CHAPTER SIXTEEN

The Midtown New York Glide Bomb Club

THE WINTER OF 1943 marked the start of the imperial age of the human computer, the era of great growth for scientific computing laboratories. It seemed as if all the combatants discovered a need for organized computing that winter. A German group started preparing mathematical tables at the Technische Hochschule in Darmstadt.¹ Japan, which had received material from the Mathematical Tables Project through 1942, formed a computing group in Tokyo.² The British government operated computing groups in Bath, Wynton, Cambridge, and London.³ Within the United States, there were at least twenty computing organizations at work that winter, including laboratories in Washington, Hampton Roads, Aberdeen, Philadelphia, Providence, Princeton, Pasadena, Ames, Lynn, Los Alamos, Dahlgren, Chicago, Oak Ridge, and New York City. Most of these calculating staffs were small, consisting of five to ten computers. Langley Field, a major aeronautical research center in Virginia, employed about a dozen such groups, each assigned to a specific research division. “Some [groups] have as many as ten computers,” explained a history of the center, “while others have one computer who often devotes a part of her time to typing and secretarial duties.”⁴ Only a few computing laboratories were as large as the New York Hydrographic Project with its forty-nine veterans of the Mathematical Tables Project or the thirty-person computing office of the Naval Weapons Laboratory at Dahlgren, Virginia.⁵

Amidst this growth of computing offices, the MTAC committee finally came to life and began to chronicle the literature of calculation. Nearly eighteen months after his confrontation with Luther Eisenhart and the National Research Council forced him to retreat, R. C. Archibald had returned to his post in the summer of 1942 and announced a new goal for the committee. “Our Guides are very slow in appearing,” he wrote. “Hence I have been led to the conviction that it would be very desirable to establish a quarterly publication called Mathematical Tables” in order to circulate the committee’s bibliographies and reports.⁶ The proposal surprised the members of the National Research Council. It would “be like issuing a professional journal,” complained the permanent secretary.⁷ After the argument over the $61.73, the council members were uncomfortable with the idea and tentatively tried to check Archibald. They approached Warren Weaver, in his role with the Rockefeller Foundation, and asked if the money granted to Archibald by the foundation could be used to finance a publication. Weaver confessed that he had a “certain horror” at being associated with Archibald’s idea, but he also stated that the Rockefeller Foundation would not stop the new periodical.⁸ The members of the MTAC committee, from L. J. Comrie to Charlotte Krampe, were slower to respond, but they generally liked the proposal. Wallace Eckert wrote that the periodical “would serve a very useful purpose” but warned that it “would probably become a financial headache” and that the “present is not the most auspicious time to start it.”⁹

Never one to wait for favorable times, Archibald pressed ahead, leaving even the most sympathetic members of his committee behind. “With the load I have to carry,” he wrote to the MTAC committee, “I can not possibly undertake either to discuss everything with you before hand or send all copy to you before publication.”¹⁰ He completed the first issue of the journal, entitled Mathematical Tables and Other Aids to Computation, in February 1943. To his credit, he recognized that the journal could not flourish if he was the sole contributor and apologized to his readers, “R. C. A. greatly regrets the apparent necessity for numerous personal contributions in this issue, as well as in the second.”¹¹ The issue contained a great deal of useful information, including lists of tables, errata, book reviews, and articles on methods of calculation. The only thing that seemed out of place was a piece devoted to the computing machines of the seventeenth century, a favorite subject of Archibald’s.

Mathematical Tables and Other Aids to Computation provided American computers with the first systematic reports on computing activities. Before the journal reached a wide audience, many computers did not know what organizations existed and what work was being done. In early February 1943, the members of a new computing group at the University of Pennsylvania did not know how they might contact the Mathematical Tables Project. One of the group’s leaders, John Brainerd (1904–1988), sent a letter to the project sponsor, Lyman Briggs at the National Bureau of Standards. Brainerd explained that he was undertaking a large computing effort for the Aberdeen Proving Ground and was searching for human computers and computing expertise. He hoped that the Mathematical Tables Project was still operating and that it might provide him with human computers or handle some of his calculations or provide him with training materials.¹² Brainerd needed especially sophisticated computers, computers with a good background in mathematics. The Mathematical Tables Project might have seemed an unlikely source of such computers, but Gertrude Blanch had initiated an extensive training program in 1941. She and other members of the planning committee developed a series of eight mathematics courses, which they offered over the lunch hour. The first course discussed the properties of elementary arithmetic; the intermediate ones covered standard high school algebra, trigonometry, and college calculus; the final course presented the methods of the planning committee: matrix calculations, the theory of differences, and special functions. The teachers treated the courses as a formal school, requiring the students to attend every session and asking them to “do a reasonable amount of ‘home work’ on their own time.”¹³

Lyman Briggs replied to Brainerd’s letter just as the Mathematical Tables Project was preparing to move from its old WPA office to the rooms rented by the Applied Mathematics Panel. He explained to Brainerd that the project had found a home for the duration of the war and was able to accept outside assignments. “I think you will be glad,” Brainerd told his colleagues, “to note the action which is being taken in connection with the computation project.”¹⁴ The enthusiasm of this initial contact quickly faded as the leaders of the two computing organizations employed different strategies in their work. Arnold Lowan, of the Mathematical Tables Project, was a classical physicist who understood the rules of divided labor. For him, computing machinery was an aid that “facilitated and abridged” the efforts of his staff. Brainerd was a professor of electrical engineering at the University of Pennsylvania. He organized his office around a large computing machine, a differential analyzer, and used human labor to compensate for the machine’s shortcomings. Brainerd’s computers were machine operators, as George Stibitz had prophesied, but these operators were not mere drudges, for they needed a thorough mathematical education in order to do their work.

In 1937, the University of Pennsylvania had acquired a differential analyzer in conjunction with the Aberdeen Proving Ground. The proving ground had financed the differential analyzer under an agreement that allowed ballistics researchers to use this machine in times of war. Until the spring of 1942, the analyzer had been used by engineering professors and graduate students. Like most university research equipment, this machine received regular but intermittent use. Four or five times a term, it would calculate a curve associated with some electrical component or circuit. Occasionally, it would serve as the object of an experiment by a graduate student interested in electromechanical controls. Once or twice a year, the university was able to rent the device to a local company. For other periods, the machine stood idle, gathering dust and dripping oil.¹⁵

In June 1942, proving ground officials notified the University of Pennsylvania that they needed to use the differential analyzer for ballistics research and offered to reimburse the school $3.00 an hour for operational costs: electricity, the wages of mechanics, supplies, and the salaries of any staff that were needed to oversee the calculations. A small group of Aberdeen researchers took the train north from the proving ground to inspect the machine. The analyzer was housed in a nondescript brick building just a few blocks from the railroad station. Their first test of the machine, a trajectory for 4.7” antiaircraft shells, was disappointing. “Upon arrival,” wrote a member of the Aberdeen staff, “it was apparent that a desirable rate of analyzer output had not been achieved.” The output from the machine substantially deviated from a hand-calculated trajectory. “The Philadelphia analyzer … has not been under the compulsion of the great accuracy demanded at Aberdeen,” observed a proving ground researcher, “and therefore has not been as assiduously cared for as the Aberdeen analyzer.” To “attempt to maintain [high accuracy] with the Philadelphia analyzer,” concluded the army, “required an exorbitantly high number of adjustments and test runs.”¹⁶

At a hastily called meeting between university officials and army officers, John Brainerd presented a plan that would produce results within 0.5 percent of hand-computed values. This plan called for a few modifications to the machine, strict operational standards, and a staff of human computers to oversee every step of the calculation.¹⁷ An early test of the new procedure achieved the specified accuracy but at the cost of substantial hand calculation. It is “desirable to expand the Philadelphia unit somewhat at once,” concluded the army, in order “to train and prepare its personnel for handling the contemplated output of the analyzer.” The calm words of the military report camouflaged the problem facing the Pennsylvania faculty. The university did not have enough college-educated computers for its analyzer staff. They had hoped to find twenty to thirty women with bachelor’s degrees in mathematics or physics, but after scouring the school’s alumna lists, they had identified only eight who held the appropriate degree. Brainerd had offered each of them a position as an assistant computer with a salary of $1,620 per annum, but he believed that no more than three or four would accept these positions. With no other obvious options, Brainerd concluded that the university would have to prepare a curriculum for human computers and operate training classes.¹⁸ He found money for this endeavor at the government’s Engineering, Science, and Management War Training Program and borrowed course materials from Aberdeen veteran Gilbert Bliss, who had taught ballistics classes to civilians at the University of Chicago.¹⁹

Brainerd’s plan had serious problems, as he freely admitted. The university lacked enough instructors qualified to teach mathematical ballistics. The only faculty willing to train the women were three retired professors, whom many judged “no longer up to the strain of teaching day long courses.”²⁰ Nothing improved the prospects for the training courses until Adele Goldstine (1920–1964) walked into Brainerd’s office in September. Goldstine was the wife of the officer that the army had assigned to monitor the computing work at the university. She was a slight woman but poised and filled with energy. She had the education that Brainerd needed, a bachelor’s degree in mathematics from Hunter College for Women in New York City, a master’s degree from the University of Michigan, and a connection to mathematical ballistics. Her husband had studied with Gilbert Bliss and had helped Bliss prepare a textbook on mathematical ballistics.²¹ Within a few weeks of her arrival, Adele Goldstine had taken command of the training program. According to her husband, she immediately “got rid of the deadwood,” the three retired professors, replaced them with two younger instructors, and helped teach the first group of students, twenty-one in number. These students completed the training that fall, swore the required oath of allegiance, and started work as computers.²²

From the start, the University of Pennsylvania recruited only “women college graduates.” The sign “Women Only” marked the door of the computing office, which was a converted fraternity house.²³ This decision was not based on any dictate from the Ballistics Research Laboratory, for the Aberdeen computing staff included both men and women.²⁴ In all likelihood, it was motivated by common stereotypes concerning office work and gender: that men were difficult to recruit for office work in wartime, that single-gender office staffs were easier to manage then mixed-gender staffs, that women were somehow specially suited for calculating.

Between classes, Goldstine spent much of her time recruiting potential computers. By the winter of 1943, John Brainerd had concluded that the university needed a staff two or three times larger than his initial estimate. They might require seventy or even eighty computers to keep the differential analyzer fully occupied and have a sufficient number of workers in reserve. In the winter of 1943, the school had less than half that number.²⁵ Brainerd returned to the University of Pennsylvania alumna lists, sent circulars to the American Mathematics Society and the American Association of University Women, and wrote to university faculty to ask the professors to volunteer their daughters or their daughters’ friends.²⁶ As a last resort, Goldstine took to the road, visiting Bryn Mawr and Swathmore Colleges in suburban Philadelphia, Goucher College in Baltimore, Douglass in New Jersey, and her own Hunter College.²⁷ “I’ve arranged to be at Queens College Tues[day],” she wrote to Brainerd from a hotel in New York, but she confessed that she did not expect much, as “next week is exam week. Also I was not able to arrange for any very effective means of advertising the job.” Even when she was able to notify students of the opportunities at the University of Pennsylvania, she found few interested applicants. At one college, she found “only 25 or so women seniors all of whom have good prospects in their own fields and so probably could not be enticed by our offer.”²⁸

Goldstine returned from her travels just as R. C. Archibald was printing the second issue of Mathematical Tables and Other Aids to Computation. Though much of the publication was devoted to traditional mathematical tables, a few articles at the back dealt with computing machinery. The first, by L. J. Comrie, explained how traditional business machines could be adapted to scientific computation. The second, by Bell Telephone Laboratories mathematician Claude Shannon, discussed the operations of the differential analyzer.²⁹ With human computers hard to find and an old analyzer struggling to meet the precision requirements, the computing staff was looking to build an improved computing machine, an electronic version of the differential analyzer. This new machine, tentatively called the Electronic Numerical Integrator and Computer, or ENIAC, would have no mechanical parts that could slip or jam or in some other way induce inaccuracy.³⁰

Even though he had an embarrassing departure from the British Nautical Almanac Office, L. J. Comrie remained the single most important source of computing information for English scientists. His company, Scientific Computing Service Ltd., was one of four major organizations that were handling ballistics, ordnance, and navigation calculations for the British government. The second group was the British Nautical Almanac Office. Like their American counterparts, these computers no longer shared the burden of producing an almanac with the French and Germans and hence had an extra burden of calculation. The third and fourth groups were the computing laboratories at the University of Manchester and Cambridge University. These two schools owned and operated differential analyzers, just like the University of Pennsylvania.³¹

In the winter of 1943, the British government formed a fifth computing office, one that could undertake general-purpose calculations for both the military and the war industries. The group, called the Admiralty Computing Service, was the creation of Donald Sadler (1908–1987), Comrie’s replacement at the Nautical Almanac, and John Todd (1915–), a professor at King’s College. Todd had been educated at Cambridge under the watchful eye of John Littlewood, the mathematician who had developed ballistics theories in the First World War.³² Todd had taken a modest interest in computing problems as a student, but he did not become fully involved with computational mathematics until 1938, when he met L. J. Comrie at a meeting of the British Association for the Advancement of Science. Comrie befriended the young mathematician, introduced him to the association’s Mathematical Tables Committee, and eventually taught him the operation of the Brunsviga calculator, repeating the lessons that he had learned from Karl Pearson.³³

39. John Todd of the Admiralty Computing Service

Todd had been drafted at the start of the war and assigned to a naval office that was studying ways of protecting ships from German mines. “I found the work boring,” he recalled, “and it was not very effective.”³⁴ Todd’s wife, the mathematician Olga Taussky (1906–1995), analyzed the vibration in aircraft structures for a government ministry. Her work produced large systems of equations with unknown values. “A large group of young girls,” she related, “drafted into war work, did the calculations on hand-operated machines.”³⁵ From observing his wife and reflecting on his own experiences, Todd concluded that the war effort would benefit from a general-purpose computing organization. “I realized that pure mathematicians, such as I,” he later wrote, “could be more useful in dealing with computational matters and relieve those with applied training and interests from what they considered as chores.”³⁶ In private, he was a little more pointed. “After a year of working for the navy, I decided that mathematicians could make tables better than physicists.”³⁷ He joined forces with the almanac director, Donald Sadler, and created the Admiralty Computing Service.

Unlike most other computing offices, the Admiralty Computing Service had two divisions, a staff of ten computers and a small group of mathematical analysts. The computers were managed by Sadler and were located in Bath, the eighteenth-century resort town where the almanac had been evacuated for the duration of the war. They occupied a prefabricated military building situated on an old Georgian estate. The computing staff consisted of students and young teachers, most of them male, who were unable or unwilling to serve in the military. Sadler described them as “nurtured by comprehensive special training,” as the skill of computation “cannot adequately be ‘picked up’ in the course of day-to-day work.”³⁸ They worked three to a room in their military hut, sharing tired desks and improvised tables. Their equipment, worn but serviceable, came from the Greenwich office of the almanac and included L. J. Comrie’s old National Accounting Machine. Work began at eight in the morning, ended at five in the evening, and continued for a half day on Saturday. The weekly schedule included time for instruction, discussion, and a meeting for the review of results. “Sadler was a real martinet for getting rid of errors,” one computer recalled. “If you made a mistake on some work and if it went out, he’d give you such a dressing down that the whole office would know.”³⁹

The second division of the Admiralty Computing Service, the mathematical analysts, worked in London and were overseen by Todd. London was a dangerous place, but it was also the home of the major scientific and engineering offices. “[John and I] moved 18 times during the war,” Olga Taussky later explained to a friend, the First World War computer Frances Cave-Browne-Cave, “and our belongings were hit by a flying bomb.”⁴⁰ Moving past the damaged buildings and the rubble in the street, Todd traveled from office to office, talking with engineers, listening to government officials, reviewing military plans. “Often we could not help them with the problems they first presented to us,” he recalled, “but I usually found a different problem that we could do.”⁴¹ For all that his clients knew, the computations were done somewhere beyond Paddington train station, where Todd began his journeys to Bath. Once or twice a week he would pass through the station, carrying requests for calculations and returning with finished results.

In the spring of 1943, Todd made the trip to Bath with John von Neumann, who had come to England in order to inspect British scientific efforts. Von Neumann then was working for the Ballistics Research Laboratory at Aberdeen and other American research projects. He had requested an opportunity to see the computing facility and L. J. Comrie’s famous accounting machine. Todd and von Neumann spent a day in Bath, talking with the computers and observing the operation of the office. On the trip back to London, the two of them discussed a new way of doing interpolation with the accounting machine. The train windows were blackened to avoid drawing the attention of German aircraft, so the two mathematicians had no distractions in the passing scenery. Taking out a piece of the “rather poor quality paper issued to government scientists at that time,” they began to prepare a computing plan. They worked as the train passed the royal castle at Windsor, the munitions plants at Slough, and the shuttered shops of Ealing. By the time the dark coaches reached the London station, they had completed their work. “It was a fixed program,” Todd wrote, but it did not quite eliminate the need for computers, as “it involved a lot of human intervention.”⁴² The experience intrigued von Neumann in a way that five years of circulars from the Mathematical Tables Project had not. Von Neumann had kept his distance from the WPA computing floor in Lower Manhattan even though he had promised to respond to Lowan’s letters. With one trip to Bath, his views changed. “It is not necessary for me to tell you what [our visits] meant to me,” he wrote to Todd after the war, “and that, in particular, I received at that period, a decisive impulse which determined my interest in computing machines.”⁴³

The two parts of the Admiralty Computing Service had obvious counterparts in the contractors of the Applied Mathematics Panel, but the American effort was far more complicated than John Todd’s organization. In England, Todd was free to make most of the key decisions, but in the United States, all requests for mathematical and computational assistance were reviewed by a committee of mathematicians. This executive committee met weekly in the conference room of the Rockefeller Foundation, a sumptuous private suite on the 64th floor of Rockefeller Center’s RCA Building.⁴⁴ Meetings would begin with a luncheon, which gave the members an opportunity to chat about the issues of the day and discuss new developments in mathematics. At an early meeting, while Rockefeller Center waiters poured drinks and brought the plates of food, one member complained of “American indifference to the German 60 ton rocket,” which he described as a false faith that the Atlantic Ocean would protect the country.⁴⁵ The mathematicians generally agreed that the German missile program was worrisome, yet they had also concluded that “the bombing of New York would be futile since an explosion outside of a building would break windows but not damage the structure itself, except very old brick types of structure.”⁴⁶

For the most part, the luncheon conversations were an opportunity to return to the summer of 1918, the season at Aberdeen that Norbert Weiner had likened to a term at an English college. In that conference room, they would not think about the carrier battles of the South Pacific, the soldiers described by Ernie Pyle in his dispatches from Europe, or the Willies and Joes that cartoonist Bill Mauldin drew for Stars and Stripes. Instead, the executive committee would turn their attention to their favorite topic, mathematics. “At lunch, there was an interesting discussion of the character of ‘probability,’” reported the Applied Mathematics Panel chair, Warren Weaver, after a meeting in the spring of 1943. Probability had become important to several projects before the panel, but practical applications were not the subject of conversation. The mathematicians were interested in the philosophical foundation of chance. Some at the meeting argued that there was no such thing as a random event and that probability was nothing more than a clever use of set theory. “As frequently happens,” Weaver observed, “the argument settled down to the question of the most useful definition or connotation of words.”⁴⁷

40. Warren Weaver being decorated for his service on the Applied Mathematics Panel

Once the meal was finished and the dessert dishes cleared from the table, the mathematicians turned to their business. The first items on the agenda were reports from the panel’s major contractors. Most of these organizations were located in or near New York City. One member of the panel mockingly referred to his research group as the “Mid Town New York Glide Bomb Club.”⁴⁸ The largest contractor was Columbia University, which was home to four different research centers: an applied mathematics group, a statistical group, a bombing studies group, and the Thomas J. Watson Astronomical Computing Bureau. It alone accounted for half of the Applied Mathematics Panel budget. In 1943, the remaining budget, save 5 percent, was spent within a one-hundred-and-fifty-mile radius of Manhattan.⁴⁹ Recipients of the panel’s largesse included the Mathematical Tables Project, New York University, Brown University, Princeton University, and the Institute for Advanced Study. There were no contracts with the University of Chicago, none with Iowa State College, and none with the University of Michigan. There was no contract for the Harvard mathematics department, until one of its faculty began raising a public fuss about the panel and Warren Weaver responded by offering the Massachusetts school a token assignment.⁵⁰

After reviewing the contractor reports, the mathematicians of the Applied Mathematics Panel turned to new requests for mathematical work. Some of the requests came directly from the military, but most originated at the war research laboratories. Each member of the panel was responsible for working with a division of the National Defense Research Committee and identifying potential projects for the Applied Mathematics Panel. As they discussed the new requests, the panel members would sketch a rough solution to the problem. Most of these solutions required little mathematical skill beyond that taught to undergraduates, but they usually demanded attention to details and the careful consideration of special situations. By the time each discussion ended, the panel members would have a sense of the effort required for the problem, the kind of individual who might handle the work, and the value of the result. They declined several projects on the grounds that they were not worth the effort.⁵¹

After they had accepted a request, the panel would assign it to one of their contractors, such as the Applied Mathematics Group at Columbia University or the Bombing Analysis Group at Princeton University. The research staff of the contractors were generally young professors or graduate students. Most were mathematicians, though several were economists, such as Milton Friedman, or engineers, like Julian Bigelow. Weaver characterized the contractor staff as “high grade persons who may admittedly not be geniuses, but who have unfailing energy, curiosity and imagination, and a reasonable set of technical tools.” The Applied Mathematics Panel rarely quibbled about the specific training of its research staff, though it did note that the most important quality for success was “the unselfish willingness to work at someone else’s problem.”⁵²

Each of the contractors maintained some kind of computing staff. The three mathematics groups at Columbia employed twenty human computers plus the tabulating machine operators at the Thomas J. Watson Astronomical Computing Bureau.⁵³ New York University built its computing staff around a young graduate student, Eugene Isaacson (1919–). Isaacson was first exposed to the methods of computation at the Mathematical Tables Project. “I learned about using the mechanical calculators and about computing from this fine team,” he would later assert. At first, he worked by himself, but he was soon assisted by Nerina Runge Courant. Courant took up the work not as a student but as a wife and a daughter. She was married to the head researcher at the university, Richard Courant, and was the daughter of Carl Runge (1856–1927), a mathematician who had refined the methods of solving differential equations. Her connections were a tie to the past, a reminder that fathers and husbands had once provided opportunities for women at the American Nautical Almanac and the Harvard Observatory. In this war, the opportunity came from the scale of the mobilization, not from family relations. When the New York University computing office expanded, adding six more computers, the school appointed Isaacson to lead the group, not Nerina Courant.⁵⁴

The Mathematical Tables Project served as the reserve computing unit for the Applied Mathematics Panel and was the second-largest item on the panel’s budget.⁵⁵ Normally, the panel would review all computing requests and forward the ones that they approved to Arnold Lowan. For some large problems, they would occasionally solicit competitive bids. In the summer of 1943, they asked three computing groups to estimate the amount of time required to produce a table of complex numbers. Responding for the Mathematical Tables Project, Lowan wrote that it would take about twelve weeks to prepare the table and check the results. At the Thomas J. Watson Astronomical Computing Bureau, the bid was prepared by Jan Schilt (1896–1982), the astronomer who had replaced Wallace Eckert as director. Schilt’s analysis suggested that the bureau’s mechanical tabulators could prepare the tables in eight and a half weeks, though the time would double if the Applied Mathematics Panel wanted the calculations checked for machine errors. The last bid came from the IBM Corporation. A company engineer estimated that IBM could complete the calculations in only seven and a half weeks and argued that there was no need to duplicate the calculations to check the results. The Applied Mathematics Panel did not see an obvious choice among the three proposals. At length, they decided that the table was not worth the expense and abandoned it.⁵⁶

Through the middle of the war, the Applied Mathematics Panel found that the expense of human computers was close to the cost of machine calculation. In a competitive bid between the Mathematical Tables Project and Bell Telephone Laboratories, Arnold Lowan estimated that it would cost $1,000 for his staff to do the work, while the computers under Thornton Fry stated that the calculations would require $3,000. The panel rejected both bids, judging that they exceeded the value of the computation. An engineer at Bell Telephone Laboratories decided to produce a machine that would “automatically grind out and record results, using third order differences.” When the news of the machine reached Warren Weaver at the Applied Mathematics Panel, he ruefully noted that the “estimated cost of [the] Gadget [was] about $3,000,” three times the bid from the Mathematical Tables Project.⁵⁷

Computing machines were more efficient than human computers only when they could operate continuously, when they could do repeated calculations without special preparations. A punched card tabulator could work much faster than a human being, but this advantage was lost if an operator had to spend days preparing the machine. The differential analyzer was proving to be a good way of preparing ballistics tables only when it could compute trajectory after trajectory with little change to the machine. The problem of solving linear equations offered the same kind of opportunity for mechanical computation, as the rules for solving such equations did not change from problem to problem. In the fall of 1943, the Applied Mathematics Panel received a request from the Army Signal Corps to compute twenty-six values from twenty-six equations. Warren Weaver noted that the scale of this problem was remarkably close to the capacity of a machine proposed by his former student, the Iowa State College professor John Atanasoff. “We have recently run into problems which necessitate the rapid solution of systems of linear algebraic equations,” he wrote to the dean of Iowa State College. “Could you inform me concerning the status of the electrical machine which Atanasoff designed for this purpose?”⁵⁸ The dean replied that the request had come too late. All that remained of the machine was a pile of scrap metal, a box of salvaged circuit parts, and the two drums that had once served as the machine’s memory.⁵⁹

Some accounts of the Applied Mathematics Panel describe the work as if it were accomplished under battlefield deadlines with late-night mathematical analyses and forced marches at computing machines.⁶⁰ In fact, much of the work, mathematical and computational, was done under strikingly ordinary conditions. For most of the war, the computers of the Mathematical Tables Project were able to work a standard shift, beginning their days at eight in the morning, ending at five, and taking an hour for lunch. Except at a few moments of crisis, the computers spent about 30 percent of their time finishing tables that they had begun under the WPA. “Gertrude Blanch abhorred a vacuum,” recalled one computer,⁶¹ so she used the old projects to keep the computers busy.⁶² The project also acted as the reserve staff for LORAN. By the summer of 1943, it provided the New York Hydrographic Office with a couple of computers each day, as well as typists, secretaries, and proofreaders.⁶³ Arnold Lowan kept a running tally of the debt, which eventually amounted to 3,150 days of labor.⁶⁴

In the late fall of 1943, the Mathematical Tables Project experienced a brief season of double-shift work, a period when the computers began calculating at 8:00 AM, finished at midnight, and went home through empty streets and cold night air. It was an experience that pulled them together and made them feel connected to the soldiers who were training for the invasion of France. They took pride in the knowledge that the calculations were intended for planners of Operation Overlord, the code name for the D-day invasion of Europe. This assignment had its origin in a bombing sortie that had failed to reach its target in France. Before heading back across the English Channel, one plane had lightened its load by dropping its bombs over the beaches of Normandy. The crew reported that their actions “set off a strange series of explosions” in the area, indicating that the beaches were probably mined. This news would have been unremarkable except for the fact that Normandy was the planned site for the D-day invasion. When the Overlord planners received this news, they decided to prepare a bombing mission to clear the defenses. The planes would drop high explosives on the beach and rely on the shock waves to detonate the mines.⁶⁵ To prepare this operation, the planners requested tables that would estimate the number of mines that could be cleared by a squadron of planes.⁶⁶

The Applied Mathematics Panel approved the request for beach-clearing tables in the fall of 1943 and assigned it to Jerzy Neyman (1894–1981), a statistician at the University of California. In many ways, he was a poor choice for the Applied Mathematics Panel, as more than one historian has noted. Neyman disliked working with the military and had “a tendency to postpone the computational chores assigned him by the panel” and instead pursue “highly general theoretical studies of great interest to statisticians but little use to practical-minded generals.”⁶⁷ He even had trouble working with other mathematicians. Neyman had originally been a subcontractor to the Princeton University research effort, but in the fall of 1943, he had called upon Warren Weaver to ask if he could be treated as an independent researcher. Weaver recorded that Neyman engaged in “considerable hemming and hawing, considerable artificial emphasis on the fact that [the Princeton mathematicians] are ‘good fellows,’” as he found the courage to explain that he had “no affinity” for the Princetonians. Weaver’s assistant, who knew that the relations between Neyman and the Princeton group had caused considerable problems for her boss, recorded that Weaver “keeps his face reasonably straight, and expresses the opinion that it may barely be possible to work out some sort of a divorce.”⁶⁸

For the mine-clearing problem, Neyman used a statistical model for “train bombing,” the practice of dropping bombs from a plane at regular intervals. He treated the train of bombs as a problem of geometric probability. The bombs became circles, which fell to their target like a handful of coins dropped on a tile floor. Some of the circles fell to the left, some to the right; some grew large, others shrank to a dot. Neyman’s analysis estimated the number of handfuls that would be required in order to cover the floor.⁶⁹ The analysis required a substantial amount of computation to move from coins on the floor to bombing tables, more than Neyman could handle by himself. He had a small computing staff in California, six students and an assistant, who shared five computing machines.⁷⁰ These students could handle small projects, but like Neyman, they were more interested in the mathematics than in the calculation and tended to defer their numerical work until the late evening hours.⁷¹

Weaver had first tried to find a punched card facility to do the mine-clearing calculations. He talked with three different groups, the University of California business office, the laboratory of chemist Linus Pauling (1901–1994) at the California Institute of Technology, and the Thomas J. Watson Astronomical Computing Bureau in New York. The University of California was unable to take the work, but the other two offices welcomed the task.⁷² “We would be very glad to team up with Neyman on any project that seems worthwhile to you,” Pauling told Weaver, adding, “The men here … have had now a great deal of experience with the use of punched card machines for mathematical calculations.”⁷³ The Watson Laboratory reported that they were doing some work for Wallace Eckert at the Nautical Almanac, “but they seem to think that this could be put to one side.” Weaver urged Neyman to send his analysis to the Watson Astronomical Computing Bureau, as the “costs are exceedingly moderate due to the fact that the IBM company furnishes all equipment, etc. so that we would need to pay only stipends of the people involved and consumed supplies.”⁷⁴

In the end, neither Pauling’s lab nor the Watson Astronomical Computing Bureau handled the computation. Warren Weaver assigned the job to the Mathematical Tables Project, and Gertrude Blanch prepared the computing plan.⁷⁵ At first, Blanch believed the work could be accomplished by a handful of her workers. Following the progress from California, Neyman soon realized that Blanch’s plan did not capture his intent. “Soon after the computations were started, it appeared necessary to alter the program,” he reported to Weaver, “which means in fact to extend it.” The new plan required more effort from the Mathematical Tables Project computers. Before long, the entire staff was spending two full shifts working on nothing but Neyman’s calculations. “I am sorry for underestimating the amount of computations done by Dr. Lowan,” Neyman apologized. In all, the calculations had consumed twenty-three times the labor that he had anticipated.⁷⁶ The final report was completed, after three full weeks of labor, on December 17, 1943.⁷⁷

As with many of the war computations produced by the Mathematical Tables Project, Blanch and Lowan sent their results to the Applied Mathematics Panel and had only the vaguest idea how they would be used. It was like sending offspring into the world and never knowing what these children would accomplish, what trials they would face, where they would make their home. At times, Lowan would comfort himself, thinking that this work was a humble but key part of the war effort. It was like the proverbial nail which, if lost, would cause the loss of a horseshoe and set in motion a chain of disasters that would precipitate the loss of a horse, a rider, and ultimately the battle itself. Lowan desperately wanted to connect the Mathematical Tables Project to the successes of the war, and so he avoided the moments of sober contemplation, which would have reminded a more secure leader that a horseshoe is generally affixed to the hoof not with a single nail but with six. Neyman’s tables represented but one way of preparing the landing site at Normandy. After surveying the beaches more closely, the planners of Operation Overlord concluded that there were no mines blocking the invasion. The bombers that would have been assigned to mine clearing were deployed against artillery batteries.⁷⁸ The computations were filed away and never used.

Just before the turn of the new year, the Applied Mathematics Panel was approached by a commander from the navy’s Bureau of Ordnance. The officer reported that the bureau wished to purchase a computing machine to handle exterior ballistics calculations, but they had “absolutely no one who can survey the machines available.” Their scientists were “inclined to favor one that uses digital computation,” but they knew little about such devices. The commander asked the panel members to prepare a report on computing machines and make a recommendation to the navy. The commander’s superiors indicated that the Bureau of Ordnance would need “the backing of an Applied Mathematics Panel recommendation in order to secure a satisfactory machine.”⁷⁹

This request was awkward for Weaver. As much as he wanted to prepare a survey of computing machines, he believed that none of the Applied Mathematics Panel scientists could produce such a report without bias. George Stibitz was the panel member best prepared to write such a report, but he was predisposed to electric machines built from relays, such as his complex calculator. That winter, he was designing a second machine with the technology. This device was an interpolator, a machine that could compute intermediate values of a function.⁸⁰ After weighing the virtues of expertise against the problems of conflicted interests, Warren Weaver asked Stibitz to prepare the review. In an attempt to ensure that the report was balanced, he asked the Bell Telephone Laboratories researcher to work with a committee that included a naval officer and an MIT professor, whom he characterized as being “familiar with the electronic type of computer and with the IBM equipment.”⁸¹

Stibitz’s committee restricted their attention to large machines, such as the calculator that Howard Aiken had begun in 1938. This machine, which had been under construction for much of the war, was nearing completion at an IBM factory. IBM engineers had tested large parts of the device and were preparing to ship it to Harvard. The committee also considered the differential analyzers that were operating at MIT, Aberdeen, and the University of Pennsylvania. The Stibitz committee ignored the ENIAC, the digital differential analyzer under construction at Pennsylvania.⁸² The project was far from finished, and hence there was not much to report. It was still classified by the army, but those outsiders who knew about it had doubts about its future. Its lead designers, J. Presper Eckert (1919–1995) and John Mauchly (1907–1980), did not have much of a pedigree. Mauchly was a former teacher at a small religious college outside of Philadelphia. He had been introduced to computational problems during the Depression, when he had organized a statistical laboratory with National Youth Administration funds.⁸³ Eckert was a recent graduate of the university’s electrical engineering program. He had been known as a clever student, but he had not been at the top of his class, nor had he ever built a large machine.⁸⁴

The report did not have much influence over the navy’s computing plans. As Stibitz was preparing the report, the Bureau of Ordnance was making arrangements to assume authority over Aiken’s machine at Harvard and was considering a more advanced version of the device.⁸⁵ Still, the navy was satisfied with the paper and circulated it to their officers.⁸⁶ Stibitz followed this review with studies of punched card equipment, relay computers, and interpolating machines. Gertrude Blanch contributed a small part to one report on computing machinery. She was asked by Stibitz to “determine which iterative [computational] methods lend themselves best to the instrumentation of a modern computing device.”⁸⁷ Given the limitations of standard punched card equipment, it was not entirely clear that any of the computing machinery would be as flexible as a staff of human computers. Blanch studied the details of the Bell Telephone Laboratories computing machines, including the new interpolator and the design for a more sophisticated calculator that was still under construction. After she grasped that these machines could perform lists of instructions, she reported that most of her “techniques should work well on relay computers.”⁸⁸

In its first year as a contractor to the Applied Mathematics Panel, the Mathematical Tables Project had drawn few signs of respect from the panel’s senior mathematicians. They seemed to view the group as a secondary research unit, an organization much inferior to Columbia and Princeton. None of the panel members had even visited the offices of their second-largest contractor, preferring instead to send Warren Weaver’s administrative assistant, Mina Rees (1902–1997), to communicate with Arnold Lowan. In correspondence they tended to call the project director “Mr. Lowan” rather than “Doctor Lowan,” the honorific they reserved for scientists that they did not know, or the unadorned “Lowan,” the form they reserved for themselves.⁸⁹ Their attitude toward the group began to change when Cornelius Lanczos (1893–1974) joined the planning committee. Lanczos was a well-respected applied mathematician and had served for a year as a research assistant to Albert Einstein. He was one of the many Jewish mathematicians who had fled Eastern Europe in the 1930s and settled in the United States. For a time, he had held a position at Purdue University, but he was a poor match for the school. “I am trying desperately to get away from here,” he had written to Einstein.⁹⁰ He was so desperate that he was willing to forgo a regular university appointment and take a position at a former relief project.

Lanczos never served as a traditional planner, never prepared a computing plan, never oversaw the computing staff. Instead, he acted like a visiting scholar, an expert on the methods of calculation who could teach new techniques to Gertrude Blanch, Ida Rhodes, and the other members of the planning committee. Starting in the winter of 1944, he offered seminars on numerical methods, advertising them through the Applied Mathematics Panel and nearby New York University. “His lectures attracted a wide audience, not only from the Project, but from mathematicians at local universities,” recalled Ida Rhodes.⁹¹ These lectures brought a small glimmer of respect from the Applied Mathematics Panel. By March, they were starting to address Lowan in more informal terms and to refer to the project as “Lowan’s Group.”⁹² More important, they were pointing to the Mathematical Tables Project as a successful computing organization. They encouraged prospective computers to visit the organization and copy its operating procedures. Among the visitors that winter was a group of scientists that was preparing to build a computing laboratory for the Manhattan Project in Los Alamos, New Mexico.

Computing laboratories were familiar institutions to the atomic scientists, as most of the major university physics departments had some kind of computing staff. Yet these academic laboratories were far smaller than the scale demanded by the effort to build the bomb. The computing office at the University of Chicago, one of the larger contractors to the Manhattan Project, consisted of just one faculty wife and a few graduate students.⁹³ The senior leaders of Los Alamos wanted to model their organization on the largest computing offices of the Applied Mathematics Panel, the Thomas J. Watson Bureau and the Mathematical Tables Project.

The Watson Laboratory received the first visitors from the Los Alamos staff, a couple named Mary and Stanley Frankel. Stanley Frankel had managed the computing bureau at the University of California that had handled the calculations for isotope separation, the problem of extracting the type of uranium that could be used in a chain reaction.⁹⁴ It was a small group with none of the equipment that could be found at Columbia. The Frankels spent about three days at the bureau, working with director Jan Schilt and a young graduate student named Everett Yowell (1920–).⁹⁵ Yowell had the rare distinction of being a second-generation computer. His father, also named Everett Yowell (1870–1959), had computed for the Naval Observatory from 1901 to 1906. The elder Yowell was part of the generation that had known Simon Newcomb, Myrrick Doolittle, and the computers of 1918 Aberdeen.⁹⁶ After his service as a computer, the senior Yowell had become a mathematics instructor at the U.S. Naval Academy and then had returned to the family home in Ohio to become the head of the Cincinnati Observatory. The younger Everett Yowell spent his youth playing in the halls and chambers of the observatory. His father taught him how to use a telescope, how to record the position of an object, how to reduce astronomical data. His texts were the classic books: Crelle’s Tables, Newcomb’s Positional Astronomy. At the age of twelve, Yowell assisted his father on an expedition to study a solar eclipse. He entered college with a firm understanding of traditional astronomy and arrived at Columbia knowing the methods of hand computers.⁹⁷

During his first year at the school, Yowell had little contact with the Watson Bureau. “I was sort of drafted as an operator during the summer of ’42,” he recalled. The facility was beginning to do calculations for war research and had lost much of its skilled staff. Eckert was in Washington, and many of the younger workers had left for the military. Yowell learned the techniques of punched card computation by studying Eckert’s Orange Book and by experimenting with the machines. Over the course of a year, he became an expert on wiring plugboards, the mechanisms that controlled the tabulators. Plugboards were flat panels, about the size of a large notebook, that were filled with holes that represented the different operations of the tabulator. By connecting the holes with short cables, Yowell could direct the flow of data through the machines and implement the methods of the Orange Book.⁹⁸

The Mathematical Tables Project received its Los Alamos visitor a few weeks later, a researcher named Donald Flanders. Knowing the limitations of punched card tabulators, Flanders was organizing a hand computing group that would be known within the laboratory as T-5. The T-5 group was a typical wartime computing office with about twenty computers.⁹⁹ It earned a certain distinction because of its association with the physicist Richard Feynman (1918–1988). Feynman was a junior staff member at Los Alamos, and he worked with Stan Frankel to prepare computing plans for T-5. One of his plans recalled the work of de Prony or the early computing floor of the Mathematical Tables Project. Feynman divided the computation into specific tasks, such as additions, square roots, and divisions, and then assigned each task to a specific computer. Like de Prony’s computers, one T-5 computer did nothing but add. A second took square roots, using a mechanical calculator. A third only multiplied.

Instead of creating computing sheets, Feynman used standard index cards to hold the results of the computations. These cards passed from computer to computer as the calculation progressed. “We went through our cycle this way until we got all the bugs out,” recalled Feynman, and it “turned out that the speed at which we were able to do it was a hell of a lot faster than the other way, where every single person did all the steps. We got speed with this system that was the predicted speed for the IBM machine.”¹⁰⁰ This claim, the notion that the T-5 computers could equal the speed of a punched card office, was tested late in the war when Feynman organized a contest between the human computers and the Los Alamos IBM facility. He arranged for both groups to do a calculation for the plutonium bomb, the “Fat Man.” For two days, the human computers kept pace with the machines. “But on the third day,” reported an observer, “the punched-card machine operation began to move decisively ahead, as the people performing the hand computing could not sustain their initial fast pace, while the machines did not tire and continued at their steady pace.”¹⁰¹

The competition between the T-5 computers and the punched card equipment is generally reported as a scientific version of the tortoise and hare fable, a story that predicted the triumph of computing machinery and a sign that human computers would soon be replaced by the electronic computer. The result can also be interpreted the other way, as suggesting that, through much of the war, human computers were closely matched to their mechanical counterparts. Since human computers did not demand the kind of preparation required by punched card machines, they outperformed the tabulators on many military calculations. The Los Alamos scientists relied on human computers to check large calculations. The plutonium bomb calculations were compared to a similar set of numbers that had been prepared on Howard Aiken’s Mark I at Harvard.¹⁰² As the war entered its last year, human computers might still be considered the equals of automatic computing machinery.