CHAPTER TWELVE

The Best of Bad Times

SPRING 1930. It was the first vernal season of the Great Depression, though the economic collapse was not yet potent enough to touch the annual meeting of the National Research Council. The council was the visible symbol of the First World War’s scientific legacy. Formed to coordinate research for the American military effort, it had grown in stature and influence during the 1920s. As part of the National Academy of Sciences, the council occupied a marble-clad building on the National Mall. The entrance to the building stood across the street from the memorial to Abraham Lincoln. Visitors to the facility passed through large, bronze doors into the building’s solemn interior. The academy’s central auditorium, which stood behind the foyer and the stairs to the executive offices, could be mistaken for the conclave of a mathematically inclined Masonic order. A high balcony of chairs circled the room, and the walls were decorated with allegorical mosaics based upon the symbols of science. The National Research Council, acting as the operating committee of the academy, was charged with the responsibility “of increasing knowledge, of strengthening the national defense, and of contributing in other ways to the public welfare.”¹ In practice, this charge meant that the senior leadership of the council would identify outstanding scientific problems and appoint committees to report on those issues. That spring, the problems of the human computers appeared on the council’s agenda when one member suggested that something should be done to consolidate the literature of calculation.

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 struggled 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 had 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

Davis emerged from the calculation with a new table of the Bessel function and the notion that he should create a compendium of mathematical tables.²⁹ He recognized that there was an epic irrationality in such an idea. “Although the machines were present in the laboratory there were no funds with which to operate them,” he wrote, “no trained personnel to hire even if funds had been available, and not the slightest chance to print and publish to the world the fruits of the heroic computation could it actually be achieved.”³⁰ Under such circumstances, most mathematicians would have not even attempted the project, but Davis believed in the idea and had the ability to make others believe in it as well. He recruited volunteer computers from among the university’s mathematics students and convinced them that a book of mathematical tables was a grand project, a goal worthy of their noblest efforts. He reported that the computers arrived in the laboratory “fired with enthusiasm” and that their calculations “filled the laboratory with their music.”³¹

The computers finished their work in 1932, three years after the stock market crash and one year after the National Research Council had decided that it was not a good time to publish a bibliography of tables. Davis estimated that it would cost $2,100 to typeset his manuscript of tables, print the pages, and bind the book, a sum that far exceeded the annual salary of a professor, yet he seemed undeterred by the economics of his project. He was a partner in a small scholarly publishing firm, a company that he had named Principia Press, after Isaac Newton’s great work. Davis confessed that Principia Press was a “reckless adventure,” as there seemed to be little demand for their eclectic list of scientific and philosophical books, but the firm had done surprisingly well in spite of the poor economic conditions. “Any one who entered a printing plant with a thousand dollars in real money,” he observed, “was a person to be met with open arms.”³² The press was able to raise enough money to publish his manuscript, which he entitled Tables of Higher Mathematical Functions.

After releasing this first volume, Davis started work on a second collection of tables. For this calculation, he paid his computers with money that he received from one of the New Deal agencies, the National Youth Administration, or NYA. The National Youth Administration was created as a “relief program for the middle class.” It provided training and educational activities for young men and women who were working to support their families. Most of the National Youth Administration activities were designed for high school students, but one of its program provided funds to employ college students. These NYA grants paid students to serve as part-time administrative aides, to work as teaching assistants, and to perform research for faculty. Like every other program of the New Deal, the National Youth Administration was a controversial activity. Many educators refused to take NYA funds, arguing that it was “the first step in the establishment of a federal education system competitive with the schools.”³³ Even at schools that could easily employ research and teaching assistants, deans often had to push their faculty to find some use for an NYA grant.³⁴

By nature, Davis should have been among the critics of the National Youth Administration. He was a political conservative and once described President Franklin Roosevelt as a “violent man, who showed the nature of his spots immediately after his election.” Yet, when Indiana University announced that it would start a National Youth Administration program, he put his political objections aside and moved “with a boldness that verged on rashness” to secure NYA funds for his computers. He suspected that “the University administration, caught without definite plans for the employment of these young people, would set them to menial tasks about the campus.” With a clear program in hand, he was able to acquire a substantial amount of the National Youth Administration funds allocated to Indiana University, though he confessed he gained “few friends by his boldness.”³⁵ In all, the National Youth Administration funds helped him produce two more volumes of tables.

The quality of Davis’s calculations was tested when Tables of Higher Mathematical Functions reached the British Nautical Almanac Office and the desk of L. J. Comrie.³⁶ “With an unknown author,” wrote Comrie, “it is desirable to check considerable parts of the tables, to see if he has the reliability of Andoyer and Peters, the proneness to error of Steinhauser, Gifford and Hayashi, or the plagiaristic tendencies of Duffield, Benson and Ives.”³⁷ These other human computers had been the targets of pointed reviews by Comrie; and Davis was to join their number. Comrie worked through the book, table by table and value by value. By recomputing 2,000 entries, he reconstructed Davis’s original computing plan, uncovered a substantial number of errors in the book, and identified the source of each mistake. Comrie noted that the pattern of errors indicated that the computers had verified their results by repeating the calculations a second time, “the poorest possible check” in his eyes. They had made mistakes in rounding the numbers and had introduced errors when they transcribed the values. Even the design of the book did not escape his attention. “The general lay-out of the tables,” Comrie wrote, “shows a lack of acquaintance with many elementary principles of tabulation, lack of consistency and lack of consideration for the user.” The review was not entirely negative, though its conclusion, that “table-lovers are assured that they should possess this work,” seemed faint praise.³⁸ Davis apparently paid due attention to Comrie’s criticism, for the second set of tables, those produced with NYA funds, had considerably fewer errors than the first.³⁹

During the first years of the Great Depression, H. T. Davis spent summers at the family home in Colorado Springs. It was a time to get away from the demands of university life, a chance to see old friends, and an opportunity to meet those who had come to southern Colorado in search of a better life. Town society included wealthy miners and poverty-stricken farmers. There were ministers hoping to find a land more spiritual and patients who hoped that the dry air might free them from tuberculosis. Among this group was a businessman named Alfred H. Cowles (1891–1984), who had survived the stock market crash with most of his fortune intact and had come to think that he might use his resources to improve the national economy.

Cowles was not formally trained in economics or in the methods of research, but he came from a successful newspaper family. The Cowles family owned the Cleveland Leader, had a substantial share of the Chicago Tribune, and also published farm papers in Washington, Oregon, and Idaho which were similar to Wallace’s Practical Farmer. Alfred Cowles had begun his career at the family paper in Spokane before deciding that he wanted to form his own business. He established an investment firm in Chicago and specialized in acquiring and restructuring small railroads. For a time, he ran a small conglomeration of southern lines that was known as the Alfred Cowles Railroad,⁴⁰ but he never entirely broke his ties with the world of journalism. His firm published a stock market newsletter that analyzed the state of the market and recommended stocks to buy or sell.

In the late 1920s, Cowles was diagnosed with tuberculosis, and as others had done before him, he moved west in search of better health.⁴¹ He withdrew from business shortly before the stock market crash of 1929, an event that caused him to think about the health of the economy as well as his own physical well-being. The initial prognoses for the market were optimistic and forecast a quick return to prosperity, but stock prices continued to fall. With time to ponder the situation, Cowles “began to feel that most of the forecasters were just guessing, himself included.”⁴² Living a life of enforced leisure, he began to sketch ideas for studying the stock market. His financial work had taught him something about correlation and statistical least squares. His first analysis was a regression model, one that simultaneously compared the predictions of twenty-four different market newsletters with the actual stock market prices. The equations required him to use least squares and demanded a substantial amount of calculation, calculation that Cowles did not know how to do.

With the resources at his command, Alfred Cowles could have easily found university researchers willing to study stock market predictions. He had connections at Yale University, where he had gone to college, and at the University of Chicago. Yet it seems that Cowles wanted to do the work himself, that he wanted to be the gentleman researcher, the amateur scholar working in semiretirement. Believing that he could do the work if he had assistance with the computations, he went in search of calculating help. He was led to H. T. Davis through a mutual friend, the director at a local tuberculosis foundation. In many ways, Davis was a good match for Cowles, for he never questioned the businessman’s approach to research. Had he been more active in the economics community, Davis might have tried to push Cowles toward a certain type of research, or he might have tried to make Cowles a silent partner in his own research. Instead, he tried to be the best help he could. “As far as I know, such a regression equation has never been made,” Davis replied, apparently unaware that Myrrick Doolittle had solved such equations by hand at the Coast and Geodetic Survey, that Howard Tolley had done similar work at the Department of Agriculture, and that George Snedecor was doing the same at Iowa State College.⁴³ “It happens, however,” Davis continued, “that a new machine is now available, a Hollerith Calculator, by means of which such a problem can be solved.”⁴⁴

In fact, Davis had little, if any, experience with “Hollerith Calculators,” as tabulating equipment from International Business Machines was sometimes called. His opinion was deduced from what others had told him or from what he read about the machines in the scholarly literature. While card tabulators could ease the labor of computing a large regression problem, they were unable to do some of the most difficult and time-consuming work, as the workers at the Iowa State Statistical Laboratory had learned. The Iowa State computers were able to use the machines only to calculate correlations and do the preliminary work for a regression problem. The final solution had to be calculated with an adding machine. To solve a regression problem with twenty-four elements could require eight or ten months of labor.

Though he knew little about tabulating equipment, Davis agreed to help Cowles build a computing laboratory in Colorado Springs. Later that summer, the two of them took the train north to Denver and visited a company that used punched card tabulators in its business. Cowles was satisfied with what he saw and leased a full set of equipment for his office.⁴⁵ Only after the tabulators arrived in Colorado Springs, perhaps as late as August, did Davis realized that the tabulating equipment could not compute a correlation or solve a regression equation. To compensate for this deficiency, he pressed Cowles to hire some of the computers that had prepared the Tables of Mathematical Functions in Indiana.⁴⁶

Cowles eventually adjusted his research plans, replacing the massive twenty-four-term regression with a series of twenty-four smaller calculations. Much of the work for these smaller calculations could be handled by the punched card equipment, leaving only a little arithmetic for the computers to do by hand. As he gathered data, he also developed a simpler way of analyzing the stock market forecasts, a method that compared the forecasts to random guesses. The calculations for this method were easily handled by the punched card machines. It was not the work that Cowles had planned to do, but it allowed him to answer the question “Can stock market forecasters forecast?” with the quick summary “Not very well.” He elaborated that “the best individual records failed to demonstrate that they exhibited skill and indicated that they more probably were the results of chance.”⁴⁷

Cowles must have known that he would never be a major economic researcher, but he wanted to be a part of the economics community and guide its research. He incorporated his office into a private research foundation, the Cowles Commission for Economic Research, and he actively reached out to scientists who were interested in economic research and organized computation. Using H. T. Davis as an intermediary, he met with James Glover, who taught actuarial mathematics and computation at the University of Michigan, and Thornton Fry of Bell Telephone Laboratories.⁴⁸ He also approached the Econometric Society, a new professional society devoted to the mathematical study of the economy, and offered to collaborate with them, to provide them with computing services, and to fund their publications. Initially, his proposal produced hesitation among the economists. One member reported that a few “became alarmed lest the Society’s good name be harmed by its implication in a venture with a man who was willing to spend a considerable sum of money in order to accomplish they knew not what purposes of his own.” The group debated the proposal among themselves before sending one of their number to meet with Cowles and to inquire about his intentions. The emissary spent a week with the businessman and concluded “that Cowles was sincerely interested in econometric research.” He urged the society to take Cowles’s money, work with his research organization, and utilize his computing staff without fearing that he would attempt to influence them or their work.⁴⁹

28. Alfred Cowles (center) with H. T. Davis (right) at Cowles’s home in Colorado Springs. Photo taken by Elizabeth Webb Wilson

At the Econometric Society, Cowles crossed paths with Elizabeth Webb Wilson, the ballistics computer of the First World War.⁵⁰ Wilson was living in Cambridge, Massachusetts, and pursuing a doctorate in economics at Radcliffe College. She was the only woman among the First World War computers to find some kind of scientific role, but her success had been shaped more by her wealth than by her wartime accomplishments. She had taught high school after the war until an inheritance from her parents left her a substantial income. Freed of the need to work, she had pursued graduate study, first at the University of Michigan and later at Radcliffe. Like Cowles, she tried to move beyond the role that wealth had brought her, though she was limited by her gender in a way that Cowles was not. Instead of financing industry, she had done calculations for the Michigan Teachers’ Annuity. Instead of commanding the Econometric Society, she had represented Michigan professor James Glover at actuarial congresses. Though she might yearn to be the leader, she would accept the role of observer and commentator.⁵¹

If “business principles were quite free to work out their logical consequences, the outcome should be to put the pursuit of knowledge definitely in abeyance,” quipped the economist Thorsten Veblen.⁵² Veblen’s nephew, the mathematician Oswald Veblen, rarely agreed with his uncle’s pronouncements, but he might have conceded the idea that commercial businesses rarely supported unfettered scientific research. The younger Veblen had spent part of the 1920s in a frustrating attempt to convince industries that supporting mathematical research was in their interest, a campaign that he called “our Debt to Mathematics.”⁵³ It proved to be a much harder task than organizing the computing staff at Aberdeen. Few industries, save those involved in power generation or aircraft production, saw any value in pure mathematics. Mathematicians found it easier to raise money for computation, as computation could support a corporate goal. Both Westinghouse and General Electric expanded their computing staffs during the 1930s, as they were involved in the construction of the large New Deal electrical projects: the Rural Electrical Association, the Tennessee Valley Authority, and the dams on the Columbia River. The two companies investigated Vannevar Bush’s new computing machine, the differential analyzer, in order to handle their engineering calculations. One of the few examples of a company funding an independent computing lab, a lab with little direct connection to company production, was the scientific computing facility at Columbia University, which was financed by International Business Machines.

The Columbia computing facility, originally known as the Columbia University Statistical Bureau, was the joint creation of a scholar and a business leader, Benjamin Wood (1892–1984), a professor at Columbia’s education school, and Thomas J. Watson, president of International Business Machines. Wood was a Texan, described by a biographer as a “towering and disciplined intellect against which sparks of imagination impinged with the force of ignition.”⁵⁴ Watson was a salesman by training, enthusiastic yet focused, and strategic.⁵⁵ The two met when Wood was studying the Alpha and Beta intelligence tests, the exams that the army had used during the First World War to screen recruits. Wood had collected hundreds of tests as his raw data. Each of these tests was graded by hand, and the results were analyzed with correlation statistics. By his estimate, it cost him five dollars in labor to process each batch of tests.⁵⁶ Thinking that there must be some way to grade the tests with a machine, Wood wrote to the presidents of ten companies, described his problem, and asked their assistance. Of the ten, only Thomas Watson responded. He had no solution to the problem, but he was intrigued with Wood’s letter.⁵⁷

29. Columbia University Statistical Bureau. Ben Wood (in dark suit) stands in the center

The story of the initial meeting between the professor and the businessman comes from Wood, who is not the most reliable witness. He liked to boast and would later attribute quotes to Watson that could not possibly have come from the leader of IBM.⁵⁸ Wood stated that the two met in a downtown business club and that he began the meeting by flattering the IBM product line, telling Watson that the tabulators could “do marvelous things in science and education, civil service, government, logistics, military, aviation, astronomy, every science in the world.”⁵⁹ No matter what Wood may have said, something in his presentation appealed to Watson. Watson’s son later wrote that the Columbia professor described a vision that was “music to the ears of a tabulating machine maker.”⁶⁰ During the meeting, Watson offered to provide Wood with punched card equipment. As Wood would later recall, “two or three weeks later, or maybe one week later, two or three huge trucks arrived at my office” and delivered what he remembered as “every IBM machine they had.”⁶¹ Of course, the installation was not quite that easy. Wood had to get permission from his dean, find space on campus, install the equipment, and find a trained operator.

Wood outlined a grand vision for the tabulating machinery. “I was planning to make tests over the whole gamut of the curriculum,” he recalled. Wood provided Watson with a basic understanding of statistical calculation as employed by social scientists and suggested new equipment that might be useful in statistical research. He also worked with IBM engineers to create a progressive digiting machine that could automatically perform multiplication and helped IBM identify a mechanism that would score standardized tests. When called upon to give a speech or demonstrate his equipment or even write a letter of recommendation for Watson’s teenage son, Wood was glad to comply.⁶² Perhaps his most important contribution was to admit into his laboratory a young astronomy professor named Wallace J. Eckert (1902–1971).⁶³

Unlike social statistics, astronomical calculation was not a growing field, and unlike the boisterous Wood, Wallace Eckert was a “small and retiring man,” characterized by one IBM historian as “so soft-spoken that he was scarcely audible.”⁶⁴ A Columbia graduate student went so far as to call him one of the “passé guys,” a scientist who looked to the past rather than anticipating the future.⁶⁵ Passé or not, Eckert came to the laboratory wanting to see how the punched card machines could handle a classic and difficult calculation, the three-body problem. The specific version of the problem was the system involving the Earth, the Sun, and the Moon. Eckert had an unusually detailed analysis of the problem, which he had obtained from Yale professor Ernest W. Brown (1866–1938). Brown had extended his analysis beyond the three bodies of the Earth, the Moon, and the Sun and included the tug from the giant planets of Jupiter, Saturn, Uranus, and Neptune as well as the slosh of the Earth’s oceans as they dragged behind the Moon. He had summarized this solution in a 660-page volume with 180 tables.⁶⁶

With Brown’s tables, a computer could determine the position of the Moon for any day and any time, but the labor was almost overwhelming. Writing from the British Nautical Almanac Office, L. J. Comrie complained that the task of preparing a lunar ephemeris from Brown’s tables required “the continuous work of two skilled computers.”⁶⁷ Comrie transferred this calculation from human computers to the punched card equipment. This new approach to preparing an ephemeris required Comrie to think in terms of operations that were not obvious to the astronomical computer. He selected the tables he needed and punched them onto a separate deck of cards. Each table represented a different force on the moon. Next, he duplicated the cards and shuffled them together, using a card sorter in a downtown London office.⁶⁸ When he was done, the first cards had the values for January 1, the next cards had the values for January 2, and so forth. In the final step of the calculation, he put the cards for each day through a tabulator in order to sum the values.⁶⁹ The process was relatively quick and possessed the added benefit that “a small change may be made in the elements and the new values of the coordinates obtained with almost no additional work.”⁷⁰

Comrie was not in a position to further develop the methods of punched card computation, as the British Nautical Almanac did not have its own tabulator. However, he sent a copy of his computing plan to Eckert, who had access to Wood’s tabulating facility at Columbia. Eckert studied Comrie’s plan and carefully duplicated the English computations.⁷¹ From this work, he slowly began to expand his skill with the tabulating equipment, learning how to handle complicated analyses and difficult computations. By the spring of 1934, he had become the expert in scientific computation with punched card equipment and had supplanted Benjamin Wood as the faculty contact with International Business Machines. That spring, IBM recognized Eckert’s growing prominence by helping him create a new facility, the Columbia University Astronomical Computing Bureau. This organization was not really a separate laboratory, for it used the same machines that were being used to tabulate educational statistics. It did have one new piece of equipment, an IBM 601 multiplying punch, which eliminated the need to do progressive digiting.

For all of the attention that International Business Machines gave to Columbia University, Benjamin Wood, and Wallace Eckert, the company considered scientific computing to be only a minor application of their equipment. In 1935, the company prepared a book to promote the use of tabulators in higher education, entitled Practical Applications of the Punched Card Methods in Colleges and Universities. The volume was edited by a company employee and was published by Columbia University Press. “So numerous are the uses of the punched card method in colleges and universities,” read the preface, “and so great the interest shown by these institutions that the creation of this volume was a logical development.”⁷² Fully four-fifths of the contributions to the book were business applications: class records, patient histories, student accounts, course registration, resource scheduling. Of the remaining fifth, most dealt with social statistics. Three entire chapters had been submitted by the statisticians at Iowa State College. Only Eckert’s chapter, buried at the back of the book, dealt with astronomy.

Eckert began to record the methods of scientific computation in a notebook which was known locally as the “Orange Book.” In the pages of this book, he described how to reduce data, create a star catalog, compare observed positions with theoretical calculations, and mechanize the solution of differential equations.⁷³ His descriptions showed how to prepare the cards and how to work with the sorters, tabulators, and punches. Through 1935 and 1936, scientists began to appear at the door of the laboratory. Some had written to ask for permission to visit; others, who may have been passing through New York or attending a conference down by one of the railroad stations, simply arrived unannounced. They talked with Eckert, handled the cards, watched the machines in operation, worked with one of the machine operators, and usually inquired if they might make a copy of some page of the Orange Book.⁷⁴

In 1936, one of Eckert’s visitors was an astronomer from the Soviet Union, the aptly named Boris Numerov. Numerov walked freely among the equipment, listened to Eckert talk about the benefits of punched card calculation, and, most likely, took copies of pages from the Orange Book. When Numerov left the lab, he apparently told Eckert that he would keep in touch or that he might write later or that perhaps he would need Eckert’s assistance in building a punched card facility in the Soviet Union. Eckert accepted the farewell, watched Numerov depart for Moscow, but never heard from him again. It was the era of the Stalinist purges, and Eckert came to believe that the Soviet astronomer had been punished or killed for inquiring about punched card tabulation. It was a misguided concern, as Numerov almost certainly had the permission of the Communist Party for his visit, but it was not without basis in fact. The threat to the astronomer came not from a visit to an American computing laboratory but from a German name for an asteroid. Numerov was arrested after the Soviet secret police learned that German astronomers had named a small planet Numerov. Concluding that anyone who received such an honor from Germany was likely a spy, the secret police had him executed.⁷⁵

Eckert may not have appreciated the politics that pulled Numerov to his doom, but he was able to recognize the forces pulling on his computing facility. By 1936, the Columbia Computing Bureau was the prominent facility for scientific computation with punched card equipment, a laboratory far more visible than the Iowa State Statistical Laboratory or the computing office at the U.S. Department of Agriculture. As the leader of the astronomical computing bureau, Eckert was increasingly identified with International Business Machines, even though he remained a member of the Columbia faculty. In his writings, however, he made it clear that he was not a blind advocate for IBM, an unquestioning promoter of tabulation equipment. “The main question in any case is not ‘can the problem be solved by these machines,’” he wrote, “but rather ‘have I enough operations of this type or that, to justify such powerful equipment.’”⁷⁶ Still, his ties with IBM were close, and when he decided to publish his Orange Book of computational methods, he used the publication services of International Business Machines rather than Columbia University Press or some other university publisher.⁷⁷

In 1933, when organized computing had taken root at Indiana University, at the Cowles Commission, and at Columbia University, the National Research Council returned to the idea of preparing a general bibliography of mathematical tables. Some on the council, including Thornton Fry, believed that Davis might be the appropriate person to head the unfinished Subcommittee on the Bibliography of Mathematical Tables and Other Aids for Computation. Others had reservations. Davis would not “be the right man to head up a committee along this line,” wrote Henry Rietz (1875–1943), a professor at the University of Iowa. He observed that Davis expressed more enthusiasm than discipline and that “Professor Davis very strongly believes that the real problem of aids to computation rests in table-making itself rather than in a comprehensive bibliography.”⁷⁸ The rest of the council reluctantly concurred and continued its search. Finally, they returned to the Aberdeen veterans and selected A. A. Bennett of Brown University, a mathematician who had worked with both Oswald Veblen and Forest Ray Moulton. “Bennett seems especially well-fitted for the work,” argued Rietz, “not only because he would probably do a scholarly piece of work, but because Brown has … the best collection of mathematical tables in connection with any university.”⁷⁹

Bennett accepted the chair of the MTAC committee in 1935, but the appointment came at a poor time for him. Along with Oswald Veblen and Gilbert Bliss, he was a consultant to the Aberdeen Proving Ground. In 1935, the proving ground had reorganized the division engaged in ballistics research and had increased the number of test firings on the artillery ranges for the first time in a decade.⁸⁰ In the years since the First World War, ballistics research had been divided into three distinct fields. The traditional computation of trajectories was now identified as external ballistics, which was contrasted with internal ballistics, the study of the stresses and pressures within a gun. The final division dealt with the physics of exploding shells and was called, appropriately, terminal ballistics. The new Ballistics Research Office had sections devoted to each aspect of the research as well as a new central computing office.⁸¹

Bennett had some initial success organizing the MTAC committee, but he was unable to give the work the kind of effort and attention that it deserved. He wrote to the Galton Laboratory at the University of London to enquire about the plans of Karl Pearson. Pearson’s son replied that his father had died the year before but that he had left a great deal of material which might be used by the new committee. Bennett also asked a half dozen individuals, including H. T. Davis and L. J. Comrie, to join him on the committee and help with the bibliography. Writing from Colorado, Davis exclaimed that “I am very much pleased to accept membership on this Committee because I believe sincerely in the importance of the project.”⁸² Comrie, however, was more circumspect. “Am I right in interpreting ‘Aids to Computation’ as meaning calculating machines?” he asked.⁸³ Only after Bennett assured him that such machines would have a place in the bibliography did he agree to serve.⁸⁴

Comrie’s ability to contribute to MTAC would be limited. The problem was not so much the economy as it was a fall from grace, a small lapse of judgment. In the winter of 1935–36, the British Admiralty discovered that Comrie had not been accurately reporting the activity of the Nautical Almanac Office. Comrie was convinced that his staff was too small and that he was unable to retain the best computers because of Admiralty personnel regulations. Unable to make his point through memos and arguments, he was trying to impress upon the Admiralty the shortcomings of their policies by delaying the release of important work. He told his supervisors that the almanac computers were overworked and unable to do certain computations when, in fact, those computations were already finished and residing in Comrie’s files.⁸⁵ The flaw in this strategy was exposed when an investigative board arrived unannounced at the almanac office. The board discovered the missing computations, charged Comrie with obstructing Admiralty work, and dismissed him.⁸⁶ “Comrie’s often-expressed complaints that the civil service regulations were petty and restrictive are given some justification by [the record],” observed historian Mary Croarken, “but it is also clear that Comrie was inept at ‘playing the game’” and working effectively within a large government organization.⁸⁷

After his departure from the British Nautical Almanac, Comrie rented a building in London and formed a private computing laboratory, the Scientific Computing Service Ltd. The company grew quickly, sustained in no little part by computing contracts from the British government, including his former employer, the Admiralty. In less than a year, he employed a staff of sixteen computers, “most of whom have academic training,” he boasted. The company handled the same kinds of calculations that were done at the Nautical Almanac Office: navigation tables, astronomical calculations, statistical summaries. Looking for commercial business, it also advertised a specialty in the analysis of questionnaires and “an advisory and investigational service relating to the purchase and use of calculating machines.”⁸⁸

Though Comrie’s new company prospered, his fall from grace had consequences. His scientific life was burdened with the need to satisfy bank officers, customers, and investors. He could no longer freely volunteer his time to scientific organizations, either the Subcommittee on the Bibliography for Mathematical Tables and Other Aids for Computation or the Mathematical Tables Committee of the British Association for the Advancement of Science. He could remain a member of both groups and could contribute to the work of each, but he could not afford to take a leadership role. In his new position, he had to earn his own way and support the economic prosperity of his company.