The Difference Engine: Charles Babbage and the Quest to Build the First Computer

The Difference Engine: Charles Babbage and the Quest to Build the First Computer

by Doron Swade

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In 1821 an inventor and mathematician, Charles Babbage, was poring over a set of mathematical tables. Finding error after error Babbage exclaimed, "I wish to God these calculations had been executed by steam." His frustration was not simply at the grindingly tedious labor of checking manually evaluated tables, but at their daunting unreliability. Science, engineering,


In 1821 an inventor and mathematician, Charles Babbage, was poring over a set of mathematical tables. Finding error after error Babbage exclaimed, "I wish to God these calculations had been executed by steam." His frustration was not simply at the grindingly tedious labor of checking manually evaluated tables, but at their daunting unreliability. Science, engineering, construction, banking, and insurance depended on tables for calculation. Ships navigating by the stars relied on them to find their positions at sea.

Babbage launched himself on a grand venture to design and build mechanical calculating engines that would eliminate such errors. His bid to build infallible machines is a saga of ingenuity and will, which led beyond mechanized arithmetic into the entirely new realm of computing. Through Ada, Countess of Lovelace and daughter of Lord Byron, we gain tantalizing insights into how at least one Victorian glimpsed the promise of what was to come. Babbage springs out of history like a jack-in-the-box: a gentleman philosopher, a tireless inventor, a vigorous socialite, and a mesmerizing raconteur. "Mr. Babbage is coming to dinner" was a coup for any hostess.

Drawing on previously unused archival material, The Difference Engine is a tale of both Babbage's nineteenth-century quest to build a calculating engine and its twentieth-century sequel. For in 1991, Babbage's vision was finally realized, at least in part, by the completion at the Science Museum in London of the first full-sized Babbage engine, finished in time for the 200th anniversary of Babbage's birth. The two quests are mutually illuminating and are recounted here by the-then Curator of Computing, Doron Swade -- one of the main protagonists of the successful resumption of Babbage's extraordinary work.

Editorial Reviews review
The Barnes & Noble Review
Computers weren't always made of silicon: For centuries, they were made of flesh and blood. Real human beings, called "computers," sat from morning until night, making calculations. One day in 1821, Charles Babbage and his friend the astronomer John Herschel, sat down to review hundreds of those calculations -- and quickly discovered errors that spoiled them beyond repair.

Said Babbage, "I wish to God these calculations had been executed by steam." And so began two obsessions: Babbage's lifelong, failed project to construct a working digital computer, and the London Science Museum's quest to build the computer Babbage could never finish. Both are chronicled splendidly in The Difference Engine.

Doron Swade, who masterminded the Science Museum's project, begins with Babbage himself -- a man who was brilliant and stubborn in equal parts. Babbage left Cambridge without his degree, having chosen a "blasphemous" proposition to defend in the public debate that would've qualified him to sit for final exams -- knowing full well that he was to be judged by a leader of Cambridge's religious community. His principled contrariness would be the hallmark of his career, ultimately alienating the political and financial supporters whose help was essential to the completion of the project.

For all that, Babbage did manage to create plans of breathtaking complexity that would have required 25,000 individual parts. Many of the calculating components were actually built -- painstakingly, one at a time, since mass-production techniques with the needed precision didn't yet exist. (Tragically, most of these items were later melted for scrap.)

Some may be discomfited by the book's assessment of Ada Lovelace, Lord Byron's daughter and Babbage's collaborator. She is often credited with outlining the key ideas that led to the modern discipline of computer programming; Doron Swade objects. "The notion that she made an inspirational contribution to the development of the Engines is not supported by the known chronology of events.... Historians close to the detail of Babbage's work express dismay at the well-intentioned but misguided tributes paid to Ada."

Some 150 years after Babbage failed, Swade and his colleagues picked up where Babbage left off. The original plans would challenge them nearly as severely as they had Babbage. Putting aside the financing issues that complicated construction of Babbage's Difference Engine No. 2, there were design issues as well. Swade's team found small problems ("a long, beautiful, helical arrangement of arms which performs no function at all") and a few larger ones -- notably, a defect in the mechanism for carrying tens that Babbage would certainly have noticed had he ever built it.

Through 1991, the team gradually improved the clanking machine's reliability, reducing the frequency of jamming -- and of problems that would send broken bronze parts shooting across the room. On November 29, 1991, the engine performed its first full, automatic, error-free calculation.

If you're in London, you can see Babbage's engine today. But seeing it only hints at the richness of his vision. To really understand the dream -- and how it became real -- you need to read The Difference Engine. (Bill Camarda)

Bill Camarda is a consultant, writer, and web/multimedia content developer with nearly 20 years' experience in helping technology companies deploy and market advanced software, computing, and networking products and services. His 15 books include Special Edition Using Word 2000 and Upgrading & Fixing Networks For Dummies®, Second Edition.

Swade's precise book is the account of a precocious Victorian dream and that dream's realization. It tells the story of mathematician and inventor Charles Babbage, who, in 1821, came up with the idea for a machine that could do computation, putting an end to mistakes and forever eliminating the tedium of double-checking figures. By 1822 Babbage had conceived and designed a mechanical computer: an enormous, crank-driven monstrosity of wheels and rods, capable of making error-free calculations and even endowed with a memory. Undiplomatic as he was, Babbage made enemies where he most needed friends. Unconvinced of his reliability—or of the usefulness of his expensive brainchild—the British government withheld funding for Babbage's "difference engine" midway through its construction, and he never saw it completed. In 1991 Swade and his colleagues at London's Science Museum got together the money to build the device for an exhibition marking the bicentenary of Babbage's birth. Dense with technical detail, the book may be slow going for some readers, although it will appeal to those with an interest in engineering or the surprisingly long history of the computer.
—Eric Wargo

Publishers Weekly
Englishman Charles Babbage (1791-1871), an eccentric, ingenious mathematician, decided that existing tables of computations included far too many errors: the day's textbooks came with errata sheets appended by more errata sheets. The inventive Babbage entered completely new territory in his struggle to design an automatic computing machine that could achieve an "absolute integrity of results," and in the 1820s he completed plans for the "Difference Engine." Swade (coauthor of The Dream Machine), an assistant director at the London Science Museum, offers an engaging biography of Babbage and his milieu (buttressed by 16 pages of b&w photos and illustrations). Babbage convinced the government to invest in his invention, but the technology of the day made it prohibitively expensive to complete the machine to his satisfaction. He went on to design the "Analytical Engine," a quicker, more advanced, more broadly applicable machine that could be programmed with punch cards to do computations and store data. Unfortunately, Babbage never got to build this second machine, either. His life was full of personal tragedy, political confrontations, the personal vendettas of colleagues and the frustration of being unable to build what he designed. In the 1980s, Swade gathered a team of experts and tried to make sense of Babbage's drawings and notes in a modern quest to construct what Babbage could not. Swade's able account of this gifted scientist, his cohorts and their curious endeavors enhances and broadens the growing body of literature on computer history. (Sept. 10) Forecast: The "technological frontier" parallels between Babbage's age and our own are becoming increasingly clear, and Swade'simmersion in and love for Babbage's project comes through here (beyond some British reserve). Of all the books this season whose flap copy compares them to Longitude, this title has one of the best shots at a similar breakout. Copyright 2001 Cahners Business Information.
Library Journal
One of the first devices to be considered an automatic digital computer was conceived by the eccentric British mathematician Charles Babbage in 1822. In Babbage's time, teams of mathematicians working around the clock with primitive calculations generated complex logarithmic and trigonometric tables manually. Noting the large number of errors in these tables, Babbage proposed building an enormous mechanical calculator that he called a "Difference Engine" to calculate them automatically. Engineer and historian of technology Swade (coauthor, The Dream Machine) tells the story of Babbage's determined efforts to construct the first computing machine, which was, unfortunately, only partially completed despite financial backing from the British government. Nonetheless, Babbage's story, set against the politics and science of the early Victorian age, is fascinating. More than 150 years after its conception, one of Babbage's Difference Engines was constructed from original drawings by a team headed up by Swade at London's Science Museum. Recommended for an informed audience. Joe Accardi, William Rainey Harper Coll., Palatiane, IL Copyright 2001 Cahners Business Information.
Kirkus Reviews
An account by London Science Museum director Swade ("Charles Babbage and His Calculating Machine", not reviewed) of the work and influence of 19th-century English mathematician and inventor who was the first to proclaim the need for computers and describe their basic features. Computing is not the same as calculating. Cumbersome mechanical calculators, capable of performing fairly impressive mathematical operations, had existed for centuries. They could not, however, perform millions of such operations-although, by the 19th century, this was precisely what was required. Many professions routinely used entire volumes filled with nothing but calculations: navigational, astronomical, logarithmic, or chemical tables. Each calculation in these massive references had been performed by hand and, inevitably, errors crept in. More errors then appeared during transcribing and typesetting. It was maddening. When Babbage proposed an immense machine that could be programmed to calculate and print continually, almost everyone liked the idea, and the British government contributed a huge (for the time) sum of money for the research and development of the scheme. Babbage spent much of his own fortune and invested decades in the research, design, toil, quarrels, and personal disasters that produced sheaves of drawings and piles of parts but no complete machine. Eventually the government stopped contributing, and Babbage died a bitter man. The author has the expertise necessary to understand his subject's ideas and, after telling the story, he asks the obvious question: Would the machines have worked? The answer comes in the final chapters, which describe a six-year effort to construct one ofBabbage's designs in time for the bicentennial of his birth in 1991. In man-hours, frustration, and sheer financial cost, the enterprise duplicated Babbage's torments almost exactly, with one exception: The machine was built. And it worked. A moving and fascinating account of a brilliant man who failed in spite of his best efforts.

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The Difference Engine, Chapter One

Chapter 1


I wish to God these calculations had been executed by steam.

— Charles Babbage, 1821

A carriage clatters to a halt outside No. 5 Devonshire Street, London. A well-dressed man in his late twenties alights with a bundle of manuscripts tucked under his arm. At the sound of the carriage, a tall gentleman comes out to greet him. The visitor is John Herschel, an astronomer, up in London from his father's house in Slough. His host is Charles Babbage, mathematician. It is summer 1821.

The two friends are pleased to see each other again. Their friendship had flowered during their undergraduate years at Cambridge, and they have stayed in close touch since. They exchange pleasantries as they go inside and swap some scientific gossip. Within a few minutes they sit down to their task in the drawing room.

Herschel divides the bundle of manuscripts equally between them. The sheets are covered with closely written calculations and lists of numbers - mathematical tables they are preparing for the Astronomical Society. The results in front of them have been calculated by 'computers'. These are not machines, but people who perform routine calculations by hand according to a fixed arithmetical procedure. The two stacks of papers contain the results of the same set of calculations carried out by different computers. If the computers have done their work perfectly, the two sets of results should be identical.

They settle in their chairs and start comparing the figures. Herschel reads a number from his sheet; Babbage checks it against the entry in front of him. Line by line they proceed in thispainstaking way. They find an error - the result in Herschel's manuscript differs from Babbage's. The computers have made a mistake. The two friends mark the entry and proceed. Concentration is intense. At times they lose track, and have to go back. More errors. Babbage becomes increasingly agitated. Finally, he can contain himself no longer. 'I wish to God these calculations had been executed by steam.'

This exasperated appeal was made when Babbage was twenty-nine. Its ramifications were to dominate the rest of his life.

The burdens of calculation had plagued many before him, and Babbage was voicing the frustrations of centuries. Relief from the tyranny of numbers was sought in early mechanical aids to counting - tally sticks, pebbles and tokens - which date back several thousand years. There was a large gap until the shift from counting to mechanical calculation seized the imagination of some of the leading intellects of seventeenth-century Continental Europe. Wilhelm Schickard, Blaise Pascal and Gottfried Leibniz devised and constructed mechanical calculators to relieve the drudgery of doing sums. Leibniz's 'reckoner' built in the late 1670s used a revolutionary device, the stepped drum, which dominated calculator design for the next two centuries. The calculators of Leibniz and Pascal were sensations. They were paraded in the palaces of royalty and adorned the drawing rooms of the aristocracy, savants and the wealthy. But they were more in the nature of ornamental curiosities - objets de salon - exquisite, delicate, unreliable and unsuited to daily use.

By 1821, when Babbage and Herschel sat down to check their manuscripts, the situation was not much improved. Thomas de Colmar had just introduced a new calculating device, the arithmometer. This was a small desktop instrument with dials, sliders and a handle which, through a series of manual operations, was capable of basic arithmetic. The early arithmometers were erratic, and it was decades before they made their mark as practical devices for routine use. Slide rules were a great boon for quick and convenient calculation, but the scales and divisions were read by eye and there was an element of subjective judgement in the last decimal places. Accuracy was typically limited to three or four figures, which was fine for some purposes, but not all.

It was not until the last decades of the nineteenth century that mechanical desktop calculators became reliable, robust and cheap enough for general arithmetic - addition, subtraction, multiplication and division. Until then, scientists, engineers, surveyors and architects relied on printed tables for mathematical functions or calculations requiring more than a few figures of accuracy. Journeymen, builders, tradesmen, merchants and excise officers turned to printed books of look-up lists and 'ready reckoners' for multiplication, multiples of fractions, conversion of units and a host of arithmetical tasks essential to their daily work. Bankers, investors, actuaries, moneylenders and clerks relied on tables of interest for returns on investment, annuities and assurance premiums. The bookshelves in studies, offices, ship's cabins and workshops groaned under the weight of volumes of tables for desk use, and well-thumbed pocket editions populated the bags and pouches of those on the move.

The need for tables and the reliance placed on them became especially acute during the first half of the nineteenth century, which witnessed a ferment of scientific invention and unprecedented engineering ambition - bridges, railways, shipbuilding, construction and architecture. The heroes of the age laid much of the foundation for modern scientific and industrial life - Michael Faraday, Charles Wheatstone, Humphry Davy, John Dalton, Isambard Kingdom Brunel, Joseph Whitworth and Charles Darwin. The nineteenth century was not only an age of reason. It was also an age of quantification in which science and engineering set about reducing the world to number. With the rise of science and the burgeoning Industrial Revolution, the need for accurate and convenient numerical calculations mushroomed.

There was one need for tables that was paramount - navigation. Navigators found their position on the open seas from the moon and the stars, and astronomical tables of the kind being checked by the two friends in 1821 were crucial for this purpose. Britain was a leading maritime nation, and accurate navigation was critical to the safety of the fleet both for the protection of the realm and for trade. The stakes were high. Capital, private fortunes and lives were at stake.

The problem was that tables were riddled with errors. Finance, trade, science and navigation were at risk from hidden dangers, and the insecurity of flawed tables undermined the certainties promised and sought by the burgeoning new sciences. When errors were found in published tables a correction sheet of errata was issued and included in the next edition, and these correction sheets give some clues to just how serious the problem was. Dionysius Lardner, professor of natural philosophy and astronomy at London University, and a prolific populariser of science, sought to expose the sorry state of affairs. He inspected a private collection of 140 volumes of tables (probably Babbage's) which had a printed area covering more than sixteen thousand square feet - the size of about six tennis courts. In a random selection of 40 volumes he found no fewer than 3,000 errors acknowledged in the errata sheets. Some of the correction sheets themselves contained rrors. Lardner ridiculed the need for errata of errata, and in the case of the Nautical Almanac - a standard volume of astronomical tables - he trumpeted the absurdity of errata of errata of errata. Lardner's case was that tables were generically flawed. Yet others argued that they were accurate enough. There was no absolutely certain way of verifying tables, and experts disagreed about whether there was a crisis at all, notwithstanding Lardner's painful expose.

The problem was not the errors already found and flagged in the correction sheets, but the insecurity of not knowing how many errors remained undetected. Herschel, writing in 1842 to the Chancellor of the Exchequer, Henry Goulburn, captured this deep anxiety of the unknown: 'an undetected error in a logarithmic table is like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks may have taken place'. News of shipwrecks was a constant reminder of the dire consequences to navigation of undetected errors. Scientific magazines buzzed with novel life-saving apparatus about which outlandish claims were made. One device offered a rubber suit with a buoyancy belt and weights to keep the hapless victim vertical. A floating store provided drinking water, food, reading material ('so that he may read the news to pass the time'), cigars, and a pipe and tobacco, as well as torches and rockets to signal the victim's position to rescuers. The kit included metal frames clad with rubber which fitted round the survivor's hands so that, when tired of reading, smoking, eating and drinking while bobbing around, he or she could go places by paddling. Another device was a buoy with sailcloth trousers, gumboots and metal hoops to protect against rocks and voracious fish. The upper section of the buoy was open and large enough to allow some freedom of movement of arms and head, as well as storage for a month's supply of food and water. A concertina cowling like that found on a modern convertible car could be pulled over as a roof in high sea. Yet other devices used pedal power for propulsion and lights for attracting attention.

The preoccupation with shipwrecks was not confined to scientific magazines and reports of sensationally impractical inventions. The Illustrated London News carried stark accounts of distressed ships often depicted in dramatic engravings. The foundering of the iron steamer Brigand was reported with an artist's rendering and a vivid eyewitness report by a survivor of 'this lamentable catastrophe'. The Brigand was only two years old, and had been built at a cost of £32,000 to ply between Liverpool and Bristol. Such reports rarely identified navigational error as the cause of disaster, nor did they specifically incriminate the accuracy of tables. But they were constant public reminders of the dangers of sea voyages, and provided a strong base from which to argue the dread consequences of erratic navigation.

The source of errors in tables was clear: human fallibility. The preparation of mathematical tables was a laborious, tedious and exacting task. For a start, mathematicians devised the formulae and the range of values the tables were to cover. This was the clever part. They then calculated the 'pivotal values' - series of numbers at relatively large intervals. Filling the gaps involved calculating all the values in between (called sub-tabulation). This was a task of awesome drudgery. Each entry in the table had to be calculated by hand, and the production of a complete table demanded the seemingly endless repetition of the same series of arithmetical steps performed on slightly different numbers. To spare themselves, the mathematicians farmed out the routine work to the 'computers' - a common reference to people who performed calculations. (Computers are not the only devices to have human antecedents. Later in the nineteenth century, 'typewriter' referred to a person who typed rather than to the machine itself. It was not unheard of for the boss to elope with his typewriter.)

It was standard practice to give the same task to two computers who would perform the same set of calculations without collaboration. The results, independently prepared in this way, would then be checked against each other. This system of error detection was not foolproof, and it was not unknown for both computers to commit the same mistake. But if independently calculated results were found to be in agreement, this established a high degree of confidence in the correctness of the entry. Any discrepancy in the two results signalled an error and the offending pair of numbers were checked for correctness. This was the stage that Babbage and Herschel had reached when Babbage was driven to proclaim what is perhaps one of the most resonant utterances of the nineteenth century in appealing to 'steam' to execute calculations.

Once checked, results were copied by hand into lists and the manuscripts given to printers for typesetting. Inevitably the process of transcription was itself vulnerable to error. The typesetter then set the results using loose metal type, in preparation for printing. A compositor read each numerical result and selected a separate piece of type for each digit in the number. Pieces of type were laid alongside one another to make up the digits of the desired number, and sets of type were blocked together in a frame to make up a page for use in a printing press. Typesetting acres of numbers is a monotonous task and one that, as ever, is liable to error. A compositor setting text into type can at least recognise meaningful groups of letters making up words. But numbers have no immediate meaning, and there is no intuitive sense of whether or not any one digit has a sensible relationship to the one before or after.

Even when printed sheets of tables finally rolled off the press, the job was not yet done. The printed copy still needed to be proof-read. Anyone faced with a sea of numbers will be daunted by the burden of verifying them. It is not only monumentally tedious, but the process of checking is itself vulnerable to error however conscientiously the task is carried out.

At each of the four stages in the manual production of tables - calculation, transcription, typesetting and proofing - errors wait in ambush. Human frailty is the enemy of accuracy. What confidence could anyone have in the integrity of the outcome?

But what of Babbage's appeal to steam? Britain was in the throes of industrial revolution. Products poured from the new manufactories, and there seemed no limit to the variety and invention of the industrial arts as new materials and processes of manufacture were exploited. Britain led the way and, as Benjamin Disraeli put it in 1838, was fast becoming 'the workshop of the world'. The essayist and historian Thomas Carlyle called the decades of upheaval 'the Age of Machinery'. Science, engineering and the flourishing new technologies held limitless promise. Machines were the obsession of the times, and the extent to which motive power and mechanism permeated life sometimes touched on the absurd. One scientific magazine proclaimed the benefits of a 'new domestic motor'. The illustration shows a woman sitting in a rocking chair darning a sock. Through a system of pulleys, levers and weights, the oscillating chair rocks a cradle with a cherubic sleeping infant, and operates a milk churn at the same time. The reporter noted:

By this means, it will be observed, the hands of the fair operator are left free for darning stockings, sewing, or other light work while the entire individual is completely utilised. Fathers of large families of girls, Mormons, and others blessed with a superabundance of the gentler sex, are thus afforded an effective method of diverting the latent feminine energy, usually manifested in the pursuit of novels, beaux, embroidery, opera-boxes, and bonnets, into channels of useful and profitable labour.

On an industrial scale the engines of change were not women, but the steam engines which powered the factories. At the time of Babbage's invocation of steam as the salvation of tables from the curse of human fallibility, steam was both the actual and symbolic agent of change and held the promise of prosperity for all.

The encounter with Herschel in 1821 when the two friends met to verify the calculations of the computers was the genesis episode in the history of automatic computation. The account given here is based on the description Babbage wrote some eighteen years after the meeting.

In a separate record written closer to the events, Babbage is less sure whether it was he or Herschel who made the seminal appeal to steam, and comments that, whoever it was, he was in any case half-joking. Despite the differences between Babbage's accounts, the essential features of the encounter are clear. The problem was the daunting handicap of human fallibility to reliable calculation. The solution was machines.

—From The Difference Engine: Charles Babbage and the Quest to Build the First Computer by Doron Swade. (c) September 2001, Viking, a division of Penguin Putnam, used by permission.

Meet the Author

Doron Swade, assistant director and head of collections at the Science Museum in London, is an engineer, historian of technology, and a leading authority on the life and work of Charles Babbage.

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