
part of the unfinished engine is one of the finest examples of precision
engineering of the time and works impeccably to this day.

The demonstration piece is the first known automatic calculator. Unlike
the desktop calculators of the time, the engine, once set up, did not rely
on informed human intervention. Thus, an operator could achieve accurate
results without any understanding of the logical or mechanical principles
involved. The opportunity to speculate about machine intelligence was not
lost on Babbage and his contemporaries. Harry Wilmot Buxton, a younger
colleague with whom Babbage entrusted many of his papers, wrote that "the
wondrous pulp and fibre of the brain had been substituted by brass and
iron; he [Babbage] had taught wheelwork to think."

Despite its impressive capabilities, the difference engine could perform
only one fixed task. Babbage's reputation as a computer pioneer largely
rests on another, more sophisticated device‹ the Analytical Engine,
conceived by 1834. He intended the Analytical Engine as a general-purpose
programmable computing machine, whose features are startlingly similar to
those of modern electronic computers. It had a basic repertoire of
operations (addition, subtraction, multiplication and division) that it
could execute in any sequence. The internal architecture of the machine
featured a separate "store" and "mill," equivalent to the memory and
processor in a modern computer. The separation of store and mill has been
a dominant design feature of electronic computers since the mid-1940s.

The Analytical Engine could be programmed by using punched cards, a
technique previously used in the Jacquard loom to control patterns of woven
thread. The Analytical Engine could take alternative courses of action
depending on the result of a calculation, enabling it to perform complex
functions. Babbage intended the machine to be able to handle up to
50-digit input numbers and 100-digit results; the output could be printed,
punched or plotted.

Although historians customarily refer to the Analytical Engine as if it
were a physical thing, it is actually a series of unbuilt designs that
Babbage refined at intervals from 1834 until his death in 1871.
Demoralized by the fate of Difference Engine No.1, he made no serious
attempt to construct a full-scale Analytical Engine. A small experimental
part of the mill that was still incomplete at the time of his death, along
with another fragment later built by Babbage's son, Henry Prevost Babbage,
are the only significant remains of his grand designs.

Work on the Analytical Engine forced Babbage to think about how to develop
mechanisms capable of automatic multiplication and division, all regulated
by a complex control system. The solutions to those problems inspired him
to design a simpler and more elegant difference engine, Difference Engine
No.2. Although the machine calculates to a precision of 31 figures,10
digits more than Babbage envisaged for Difference Engine No. 1, it
contains only one third as many parts. Babbage drew up detailed plans for
the second machine between 1847 and 1849 and offered them to the government
in 1852 but received no encouragement. So things stood for nearly a
century and a half.

During several visits to London beginning in 1979, Allan G. Bromley of the
University of Sydney in Australia examined Babbage's drawings and notebooks
in the Science Museum Library and became convinced that Difference Engine
No. 2 could be built and would work. I had independently read of
Babbage's hapless fate and become deeply puzzled as to why no one had tried
to resolve the issue of Babbage's failures by actually building his engine.

In 1985, shortly after my appointment as curator of computing, Bromley
appeared at the Science Museum carrying a two page proposal to do just that.
He suggested that the museum attempt to complete the machine by 1991, the
bicentenary of Babbage's birth. Bromley's proposal marked the start of a
six-year project that became something of a personal crusade for me. The
saga of our effort to construct the difference engine is one worthy of
Babbage himself. We embarked on a complex engineering project that took us
into unknown technical territory and confronted us with mechanical
conundrums, funding crises and the intrigues inherent in any major venture.

Difference Engine No. 2 was clearly the engine of choice for the project.
The associated set of drawings is intact whereas those for Difference
Engine No. 1 show regrettable gaps. Difference Engine No. 2 is also a
more economic design. Cost and time constraints argued in favor of
ignoring the printer and concentrating on the rest of the engine. The
printer is composed of about 4,000 parts and would be a sizable engineering
project in its own right.

The documentation for Difference Engine No. 2 consists of 20 main design
drawings and several tracings. As we pored over those drawings, my
colleagues and I discovered several flaws in the plans, in addition to
those identified by Bromley. One major assembly appears to be redundant.
Other mechanisms are missing from the design. For example, the initial
values needed to begin a calculation are entered by unlocking the columns
and manually rotating each of the freed figure wheels to the appropriate
positions. Babbage omitted a means of locking the columns after they were
set, so the setting-up procedure was self-corrupting.

The most serious design lapse concerned the carriage mechanism. This
crucial component ensures that if, in the course of an addition, the value
on a figure wheel exceeds 10, then the next higher figure wheel (indicating
numbers 10 times larger) advances one digit. The most extreme test of the
carriage mechanism occurs when a 1 is added to a row of 9's. Babbage
solved the carry problem in an exquisitely innovative manner. During the
first part of the calculating cycle, the engine performs a 31-digit
addition without carrying the 10's, but every figure wheel that exceeds 10
sets a spring-loaded warning device. In the second part of the cycle each
armed warning device allows a rotating arm to advance the next higher
figure wheel by one position.

Unfortunately, the configuration of the carry mechanism shown in Babbage's
design drawings is unworkable. The direction of rotation of the figure
wheels is incorrect, and the warning-and-carry mechanism could not function
as drawn. The source of these shortcomings stimulated considerable
speculation. We considered the possibility that errors were introduced
deliberately as security against industrial espionage. More likely, some
flaws were design oversights, and others were inevitable drafting and
layout errors.

None of the design problems we found in Difference Engine No.2 compromised
its overall logic or operational principles, and we managed to devise
solutions for all. Unnecessary mechanisms were omitted. The missing
locking assemblies for the figure wheels were devised and, where necessary,
their motions derived from those of neighboring pieces. Bromley solved the
carry-mechanism problem by mirror-reversing the incorrectly drawn parts and
altering their orientation. The introduction of a four-to-one reduction
gear in the drive allayed skepticism about whether the massive Difference
Engine No. 2 could be driven by hand. This change made the drive handle
four times easier to turn but caused the engine to run four times slower.

Implementing the solutions raised a significant philosophical dilemma.
Could we make these alterations without compromising the historical
authenticity of the result and, with it, the mission of proving that
Babbage's engines were logically and practically sound? We solved this
problem by adhering to Babbage's own design practices and strictly
confining ourselves to techniques or devices available to Babbage. We also
planned the revisions to Babbage's design so that every mechanism we added
could be easily removed.

In 1989 we built a small trial assembly at the Science Museum to verify the
logic of the basic adding element and to confirm that the carry mechanism
operated correctly. The assembly adds a two-digit number to another
two-digit number and takes account of any carry from units to tens and from
tens to hundreds. The finely finished device went a long way toward
convincing sponsors and colleagues that our project involved an engineering
aesthetic as well as an intriguing historical thesis. The trial piece
later proved an invaluable aid for visualizing the machine's operation and
for testing the first sample parts.

To build Difference Engine No. 2 and to estimate the cost of manufacturing
it, we needed full-dimension drawings of its parts. Late in 1989 we
contracted a specialist engineering company to produce a set of drawings
using Babbage's original set as the authoritative source. Missing
information‹detailed dimensions, choice of materials, tolerances, methods
of manufacture and a great deal of fine detail‹had to be supplied.

Dimensions for the individual parts were obtained by measuring and scaling
the original plans. The engineering company produced 50 new drawings that
fully specified each of the engine's 4,000 parts. Surviving mechanical
assemblies show that Babbage constructed his parts from bronze, cast iron
and steel. Bromley and Michael Wright of the Science Museum offered advice
regarding which material to use for each part. Our colleagues at the
Imperial College of Science and Technology analyzed the composition of the
components of Difference Engine No.1 to guide us in selecting an
appropriate modern bronze.

No attempt was made to use period machinery in the manufacture of parts.
The engine's 4,000 components embody only about 1,000 different part
designs, so there is a high degree of repetition. We unashamedly relied on
modern manufacturing techniques to produce the many identical parts. We
also welded parts that Babbage would have forged. But we scrupulously
ensured that Babbage could have produced components of the same precision,
though possibly by other means.

Specifying the precision with which parts should be made proved less
problematic than we first feared. Bromley and Wright had measured parts
from Difference Engine No. 1 and found that Clement achieved repeatability
of 1.5 to 2.0 thousandths of an inch, belying the popular belief that
mid-19th century mechanical engineering lacked the precision necessary for
building Babbage's devices. We adopted a modern engineering standard,
confident that it was within the limits of what 19th century craftsmen
could achieve. The process of producing the 50 modern mechanical drawings
took about six months and was substantially complete by January 1990.

We were determined to secure a fixed-price contract for manufacture and
assembly so as not to repeat Babbage's sorry tale of open-ended expense.
After some hard negotiation, the Science Museum and the specialist company
agreed to a price and to a set of provisions to cushion against unforeseen
technical difficulties. The Science Museum committed to underwrite the
costs against pledges from a group of five sponsoring computer companies:
ICL, Hewlett Packard, Rank Xerox, Siemens Nixdorf and Unisys.

Then, in June 1990, just as the final contract was about to be signed, the
company involved went bankrupt after 35 years in business. Reg Crick and
Barrie Holloway, the two engineers on the Babbage project, were fired on
Thursday, June 7. Unless orders were placed with contractors by close of
business the following day, we would incur cost penalties and have to
embark on another round of financial negotiation which would have
jeopardized our goal of completing the project in time for the Babbage
bicentenary. Officials at the Science Museum interviewed Crick and
Holloway on the morning of June 8; by lunchtime they were museum employees.
We spent the day frantically writing out part orders for subcontractors and
drafting contract terms. At 5:30 P.M., I sprinted to the post office to
mail the drawings and orders to the component manufacturers. We made the
deadline by minutes.

Difference Engine No. 2 was built in public view in the Science Museum.
Fitting and assembly commenced in November and was completed in May 1991.
The engine became the centerpiece in the exhibition Making the Difference:
Charles Babbage and the Birth of the Computer, which opened on June 27,
1991. Even then, the project kept us on tenterhooks. The three-ton
Difference Engine No. 2 had not yet performed a full calculation, and it
kept jamming unaccountably. We developed debugging techniques to track the
source of the jams and continued to work on the machine during the
exhibition. On November 29, 1991, less than a month before Babbage's 200th
birthday, the machine completed its first full-scale successful
calculation. It produced the first 100 values in the table of powers of
seven and has functioned without error ever since. The engine ended up
costing just under £300,000 ($500,000).

Our project illuminated several aspects of Babbage's skills as a designer
and engineer. Historians of technology have debated whether the high
standards of precision that Babbage demanded were necessary or were the
product of misguided perfectionism. Some researchers have pointed out that
cruder engines had been built to good effect. Georg and Edvard Scheutz, a
Swedish father-and-son team who were inspired by an account of Babbage's
work, built three difference engines, mostly of their own design. The
first of these, completed in 1843, had a wood frame and was made using
simple hand tools and a primitive lathe. Despite its comparatively rough
construction, the Scheutzes' machine performed successfully before the
Swedish Royal Academy.

Babbage's difference engines were larger and more sophisticated than those
attempted by the Scheutzes, however. Our experiences constructing
Difference Engine No. 2 underscored the importance of exacting standards.
We had expected that repeat parts made using computer controlled machines
would be sufficiently identical to be interchangeable. This proved not to
be the case. Fine tweaking of components to tolerances of no more than a
few thousandths of an inch proved necessary, especially for the proper
operation of the carry mechanism. Babbage's insistence on high precision
was evidently based on sound engineering judgment.

Constructing Difference Engine No. 2 revealed subtleties and ingenuity in
Babbage's design not immediately evident in the drawings. The project also
gave us tremendous respect for Babbage's ability to visualize the operation
of complex mechanisms without the aid of physical models. We hope to
extend our explorations of Babbage's elegant designs; to do so, we are
currently trying to attract sponsorship to build the printer. In the
meantime, we marvel at the physical realization of plans that Babbage drew
up nearly 150 years ago. Difference Engine No. 2 stands as a splendid
piece of engineering sculpture, a monument to the rigorous logic of its
inventor.