Following his graduation, de Prony had hoped to live in the capital and pursue scientific research, but the conventional assignment for young engineers was a term of service in the field. He fulfilled his duty and found a way back to Paris by taking an appointment as an inspector, an officer who critiqued the mathematical analyses of other engineers and verified calculations. Though the assignment involved no independent work, he found it a pleasing activity, reporting that “happy circumstances then put me in contact, with the most distinguished savants of the capital.” It also brought him into contact with foreign savants, including Nevil Maskelyne. De Prony met Maskelyne when the corps decided that it needed to remeasure the difference in longitude between Paris and London. Beyond the intellectual challenge of this work, an accurate measurement of the difference would allow French surveyors to use the British Nautical Almanac in their work and enable the Académie des Sciences computers to compare their tables with the output of Maskelyne’s computers. As part of the effort to measure the difference between the two capitals, de Prony traveled to Greenwich, met Maskelyne, and inspected the work of the almanac computers.26
De Prony had become leader of the Bureau du Cadastre because of a cautious and uneasy relationship between the corps engineers and revolutionaries. The revolutionaries were wary of the corps, their uniforms, and their fleur-de-lys buttons, yet they needed the services of corps officers and could not easily dismember the group. In an attempt to weaken the authority of the corps, the revolutionary government tried to disperse the officers, most of whom resided in Paris, and have them take positions in the countryside.27 In early 1791, the government ordered de Prony to move to southwest France but found that he was unwilling to take the assignment. “I have received your letter, informing me that I am appointed engineer-in-chief for the departement of the Pyrenees,” he wrote to his superintendent. “In these circumstances, I beg you to permit me to remain in Paris.” He argued that he was working on two reference books that would be difficult to complete without the resources found in the capital. Claiming that the research had “already cost me many sleepless nights,” he stated that he was willing to forgo a formal assignment so long as he could stay in Paris and continue with his research. After a brief confrontation, a senior officer intervened and gave de Prony the job at the Bureau du Cadastre.28
In ordinary times, de Prony would have been responsible for organizing surveying teams and dispersing them across the country, but 1791 was no ordinary time. The dangers of civil unrest forced de Prony to keep the survey teams in Paris and occupy them with “tasks of public usefulness.”29 Under these circumstances, he sought or accepted the task of preparing the trigonometric tables for the decimal grade system of angle measure. De Prony wrote that the assignment “over-burdened” him.30 The Académie des Sciences wanted the work done quickly and required that the final tables leave “nothing to be desired in accuracy.”31 As he contemplated the work before him, he devised a plan based upon the first chapter of The Wealth of Nations. A French commentator has suggested that de Prony approached the book haphazardly, the way one might flip open a Bible to search for an inspiring verse. “He opened it at random and his eye fell on the first chapter, which was called A Treatise on the Division of Labor, and which cited the example of making pins.”32 It is a dramatic rendition of the story, but it overlooks the long-standing influence of The Wealth of Nations upon the engineers in the Corps des Ponts et Chaussées. The book had circulated among the officers during the early 1780s and was probably an old and familiar friend to de Prony.33
De Prony recalled that the pin example provided the insight he needed. “Suddenly,” he wrote, “I conceived how I might apply the same method to the work which had burdened me.” Referring to one of the tables he needed to compute, he recorded that his bureau “could manufacture logarithms as easily as one manufactures pins.”34 His recollection of the event ignores a great deal of hard work and gives his accomplishment a patina of false confidence. The structure of de Prony’s computing office cannot be easily seen in Smith’s example. His computing staff had two distinct classes of workers. The larger of these was a staff of nearly ninety computers. These workers were quite different from Smith’s pin makers or even from the computers at the British Nautical Almanac and the Connaissance des Temps. Many of de Prony’s computers were former servants or wig dressers, who had lost their jobs when the Revolution rendered the elegant styles of Louis XVI unfashionable or even treasonous.35 They were not trained in mathematics and held no special interest in science. De Prony reported that most of them “had no knowledge of arithmetic beyond the two first rules [of addition and subtraction].”36 They were little different from manual workers and could not discern whether they were computing trigonometric functions, logarithms, or the orbit of Halley’s comet. One labor historian has described them as intellectual machines, “grasping and releasing a single piece of ‘data’ over and over again.”37
The second class of workers prepared instructions for the computation and oversaw the actual calculations. De Prony had no special title for this group of workers, but subsequent computing organizations came to use the term “planning committee” or merely “planners,” as they were the ones who actually planned the calculations. There were eight planners in de Prony’s organization. Most of them were experienced computers who had worked for either the Bureau du Cadastre or the Paris Observatory. A few had made interesting contributions to mathematical theory, but the majority had dealt only with the problems of practical mathematics.38 They took the basic equations for the trigonometric functions and reduced them to the fundamental operations of addition and subtraction. From this reduction, they prepared worksheets for the computers. Unlike Nevil Maskelyne’s worksheets, which gave general equations to the computers, these sheets identified every operation of the calculation and left nothing for the workers to interpret. Each step of the calculation was followed by a blank space for the computers to fill with a number. Each table required hundreds of these sheets, all identical except for a single unique starting value at the top of the page.
Once the computers had completed their sheets, they returned their results to the planners. The planners assembled the tables and checked the final values. The task of checking the results was a substantial burden in itself. The group did not double-compute, as that would have obviously doubled the workload. Instead the planners checked the final values by taking differences between adjacent values in order to identify miscalculated numbers. This procedure, known as “differencing,” was an important innovation for human computers. As one observer noted, differencing removed the “necessity of repeating, or even of examining, the whole of the work done by the [computing] section.”39
The entire operation was overseen by a handful of accomplished scientists, who “had little or nothing to do with the actual numerical work.” This group included some of France’s most accomplished mathematicians, such as Adrien-Marie Legendre (1752–1833) and Lazare-Nicolas-Marguerite Carnot (1753–1823).40 These scientists researched the appropriate formulas for the calculations and identified potential problems. Each formula was an approximation, as no trigonometric function can be written as an exact combination of additions and subtractions. The mathematicians analyzed the quality of the approximations and verified that all the formulas produced values adequately close to the true values of the trigonometric functions.
Joseph Lalande visited the Bureau du Cadastre in 1794, after the computers had been working for nearly two years. He probably saw only the office of de Prony and his planners. No record has been found of a centralized computing floor for the former hairdressers.41 Given the size of the computing staff and the tradition of cottage work, it is likely that the computers did their calculations at home. Lalande, who had become the éminence grise of French astronomy, reported that de Prony’s computers were “producing seven hundred results each day.”42 At that pace, they could have duplicated Clairaut’s calculations for Halley’s comet in about a week
. Perhaps more to the point, if Lalande, Lepaute, and Clairaut had been asked to prepare de Prony’s decimal trigonometry tables, they would have spent a century and a half sitting at their table in the Palais Luxembourg.
Lalande’s visit seems to have marked a high point of the cadastral computers. In 1795, the revolutionary government instructed de Prony to prepare the tables for publication “at the expense of the nation,”43 but by the time de Prony completed the work, the nation was not all that interested in paying for the new trigonometry. Decimal angle measure was not included in the law implementing the new metric system, which was passed by the National Assembly on August 1 of that year.44 “In the face of popular indifference and hostility,” wrote historian Ken Alder, “the government began to lower its sights.”45 Officials had difficulty enforcing the use of metric measures in Paris, and there is little evidence that it penetrated into the countryside.
De Prony kept his project in operation through 1800 or 1801, even though it appears that most of the work had been completed by 1796. Even before the typesetters began work on the tables, de Prony’s publisher began to promote the new trigonometric functions with the story of their creation. According to the advertisement, de Prony had created a new “process of manufacturing” that was “strange in the history of science, where there is no other example.” The publisher argued that the tables would never have been created “if M. de Prony had not had the fortunate idea of applying the powerful method of division of labour,” but such words could not bring the tables into print.46 The publisher was bankrupted during a national fiscal crisis. The French government, then led by Napoleon, had no interest in completing the work. De Prony retained the nineteen-volume manuscript and made occasional, though fruitless, efforts to publish it.47
The story of Gaspard de Prony and his computers at the Bureau du Cadastre would have been little more than an odd footnote to the history of economics were it not for the attention of Charles Babbage. Babbage is generally remembered as a mathematician and as a designer of early computing machinery, but he was a broad and eclectic scholar whose interests ranged from mathematics and astronomy to economics and railroad construction. To a certain degree, he fit the stereotype of the Victorian gentleman scientist. He had been educated at Cambridge in the canonical works of Newton and Halley; he possessed a comfortable, though not extravagant, income that allowed him to pursue his own interests; he lived in London and mingled freely with the country’s political and intellectual elite. In some ways, he was more interested in the organizations and institutions of science than he was in the science itself.48
Babbage arrived in London in 1814, finished with his Cambridge studies and newly married. He applied to be a computer at the Royal Greenwich Observatory, but friends encouraged him to direct his talents elsewhere.49 Looking for ways to establish a reputation as a scientist, Babbage decided to give a series of public lectures on astronomy. His mathematical training was deeply connected to astronomical problems, but that training did not make him an expert on stars and comets and planets. In preparing the lectures, he relied on the advice of more accomplished colleagues, notably a college friend, John Herschel (1792–1871), and Herschel’s aunt, Caroline Herschel (1750–1848). The two were members of England’s premier astronomical family. William Herschel (1738–1822), the father of John and the brother of Caroline, had discovered the planet Uranus in 1781. Caroline Herschel had served as her brother’s assistant before she became recognized for discovering comets and cataloguing nebulae.50
5. Charles Babbage
Babbage’s lectures brought him to the attention of a group of businessmen and amateur astronomers who were organizing a society for “the encouragement and promotion of Astronomy.” This group, originally called the Astronomical Society of London, invited Babbage and John Herschel to their first meeting. This meeting was held in January 1820 at a tavern situated among the business houses of central London. Most of the founders had some connection to ocean trade and the problems of celestial navigation. They were merchants, currency traders, stockbrokers, and business teachers.51 Though many of them were comfortable behind the lens of a telescope or computing the orbit of a planet, they described astronomy as if it were another commercial endeavor. The language of Adam Smith and divided labor permeated their words and sentences. They stated that the society would coordinate the “labours of insulated and independent individuals” and that they were “ready and desirous to divide at once the labour and the glory” of celestial observation. Their descriptions of the society suggest that they had some first-hand experience with the problems of management, for they wrote of the need “to preserve a perfect unity of design” while simultaneously preventing the loss of effort.52
In 1821, Babbage and Herschel agreed to undertake one of the first projects sponsored by the society, a set of mathematical tables that would augment the material in the British Nautical Almanac. The two college friends prepared a computing plan and hired a pair of computers to produce two independent versions of the table. Once the computers had finished their work, Babbage and Herschel compared the results. Sitting together, one of them read aloud the values from his version of the table. The other held the second table and confirmed each number. “Finding many discordancies,” Babbage later wrote, “I expressed to my friend the wish that we could calculate by steam.”53 He would point to this work as the start of his study of computing machines, but he would repeat at least two inconsistent versions of this story. A second narrative placed his moment of insight during his student days in Cambridge. Both versions suggested that the idea to design a computing machine grew out of a desire to improve the accuracy of calculation. As Babbage would acknowledge, he was neither a trained engineer nor a skilled machinist.54 His design for a computing engine would be based upon the division of labor, though not upon Maskelyne’s ideas but upon those of de Prony.55
Babbage knew of de Prony and the cadastral computers when he and Herschel prepared their tables in 1821. He may have seen the manuscript tables when he visited Paris with his wife in 1819, or he may have learned of the computing effort when de Prony asked a wealthy English physician to help publish the tables.56 Babbage was little interested in the decimal trigonometry tables but clearly understood the benefits of de Prony’s organizational plan. He wrote that de Prony’s experience showed that the division of labor was not restricted to physical work but could be applied to “some of the sublimest investigations of the human mind,” including the work of calculation. After his own attempts at calculation, Babbage turned to de Prony’s analysis and took the division of labor to its next logical step, the invention of a machine to “facilitate and abridge” the work.57
When he began work on his calculating machine, Babbage was following a path that was already well marked. Inventors in both England and the United States had built machines based upon Adam Smith’s example of the divided labor in pin manufacture. Their machines followed each step that Smith had identified in The Wealth of Nations. They cut a roll of wire into fixed lengths, sharpened one end of each wire segment, affixed a head to the other, and placed the finished pin in a paper holder. Babbage took the opportunity to study one of these pin-making machines and reported that “it is highly ingenious in point of contrivance,” especially interesting “in respect to its economical principles.”58
Babbage designed a machine that might be considered more flexible than the pin-making machines. Rather than analyze the equations that had been used to create a specific table, such as the decimal trigonometry tables, he considered a single computational technique that could be applied to many kinds of calculation. The technique that he chose was a process of mathematical interpolation known as the finite difference method. The finite difference method is one way of computing intermediate values of a table, such as the intermediate positions of the moon that Nevil Maskelyne’s computers prepared for the British Nautical Almanac. It is especially amenable to the division of labor because it reduces the entire process into the s
imple operation of addition. A simple application of this method can compute a list of the squared integers (4, 9, 16, etc.) without performing a single multiplication. First, one computes a list of the odd integers: 1, 3, 5, 7, 9, etc. This can be done by starting with the number 1 and successively adding 2: 1 + 2 = 3, 3 + 2 = 5, 5 + 2 = 7. Once this has been completed, one can sum the list of odd integers to get the list of squares: 1 + 3 = 4, 4 + 5 = 9, 9 + 7 = 16, and so on.
Though Babbage’s machine would be far more complicated than the pin-making device, it was simpler in one respect. The pin machine needed to perform four different fundamental operations. Babbage’s machine would only need to do one: addition. Babbage started with a geared adding mechanism originally developed by Blaise Pascal (1623–1662) in 1642,59 improved the design, and cascaded the devices so that the results of one addition would be fed to the next. To create a list of squared integers, one mechanism would repeatedly sum the number 2 to create new odd numbers. The next mechanism would sum the odd numbers to create the squares. By the spring of 1822, Babbage had completed a demonstration model of his machine, which he named the “Difference Engine.”
The London of 1822 was wholly unprepared for Babbage’s machine. It was a world of gaslights and horse-drawn carriages, of servants and walking sticks. Most residents had not yet seen a steam locomotive, as the city’s first railroads were still under construction.60 Though the idea of the adding machine was one hundred and eighty years old, there was none to be bought or sold. The first commercial machine, which would be produced in France, existed only as a crude prototype.61 Babbage anticipated that his machine might be met with disbelief or even opposition. He cautiously approached the Royal Society, recognizing that the organization might be able to help him promote his machine. His letter to the society president made conservative claims and acknowledged that Royal Society members might not believe it possible to create a machine that could handle such complex calculations without supervision. He tried to disarm potential criticism by invoking Jonathan Swift: “I am aware that the statements contained in this Letter may perhaps be viewed as something more than utopian, and that the philosophers of Laputa may be called up to dispute my claim to originality.”62
When Computers Were Human Page 5
