When Computers Were Human (19 page)

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 they 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

Florence Weldon proved to be a greater help to her husband than Galton's committee. “The committee did not possess a mathematician to put on the break,” claimed Shaw's friend Karl Pearson, “and Weldon attempted too much in too short a time.” As W. F. Raphael Weldon began to publish his results, he was met by the same kind of hostility that had greeted the calculations of Halley and Clairaut. W. F. Raphael Weldon's work was far from perfect, and his mathematical formulas did not always demonstrate the properties he had hoped to illustrate; but the response to his work was not in proportion to its flaws. “The very notion that the Darwinian theory might, after all, be capable of statistical demonstration seemed to excite all sorts and conditions of men to hostility,” observed Pearson. W. F. Raphael Weldon worked with the committee through the mid-1890s and then took a position at Oxford University.
²³

The methods of organized statistical calculation, especially the calculation of correlation values, developed in the laboratory of Karl Pearson at the University of London. Pearson was a professor of mathematics, but he had broad interests that ranged from history and politics to religious faith and the relations between the sexes.
²⁴
Born Carl Pearson, he was the son of a London attorney and the product of a traditional Cambridge mathematics education, including the third-place finish on the Tripos. As a young man, he had a crisis of faith that caused him to abandon conventional Christianity and embrace socialism. After two years of study in Germany he adopted the German spelling of his first name,
Karl
.
²⁵
Pearson was a radical but not a bomb thrower. George Bernard Shaw described such people as Pearson as “unconventional in a conventional way.” “[He] was in many ways poorly socialized,” observed his biographer, Ted Porter, “a thoroughly original character who, while drawing deeply and repeatedly from the cultural resources of his time, rejected many of the conventions of his class and profession.”
²⁶
Before turning his attention to statistical theory, he wrote books on the philosophy of science and organized a selection of his friends into a Men and Women's Club. According to a historian of the club, “discussions ranged from sexual relations in Periclean Athens to the position of Buddhist nuns, to more contemporary discussions of the organization and regulation of sexuality, particularly in relation to marriage, prostitution, and friendship.” Pearson's presentations were highly intellectual, often laced with Darwinian ideas, and were occasionally beyond the grasp of other club members.
²⁷

Pearson's influence over the practical issues of computation began in 1895, when the Royal Society added Pearson to the Committee for Conducting
Statistical Inquiries into the Measurable Characteristics of Plants and Animals. Pearson was not particularly impressed by the organization of the group or its method of operation. He later recalled that “Weldon's work was hampered by the committee” and suggested that the members had neither the inclination nor the ability to help him.
²⁸
Pearson's contribution to the group was a mathematical formula for correlation, a formula that turned correlation analyses from a lengthy graphical procedure requiring a certain judgment to a straightforward equation. This formula required the computers to summarize the data in five quantities. In Galton's example, two of the quantities were computed from the children's heights, two more came from the mid-parent heights, and the last was calculated from products of the two sets of data. A final computation of four multiplications, three subtractions, one square root extraction, and a long division produced the correlation value.
²⁹

The formula for correlation became one of the first mathematical tools for a small computing group that Pearson formed at the University of London in an organization he would call the “Biometrics Laboratory.” “All the work of computing undertaken in my Department,” Pearson explained, “[was] entirely done by volunteer workers,” a group of computers that included students, friends, relatives, and his wife.
³⁰
Though Pearson dominated the group, he liked to think that they were all collaborating as equals. The first large project of this group began in the summer of 1899. At “Hampden Farm House in the Chilterns,” he reported, “we had at our disposal a considerable strip of garden covered with Shirley poppies.” The poppies, with their distinctive seed pods, provided the basic material for a study of inheritance. Pearson recruited fifteen friends to help with the research, a collection of eight men and seven women that included the Weldons. Several of this group had been members of the Men and Women's Club. Pearson treated this project as a socialistic endeavor, an effort in which all contributed equally. Though he was directing the work, he took his turn with the more mundane tasks, such as tending the plants, measuring specimens, and harvesting the seed.
³¹