When Computers Were Human
Page 23
The proposal before the National Research Council was simple and straightforward. It would establish a committee to prepare a bibliography of the mathematical tables that had been published in scientific journals. There was, of course, no single literature of computation. Tables and articles on computation could be found in dozens of scholarly publications, including the Astrophysical Journal, the Transactions of the Cambridge Philosophical Society, Biometrika, the Journal of the Optical Society of America, and the Proceedings of the Royal Artillery Institution. In addition to a summary of these journals, the proposal asked for a report on “automatic calculating machines, harmonic analyzers,” and “special graphical device machines of all kinds.”2 These devices were called, in the language of the day, “aids to computation,” hence this compilation would be prepared by a committee with the unwieldy name of the “Subcommittee on the Bibliography of Mathematical Tables and Other Aids to Computation,” a title that would quickly be shortened to the initials “MTAC.”
“Was it Dr. Veblen who initiated this suggestion?” asked Floyd K. Richtmyer (1881–1939). Richtmyer, a professor from Cornell University and an officer of the council, had been asked to find someone who might organize the MTAC committee. Technically, the answer to his question was no, as the idea had been suggested by a consultant to the Nautical Almanac Office, but the proposed committee clearly bore the influence of Veblen and the Aberdeen veterans. One of Veblen’s former assistants within the Army Ballistics Office, Gilbert Bliss from the University of Chicago, served on the National Research Council and championed the proposal. Veblen, though not the instigator of the idea, knew of the plan, approved of it, and suggested several individuals who might serve on the committee.3
As Richtmyer sought a leader for this group, he received a letter from the director of the Yale Observatory, informing him that an English mathematician, misidentified as “Karl Pierson,” had already prepared a bibliography of tables. The letter reported that one volume of the work had already appeared—the pamphlet on logarithm tables that was published in the Tracts for Computers—and that this booklet was one “that astronomers, at least, have frequently used.”4 Richtmyer replied that he was “much indebted” for the information. If Pearson had created a full bibliography, he felt that there would not be a need to create a new one, for “duplication of effort, particularly in a matter like this, is highly undesirable.”5
After a quick review of Pearson’s work, Richtmyer concluded that the Tracts for Computers was not a complete bibliography and that there was still plenty of work for the proposed MTAC committee. He then returned to the search for a committee chair. He had two candidates for the position, Thornton Fry of Bell Telephone Laboratories and Vannevar Bush (1890–1974), a professor of engineering at the Massachusetts Institute of Technology.6 Of the two, Bush was the more intriguing choice. He had recently built a computing machine that could solve differential equations, the equations of planetary orbits, artillery trajectories, and electrical devices. His machine was called a “differential analyzer,” though many a commentator would note that it neither differentiated nor analyzed. It used spinning disks and rotating drive shafts to represent mathematical quantities, and it solved differential equations with a technique that was analogous to the method that Andrew Crommelin had used to predict the return of Halley’s comet in 1910. However, as the machine worked with motions and not with numbers, it recorded solutions as a graph drawn by a mechanical pen.7
Bush’s differential analyzer had received much attention from engineers and industrial scientists. The computing division of General Electric had taken an interest in the machine and had used it to do several computations.8 However, after discussing the merits of Bush and his invention, Richtmyer concluded that the MIT professor was the wrong person to chair the MTAC committee. Bush was not much interested in mathematical tables, and the differential analyzer seemed to be a “special machine and is not likely to be available for general laboratory purposes.”9 With Bush eliminated, Richtmyer turned to Thornton Fry and asked him to lead the group.
“I would like to cooperate if possible,” Fry responded, but “I think I had better get a clearer picture of just what this … will involve before agreeing to take it on.”10 In part, he was being cautious, as American Telephone and Telegraph had first command on his loyalty, but he was also opening a negotiation, probing the National Research Council to determine what resources might be at his disposal if he agreed to prepare the bibliography of tables. Fundamentally, he did not like the idea of producing a bibliography and argued that it was only “the distasteful but necessary first step in a program of producing the numerical tables.” He especially disliked the second part of the committee charge, the review of computing machinery. Such a review, he complained, “would have to contain a certain amount of comparative criticism to which exception would undoubtedly be taken by every manufacturer whose product was adversely mentioned.”11
There “is no doubt that a very definite need exists for more complete mathematical tables of certain types,” Fry concluded. He suggested that the new committee should “map out the need [for new tables] and apportion the work to various people so as to avoid duplication and secure the maximum possible results from the effort expended.” He noted that there were many skilled computers who might contribute to such a National Research Council project. He could volunteer the services of Clara Froelich and the other staff at Bell Telephone Laboratories. Karl Pearson, though quite senior, might be willing to contribute. L. J. Comrie, at the British Nautical Almanac, would certainly be interested. Fry thought that he might be able to entice some contributions from Aberdeen veterans, such as A. A. Bennett (1888–1971). Bennett had served as the chief mathematical assistant to Forest Ray Moulton and had made substantial contributions to Moulton’s revised theory of ballistics. He now held a position at Brown University and was also a special consultant on computation to both the army and General Electric.12 There were even some new faces that might lend their effort, such as Indiana University professor Harold T. Davis (1892–1974). After stating his vision, Fry indicated that he would be willing to chair the MTAC committee and produce a bibliography if “the committee in question shall carry forward some such program as that which I have outlined.”13
Richtmyer was sympathetic to Fry’s idea, as the National Research Council had undertaken similar cooperative activities in the past. During the 1920s, the council had sponsored a multivolume handbook of data for scientists and engineers. This project, called the International Critical Tables of Numerical Data, Physics, Chemistry and Technology, had been praised by scientists in the United States, Europe, and Japan, but it had proven to be an expensive undertaking. The publication had cost $177,000 even though all of the contributors had worked as volunteers. The funds had been donated by “those appreciating its importance and in a position to make the necessary investment,” as the National Research Council had no funds of its own. Two hundred and forty-four organizations had donated to the project, although the bulk of the money had come from a single source, the Carnegie Institution of Washington.14 Richtmyer was confident that the council could find similar funds for Fry’s project and asked the mathematician from Bell Telephone Laboratories to describe his idea more fully and prepare a budget for the project.15
Fry, engaged in other activities at Bell Telephone Laboratories, delayed his reply for five months. As a consequence, he lost a moment of opportunity. By the time that he presented his plan, the council was feeling the full impact of the economic depression. Richtmyer told him that the National Research Council was “not at the moment in a position to finance a more ambitious program, desirable as such a program obviously is.” He asked Fry to consider producing only the bibliography, “in spite of the fact that this proposal falls far short of the plan which you outlined in your letters to me.”16 However, events were moving too quickly. Before Fry could reply, the council withdrew the offer. Feeling awkward about conveying the news to Fry, Richtmyer struggle
d to find his words. “Partially on account of developments since we began to consider this project,” he wrote, “it may turn out that we shall not wish at the present time to form a committee even for the preparation of the Bibliography.”17 Fry did not even bother to reply to this letter but stuffed it in his files.
In the summer of 1931, when Richtmyer withdrew his offer to Fry, neither the National Research Council nor anyone else appreciated the potential opportunities for human computers that would be offered by the Great Depression. The difficult times encouraged new applications of the computing methods that had been developed during the First World War. The statistics of hog production could analyze the collapse of industrial production or the growing reach of poverty. The mathematics of exterior ballistics could help identify the trajectory of the stock market. Rather than being a hindrance to large computing projects, as Richtmyer feared, the economic collapse encouraged the formation of large computing staffs, since rising unemployment reduced the cost of labor.
The issues that had encouraged the National Research Council to form the MTAC committee did not vanish when they withdrew their offer to Thornton Fry. As computing groups grew and expanded, they looked for the kinds of activities that could be found in the more established disciplines of astronomy or physics or electrical engineering. They desired a unified literature, textbooks, standard ways of training computers, journals to disseminate new ideas, and a professional society that might identify pressing research problems. Such institutions would not appear overnight, as the National Research Council’s actions concerning the MTAC committee portended. Human computers would have to make due with interim solutions while they worked to establish computing as a more formal scientific field. Their efforts were complicated by the fact that the same forces that encouraged the expansion of computing laboratories also encouraged the development of computing machinery. At times, it appeared that scientists were caught between two contradictory trends. The first trend was the effort to elevate the status of those who worked with numbers. The second trend pushed human computers to the margins of scientific laboratories and replaced them with precise, unfailing machines.
Harold Thayer Davis, professor of mathematics at Indiana University, shared his last name with the founder of the American Nautical Almanac, Charles Henry Davis, but the two had no direct family connection and had little in common. Charles Henry was a naval officer, a member of the Boston elite, and a highly disciplined scientist. Harold Thayer, or H. T., was a reluctant soldier, the son of a western land speculator, and a self-described “ultra-crepidarian,” a shoemaker who would not “stick to his last,” a workman unable to focus on the tasks he had been trained to do.18 At different times in his life, he showed the prospects of becoming a classical scholar, a physician, and even a billiards player. The strongest connection between H. T. and Charles Henry was a common interest in scientific computation. Mathematical calculation was the “open sesame,” wrote H. T. Davis, “to many undiscovered areas of human knowledge.” Though H. T. would never form a computing organization as important as the Nautical Almanac Office of his namesake, he would prove to be adept at performing large calculations under difficult circumstances.
H. T. Davis was born in Beatrice, Nebraska. His grandparents had come west to make their fortune in cattle and gold, but great wealth had eluded them. His mother was the daughter of a farmer. His father was the city treasurer. When Davis was young, his family moved first to Idaho and then to Colorado in search of a more healthful climate for his father, who suffered from asthma. He entered college in 1910, shortly after Halley’s comet receded from sight. “As viewed from Cañon City,” Davis later recalled, “[the comet] hung just above the western mountains with a brilliant head and a tail that swept across the sky through an arc of 130 degrees.” He speculated that the return “might be chosen as the beginning of an epoch in science that has had no parallel in the history of the world.” But at the time, he had no interest in studying science. When he entered Colorado College that fall, he intended to study history, literature, and economics rather than mathematics and computation.19
Davis became interested in computation after his father fell ill in 1912. Needing to provide for his family, Davis left college and took a job with a civil engineer. The engineer was grading land and needed an assistant to measure newly excavated drainage canals and compute the amount of soil that had been removed. Davis spent several weeks diligently tracing the topography of the land and slowly summing up the volume of dirt. As he grew tired of the drudgery, his “ingenuity was awakened,” and he saw a new way to organize the calculations. As he recalled the event, his plan reduced weeks of work to a task requiring “two or three hours.”20
When his father recovered his health, Davis returned to Colorado College with a new interest in mathematics and computation. He graduated with a degree in mathematics and spent two years teaching the subject at a local high school. When one of his professors took a job at Harvard, Davis followed him in order to study for a master’s degree. He arrived in Cambridge in 1917, just as the United States was entering the First World War. Unlike Oswald Veblen or Norbert Wiener or Elizabeth Webb Wilson, Davis originally had no interest in going to war. He believed that America should stay out of Europe’s problems and that President Woodrow Wilson was a “dangerous demagogue”; but during the summer of 1918, he had a change of heart and enlisted in the army. It was a conversion of little consequence, for the armistice was declared while he was at a training camp in South Boston.21
Returning to Harvard, Davis was drawn to empirical subjects, rather than the more theoretical topics that had been introduced by German mathematicians some twenty-five years before. While studying theorems and proofs, he complained that “one grew sick, indeed, at the torrent of abstract symbolism which was poured forth at every [mathematical] seminar.” His studies combined the two central methods of scientific calculation, statistical methods and calculus-based methods. He took classes with a mathematical statistician and worked in a Harvard statistical laboratory. “It was in this laboratory,” he remembered, “that [I] first saw [a] multiplying machine, a nice, black, shiny Monroe calculator, which operated with a crank.” When the time came for his master’s exam, his professors asked him to undertake a broad survey of the computational methods and to show how to compute a class of functions called elliptic integrals. Writing of the experience in the third person, as he often did when describing his life, he said that “the subject suited his taste and he undertook it avidly.”22
From Harvard, Davis went first to the University of Wisconsin to begin doctoral studies and then to Indiana University to teach. He had not finished his doctorate when he arrived at Indiana, but he had taken the job in order to support his new wife and family. The country was in the midst of an economic recession, the difficult time that followed the end of the First World War. Davis was grateful for a university job, but he was surprised at the relative poverty that he found on the campus. Once the university had been the promising new school of the Midwest, but its fortunes had fallen. Davis reported that the department of mathematics “was housed in a single dingy room in an old building used mainly by chemistry. Desks were crowded together and the author found space for only a small table in the place assigned to him.”23 The university president admitted that young faculty members worked so hard that they had “little leisure, little energy left. [They] can not brood by the hour over [their] own studies as a man must to grow rich in them.”24
In spite of the conditions at Indiana University, Davis remembered the school as a place of great freedom, an opportunity to “go his own way and explore those paths into which his own interest and his own imagination” directed him. In 1927, with his doctoral work behind him, Davis decided that he wanted to build a statistical computing lab like one that he had once used at Harvard. The national economy had recovered, but Indiana University had no money to support his research. Davis was able to acquire some funds from a local charity, a foundation that ha
d been created by a grateful alumnus of the university. The grant was small, a “few hundred dollars at most,” but it allowed him to acquire “a battery of electrically driven Monroe calculators.” The dean of the business school found a room for the new laboratory in the attic of the library, a space previously used as an artist’s studio. The university offered $86 to give the walls a fresh coat of paint, install electric lights, and provide some tables for the machines.25
Thornton Fry once quipped that H. T. Davis computed “various things as they occurred to him.”26 The first test of the new computing lab came from the physics department. One of the physicists was experimenting with beams of light. Davis was attracted to one experiment that produced a “beautiful circular pattern with seventy rings, which broadened as they neared the circumference.” The physicist wanted to compute the amount of energy in each ring as a way of testing the wave theory of light. The problem had nothing to do with statistics, but Davis saw that the calculation would provide “an immediate use for his machines” and volunteered to do the work.27
The calculation required Davis to use some values of the Bessel function, the function that had been tabulated by the Edinburgh Mathematics Laboratory and the British Mathematical Tables Committee. Finding none of these tables in the Indiana University library, Davis decided that he would create a new table for his own use. He became absorbed in this extra task, preparing pages of Bessel functions that would not be needed for his calculation. Only after the table was complete did he return to the original physics problem. When all the work was done, Davis and his colleague discovered that the final values for the energy in the light did not match the empirical measurements from the experiment. The two reviewed the figures, looking for an error in the calculations, but found nothing of significance. They eventually realized that Davis had used an incorrect value for the frequency of the light. At this point, they had two ways to adjust their results. They could either recalculate the energy levels using the correct frequency or redo the experiment using light that matched the frequency from the calculation. Davis conceded that repeating the experiment would be “arduous,” but he claimed that it would be easier to adjust the experimental mechanism than to perform the calculations a second time. His colleague eventually agreed with this reasoning, returned to the laboratory, and performed the experiment with the new frequency of light. This time, reported Davis, “the experimental evidence and the mathematical values coincided exactly.”28