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Unformatted text preview: Redeeming Charles Babbage’s Mechanical Computer A successful eﬁfort to build a working, three—ton
Babbage calculating engine suggests that history
has misjudged the pioneer of automatic computing harles Babbage is celebrated as the great ancestral ﬁgure in the history of computing. The de
signs for his vast mechanical calculators
rank among the most startling intellec
tual achievements of the 19th century.
Yet Babbage failed in his efforts to real
ize those plans in physical form. Histo
ries of computing routinely assert that
Babbage faltered primarily because the
demands of his devices lay beyond the
capabilities of Victorian mechanical en
gineering. Curiously, no contemporary
evidence supports that view. In 1985 my colleagues and I at the Sci
ence Museum in London set out to re
solve or at least illuminate the question
by building a fullsize Babbage comput
ing engine based on his original de
signs. Our endeavor ﬁnally bore fruit in
November 1991, a month before the bi
centenary of Babbage's birth. At that
time, the device—known as Difference
Engine No. 2—ﬂawlessly performed its
ﬁrst major calmlation. The success of
our undertaking affirmed that Babbage‘s
failures were ones of practical accom
plishment, not of design. Those failures have become inextri
cably associated with his creative ge DORON D. SWADE is both an electron
ics engineer and a historian of comput
ing. He has been senior curator of the
computing and control section of the Sci
ence Museum in London since 1985 and
has published articles on curatorship
and on the history of computing. He has
recently written two books: Charles Bab
bage and His Calculating Engines, which
accompanies the Babbage exhibition that
Swade curated, and, in collaboration with
Jon Palfreman, The Dream Machine: Ex
ploring the Computer Age, a companion
to the television series of the same name.
Swade led the project to construct a full
scale Babbage calculating engine. by Doron D. Swade CHARLES BABBAGE sat for this daguer
reotype around 1847, the year he began
work on Difference Engine No. 2. nius. Babbage, proud and principled,
was famed for the vigor and sarcasm
of his public denunciations of the sci
entiﬁc establishment. The demise of his
engine project added a sense of injus—
tice, bitterness and even despair to his
celebrated diatribes. Since then, he has
acquired an image of testiness and ec
centricity; the ﬁrst biography of Bab
bage, written by Maboth Moseley and
published in 1964, was titled Irascible
Genius: A Life of Charles Babbage, Inven
tor. 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 calcu
lation arose from the exasperation he
felt at the inaccuracies in printed math
ematical tables. Scientists, bankers, ac
tuaries, navigators, engineers and the
like relied on such tables to perform
calculations requiring accuracy to more 86 SCIENTIFIC AMERICAN February 1993 than a few ﬁgures. But the production
of tables was tedious and prone to er
ror at each stage of preparation, from
calculation to transcription to typeset
ting. Dionysius Lardner, a wellknown
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 tabu
lar errors. He traced clusters of errors
common to different editions of tables
and deduced where pieces of loose type
had been incorrectly replaced after fall
ing out. On one occasion, he collaborat
ed with John Herschel, the renowned
British astronomer, to check two inde
pendently prepared sets of calculations
for astronomical tables; the two men
were dismayed by the numerous dis
crepancies. “I wish to God these calcu
lations had been executed by steam!"
Babbage exclaimed in 182 1.
Mechanical computers should, Bab
bage 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 transcrip
tion and typesetting errors by automat
ically impressing the results of its cal
culations onto papierméiché 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 experimen—
tal model intended to carry him toward
his goal. He called his mechanical cal—
culator a “difference engine” because it
is based on a mathematical principle
known as the method of ﬁnite differ
ences. The method permits one to de—
termine successive values of polynomi
al functions using only addition [see
box on page 90]. Multiplication and di— vision, which are far more difﬁth 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 de
gree of conﬁdence that all previous val
ues are also correct. For economy of design, Babbage's dif
ference engines use the decimal number
system rather than the binary system
common to modern electronic comput
ers. 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 rep
resented by the angular rotation of the
associated ﬁgure wheel. The engine’s
control mechanism ensures that only
wholenumber values, represented by
discrete positions of the ﬁgure wheels,
are valid. Babbage boasted that his ma
chines would produce the correct result
or would jam but that they would never
deceive. Babbage's most ambitious venture to
construct a fullscale calculating device DIFFERENCE ENGINE NO. 2 was constructed in public view at
the Science Museum in London. Here the two engineers who
built it, Barrie Holloway (left) and Reg Crick (right). Perform was devoted to the illfated Difference
Engine No. 1. His efforts foundered in
1833 after a decade of design, devel
opment and component manufacture,
not to mention vast expense. The proj
ect 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 re
mained tantalizingly unresolved is
whether the circumstances surrounding
the collapse of the project concealed
the technical or logical impossibility of
Babbage's schemes. ifference Engine No. 1 consists
D of a basic adding element, re peated many times over in an
arrangement that embodies the meth
od of differences. The size and com
plexity 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 enor
mously expensive. When Clement’s last
bill was paid in 1834, the cost totaled
£17,470. For comparison, the steam lo
comotive John Bull, built in 1831, cost
all of £784. Clement completed about 12,000 of
the 25,000 parts required for Differ
ence 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 Roy
al, who pronounced Babbage's engine
”worthless.” The failure to complete the
difference engine was the central trau
ma in Babbage's scientiﬁc life; it is a top
ic he returns to repeatedly in his writ
ings as though unable to reconcile him
self to the dismal outcome. The years of work on Difference En
gine No. 1 did produce one noteworthy,
tangible result. In 1832 Clement assem
bled a small section of the engine, con some essential adjustments. Babbage also designed a print—
ing mechanism for the difference engine, but because of lim
ited time and money, the printer has not yet been built. SCIENTIFIC AMERICAN February 1993 87 sisting of about 2,000 parts, as a demon
stration piece. This ﬁnished part of the
unﬁnished engine is one of the ﬁnest ex
amples 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 en
gine, once set up, did not rely on in
formed human intervention. Thus, an
operator could achieve accurate results
without any understanding of the logi
cal or mechanical principles involved.
The opportunity to speculate about ma
chine intelligence was not lost on Bab—
bage and his contemporaries. Harry Wil
mot Buxton, a younger colleague with
whom Babbage entrusted many of his
papers, wrote that “ the wondrous pulp
and fibre of the brain had been substi
tuted 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 En»
gine as a generalpurpose programma
ble computing machine, whose features
are startlingly similar to those of mod
ern electronic computers. It had a basic
repertoire of operations (addition, sub
traction, 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 proces
sor in a modern computer. The separa
tion of store and mill has been a domi
nant design feature of electronic com
puters since the mid19408. The Analytical Engine could be pro grammed by using punched cards, a
technique previously used in the Jac
quard 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. Bab
bage intended the machine to be able
to handle up to 50digit input numbers
and IOUdigit results; the output could
be printed. punched or plotted.
Although historians customarily re
fer 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. l, he made no se
rious attempt to construct a fullscale
Analytical Engine. A small experimen
tal part of the mill that was still incom
plete at the time of his death, along with How Babbage’s Difference Engines Work 88 hown below is one of Babbage’s 20 main drawings of Difference Engine No. 2, which he drafted in 1847. The
machine is operated by means ofthe handle on the right.
Turning the handle rotates a vertical stack of 14 pairs of
cams that determine the action and timing of the calculat
ing cycle. Numbers are stored and operated on in eight ver
tical columns, each of which contains 3] engraved figure
wheels. The least significant digit of a number is stored at
thebottom ofthe column, the most significant digit at the
top. The initial values for a calculation are entered by un
locking the ﬁgure wheels and rotating each one by hand to
the appropriate decimal value. Below the ﬁgurewheel col
umns are a set of racks and levers that, when activated by
links from the cams, lift, lower and turn the vertical axes, thereby carrying out the addition of differences. Difference
Engine No.2 does not add numbers in sequence from right
to left, as one might expect. Instead values from oddnum
bered columns are added to evennumbered columns dur—
ing the first halfcycle; evennumbered columns are then
added to oddnumbered columns during the second half
cycle. This technique signiﬁcantly reduces the time required
for a calculation. A similar approach, known as pipelining,
is used in modern electronic computers. The printing
assembly, located at the left, is directly coupled to the last
column of ﬁgure wheels, which bear the ﬁnal result ofthe
calculation. Each turn ofthe handle produces one 30digit
value in the table of differences and automatically prepares
the machine to generate the next number. FIGURE
WHEEL
COLUMNS HANDLE PRINTER SCIENTIFIC AMERICAN February 1993 l another fragment later built by Bab
bage'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 mul
tiplication and division, all regulated by
a complex control system. The solutions
to those problems inspired him to de
sign a simpler and more elegant differ
ence engine, Difference Engine No. 2. Al
though the machine calculates to a pre
cision of 31 ﬁgures, 10 digits more than
Babbage envisaged for Difference En
gine 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 begin
ning in 1979, Allan G. Bromley of the
University of Sydney in Australia exam
ined Babbage‘s drawings and notebooks
in the Science Museum library and be
came convinced that Difference Engine
No. 2 could be built and would work. I
had independently read of Babbage's
hapless fate and become deeply puz
zled as to why no one had tried to re
solve the issue of Babbage's failures by
actually building his engine. ment as curator of computing, Brom
ley appeared at the Science Muse
um carrying a twopage proposal to do
just that. He suggested that the muse
um attempt to complete the machine
by 1991, the bicentenary of Babbage’s
birth. Bromley's proposal marked the
start of a sixyear 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 conun
drums, 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 En—
gine N0. 2 is also a more economic de
sign. Cost and time constraints argued
in favor of ignoring the printer and con
centrating on the rest of the engine. The
printer is composed of about 4,000
parts and would be a sizable engineer
ing project in its own right.
The documentation for Difference
Engine No. 2 consists of 20 main de—
sign drawings and several tracings. As In 1985, shortly after my appoint WORKING PART of Difference Engine No. 1, assembled by Joseph Clement in 1832,
is the ﬁrst known automatic calculator. Its ﬂawless operation strongly supports
Babbage’s conviction that building a fullsized engine was a practical prospect. we pored over those drawings, my col
leagues and I discovered several ﬂaws
in the plans, in addition to those iden
tified by Bromley. One major assembly
appears to be redundant. Other mecha
nisms are missing from the design. For
example, the initial values needed to be
gin a calculation are entered by unlock
ing 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 settingup proce—
dure was selfcorrupting. The most serious design lapse con
cerned 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 car ry problem in an exquisitely innovative
manner. During the ﬁrst part of the cal
culating cycle, the engine performs a
31digit addition without carrying the
10’s, but every ﬁgure wheel that ex
ceeds 10 sets a springloaded warning
device. In the second part of the cycle,
each armed warning device allows a ro
tating arm to advance the next higher
ﬁgure wheel by one position. Unfortunately, the conﬁguration of
the carry mechanism shown in Bab
bage’s design drawings is unworkable.
The direction of rotation of the ﬁgure
wheels is incorrect, and the warning—
andcarry mechanism could not func
tion as drawn. The source of these short
comings stimulated considerable spec
ulation. We considered the possibility
that errors were introduced deliberate
ly as security against industrial espi
onage. More likely, some ﬂaws were de
sign oversights, and others were inevit
able drafting and layout errors. SCIENTIFIC AMERICAN February 1993 89 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 omit
ted. The missing locking assemblies for
the ﬁgure wheels were devised and,
where necessary, their motions derived
from those of neighboring pieces. Brom
ley solved the carrymechanism problem
by mirrorreversing the incorrectly drawn
parts and altering their orientation The
introduction of a fourto—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 com
promising the historical authenticity of
the result and, with it, the mission of proving that Babbage's engines were log
ically and practically sound? We solved
this problem by adhering to Babbage’s
own design practices and strictly con
ﬁning ourselves to techniques or de
vices available to Babbage. We also
planned the revisions to Babbage's de
sign so that every mechanism we added
could be easily removed. bly at the Science Museum to verify the logic of the basic adding ele
ment and to conﬁrm that the carry
mechanism operated correctly. The as
sembly adds a twodigit number to an—
other twodigit number and takes ac—
count 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 aes
thetic as well as an intriguing historical
thesis. The trial piece later proved an I n 1989 we built a small trial assem Mathematical Principles of the Difference Engines abbage’s difference engines are so called because they use the method of
ﬁnitedifferences to ﬁnd the value of certain mathematical expressions. 90 The method is used below to produce the table of cubes (y = x3). The ﬁrst dif
ference is found by subtracting successive pairs of cubes. The same procedure
is applied to pairs of ﬁrst differences to derive second differences. When the
process is repeated for the second differences, one ﬁnds that the third differ—
ence is constant and equal to six. This information makes it possible to gener—
ate the rest ofthe table of cubes by reversing the differencing procedure. For
example, adding six to the second difference (I 8) gives the new second differ
ence (24); adding this to the ﬁrst difference (3 7) yields the new ﬁrst difference
(61). Finally, adding this to the last cubed number (64) gives the next number
in the sequence, 125 or 53. The procedure can be repeated indeﬁnitely to gen
erate as many terms as desired using only repeated additions. The method of differences can be applied to any of the mathematical func
tions known as polynomials, which hav...
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