CHAPTER SIX

Looking Forward, Looking Backward: Machinery 1893

ON A TYPICAL WORKDAY in 1881 or 1882, Rhoda Saunders would begin her calculations in the Harvard Observatory computing room by picking up her pen, uncorking her bottles of ink, one black and one red, and opening her computing book. All of these objects would have been familiar to Edmund Halley in the seventeenth century or Nicole-Reine Lepaute in the eighteenth, but each had been subtly changed by industrialization. Saunders’s pen had a preformed steel nib that easily outlasted the hand-cut point of a goose quill. Her bottles of ink were commercially produced and varied little from batch to batch. The lines in her computing book, printed by a mechanical press, were straight and true, without any of the wiggles or cramped margins found on the hand-ruled sheets of Nevil Maskelyne or Maria Mitchell.

The uniformity that could be found in Saunders’s mass-produced writing implements could also be found in a new generation of computing tools. The slide rule, which became popular in the United States during the 1880s, was a mass-produced version of a 1622 invention.¹ The original slide rule had been created by the English mathematician William Oughtred (1574–1660), who used the concept of logarithms. Logarithms were a new discovery in the early seventeenth century. They are special values that converted multiplication into addition. For any number, a mathematician could find a corresponding logarithm. For example, the logarithm of 2 is .3010, while the logarithm of 3 is .4772.² By adding the two logarithms, we get .7782, which is the logarithm of 6, the product of 2 and 3. Oughtred created his rule by inscribing two rods with logarithmic scales that resembled the scales of an ordinary ruler, except that the space between numbers grew smaller and smaller as the values increased. By sliding these two rods, Oughtred could add two logarithms or, equivalently, multiply two numbers.

The slide rules of Oughtred and other seventeenth-century scientists were expensive, hand-crafted devices, each one designed for a specific kind of problem. Isaac Newton created a rule with three slides that could be used to solve cubic equations. England’s first Astronomer Royal, John Flamsteed (1646–1720), purchased a special rule for astronomical calculation.³ Only with the invention of precision ruling machines that could cut logarithmic scales did these rules become common. These machines started appearing in the early nineteenth century. By 1833, slide rules were so inexpensive that Gaspard Riche de Prony could report that Parisians are “commonly using ‘sliding rules’ at all levels, including shop keepers and artisans.”⁴

In the United States, “interest in the slide rule was awakened in about 1881,” according to an early historian of mathematics. Again, the driving force behind the adoption of the slide rule was a manufacturing economy that could produce them in large quantities. During the 1880s, slide rules were introduced in the American university curriculum, and they started to appear in the engineering literature. Most American scientists adopted a standard version of the slide rule known as the “Mannheim rule,” named after its designer, a French army officer.⁵

Slide rules were used only sporadically by the observatories and almanacs because they could not perform calculations to the precision needed by astronomers. A good slide rule operator could get an answer to two or three digits of precision. Observers and astronomers often wanted each calculation accurate to six or eight digits. The astronomical computers were more open to the geared adding machine. Like the slide rule, the adding machine was a seventeenth-century curiosity that became an important tool only after it encountered nineteenth-century methods of mass production, especially the development of interchangeable parts and high-precision manufacturing. The adding machine can be traced to the same geared mechanism of Blaise Pascal that inspired Babbage’s Difference Engine. Pascal’s device consisted of eight geared wheels, each marked with the digits from 0 to 9. An operator would add two numbers by turning the wheels. Once a wheel had completed a full cycle, moving through the numbers 1 through 9 and returning to zero, it would trip a carry mechanism that would advance the neighboring wheel by one place. Pascal tried to manufacture his machine and sell it, but he was unable to build a robust device that would produce reliable results in the hands of others. As the historian Michael Williams has observed, “The mechanism, although ingenious, is rather delicate and prone to giving erroneous results when not treated with the utmost care.”⁶

The first adding machine to achieve large sales, the French Arithmometer, was a contemporary of the Scheutz difference engine. It was developed by Charles Xavier Thomas de Colmar (1785–1870) during the 1840s. De Colmar, an actuary, attempted to sell his first machines to insurance firms but found it difficult to convince business owners that they could benefit from a machine that could do arithmetic. “It was not enough to see need,” wrote James Cortada, historian of the adding machine industry; “the [adding machines] had to be sold.”⁷ De Colmar began to find a market for his machines only after he displayed them at the Paris Exhibition of 1867.⁸ He drew visitors to his presentation with a giant Arithmometer, a machine approximately the size of a piano. His standard machine, which was only about two feet long, was purchased by customers from France, Britain, and even the United States.

Unlike the slide rule, the de Colmar adding machine could compute to high precision. By 1878, a British scientist observed that “English astronomers are now just beginning to use [the arithmometer] for the tedious computations continually going on in observatories.”⁹ Demand for de Colmar’s machine began to grow in the late 1880s, largely driven by the expansion of office work. The decade produced several improvements to calculating machines, including lightweight adding mechanisms and keyboards for entering numbers. In the United States, the adding machine industry took root in the new industrial cities of St. Louis and Chicago. These cities were railroad hubs and supported substantial populations of skilled mechanics and adventurous businessmen, “the hopeful and the hopeless—those who had their fortune yet to make and those whose fortunes and affairs had reached a disastrous climax elsewhere.”¹⁰ They produced industry pioneers such as Frank Baldwin (1838–1925), William Seward Burroughs (1855–1898), and Dorr E. Felt (1862–1930). Baldwin created a lightweight machine that resembled a hand-cranked coffee grinder that had been laid on its side. Burroughs designed a more substantial machine for banks. His device, also named the Arithmometer, stood four feet tall on long legs and was covered by ranks of buttons that were labeled with the numbers 0 to 9. Felt called his device the Comptometer.¹¹ It was about the size of a cigar box and weighed no more than a college dictionary. It was the first machine purchased by one of the major computing laboratories. In 1890, the Coast Survey computers acquired one for Myrrick Doolittle, who used it to adjust triangulations with his method of least squares. The next year, the Coast Survey Comptometer was joined by a Burroughs Arithmometer.¹²

The last of the new computing machines, the punched card tabulator, was developed at the same time that Baldwin, Burroughs, and Felt were building their first adding machines. Like the slide rule and the adding machine, it combined ideas from older technologies with the new methods of mass production. Punched cards had been developed to control looms in the early nineteenth century. The tabulator had a geared counting mechanism, like the mechanism of Pascal. The influence of mass production came not from machine tools or the concept of interchangeable parts but from the mass processing of data at the United States Census Office. The Census Office was assembled every ten years to fulfill the constitutional requirement of enumerating the American population. Over the ten censuses that had been performed since 1790, the office had developed an elaborate system of clerks and forms to summarize the population counts. Through the 1880 census, the office employed no real machine to assist the work beyond a frame that held a role of paper.

One of the workers at the 1880 census was Herman Hollerith (1860–1929), a recent graduate of the Columbia University engineering school. Hollerith would later recall that his interest in mechanical tabulation began on a day when he was inspecting the office operation with the census director. Watching the clerks repeat similar operations again and again, the director remarked that “there ought to be a machine for doing the purely mechanical work of tabulating population and similar statistics.”¹³ It took three years for Hollerith to conceive the basic principles of a mechanical tabulating device and refine these ideas into a workable system. In later years, he would claim that he found his inspiration by watching a train conductor punch holes in a ticket. By 1885, he was recording data as holes in cards, where each card held information for a single person. Was the subject female? There was a hole to punch. Was she a resident of Massachusetts? There was another hole to punch. Did she own property? There was a third hole to punch. His tabulator read the data from each card. The card was placed on a little frame, and an array of wires was lowered upon it. If the wire encountered a hole, it would complete a circuit and advance a counter. If it encountered cardboard, it would do nothing.¹⁴

Hollerith tested his tabulating system in 1886 by computing vital statistics for Baltimore, the numbers of births and deaths in the city. The test gave him an opportunity to see how his machines would fare in a production situation and correct any design flaws. The Census Office followed the progress of the test and the accomplishments of the machines. In 1889, they gave the machine a formal trial for the 1890 census and compared it with two other methods that had been proposed to tabulate the records. Of the three, Hollerith’s method was the only one that involved a new computing machine. The director of the census judged that the three “methods have certain features in common,” as each recorded the census information on cards and then sorted the cards to tabulate the data. The other two methods sorted the cards by hand and then used racks or preprinted paper forms to make the final counts. When the three systems were compared in a trial, Hollerith’s system proved to be twice as fast as the other two. “The total probable saving,” wrote the director of the census, “from the use of punched slips and the electrical counting-machine would amount to $579,165,” enough money to pay the salaries of five hundred census clerks.¹⁵

15. Hollerith punched card tabulator and operator

In early 1890, when the tabulating machines were installed in the Census Office, they created a sense of mystery and reverence among some of the staff. “One who has not had personal experience in handling cards cannot conceive the stimulating effect which they have upon the imagination of the statistical computer,” wrote one worker. He described the cards as images of living beings “whose life experience is written upon their face in hieroglyphic symbols.” The tabulating machines, which not only counted the cards but also sorted them into little bins, seemed to presage a final judgment. One human computer claimed that the sounds of the tabulating machine were “the voice of the archangel, which, it is said, will call the dead to life and summon every human soul to face his final doom.”¹⁶

The tabulators were not motor driven and hence did not produce the roar of a machine shop, but they made a loud click each time the wires descended upon the card and rang a bell to signify that the data had been counted. A visitor to the Census Office recorded that the facility was far noisier than an ordinary office. “Upon first entering the [computing] room,” he wrote, “the whizzing of the electric fans and the ringing of bells, which are attached to each machine and respond to every touch upon the keys, are confusing.” The Census Office paid a weekly lease on the machines and was eager to complete the tabulation as quickly as possible. Clerks were required to punch 700 records a day. Tabulator operators processed 50,000 records on each shift. The visitor observed that the census director demanded so much of the staff that many workers lasted only a few days and that, finally, “none but the industrious are left.”¹⁷

The Hollerith tabulators received their first public display at the World’s Columbian Exposition, the Chicago World’s Fair of 1893. Hollerith was a reluctant participant, perhaps concluding that his invention would be overlooked at an event that offered 65,000 individual exhibits spread over a 633-acre campus.¹⁸ “He doesn’t want to go one bit,” his mother-in-law recorded, “and will only exhibit his machines in the Census Office exhibit.” His machines were rewarded with a bronze medal as a “novel electrical tabulating system,” but scientific computing and computing machinery were only a small part of the exhibit.¹⁹ The Hollerith machines occupied one corner of the government display. Slide rules from Germany and America could be found between bolts of cloth and gleaming steam engines. The adding machines invented by Dorr Felt and William Burroughs were grouped with accounting ledgers and wooden desks. The U.S. Navy gave a small case to the American Ephemeris and Nautical Almanac as part of a grand display of naval power. The Coast and Geodetic Survey proudly showed its maps and field instruments to the visitors, but only a discerning observer would have appreciated that the agency had a large computing office.²⁰

“The Exposition itself defied philosophy,” wrote historian Henry Adams. “Since Noah’s Ark, no such Babel of loose and ill joined, such vague and ill-defined and unrelated thoughts and half-thoughts and experimental outcries as the Exposition, had ever ruffled the surface of the Lakes.”²¹ For all of its importance to Chicago and to American culture, the exposition was only a trade show, a grander version of the American county fair. The direct connection to the rural agricultural shows could be found at the south end of the grounds, where farmers displayed well-scrubbed hogs and carefully nurtured ears of corn. Perhaps the only common theme to be found in the exposition were the statistics of economic growth that accompanied almost every product. Exhibitors used numbers to describe the cost of their products, the value of labor they would save, the lives they would improve, and the profits they would make. Henry Adams confessed that he stood before one exhibit and was “obliged to waste a pencil and several sheets of paper trying to calculate exactly when, according to the given increase of power, tonnage, and speed, the growth of the ocean steamer would reach its limits.”²² An extreme use of statistics could be found in the German pavilion, where Krupp Industries displayed a new cannon that weighed 42 tons, had a 17-inch bore, and could throw a 2,300-pound projectile 16 miles at a cost of $1,259 per shot. In jest, Krupp engineers had suggested that the exposition committee might fire the gun at the conclusion of the fair, as they had calculated that the “concussion would undoubtably knock down all the great buildings in Jackson Park and thus save a lot of labor in their removal.”²³

16. Exhibit hall of the World’s Columbian Exposition

Taken by themselves, these commercial statistics offered little to human computers, as they were not considered to be part of scientific calculation. When placed in the larger context of the fair, the presence of social statistics suggested that many individuals and organizations were attempting to bring the precision of scientific calculation to the phenomena of social, economic, and personal life. The use of statistics was clearly seen at the intellectual part of the exposition, a series of meetings called the World’s Congress Auxiliary. The Congresses, as they were called, were held at the newly finished Art Institute building in center-city Chicago rather than at the fairgrounds. In contrast to the fair directors, who were most interested in material products and inventions, the Congress organizers took as their motto “Not things but men; not matter but mind.” Between May and October, there were 1,200 separate meetings that covered almost every aspect of human endeavor. Some of these congresses were conferences of existing professional organizations, while the rest were special events that covered topics such as women’s rights, religion, art, philosophy, engineering, history, literature, and science.²⁴

The Congress most directly related to computation, the meeting on mathematics and astronomy, revealed signs of a split between the two disciplines, the decline of an old alliance that had nurtured human computers. Representatives of the astronomers and the mathematicians had agreed to hold a single meeting, but there was no Benjamin Peirce, no central figure to pull the groups together. The mathematicians, desirous of showing their independence and sophistication, were discussing the theorems and proofs of German mathematics. It was a time when German scholarship, particularly German scientific research, “became the focus of extravagant excitement and admiration.”²⁵ German mathematicians emphasized abstraction, generality, rigor, and formal proofs. Of the forty-six mathematical speakers at the Congress, half came from Germany. Congress organizers were so interested in German methods that they arranged for a special train to take them to the fairgrounds so that they might study a display prepared by the German universities of Göttingen, Bonn, and Berlin.²⁶

At the Mathematics and Astronomy Congress, the established computing offices could offer nothing that could compare to the German speakers. The first American to address the group was the librarian of the Coast and Geodetic Survey Office, Artemas Martin (1835–1918). Martin was the kind of mathematician that had once been common in the United States. He had been raised on a farm in western Pennsylvania and had taught himself the basic elements of mathematical practice. While selling produce at a local market, he would fill the margins of his account books with mathematical problems and their solutions.²⁷ Though he was well known for his “rare and happy faculty of presenting his solutions in the simplest mathematical language,” his contributions seemed overwhelmed by those of the German contributors.²⁸

The astronomy talks were also divided between the old and the new. The senior astronomers were more interested in the new methods of astrophysics than in the classical calculations of positional astronomy. Edward Pickering, whose computing floor at Harvard remained one of the largest astronomical computing groups, talked about his analysis of the light reflected from the moon, an analysis that identified the chemical composition of the lunar surface. The discussion of calculation was left to the junior astronomers: a French computer, Dorothea Klumpke, from the Paris Observatory; Maria Mitchell’s replacement at the Nautical Almanac Office, David Todd; and Harvard computer Wilhemina Fleming.²⁹

The Congress on Electrical Engineering, which was held the same week as the Mathematics and Astronomy Congress, suggested that organized computing was starting to move into the commercial and manufacturing applications of science. An employee of the new General Electric Company, the engineer Charles Steinmetz (1865–1923), gave a talk on the mathematical model of alternating current. Near the end of his presentation, he described his company’s computing division. For those familiar with the computing offices of observatories and almanacs, the name was misleading, for the division had no large staff of human computers. The computing division consisted of a small staff of engineers who reviewed the designs of electrical circuits, motors, controllers, and other devices. Using the techniques that were being developed by Steinmetz and others, these engineers verified that the electrical devices would behave as they were intended to behave. This work required a lot of calculation, but for the moment, all of the arithmetic was handled by the engineers themselves. A decade would pass before they would divide the work with a staff of human computers.³⁰

The Congress on History provided a starting point for the use of numbers in the social sciences and the need to process large amounts of statistical data. The congress included a paper by University of Wisconsin professor Frederick Jackson Turner, who began his talk by referring to the reports of the 1890 census. Using numbers that had been tabulated by Herman Hollerith’s machines, the reports stated that the United States no longer had a large area that could be considered an unpopulated frontier. “This brief official statement marks the closing of a great historic movement,” observed Turner to his audience. “Up to our own day, American history has been in a large degree the history of the colonization of the Great West.”³¹ Turner’s conclusion may have surprised his audience, but it built upon a traditional relationship between statistics and the discipline of history. Through the end of the nineteenth century, the study of statistics was related more closely to historical research than to mathematical study. The term “statistics” was taken to mean the numbers of the state, the numbers that described the strength, wealth, and health of a country.³² Most of the early American statisticians were either physicians or historians. The physicians were using numbers to measure problems of public health, while the historians were interested in social stability.³³ The Statistical Congress at the fair spent little time on mathematical issues and debated how numbers could be better used for governance and management.³⁴

By 1893, statistical methods had begun to spread to other fields of research, notably economics, agricultural research, and the field that would ultimately be named “Sociology.” The Congress on Social Progress caught the first discussions of this new discipline. One of the key speakers, the Chicago social worker Jane Addams (1860–1935), based her ideas on the practical needs of the city dwellers, but she reached for a deeper understanding of society that could only come through numbers. She not only spoke of individual cases that appeared at Hull House, the institution that she had founded, but also tried to give a fuller picture of social needs in the city of Chicago. Her ideas were echoed in other discussions that touched upon social issues, notably the Congress on Women’s Progress and the Congress on Labor.³⁵

Henry Adams, who spoke at the History Congress, clearly saw the rising importance of statistics and numbers in the study of social life but was uncomfortable with such tools. “At best [I] could never have been a mathematician,” he wrote, “but [I] needed to read mathematics, like any other universal language, and [I] never reached the alphabet.”³⁶ Numbers tended to suggest a scientific certainty, fundamental laws, ultimate goals. To him the fair and congresses suggested that Americans seemed to be “driving or drifting unconsciously to some point in thought, as their solar system was said to be drifting towards some point in space,”³⁷ but he could not identify that point. Within the field of computation, it is hard to find a single idea at the fair that summarized the position of human computers in 1893. One can find the influence of the traditional computational fields: astronomy, calculus, surveying, and navigation. Equally prevalent were the new ideas of German mathematics, social science, mathematical statistics, and computing machinery. Tying these themes together were the familiar strands of mass production and the division of labor. By 1893, most observers could see that the industrial economy had both benefits and drawbacks. Companies rewarded their workers unequally. Factory methods eliminated some of the skills that workers had passed from generation to generation. The industrial economy had only a few places for women, even though colleges were educating women in record numbers. Industrial leaders, including scientists, could develop products and ideas that were not always beneficial to society as a whole. The innovations in scientific calculation that came with mass-produced calculating machines were not as easy or as obvious as the lessons in divided labor. If they were headed toward a single point in space, that point encouraged the expansion of scientific methodology to problems beyond astronomy, the demand to use resources efficiently in research, and the requirement to have accurate results.