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Babbage - Redeeming Charles Babbage’s Mechanical Computer...

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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 full-size 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 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 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 papier-méiché 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 whole-number 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 full-scale 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 ill-fated 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 general-purpose 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 mid-19408. 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 50-digit input numbers and IOU-digit 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 full-scale 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 figure-wheel 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 odd-num- bered columns are added to even-numbered columns dur— ing the first half-cycle; even-numbered columns are then added to odd-numbered 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 30-digit 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 two-page 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 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 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 full-sized 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 setting-up proce— dure was self-corrupting. 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 31-digit addition without carrying the 10’s, but every figure wheel that ex- ceeds 10 sets a spring-loaded 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— and-carry 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 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 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 two-digit number to an— other two-digit 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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