When Computers Were Human

by David Alan Grier

  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 a
nswer 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, ex. 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:

  Black plus black is black.

  Red plus red is red.

  Black plus red or red plus black, hand the sheets to group 2.64

  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