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 mi
litary 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 a
ssume 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.
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