When Computers Were Human

by David Alan Grier

  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.

  CHAPTER SEVEN

  Darwin’s Cousins

  I was quite certain that … the contemporary woman would find her faculties clear and acute from the study of science. …

  Jane Addams, Twenty Years at Hull House (1910)

  IN 1894, when the playwright George Bernard Shaw (1856–1950) needed to invent a character that captured the challenges faced by the young women of his age, he made her a mathematician. Vivian Warren, the central character of the play Mrs. Warren’s Profession, is a graduate of Newnham College, a women’s school at Cambridge. Such colleges were still new in the 1890s and were trying to find their way amidst the older and wealthier men’s schools. One measure of success for the women’s schools was the scores of their students on the Tripos, the Cambridge mathematical honors exam. In 1890, a Newnham student had drawn national attention by besting all of her male peers and achieving the top score on the Tripos, an achievement that would have made her First Wrangler but for her gender.1 In Mrs. Warren’s Profession, Shaw has the fictional Vivian Warren achieve the third-highest score on the exam, a detail that was probably added in consideration of Shaw’s friend, the mathematician Karl Pearson (1857–1936). When Pearson was a student at Cambridge, he had been the Third Wrangler in the Tripos.2 As a friendly jab at Pearson, who was somewhat sensitive about the fact that he did not get the top score on the exam, Shaw has Warren confess that she took the Tripos exam only because her mother agreed to pay her fifty pounds “to try for fourth wrangler or thereabouts.” Even though she bested her goal, Warren concludes that the Tripos “doesn’t pay. I wouldn’t do it again for the same money.”3

  In Mrs. Warren’s Profession, Vivian Warren is identified as an actuary, but she does the work of a human computer. She describes her work as “calculations for engineers, electricians, insurance companies, and so on.” In one speech, she talks about how much she enjoys working in an actuarial office in the city of London. Her days are spent in calculations. “In the evenings we smoked and talked, and never dreamt of going out except for exercise. And I never enjoyed myself more in my life.”4

  The play opens with the trappings of a domestic comedy: a young woman, a young man, a country house, a wise friend, and a mother, the Mrs. Warren of the title. As the plot unfolds, we learn that Mrs. Warren is not simply a wealthy landowner but also a former prostitute and the manager of a brothel. As Vivian Warren learns her mother’s story, she systematically rejects the other characters of the play and retreats into mathematics, as if it is the only thing that is pure and untainted. Her suitor is the easiest thing to reject, as he proves to be her half brother. She also declines a marriage with the brothel’s financier, rejects the conventional advice of the wise friend, and firmly expels her mother from her life.5

  Like Vivian Warren, the new computers of the 1890s were college graduates, though none left a record quite so dramatic as the one described in Shaw’s play. Many were graduates of the new women’s colleges: Newnham and Girton at Cambridge, Bedford in London, Radcliffe and Bryn Mawr in the United States. Most of these colleges had been formed in the late 1870s or early 1880s. Though only a small fraction of their students studied science, the numbers were growing, as were the expectations that the graduates would find useful work. “If it had been wasteful in the 1870s for women to sit idly home,” wrote the historian Margaret Rossiter, “it was much more intolerable for college graduates to lack useful and respectable work.” Rossiter notes that women moved quickly into laboratories but that they were “introduced in ways that divided the ever-expanding labor but withheld most of the ever precious recognition.”6 For the women of the 1890s, the social and biological sciences offered new opportunities for employment. These fields were incorporating new methods of statistical analysis, methods that required not only the traditional measuring of samples and tabulating of data, but also the more sophisticated calculations of the new mathematical statistics.

  The advance of statistical analysis was closely tied to Charles Darwin’s theory of ev
olution in much the same way that astronomical calculations were linked to Newton’s fundamental laws of motion. Darwin’s theory suggested that biological organizations were shaped by the force of natural selection, that natural selection was still operating in the nineteenth century, and that the effects of natural selection might be measured in both animals and people. If it could be measured, it might provide an explanation for a host of biological and social phenomena, just as Newton’s theory of gravitation provided an explanation for Halley’s comet. Darwin claimed that evolution could explain the size and shape of animals. His followers speculated that evolution might explain differences in intelligence, behavior, and even social standing. “Those whom we called brutes,” quipped George Bernard Shaw, “had their revenge when Darwin shewed us that they are our cousins.”7

  One of Darwin’s human cousins, Francis Galton (1822–1911), worked to find a mathematical way of verifying the presence of natural selection. Galton has been portrayed as “a romantic figure in the history of statistics, perhaps the last of the gentlemen scientists,”8 a characterization that describes his family background and captures the unorganized nature of the science he pursued. His father was a wealthy Birmingham banker, and his mother was the daughter of a wealthy physician and the aunt of Charles Darwin. He had enrolled in Cambridge with the intent of taking the Tripos and pursuing a career in mathematics. The strain of study broke his health and forced him to temporarily withdraw from school. “It would have been madness to continue the kind of studious life that I had been leading,”9 he concluded. After a year of rest, he returned to Cambridge and completed an ordinary degree, without taking the Tripos and without honors.10

  Without an honors degree, it would have been difficult for Galton to find an academic appointment. Like Charles Babbage, Galton had inherited a substantial fortune, and again like Babbage, he used his funds to finance his interest in science. He spent several years traveling through the Middle East and recording his observations of the land and its inhabitants. At times, his travels seemed to be more a rite of passage for a wealthy young man than a genuine scientific expedition. The historian Daniel Kelves reported that Galton sailed down the Nile River “lazing the days away half dressed and barefoot.”11 The trip was not entirely an adventure, for Galton brought a modicum of rigor to his work. Writing his brother from East Africa, he reported, “I have been working hard to make a good map of the country and am quite pleased with my success. I can now calculate upon getting the latitude of any place, on a clear night to three hundred yards.”12 He did not suggest that he had mastered the more difficult calculation of longitude.

  In his records of the trip, Galton shows that his ideas on quantification were crude and often uncertain. In one episode, often retold, his work could have been lifted directly from Jonathan Swift’s description of Laputa. In East Africa, Galton reported to his brother that he had found a community in which the women “are really endowed with that shape which European milliners so vainly attempt to imitate,” adding that they had “figures that would drive the females of our native land desperate—figures that afford to scoff at Crinoline.” To quantify the shape of these women, Galton had measured the dimensions of their bodies as the Laputan tailor had measured Gulliver. “I sat at a distance with my sextant, and as the ladies turned themselves about, as women always do to be admired, I surveyed them in every way.” Once he had recorded the angles, he “subsequently measured the distance of the spot where they stood—worked out and tabulated the results at my leisure.”13 If Francis Galton had moved in literary circles and had been as familiar with Charles Dickens as he was with Charles Darwin, this letter might be considered a joke, a satire on scientific practice, a sly way of telling his brother that he had spent the day studying half-naked women with a telescope.14

  Upon his return to England, Galton found a position at the Kew Observatory, a government-funded weather research station. He spent most of his time testing new meteorological instruments, but he found some time to consider problems that were suggested by the different sizes and shapes of the Africans.15 He tried to put his investigations in the context of Darwin’s theories and tried to derive mathematical methods that would verify the action of natural selection. At first, he attempted to find a way of measuring economic and social success across the generations of a single family. “As a statistical investigation, it was naive and flawed,” wrote historian Steven Stigler, “and Galton seems to have realized this.”16 In his second approach to this subject, he considered physical traits, such as those he had measured with his sextant in East Africa. The standard methods of statistics were largely confined to the tabulation of data and gave him no obvious way to approach the problem.

  Galton was more comfortable with graphical techniques than with computations or formulas. In one problem, he used a graph to find a mathematical relationship between the heights of parents and the heights of their fully grown sons. His set of data included measurements on 928 people, 205 pairs of parents and 518 sons. His first step was to reduce the heights of the two parents to a single value, a value that he called the “mid-parent.” The mid-parent was an average of the values with a slight adjustment to place the mother’s height on the same scale as the father’s. Once he had computed the mid-parent value, he paired this value with the height of the son and created a graph. “I began with a sheet of paper, ruled crossways, with a scale across the top to refer to the statures of the sons,” he explained.17 The scale down the side referred to the mid-parents. For each pair of data, he drew a small pencil mark on the grid.

  The final picture looked like an oval. Tall parents tended to have tall sons, and short parents seemed to produce short sons. He summarized that relationship by drawing a line from one of the narrow ends of the oval to the other, a line that split the oval in half. The slope of that line, when adjusted for scale, would be known as the correlation coefficient.18 A correlation value close to 1 indicated that the quantities would be highly related. A value close to zero indicated that they had no relation. Unsure of the underlying mathematics, he turned to a Cambridge mathematician, who confirmed the “various and laborious statistical conclusions with far more minuteness than I had dared to hope.”19 In confirming the work, the Cambridge mathematician could produce no simple formula for the correlation coefficient. The only way that Galton could compute a correlation was to draw the picture with its ovals and lines. That restriction did not seem to bother him, as Galton at first believed that he had solved a special problem with limited application. It took him about five years to appreciate that he had created a general method for studying any statistical data that shared the same mathematical properties as his height data. “Few intellectual pleasures are more keen,” he wrote, “than those enjoyed by a person who … suddenly perceives … that his results hold good in previously-unsuspected directions.” Still, he was embarrassed that he had not recognized the importance of his discovery and confessed fear that “I should be justly reproached for having overlooked it.”20

  Galton’s influence on organized computation began in December 1893, when he established the “Committee for Conducting Statistical Inquiries into the Measurable Characteristics of Plants and Animals.” This committee, which reported to the Royal Society, was a test of organized scientific research. It was a time of “trial and experiment,” wrote one observer. “The statistical calculus itself was not then even partially completed,” and “biometric computations were not reduced to routine methods.” The first work of the committee was to support the research of the biologist W. F. Raphael Weldon (1860–1906). Weldon had discovered the methods of Galton in the late 1880s and applied them to the study of shrimp and crabs. He “was on the look-out for a numerical measure of species,” wrote one biographer, and sought in his measurements evidence that one type of animal was evolving into two species. He was an energetic researcher and pushed the committee beyond its ability to support his work. None of the members could provide the mathematical advice he needed, though th
ey did “ask for a grant of money to obtain materials and assistance in measurement and computation.”21

  Through most of his early research, Weldon’s chief computer was his wife, Florence Tebb Weldon (1858–1936). Florence Weldon was one of the first college-educated human computers. She had graduated from Girton College at Cambridge, a companion to Newnham. By working for her husband, Florence Weldon received little recognition but probably found a substantial scope in her scientific work. She did the same tasks that her husband handled. The two of them spent their summers traveling around England and visiting Italy. Typically, they would collect about a thousand specimens, clean the animals, and measure them. In an early study, they took twenty-three measurements on each specimen. Wife and husband shared the labor of research, tabulated the results, and calculated averages, “doing all in duplicate.” They “were strenuous years in calculating,” recorded a friend. “The Brunsviga [calculator] was yet unknown to the youthful biometric school.” The Brunsviga, a favorite of English statisticians, was similar in design to the machine invented by Frank Baldwin in St. Louis. It was small and light and used sliding levers, rather than keys, to record data. Having no calculating machine of any kind, the Weldons “trusted for multiplication to logarithms and [the tables of] Crelle.”22