The first third of this book, which deals with computation from the start of the eighteenth century up to 1880, treats the first theme, the division of labor. During this period, astronomy was the dominant field of scientific research and the discipline that required the greatest amount of calculation. Some of this calculation was done in observatories for astronomers, but most of it was done in practical settings by individuals who used astronomy in their work, most notably navigators and surveyors. It was a period when the borders of scientific practice were not well defined and many a scientist moved easily through the learned disciplines, scanning the sky one night, navigating a ship the next, and perhaps, on the night following, designing a fortification or preparing an insurance table. The great exponent of divided labor, the Scottish philosopher Adam Smith (1723–1790), wrote The Wealth of Nations during this period. Smith discussed the nature of divided labor in scientific work and even commented briefly on the nature of astronomy. The astronomers of the age were familiar with Smith’s ideas and cited them as the inspiration for their computing staffs.
The second third of the book covers the period from 1880 to 1930, a time when astronomy was still an important force behind scientific computation but was no longer the only discipline that required large-scale calculations. In particular, electrical engineers and ordnance engineers started building staffs to deal with the demands of computation. The major change during this period came from the mass-produced adding and calculating machines. Such machines have histories that can be traced back to the seventeenth century, but they were not commonly found in computing offices until the start of the twentieth century. While these machines decreased the amount of time required for astronomical calculations, they had a greater impact in the fields of economics and social statistics. They allowed scientists to summarize large amounts of data and to develop mathematical means for analyzing large populations. With the calculating machines came other ideas that we associate with mass production, such as standardized methods, generalized techniques, and tighter managerial control.
The final third of the book discusses computation during the Great Depression, the Second World War, and the early years of the Cold War. It was at this time that human computers attempted to establish their work as an independent discipline, distinct from the different fields of scientific research and even from mathematics itself. This activity required human computers to create a literature of computation, define formal ways of training new computers, and create institutions that could support their work. Historians discuss such subjects under the topic of “professionalization,” a term that suggests independence, societal respect, and control of one’s activities. In the case of the human computer, professionalization produced no independence, little respect, and nothing that could be characterized as self-governance. Professionalization came just as human computers were being replaced by computing machines that were built with tubes, powered by electricity, and controlled by a program.
The story of the human computer is connected to the development of the modern electronic computer, but it does not provide the direct antecedent of the machines that were built for scientific and business calculation in the last half of the twentieth century. To be sure, the two stories twist about each other, touching at regular points and sharing ideas with the contact. The developers of electronic computers often borrowed the mathematical techniques of hand calculation and, from time to time, asked human computers to check some number that had been produced by their machines; however, few human computers contributed to the invention of electronic computing equipment, and few computing offices were connected to machine development projects. It is best to view the human computing organizations as the backdrop against which the story of electronic computers unfolds. Human computers plugged away at their calculations with little influence over those engaged in machine design. Most computers were intrigued with the electronic computing machines and looked forward to using these devices, but they would prove to be the secondary characters in the narrative, the Rosencrantz and Guildenstern instead of the Hamlet and Ophelia. The human computers occupied a small corner of the stage, somewhat unsure of their role, as engineers developed electronic replacements for the computing laboratories and their large staffs of workers.
This book attempts to invert the history of scientific computing by narrating the stories of those who actually did the calculations. These stories are often difficult to tell, as the vast majority of computers left no record of their lives beyond a single footnote to a scholarly article or an acknowledgment in the bottom margin of a mathematical table. Furthermore, the few surviving human computers often failed to appreciate the full scope of what they did. As often as not, they would deflect inquiries with remarks like “It was nothing” or “You should have asked my supervisor about that.” The stories unfolded in unusual ways from unlikely sources. There was a bound volume of correspondence in the Library of Congress, the cassette tape that had been carefully guarded by a family, a scrapbook that had been long filed away, the box of records with the confusing label on the shelves of the National Archives, the correspondence from an obscure university official, and the four-hour telephone conversation with a man on a hospital bed. Each of these stories illustrated a different aspect of the human computer, but each, in its own way, returned to the statement of a grandmother, “You know, I took calculus in college.”
PART I
Astronomy and the Division of Labor 1682–1880
If your wish is to become really a man of science and not merely a petty experimentalist, I should advise you to apply to every branch of natural philosophy, including mathematics.
Mary Shelley, Frankenstein (1818)
CHAPTER ONE
The First Anticipated Return: Halley’s Comet 1758
When they come to model Heaven
And calculate the stars, how they will wield
The mighty frame …
John Milton, Paradise Lost (1667)
OUR STORY will begin with a comet, a new method of mathematics, and a seemingly intractable problem. The comet is the one that appeared over Europe in August 1682, the comet that has since been named for the English astronomer Edmund Halley (1656–1742). This comet emerged in the late summer sky and, according to observers at Cambridge University, hung like a beacon with a long, shimmering tail above the chapel of King’s College. To that age, comets were mysterious visitors, phenomena that appeared at irregular intervals with no obvious explanation. Their origins, substance, and purpose were matters of pure speculation. Some thought that they were wayward stars. Others suggested that they might originate in the atmosphere, each a burning piece of Helios’s chariot, perhaps, that had been caught between the earth and the moon.
The only aspects of the 1682 comet that could be studied with certainty were its position against the fixed stars of night and the length of its tail. The young Edmund Halley recorded both measurements on at least seven distinct nights that summer. He was a gentleman of private life, possessed of an independent income and a new house in a prosperous village just north of London. His collection of scientific instruments included a sextant, a small telescope mounted on an arc of a circle, which allowed him to measure the distance of the comet’s head from nearby stars. His measurements were not in miles or meters or light-years but in degrees of an angle. His home marked the joint of that celestial angle. One leg stretched from the earth to the head of the comet. The second leg reached to a star, the end of the tail, or some other reference point. The work required patience and a steady hand. By the time the comet vanished, Halley had traced its path across the sky and recorded the advance and retreat of the tail. At the time, it was not entirely clear what Halley might do with these measurements. If they had been the measurements of a planet, he might have computed an orbit, but few believed that comets moved in ellipses around the sun as the planets did. Halley had other interests to pursue, so he put his comet data away for future use.
2. Halley’s comet over
Cambridge, 1682
The new method of mathematics was calculus, a subject then known in England as fluxions. Calculus is the mathematics of physical activity, the mathematics of change. It probes the nature of movement by dividing it into smaller and smaller steps and then reassembling these tiny units into surprisingly elegant and simple expressions. The techniques of calculus had their origin in an attempt to explain the motion of the planets by physical laws rather than by the arbitrary actions of superhuman beings. The English proponent of calculus was Isaac Newton (1642–1727), who developed the method while he was writing his masterwork, Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), a book commonly called Principia. In Principia, Newton explained that he was attempting to analyze “the motions of the planets, the comets, the moon, and the sea,” the last term referring to the movements of the tides.1 In the central part of the book, Newton considered the motion of two objects under the influence of a single universal force, which he called gravity. The two objects might be the moon and the earth, a planet and the sun, or even a comet and some other celestial object. In these circumstances, Newton argued that gravity impels the bodies to follow certain kinds of paths: the gentle bend of the hyperbola, the tight hairpin of a parabola, and the cyclical orbit of an ellipse.
The intractable problem appeared when the calculus of Newton met the comet data of Halley. Halley called upon Newton in 1684, when Principia was nothing more than a collection of notes. He helped Newton prepare the final manuscript for publication in 1687 and promoted Newton’s ideas at the Royal Society, the central organization of seventeenth-century English science. Though he frequently thought about the problems of comets and astronomy, he let thirteen years pass after his initial observations in 1682 before he undertook a serious analysis of his data. During those intervening years, he had other problems to keep him busy. He served as clerk to the Royal Society and as the editor of its journal, Philosophical Transactions. He also studied a number of other scientific problems, such as the design of diving bells and the mathematics of finance.
In September 1695, Halley returned to his comet data and attempted to validate the statements that Newton had made about comets in Principia. Newton had speculated that comets moved in parabolas around the sun, narrow curves that started at a distant point in the universe, sped past the earth, turned sharply at the sun, and then rushed back to the void whence they came. It seemed a plausible theory, but he had never done the analysis to verify it.2 Halley spent about a month working with the measurements from four different comets, trying to identify the path that each object made through the solar system. From an individual comet, he would select three observations, each recorded on a different day. From these numbers he computed the parameters of a parabolic curve. Newton had done this sort of work with graphs, but after a little practice Halley could report, “I am now become so ready at the finding a Cometts orb by calculation.”3 Once he had calculated the parabola, he adjusted the curve by comparing it to the other observations of the comet. If he found that all of the observations were close to the parabola, he would conclude that he had found the proper path. If he discovered that some of them fell at a distance from the curve, he would attempt to adjust the parameters in order to bring the parabola closer to the observations.
The procedure worked well for the first three comets: one observed by Newton in 1664, a second that Halley had observed just before the 1682 comet, and a third that had appeared shortly after.4 Each of these objects seemed to followed a parabolic curve. When Halley began to work on the 1682 comet, the comet that he had observed from his home, he altered his methods. He chose to fit the data to a closed ellipse rather than an open-ended parabola. Halley’s biographer has noted that this idea did not come from calculation but was “based upon somewhat inspired insight.”5 Halley had noted that the 1682 comet followed a path that had been traversed by two earlier comets, one observed in 1531 by the German astronomer Peter Apian (1495–1552) and a second recorded in 1607 by Johannes Kepler. With his 1682 data, Halley computed the values for an elliptical orbit and then compared the curve to the earlier observations. Pleased with the results, he wrote to Newton, “I am more and more confirmed that we have seen that Comett now three times since ye Year 1531.”6
Though he was certain that the 1682 comet orbited the Sun, Halley recognized that his calculations did not prove his claim. His work did not address a substantial inconsistency in his data. Seventy-six years separated Apian’s observations from those of Kepler. Only seventy-five years passed between Kepler’s sighting and Halley’s data from 1682. The analysis suggested that the comet should have a fixed period, that it should return without fail every seventy-five years. Halley speculated that the discrepancy might be caused by the gravitational pull of the outer planets, forces which could easily disturb the orbit of the comet and change the date of its return. Writing to Newton, he asked, “When your more important business is over, I must entreat you to consider how far a Comet’s motion may be disturbed by the Centers of Saturn and Jupiter, particularly in its ascent from the Sun.”7
Newton responded quickly, but his reply was vague and unhelpful. “How far a comet’s motion may be disturbed,” he wrote to Halley, “cannot be affirmed without knowing the Orb of ye Comet & times of its transit through ye Orbs of [the two planets].”8 Once Saturn and Jupiter became part of the equations, the calculations were no longer straightforward and could not be handled by a single astronomer in his spare minutes and hours. The Sun, Saturn, and Jupiter form a three-body system, three objects moving through space, each exerting an influence upon the other two. Newton had been unable to find a simple expression that described the motion of such a system, even though he had been able to find solutions for two bodies in motion. In his best effort, he had devised an approximation that crudely described the movement of three bodies, but this expression was not precise enough to explain the variation in the comet’s period.9
The lack of a simple solution to the three-body problem stymied Halley’s calculations, but it did not shake his faith. He freely discussed his ideas in public and published his theory of comets in Astronomiae Cometicae Synopsis (A Synopsis of the Astronomy of Comets).10 In this book, he claimed that he could “undertake confidently to predict the return” of the comet in 1758. Some scholars noted a lack of mathematical rigor in Halley’s analysis and questioned this claim. Responding to the criticism, Halley weakened his statements, claimed that the comet might return at any time within a 600-day period that began in 1757, and replaced his confident prediction with a sentence that began, “I think, I may venture to foretell” the return of the comet.11
From time to time, Halley tried to improve his predictions for the 1758 return. He made little progress, as he was unwilling, or perhaps unable, to refine his estimates into a detailed computation. His final effort occurred in about 1720, just before he became Astronomer Royal and director of the Royal Observatory in Greenwich. For this calculation, he had a new approximate solution for the three-body problem of Saturn, Jupiter, and the Sun. From this solution, he deduced that the comet was pulled farther from the Sun after its 1682 return and hence would require more time to traverse its path. It was one more crude estimate, but it would stand as his final word on the subject. In his last revision of his Astronomiae Cometicae, which was published after his death in 1742, he announced that his comet would return “about the end of the year 1758, or the beginning of the next.”12 With this opinion on the subject, he bequeathed the comet to future generations. “Having touched upon these things,” he wrote, “I shall leave them to be discussed by the care of posterity, after the truth is found out by the event.”13
Posterity made the return of Halley’s comet a test for Newton’s theory of gravitation. Newton’s “followers have, from his principles, ventured even to predict the returns of several [comets],” wrote the Scottish philosopher Adam Smith (1723–1790), “particularly of one which is to make its appearance in 175
8.” If scientists could predict the date of return, they would take the agreement between prediction and observation as evidence that Newton’s ideas on gravity were correct. If the predicted date did not coincide with the actual date, then they would conclude that other forces were at work in the universe. Smith believed that Newton’s analysis was probably correct. “His system,” he stated, “now prevails over all opposition, and has advanced to the acquisition of the most universal empire that was ever established in philosophy.” However, Smith was not willing to accept the prediction for Halley’s comet without a proper test. “We must wait for that time before we can determine, whether his philosophy corresponds as happily to [comets] as to all the [planets].”14
A thorough test of the gravitational theory required computational techniques beyond the mathematics that Halley had used for his initial analysis of the comet. Newton’s calculus would never provide a simple way to describe the motion of three or more bodies and hence would never give an accurate date for the comet’s return. The only way to determine the comet’s orbit was to substitute brawn for brain, to divide the comet’s progress into tiny steps, analyze the forces pulling on the comet, and then combine these steps into a serviceable whole through the tedious process of summation. “What immense labor,” wrote one astronomer, “what geometrical knowledge did not this task require?”15 Among the astronomers that followed Edmund Halley, few even considered undertaking the labor. Only one, a French mathematician named Alexis-Claude Clairaut (1713–1765), made a serious attempt to predict the date of the 1758 return, an attempt that required both a computational technique beyond those developed by Newton and the means of dividing the work among computing assistants.
When Computers Were Human Page 2
