When Computers Were Human (49 page)

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.”
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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.”
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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.
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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.
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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.
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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.”
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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.
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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.
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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.
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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.
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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.
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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?”
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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.
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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.
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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,
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so she used the old projects to keep the computers busy.
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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.
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Arnold Lowan kept a running tally of the debt, which eventually amounted to 3,150 days of labor.
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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.
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To prepare this operation, the planners requested tables that would estimate the number of mines that could be cleared by a squadron of planes.
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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.”
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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.”
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