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
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