CHAPTER THIRTEEN

Scientific Relief

MALCOLM MORROW (1906–1982) was the faceless bureaucrat of computation, the government worker who created the largest human computing group of the 1930s but left little record of himself. He lived in a working-class district of Washington, D.C., only a few blocks from the original Naval Observatory and the building that had once housed Simon Newcomb’s Nautical Almanac Office.¹ He held jobs in several of the New Deal agencies and eventually settled into the executive office of the Work Projects Administration (WPA)² as an assistant statistician. His title gives us little information about his mathematical ability, as the WPA employed many assistant statisticians. Some were nothing more than clerks. Some were project managers. Some prepared questionnaires. Only a few were employed in the analysis of data.

Morrow’s WPA was the largest and most developed of the New Deal’s relief agencies. Formed in 1935, it was Franklin Roosevelt’s third attempt to reduce unemployment through the construction of public works. The WPA operated offices in each of the forty-eight states, as well as an extra office in New York City, that provided funds for projects judged to be in the public good. The WPA paid for parks and bridges in New York City, sidewalks in Michigan, dams in Texas, city offices in Los Angeles, 226 hospitals, 1,000 libraries, 1,200 airport buildings, 2,700 firehouses, 9,300 auditoriums. WPA workers renovated the army’s research facility at the Aberdeen Proving Ground, repaired the Naval Observatory in Washington, and constructed a new building for the Iowa State Statistical Laboratory.³

In general, the WPA did not manage the projects that operated under its name. It provided only wages for workers. Local organizations would identify appropriate projects, develop plans, and pay for any necessary materials. Only rarely would the WPA staff in Washington plan and manage a project without the assistance of a local sponsor. Those projects that were directly overseen by the WPA tended to be national in scope, such as the Federal Theater Project and the Federal Writers’ Project. The theater project supported performing arts across the country and proved to be a controversial activity. While only a few of the theater productions had any political content, notably Orson Welles’s The Cradle Will Rock and Sinclair Lewis’s It Can’t Happen Here, the project was the target of conservative critics who claimed that the government-supported artists were promoting liberal ideas and undermining American society. Eventually, the critics found enough support within Congress to terminate all WPA theatrical productions.

The writers’ project generated less controversy, but it experienced serious operational problems. The project was intended to support regional authors by having them create guidebooks for each state of the union. The Washington WPA office provided a style manual that described how the “geographic, historic, cultural, social, recreational, industrial and commercial information should be assembled.” In spite of the best intentions, the project was unable to recruit sufficient regional talent to prepare the guides. Not wanting to see a visible project fail, the WPA administrators had many of the guidebooks rewritten “by experienced writers drawn from New York City and other centers, who were paid for their work on a non-relief basis.”⁴

Among the tens of thousands of WPA projects, there were about 2,400 that supported scientific research. Future Nobel laureates Glenn Seaborg and Luis Alvarez at the University of California are on the list of those who received WPA assistance.⁵ WPA funds paid the salaries of laboratory workers in much the same way that the National Youth Administration had provided funds for student assistants. Most WPA-sponsored science involved large statistical studies of social or economic problems.⁶ Malcolm Morrow’s division of the WPA, the Central Statistical Office, oversaw most of these projects. This office suggested possible studies, reviewed proposals from universities and state agencies, and granted funds that would pay for workers to conduct surveys, collect information, tabulate data, and analyze the results. The Iowa State Statistical Laboratory was a major beneficiary of the Central Statistical Office. It received WPA money to summarize harvests, measure farm income, and analyze the extent of rural poverty.⁷

Sometime early in the operation of the WPA, perhaps in the summer of 1935 or the winter of 1936, the staff of the Central Statistical Office became engaged in a discussion of mathematical tables. As they were starting to oversee a large number of statistical studies, they thought that it might be useful to provide a standard set of mathematical tables to each of the projects and to each of the regional WPA offices. If all of the statistical projects had the same tables of logarithms and probability functions, then the Central Statistical Office could compare the results of the different studies with a little more confidence. This idea produced no immediate action, as the office had more pressing things to do, but it was revived in the fall of 1937 when the nation entered a new period of economic hardship. After three years of tentative growth, the economy had begun a contraction that was quickly labeled the “Roosevelt Recession.” Faced with growing unemployment and greater labor unrest, the WPA began looking for new projects in order to expand the number of relief jobs. With winter approaching, they needed to identify activities that could operate during the cold months.⁸ The construction jobs, which constituted 75 percent of the WPA projects, were curtailed between late fall and early spring. As WPA officials evaluated different ideas, they recognized that a computational project could employ a large office staff and assigned Malcolm Morrow the task of organizing such a group.

The mechanics of starting a new project were fairly simple. Morrow needed to find office space, acquire the necessary furniture, and notify the local WPA office that he could accept a staff of qualified workers. The local office would send him as many people as he needed from those who had applied for relief jobs. The difficult part of Morrow’s assignment was the task of finding a sponsor, a scientific organization that would accept the project, oversee the computations, and provide the appropriate mathematical expertise. He started looking for a sponsor at the institution that considered itself to be at the center of American scientific research, the National Academy of Sciences. The academy building stood just a few blocks from the mammoth headquarters of the WPA, so one day in late October, Malcolm Morrow left his desk early and called upon Albert Barrows, the permanent secretary of the National Academy, and asked for assistance.

Morrow began his presentation slowly, stating ideas that were familiar to many of the scientists who worked with the academy. He reported that the statisticians on the WPA staff felt that “there was a very large amount of work, which can be done to improve the mathematical basis on which a great deal of other scientific work depends.” He noted that there were substantial errors “in a number of the standard mathematical tables” and that the “tables already in use ought to be greatly extended,” as more scientists were employing them in their research. Reaching his central point, he told Barrows that the WPA was planning to build a large computing center in New York City. The center would prepare mathematical tables for use “not only by mathematicians and astronomers, but also by surveyors, engineers, chemists, physicists, biometricians, statisticians, etc.” If they were successful, it would be the biggest computing organization in history, a group that might “employ a thousand people, as well as experts to advise.” All of the computers, of course, would be drawn from New York’s unemployment rolls, but he assured Barrows that there would be calculating machines and a “training school to initiate employees.” The new center would be an expensive operation, Morrow conceded, but New York City had $2.3 million available for relief. He implied that a large part of this money “could be devoted to this project.”⁹

After describing a computing facility nearly as fantastic as Lewis Fry Richardson’s weather computing room, Morrow retreated to a more practical realm and admitted that the project would begin on a small scale, perhaps “50 employees under the supervision of technical directors and office managers.” Coming to the key question of the meeting, he asked Barrows if the National Academy of Sciences would be willing to appoint an advisory committee to the computing center, a group that would identify projects for the computers and help prepare computing plans.¹⁰

In general, the members of the National Academy of Sciences belonged to a class that distrusted Franklin Roosevelt and disliked the idea of government-sponsored work relief. They joked that the initials “WPA” stood for “We Poke Along” and claimed that the public works projects were nothing more than an attempt to buy votes for the Democratic Party. This view of work relief was so pervasive among the secure classes of American society that twenty years after the end of the Great Depression, the novelist Harper Lee could damn a character by claiming, “He was the only man I ever heard of who was fired from the WPA for laziness.”¹¹ If Barrows held such impressions about work relief or the WPA, he was able to put them aside as he summarized the meeting for academy president Frank Lillie (1870–1947), a University of Chicago zoologist. “Mr. Morrow (a man I should judge of 40 or 45 years of age) impressed me as competent to discuss this project,” he wrote.¹²

Lillie responded to Morrow’s visit by sending a note to the chief statistician of the WPA. “I wish to assure you that we shall be most happy to render any service within our power,” he wrote; “the National Academy of Sciences in its part would be glad to appoint a committee of mathematicians to advise on specific undertakings.”¹³ Lillie named no names, but he and Barrows had already discussed possible candidates for such a committee, including Oswald Veblen, Vannevar Bush, Harold T. Davis, and James Glover.¹⁴

When Malcolm Morrow ended his meeting at the National Academy of Sciences, he had told Barrows that there was “an element of urgency in organizing the matter because of the impending election of mayor in New York City,” and he had asked that “no intimation of consideration of the project be permitted to be made publicly or find its way into the channels of the press.”¹⁵ The WPA computing office, tentatively called the Project for the Re-computation of Mathematical Tables, was not an ordinary scientific project that was supported by a university or funded by industry. It was going to be a federal project in a city where Democrats and Republicans fought over federal funds and where the outcomes of such battles could have national repercussions. Morrow was probably concerned about protecting his project, getting the computing office established before some city agency attempted to capture its budget for another purpose. The sitting mayor of New York City, Fiorello La Guardia, was an ally of Franklin Roosevelt and willing to have projects managed from Washington.¹⁶ His opponent, a member of the city’s Tammany Hall political organization, was not as sympathetic to the Roosevelt administration and might be able to redirect the project funds to some organization with no qualifications other than ties to Tammany Hall.¹⁷

After his meeting at the National Academy of Sciences, Morrow traveled to New York City, hoping to persuade one of the city’s universities to sponsor the project. Columbia University was the most likely choice, as they had a strong mathematics department and housed the offices of the American Mathematical Society. However, its faculty already operated the Columbia Computing Bureau with its tabulating machines. They showed no interest in sponsoring a large group of human computers. Morrow then approached New York University and proposed that the school provide space for the computers and mathematicians to manage the calculations. Though university officials were interested in the project, they felt that they could not provide the necessary funds and declined the offer.¹⁸

As the date of the mayoral election approached, Morrow had no sponsor for the project, no site to house it, and no plans for its operations. At the National Academy of Sciences, which had received no report from Morrow after his initial visit, secretary Barrows voiced a growing skepticism about the idea. “I still have the feeling,” he complained, “that this is one of those matters which they would not be able to complete if started.”¹⁹ Morrow found his sponsor three days before the November election. After finding no help in New York, he returned to Washington and convinced the director of the National Bureau of Standards, the physicist Lyman Briggs (1874–1963), to manage the new computing organization.²⁰

Briggs had both the technical background and the political experience for such an assignment. As a physicist, he knew how hard it could be to prepare a useful, error-free table. From his years with the Bureau of Standards, he understood that government support for science was unstable in the best of times and hostile in the worst. Since its founding in 1901, the bureau had been repeatedly attacked by congressional critics, who had argued that the government should not be involved in research and should not set standards for private industry. In 1933, Congress cut the budget of the National Bureau of Standards in half. “It was a bitter experience for us,” Briggs recorded. “More than one third of our staff was dropped on a month’s notice.”²¹ Attempting to sustain the bureau, he discovered that he could obtain relief grants to replace some of his lost budget. Money from the Civil Works Administration and the Public Works Administration, predecessors of the WPA, was used to clean and repair bureau buildings.²² “Several of the abler mechanics and technicians of the Bureau,” wrote one historian, “let go earlier, found their way into [maintenance work] and tarried there until they could be restored to the Bureau payroll.”²³

In agreeing to sponsor the WPA computing project, Briggs extracted concessions that New York University was unable to get. He would manage the project, recruit senior personnel, and provide scientific expertise, but he would provide no money for the group. The WPA would fund the entire budget for the project. Furthermore, Malcolm Morrow, who had identified himself as the project leader, was relegated to administrative issues, such as finding a suitable office, handling WPA paperwork, and communicating with the New York City relief agencies. This agreement was consummated so quickly that Morrow apparently failed to tell Lyman Briggs of his contacts with the National Academy of Sciences, for the politically astute Briggs made no effort to contact Albert Barrows or Frank Lillie. With no information from either Briggs or the WPA, the senior members of the academy naturally concluded that the relief agency had been unable to organize the computing project. “Since the day Mr. Morrow was in here saying we were to get a letter the next day, I have wondered what has happened to him,” commented one member of the Academy staff. “He seems to have disappeared off the horizon.”²⁴

It would have been best for the Mathematical Tables Project if Lyman Briggs had been able to recruit an established computer to be its leader. If the project had been led by Oswald Veblen or even H. T. Davis, it would have started operations with strong connections to the scientific world. However, the idea of leading a work relief project appealed to few scientists, and Lyman Briggs had to turn to the ranks of the underemployed, the scientists who were not able to find a position at a top college or university. The path that led him to choose Arnold Lowan (1898–1962) as project director is no longer well marked. It may have involved Oswald Veblen, probably passed through Columbia University, and almost certainly involved thermodynamic calculations, the computations of heating and cooling.

In the fall of 1937, Arnold Lowan was holding two part-time teaching positions. By day, he taught physics and mathematics at Yeshiva College in Manhattan. At night, he taught the same subjects at Brooklyn College.²⁵ He had immigrated to the United States in 1924, fleeing anti-Semitic pogroms in his home country of Romania and rushing to reach New York before a new law restricted immigration from Eastern Europe.²⁶ He was a desirable immigrant, a chemical engineer, but he had waited four years before he found professional employment, a period he would never describe on any of his resumes or reminiscences of the time. He likely spent the time among the immigrant Jews of Brooklyn or Manhattan’s Lower East Side, learning English and becoming acclimated to the United States. If he was employed during this time, he was likely doing manual labor or other work that he considered subprofessional. The first job he was willing to identify was one he took in 1928 with a utility contractor, working as what he called a combustion engineer. He described his job in grand terms, claiming that he was researching the “thermodynamics of gaseous hydrocarbons,” while he was actually working with coal gas furnaces and boilers.²⁷

30. Arnold Lowan, director of the Mathematical Tables Project

The salary he gained from tending furnaces by day allowed him to study physics by night. He took a master’s degree from New York University and then transferred to Columbia University in order to earn a doctorate. “He certainly has great industry and perseverance,” remarked a Columbia physicist, and “in the main [he] follows out his own ideas.” At a time when the brightest students were looking at problems that would lead to the subjects of relativity and quantum physics, Lowan turned to conventional thermodynamics, the study of heat. Though he rarely asked the Columbia faculty for guidance, he did become acquainted with one of the veterans of the Aberdeen Proving Grounds, a physicist who had served as Oswald Veblen’s assistant during the First World War. This connection gave Lowan a brief entry into the senior ranks of American scientists, a postgraduate fellowship at the newly formed Institute for Advanced Study in Princeton, where Veblen was on the faculty.²⁸

At the institute, Lowan seems to have kept to himself and rarely interacted with the other researchers. He spent his year developing his ideas on thermodynamics and completing a large calculation that described the cooling of the earth. In all, he did the research for ten scientific papers, each of which involved extensive numerical work. He may have been overawed by scientists like Veblen and Albert Einstein, or he may have had difficulty communicating with others, or he may simply have lacked the background to deal with research problems in the new fields of physics.²⁹ Judging from his later letters, he clearly spent some time with Einstein, Veblen, and the Hungarian mathematician John von Neumann (1903–1957), but not enough to be their friend or even their familiar. In 1934, when Lowan’s fellowship ended, they were unable or unwilling to help him find a job at a research university. With the lingering depression, budgets were tight; Lowan could not find any full-time job in physics. Instead, he took his two part-time teaching positions.

There are three plausible routes that might have led Lyman Briggs to Arnold Lowan. The shortest begins with Oswald Veblen, the great computer of the First World War, who would have recalled Lowan’s computational work at the Institute for Advanced Study. The second path is more complex, but it was suggested by one of the WPA workers. This path begins with one of Lyman Briggs’s assistants, a geologist who had prepared mathematical tables for the Smithsonian. For this path to work, the geologist would have to have read Lowan’s articles on the cooling of the earth and appreciated the extensive computations. The final path leads through Columbia University. Briggs may have simply asked the Columbia faculty or the American Mathematical Society if they knew of anyone qualified to run a computing organization.³⁰ No matter how Briggs was introduced to Lowan, he could not have found a leader better suited for the Mathematical Tables Project. Lowan was ambitious to make a reputation as a scientist and was not repulsed by a work relief job.

Lowan joined the Mathematical Tables Project in late November 1937 and was told to begin operations in the first months of the new year. The project office would be one floor of an industrial building on the west side of Manhattan, not far from Times Square. Arnold Lowan found a used desk to serve as his work area, placed it in a corner of the empty space, and started to make his plans. He would be the executive of the group, the administrator who would deal with budgets, personnel, correspondence with the public, and any communications from the Bureau of Standards. His first problem was to find more mathematical talent, a technical director to analyze the computations and prepare the detailed computing plans. Almost immediately, he hired two graduate students from Brooklyn College, but they acted as personal assistants, not mathematical leaders. His technical director needed to hold a doctorate and should know something about the operations of a large office. He probably had no idea where to search for such an individual and must have been surprised to find one in his night class at Brooklyn College.³¹

That fall, Lowan was teaching a course on the subject of relativity, an elementary presentation designed for individuals who were trying to expand their horizons. Most of the students came from day jobs in Manhattan. Sitting near the back was a short woman who wore the kind of business dress that could be washed in a bathroom sink and dried overnight. On most nights, she seemed a little tired and not especially engaged in the subject. When it was cold or raining, she did not attend the lecture at all. Lowan paid little attention to her until he began to grade the homework papers. Her mathematical reasoning was the work of a professional. It identified all the assumptions, moved through each step of the analysis, and presented the solutions in a clear manner. As the student used mathematical concepts that had not been presented in class, Lowan suspected that she was receiving outside assistance. He traveled to and from campus on the same bus line as this student, so one night after class, he sat next to her and tried to start a conversation. At first, the student was reluctant to speak, as if she was unsure of Lowan’s motives. After some coaxing, she began to relax and tell her story.

The student’s name was Gertrude Blanch (1896–1996), and she confessed to Lowan that she held a doctorate in mathematics. She had been born Gittel Kaimowitz in Kolno, Poland, a Jewish settlement near the Russian border. Like most such communities, it had suffered the czarist pogroms, and her family had fled to the United States. Her father had come first, followed by her mother and finally, in 1907, by Blanch and her sister. The family had settled in Brooklyn, which was considered a “pastoral neighborhood” compared to the tenements of the Lower East Side.³² Blanch, who had the opportunity, rare for a Jewish girl, of attending school in Poland, settled easily into the public school system. She completed the primary curriculum in three years and gained admittance to Brooklyn’s Eastern District High School.³³

31. Gertrude Blanch, lead mathematician of Mathematical Tables Project

Blanch rushed through her high school studies. “It was up to me to get a job as soon as possible,” she recalled. Her father’s health was declining, and when he died, just at the time of her graduation, all hope of attending college died with him. To support her mother, she took a job with a Manhattan hat dealer named Jacob Marks. “He would export things,” she said, “and I would organize the transactions for them. It was paperwork. They paid me very well.”³⁴ She mastered the computations for foreign currency payments, gained added responsibility, and acted as Marks’s office manager. While she was working, she assembled a small library of mathematical books, reminders of the subject she most loved in school. Many of them were commercial tracts, the kind that were distributed by adding machine manufacturers or sold by business teachers trying to improve their income. They explained various accounting computations, such as the cost of money or the depreciation of stock. They showed how to simplify calculations, check values, and reuse results.³⁵

For fifteen years, Gertrude Blanch worked for Mr. Marks. She watched the men of her generation march off to war and heard of the new opportunities for college-educated women, but she was unable to leave her office and her responsibilities to her family. Only after her mother died in 1927 was she able to begin a new life. She cleaned her parents’ apartment for the last time, accepted an invitation to live with her sister’s family, and enrolled in her first courses at New York University. When she announced to Mr. Marks that she was quitting her job in order to attend college, he countered that he would pay her tuition if she would attend night school and spend the days at his company. She accepted the offer and graduated four years later with a degree in both mathematics and physics. Her diploma was awarded with highest honors, “summa cum laude,” and she was inducted into the national Phi Beta Kappa honors society.³⁶

Blanch wanted to attend graduate school, but she knew that it would be a gamble, a risk that would hazard all her resources. In the United States, there were little more than a hundred female mathematicians, most of whom were relegated to limited roles in the profession.³⁷ The odds were lengthened by her Jewish heritage and her age. At thirty-six years, she was a full decade older than most graduate students. “Science is a young man’s game,” wrote the mathematician G. H. Hardy. Citing Isaac Newton as an example, Hardy had claimed that the great mathematician “recognized no doubt by the time that he was forty that his great creative days were over.”³⁸ As Blanch prepared for further schooling, she recognized that her scientific career would have barely started when she reached her fortieth birthday.

Before she departed for graduate school, she made her immigrant background less obvious by Americanizing her name. She had long been known as Gertrude instead of Gittel. Informally, she had occasionally used Cassidy instead of Kaimowitz for a last name.³⁹ When she came to choose a permanent last name, she selected the birth name of her mother, Dora Blanch.⁴⁰ She was not a feminist, as modern scholars would define the term, and later in life she would dismiss the idea that she had been limited by her gender. As she pondered her choice of graduate schools, she was aware that many of the best graduate programs were closed to her. Princeton University, where Oswald Veblen taught, did not admit women. Harvard educated women only through the back door of Radcliffe College. Even the most liberal of graduate programs, such as the graduate school of the University of Chicago, had their limits. Chicago gave more PhDs to women than any other school. Still, Blanch observed, “All things being equal, they would choose a male student.”⁴¹ The university offered her admission to the mathematics program, but when she asked for a fellowship, they told her that “scholarships to women were given out only in very rare circumstances.”⁴² Instead, she chose to attend Cornell University, which also offered no scholarship but welcomed women and also had a substantially lower tuition.

Cornell proved to be a good choice for her. “They appreciated me,” she recalled, “to the extent that I contributed as much as any other student. I can’t claim discrimination while I was studying.”⁴³ Her doctoral advisor was Virgil Snyder, a past president of the American Mathematical Society. Snyder, like James Glover at Michigan, advocated mathematical education for women and guided the graduate study of several female students. Blanch would later write that she was “deeply grateful to him for unfailing encouragement.”⁴⁴ She also found support in a small club for women graduate students. Every few weeks, these women met to socialize, talk about their lives, and share the lessons of graduate school.⁴⁵ She enjoyed graduate school, with its seminars and discussions and parties, even though the failing economy made study increasingly difficult for her. As her resources began to wane, the university found a fellowship that allowed her to continue her studies uninterrupted. During the most difficult times, she had to purchase food on credit from the university’s agricultural school.⁴⁶

When Blanch completed her degree in 1936, she found a temporary position at Hunter College for Women, a job which paid the “munificent sum of thirty dollars a week.”⁴⁷ It proved to be only a brief respite from the problems of the Depression and the limitations imposed upon women scholars. She spent much of the year searching for a permanent university job and completing dozens of applications. She stopped only when Cornell University refused to issue any more transcripts, claiming that her “requests have been excessive.”⁴⁸ No school offered her a position, so she turned to the employment ads in the New York Times. She applied to be the office manager for a company that made cameras for color photography. In her letter to the firm, Blanch explained that she was a Cornell graduate but never stated that she had a doctorate in mathematics. She was invited for a job interview in a pleasant mid-Manhattan office with carpets, “wall paneling and wainscoting.”⁴⁹ The senior manager, who was conducting the interview, remarked that the company had received fifty letters of application for the position but that Blanch’s was one of two “written in good English.” The manager also said that she was grateful to see that Blanch “was carrying The Nation under her arm,” a sign that Blanch was not Catholic and hence not Irish.⁵⁰

When the company offered her the job, Blanch accepted it and settled into the familiar routine of correspondence, scheduling, and bookkeeping. As the work demanded nothing of her mathematical skills, she decided to take a course at Brooklyn College. Scanning the list of what was offered, she decided that Lowan’s class would be the most interesting, even though she recalled, “It was very elementary,” an assessment that must have made Lowan wince.⁵¹

Blanch finished her story just as the bus trip ended, and the two of them started on their separate ways. Nothing more was said that evening except a pleasant farewell and a hope that Blanch might attend the next lecture. One week later, when she arrived at class, Lowan asked if he could again accompany her home. On this trip, he told her about the WPA and its plans for a computing laboratory. He explained that the computing project was being sponsored by the National Bureau of Standards and that he was the executive director. As the journey came to an end, “he asked me if I would join the project,”⁵² Blanch recalled. Two bus trips through the night did not provide her with enough information to make a decision, so she asked Lowan if she could delay her answer until she had had an opportunity to visit the office of the Mathematical Tables Project.

The following week, with the weather growing cold and the class term coming to an end, Blanch and Lowan took the train to Manhattan and walked past empty warehouses and closed machine shops to the building that housed the project office. Lowan showed her to the elevator, which had been designed for moving equipment. It had an open cage and rose slowly past exposed concrete beams and dangling light fixtures. When they reached the top and Lowan opened the gate, Blanch could see that dust covered the concrete floor and that the only furniture, beyond Lowan’s corner desk, was a mismatched collection of battered and weary tables. The windows near the staff desks were streaked with dust and dirt. Ceiling lamps gave a harsh and unpleasant glare. Permeating the air was the lingering odor of machine oil, yet something in this scene told Blanch that the WPA might represent her best chance to become a mathematician, the final gamble that might give her a place in the world of science. Before she left the building, she had “decided to resign from my job in my beautiful office and to join Lowan and go up the freight elevator.”⁵³

It would take more than simple determination to get the project going. Lowan needed to find more furniture for the office and purchase supplies. Blanch needed to learn the literature of computation and begin preparing computing plans. Most important, both of them needed to complete the work that Malcolm Morrow had begun three months before. From the scientific community, they needed to solicit a list of tables that could be used by practicing scientists and yet be prepared by a large staff of untrained computers. Morrow had asked the National Academy of Sciences to appoint a special committee to provide this advice, but Lyman Briggs, the new sponsor of the project, knew that such a committee already existed, the Subcommittee on the Bibliography of Mathematical Tables and Other Aids to Computation, MTAC. Briggs contacted A. A. Bennett, the committee chair, and scheduled a meeting for the group in the offices of the National Bureau of Standards. The only member who declined to come was L. J. Comrie, who informed Briggs that he was interested in the project but could not afford to travel from England.

Briggs convened the meeting on January 28, 1938, only three days before the start of operations. H. T. Davis was present, as were A. A. Bennett and a second Brown University mathematics professor, Raymond Claire Archibald (1875–1955). Briggs began by introducing the committee to Malcolm Morrow, even though it was the last time that the WPA statistician would have anything to do with the project. Arnold Lowan, who had traveled from New York for the meeting, sat quietly in the room and listened to Briggs present the goals for the group. When his turn came to speak, Lowan described the plans for the first calculation, a table of the first ten powers of the integers from 1 to 1,000. This table was a relatively simple project that involved none of the difficulties that would be found with more complicated functions. It extended a table that had been created in 1814 by Peter Barlow (1776–1862), the nineteenth-century computer who claimed that calculation was nothing but “persevering industry and attention.”⁵⁴ Each entry in the table required only a single multiplication. The square of a number was computed by multiplying one number by itself. The cube was computed by multiplying the square by the original number, and so on.⁵⁵

The committee accepted Lowan’s proposal and moved to consider other tables for computation. They recommended that the second project be a detailed table of the exponential function, e^x. The committee gave Lowan a rough idea of how the table should be structured and suggested ways of computing it. By the end of the day, they had identified twenty functions for Lowan, a list that could keep the project busy for two or three years. The meeting closed with a final recommendation that Lowan coordinate his efforts with the work being done by the Mathematical Tables Committee of the British Association for the Advancement of Science.⁵⁶

Initially, the discussions with the Subcommittee on the Bibliography of Mathematical Tables and Other Aids to Computation seemed to give the new WPA project a good connection with the scientific community through the National Academy of Sciences and the National Research Council. When the academy leadership finally learned of the meeting, they gave their blessing to the project and expressed their approval of the advice given by the MTAC committee.⁵⁷ However, such generosity was not as strong as Arnold Lowan might have liked, and it certainly did not extend to all levels of the organization. Later that winter, when the National Research Council reviewed the progress of the MTAC committee, some members were distressed to learn of the January meeting. When one council member gave a quick description of the meeting in Lyman Briggs’s office, another snapped that the WPA had “no connection with work assigned to committee” and that “the Committee work should be limited to a bibliography.”⁵⁸

On February 1, the WPA began to send workers to the Mathematical Tables Project office. Those who took WPA jobs were desperate for work. They lived at the edge of poverty and usually had held no stable job for a long time. The WPA’s figures suggested that 90 percent of them lacked the skills that would gain them employment with a private firm.⁵⁹ Gertrude Blanch, who had a tendency to see the best in anyone, recalled that “among them we found some very good material. Most of them were willing to learn, but we knew that we couldn’t expect too much.”⁶⁰ Though such native grace made her job a little easier, it did not allow her to be complacent or to feel sorry for her workers. She had less than five months to turn these workers into human computers. The WPA had authorized funds for the Mathematical Tables Project only through June 30. By then, if she could not demonstrate that her computers were producing useful public works, funds would be terminated and the project ended.

The most detailed picture of the computing floor in its first year comes from Blanch’s closest friend at the project, Ida Rhodes (1901–1986). Rhodes did not join the project until 1940, but she would be Blanch’s confidant for nearly forty years. She was outgoing while Blanch was retiring, flamboyant when Blanch was reserved, and critical when Blanch might have been gentle. Blanch generally approved Rhodes’s accounts of the Mathematical Tables Project. “She had a way of getting across a point,” Blanch recalled, “in a way that no one else could, all with a sense of humor.”⁶¹ Some of Rhodes’s stories contradict the administrative record of the WPA, but those that agree with other accounts of the project offer a bleak portrait of that first winter. “Many of our workers were physically ill,” Rhodes reported; “arrested TB cases, epileptics, malnourished persons abounded.” She seemed to delight in remembering that some of the computers had engaged in “several types of perversion and vice.” Those who were hardest to engage, those who were “most pitiful,” in her words, were the workers who had “lost their self respect in that horrible year.”⁶²

By early spring, Blanch was working with a computing staff of one hundred and twenty-five, a number far short of the thousand Morrow had promised, but it was as large a computing force as had ever been assembled. The operations of the Mathematical Tables Project were overseen by a planning committee, a group of six mathematicians who prepared the computing plans. In theory, the planning committee was chaired by Lowan, but Blanch generally ran the group. Each member of the committee would take responsibility for one computation, researching the background for the table, recommending a certain mathematical approach, preparing worksheets for the computers, and checking the final results. One committee member oversaw the operation of the “computing floor,” as the bulk of the computers came to be called. In addition, the planning committee worked with two smaller computing groups, the special group and the checking group. The special group tested methods, calculated initial values, and did other work for the planning committee. The checking group worked with the finished worksheets and with the final proofs for the tables. In 1938, the computers of these last two groups were the only ones who had access to the project’s three adding machines.⁶³

32. Computing floor of the Mathematical Tables Project

Blanch divided the computing floor into four groups, one for each of the arithmetical operations. The largest group, identified as group 1, did addition only. A slightly smaller group, group 2, did subtraction. Group 3, which had about twenty computers, multiplied numbers by a single digit. The elite of the computing floor was the tiny group 4. Its members did long division. She isolated each group within the Mathematical Tables Project office. She placed group members at long tables facing a wall. On the wall she put a poster to remind the computers of the basic rules of arithmetic. Few of them had completed high school, and fewer still could be trusted to work without direction. Since most did not know how to manipulate negative numbers, she devised a scheme that used black pencils to record positive quantities and red pencils to record the negatives. The wall posters described how to handle numbers of different colors. The poster for the addition group read:

The worksheets had been duplicated on a mimeograph machine. “They generally had 100 lines and were on graph paper,” explained a veteran of the project.⁶⁵ Whenever possible, Blanch tried to replace complicated operations with repeated additions. It was an approach that mimicked her driving habits. Family members remarked that she would go to great lengths to substitute three right turns for a single left-hand turn across traffic.⁶⁶ Because the computing floor had one section for each operation, she could leave some multiplications and divisions on the worksheets. The sheets circulated through all four groups on the floor, often wandering through each section several times before the work was complete. For example, a sheet might start in the addition group and then move to the multiplication group after all the initial additions were done. “The human computers who liked boring work, did calculations vertically,” observed a planning committee member. “They did 100 operations before they moved to the next column.”⁶⁷

When the worksheets returned to the planning committee, they were checked for errors. Blanch and Lowan went to extraordinary lengths to find every possible mistake, including errors created in transcribing the values to the final table. Behind their efforts was the knowledge, rarely mentioned, that one poorly computed table could permanently damage their reputation and limit their acceptance within the scientific community. “We had very little equipment,” reported Gertrude Blanch, “and a lot of supervisors who thought that this was another boondoggle project.”⁶⁸ The first defense against errors was found within the worksheets. Blanch designed them in such a way that elementary mistakes in calculation could be quickly identified. The computers filled in a grid of numbers. The last column of this grid had to match a set of predetermined values, numbers that had been computed by the planning committee or one of the special computing groups. If they did not match, the sheet contained a mistake in calculation.

Some computers attempted to avoid the discipline imposed by the worksheets. Recognizing the structure of the sheet, a worker could put the predetermined values in the last column and then fill the remaining blanks with any values that seemed appropriate. This did not happen often, given the quality of the final tables, but each member of the planning committee could recall at least one incident of cheating. Blanch remembered two women who submitted falsified worksheets. “You can’t cheat in those things,” she said flatly. “It comes out almost immediately. Well, these girls were fired immediately.”⁶⁹ The other examples of cheating or carelessness also ended in dismissals. One resulted in the departure of a planning committee member.⁷⁰

Blanch checked each calculation with six or eight different procedures. Some of the procedures were based upon the mathematical properties of the function they were tabulating. All tables were checked with the technique known as differencing. Differencing had been used by the computers of de Prony and Maskelyne, but it reached a new level of sophistication in the hands of Gertrude Blanch. It reversed the method on which Charles Babbage based his difference engine. Babbage had shown that many functions could be reduced, through the method of finite differences, to a series of repeated additions of constant terms. Blanch used this technique to check tables by repeatedly taking the differences of adjoining terms. In a table of cubes, the first five values are the numbers 1, 8, 27, 64, and 125. The first differences are 8 − 1, 27 − 8, 64 − 27, and 125 − 64, or 7, 19, 37, and 61. If we repeat the process and take adjoining differences of these values, we get 19 − 7, 37 − 19, and 61 − 37, or 12, 18, and 24. In one final set of differences we get 18 − 12 and 24 − 18, or the numbers 6 and 6. If one of these third differences were not 6, then one of the original values in the table would be in error. For most functions tabulated by the Mathematical Tables Project, the sixth or seventh repeated difference would produce a list of nearly constant numbers. Any significant variation would indicate an error in the calculations.

By WPA regulation, the human computers worked thirty-two hours a week. They were supposed to spend the remaining time looking for permanent employment. This limitation on the program gave Blanch the opportunity to study the worksheets when the computing floor was silent. She spent many an evening hour checking calculations and preparing new worksheets for the next day. She seemed to enjoy the quiet time after the computers left for the day, when there were no workers to encourage, no questions to answer, no formulas to explain. The office was quiet, and she could concentrate on mathematics.

The Mathematical Tables Project finished the table of powers in early April 1938, printed the manuscript with a mimeograph stencil on rough sheets of paper, and bound the pages with a cardboard cover. A few of the numbers were a little difficult to read. Prominently displayed on the face of the book was a WPA seal, a small rectangle that identified it as the product of a relief effort. Lowan and Blanch claimed that there were no errors in the table, a claim that was tested when a copy reached the desk of L. J. Comrie in England. Comrie reviewed the entire work, checked every value with a difference test, and concurred that the table was entirely free of errors.⁷¹

Finishing the first table was a relief to the entire group and created what Blanch called a sense of “heartwarming camaraderie” among the staff.⁷² It steeled their courage for their second project, creating tables of the exponential function, e^x. The exponential function is harder to compute than a simple power of an integer. It is the inverse of the logarithm and can be expressed as the sum of an infinite number of terms, e^x = x/1 + x²/2 + x³/6 + x⁴/24 and so on, continuing in the same pattern. In practice, a computer does not need to deal with an infinite number of operations, as the terms eventually become so small that they can be safely ignored.

The computers began working on the exponential calculations in the early spring, while they were still working on the powers of integers. It seemed important that this project be under way when the WPA reviewed the progress of the group in June. For all the anxiety among the planning staff, the review proved to be quick and perfunctory. The WPA officials reported that they were satisfied with the accomplishments of Blanch, Lowan, and the human computers and approved another six months of budget for the group.⁷³ With the future of the project on a stronger financial foundation, Lowan was able to arrange for Columbia University Press to publish the tables from the project.

While Blanch was preparing computing plans and directing the daily operations of the human computers, Lowan was attempting to bring the Mathematical Tables Project to the attention of American scientists and engineers. His first problem was to overcome the stigma of the WPA. His second was to show that his group could equal the accomplishments of the two other scientific computing organizations in New York City. Thornton Fry, Clara Froelich, and the other Bell Telephone Laboratory computers worked two miles south of the Mathematical Tables Project office. Wallace Eckert and the Columbia University Astronomical Computing Bureau sat a slightly greater distance to the north. Both had reputations that Lowan would have liked to equal.

Beginning in the fall of 1938, Lowan began to promote his project as a general-purpose computing office for the nation’s engineers and scientists. He prepared mimeographed circulars, using the same machines that reproduced his computing sheets, and mailed them to universities, government offices, manufacturers, and every scientist he could name.⁷⁴ In general, these efforts at self-promotion were frustrating affairs, as he might have learned from anyone who dealt with direct mail advertisement. He often posted one hundred or two hundred letters in a month and received not a single reply. When he did receive a reply, he was usually disappointed. Lowan received requests to prepare salary tables, to tabulate data, and to do simple calculations for other WPA projects. In general, he tried to decline such work by citing the WPA requirement that all products needed to be “widely usable.”⁷⁵ However, he quickly learned that he was part of a government organization that could be subject to political pressure. More than once, a rejected request returned to his office in the form of a letter from Lyman Briggs. These letters reminded Lowan that the Mathematical Tables Project received government funds and that it would be well advised to honor the request, no matter how uninteresting it might be.⁷⁶

The few letters from well-reputed scientists could be tantalizingly sad, like the gentleman caller who offers a moment of hope and happiness and promise before disappearing. In response to a circular, John von Neumann wrote, “Many thanks for the announcement of your project. I am much interested in your program and should like to get your material.” He ended the letter, “I may have some remarks and suggestions in connection with these things and will write to you concerning them before long.”⁷⁷ As Lowan had known von Neumann at the Institute for Advanced Study, he had some reason to expect that the mathematician would act on his promise, but the weeks passed, and the Mathematical Tables Project received no further correspondence.

The one scientist who offered more than hope was Philip Morse (1903–1985), a professor of physics at the Massachusetts Institute of Technology. “I have been in charge of a number of similar projects,” he wrote, and felt “that I should get in touch with you.” With no more introduction or pleasantries, he then described a lengthy calculation, acknowledging at the end that “this calculation has no particular difficulties but requires considerable man-hours and if you are in a position to be of help, this help would be welcomed.” Such interest was well received by Lowan, Blanch, and the rest of the senior staff, but it was accompanied by an embarrassing query. Morse ended his letter by stating, “I will be very pleased to know just what sort of arrangements you make on calculating facilities and in general how you operate.”⁷⁸

Lowan responded quickly, assuring Morse that his group would be happy to compute for anyone at the Massachusetts Institute of Technology. He gave a brief overview of the Mathematical Tables Project, telling Morse that “we are operating with a staff of 110 workers under the supervision of a planning section of which I am in charge.” He mentioned nothing about worksheets or relief workers. When he reached the topic of machinery, he equivocated. “Most of the work is, of course, done with the aid of calculating machines.”⁷⁹ Strictly speaking, the statement was true, as the project’s three adding machines contributed indirectly to everything that the staff did. However, the bulk of the calculations were done with only paper and pencil.

We do not know when Morse learned the true nature of the Mathematical Tables Project computers. He was unusually well connected in the scientific community and may have known from the start that Lowan was stretching the truth. He never criticized Lowan, never suggested that there was anything wrong with the project. In fact, he seemed to grasp innately the nature of the group. In his second letter to Lowan, he said that he had “one or two other sets of calculations which I want to suggest to you in the next month or so” and that he would “consult with a number of the other members of the Physics and Mathematics Departments here and at Harvard in order to submit to you a program that is not a set of personal interest.”⁸⁰

The last phrase in Morse’s letter was important. Lowan had to establish that every calculation was of general interest and would benefit more than a single scientist or engineer. None of the tables could be copyrighted, as they had been prepared with public money. It was one of the WPA policies that governed his actions as long as he accepted their money. The WPA also required that he use labor-intensive methods, in order to employ the greatest number of people, and restricted the number of female employees to about 20 percent of his staff, an attempt to prevent one household from receiving two sets of benefits.⁸¹ Every request for scientific calculation had to follow the WPA rules, even if that meant using methods that seemed archaic or unsuited to 1930s research.

Morse never seemed to be bothered by the WPA restrictions. He proved to be a tireless ally and a key link to the scientific community. He helped bring the group its first important scientific computation, a problem posed by the Cornell physicist Hans Bethe (1906–). Bethe was studying the processes that produce solar energy. In order to understand these reactions, he needed a table that would show the internal temperature of the sun, beginning at the outer edges and moving inward to the core. Since these measurements could not be taken directly, they had to be computed from a mathematical model.⁸² Bethe claimed that the calculations were not “prohibitively laborious” but were so difficult that no one had attempted the work without first substantially simplifying them.⁸³

Lowan eagerly agreed to undertake the project, for the work would bring the Mathematical Tables Project to the attention of astrophysicists and might also show that the group was as capable as the Columbia Astronomical Computing Bureau. If he expected that the calculations would be done quickly, he was mistaken. After the planning committee reviewed the plan, they had a half dozen questions for Bethe. They asked Bethe to verify equations and check key values. The calculations involved a three-dimensional system of differential equations, the form of equations found in Richardson’s weather model. Though the equations were simpler than those posed by Richardson, they still demanded a great deal of work. If the starting values were wrong, the effort would be wasted. Not even Hans Bethe could adjust the sun and bring it into agreement with a mistaken calculation.

In the end, Gertrude Blanch decided to do all the computations herself. She concluded that she could calculate the tables in the time that it would take her to prepare worksheets for the computing floor.⁸⁴ The calculations took about three weeks of effort. Bethe was impressed with the results, calling them the “first modern determination of the temperature of a star.”⁸⁵ The table was published in the Astrophysical Journal, which must have pleased Lowan. It was the first major publication to come from the project. Perhaps more important, it brought attention from a major physics department. Bethe reported that his colleagues had taken a look at the group’s first tables and that “the department has decided to order copies of them.”⁸⁶

By this time, the project’s second volume, Tables of the Exponential Function, had appeared in print. Compared to Karl Pearson’s Tracts for Computers or H. T. Davis’s Tables of Higher Mathematical Functions, this new volume received serious attention from the scientific press. Though book reviewers inevitably mentioned that the volume had been produced as a relief project, they generally treated it with respect. The review in the widely circulated American Mathematical Monthly was positive, though perhaps not as enthusiastic as Lowan might have liked. The reviewer, John Curtiss (1909–1977) of Northwestern University, noted that the book claimed to be “entirely free from error.” If he had been L. J. Comrie, he would have tested this assertion. As he was not, he was willing to concede that “the precautions taken seem to give considerable weight to this claim.”⁸⁷

John Curtiss’s review was an important milestone for Blanch and Lowan, evidence that they had done their job well, had met the requirements of the WPA, and had created an organization that could produce something of value to at least a few scientists. Nevertheless, the project was still a work relief effort. It still occupied a dirty industrial loft in an unattractive part of Manhattan. Each week, the members of the computing floor collected their wages hoping that by the next payday they would have a full-time job with some employer that was not the WPA.