The last computing machine of 1937 moves one step further from the offices of human computers, though it remained tied to the kinds of calculations that were being done by human computers. It was conceived at Harvard University by a graduate student in the school’s electrical engineering program. The student, Howard Aiken (1900–1973), was studying the actions of electrons in vacuum tubes. The mathematical expressions that described the electrical forces inside a vacuum tube were a messy set of differential equations. Like all other problems driving the development of computation, they could not be solved in a simple, symbolic fashion. In common with the equations of Richardson’s weather model, they described a phenomenon in three dimensions and would have required a substantial computing staff to calculate the solution. Harvard had access to funds from the National Youth Administration to pay the salaries of human computers, but such assistance was not sufficient for Aiken. “At the present time,” he wrote, “there exist problems beyond our ability to solve, not because of theoretical difficulties but because of insufficient means of mechanical computation.”35
Like Atanasoff, Aiken turned from the problems of physics to the problems of calculation. He designed a machine that used gears and wheels but had a special control mechanism that provided “automatic sequencing.”36 This mechanism would read a series of instructions from a paper tape and would direct the machine to perform those instructions. These instructions were almost a program, as we now use the term. By changing instruction tapes, the operator could make the machine perform complex arithmetic, solve simultaneous equations, compute orbits and trajectories, and reduce data.37 In many ways, Aiken’s idea was similar to Charles Babbage’s second computing machine, the one he had called the Analytical Engine. Aiken discovered the work of Babbage while he was preparing the basic outline of his machine. He was even able to inspect a partial adding mechanism that had been built according to Babbage’s specifications by his son. This connection between the nineteenth-century mathematician and the emerging computing machines is superficial, according to Aiken’s biographer, I. Bernard Cohen. “At that time [Aiken] did not have a detailed and accurate knowledge of the purposes and principles of operation of Babbage’s two proposed machines.”38
Aiken accomplished what Babbage could not: he built a working relationship between a commercial business and a scientific computing laboratory. In 1937, Aiken was older than most graduate students. Cohen has characterized him as “tall, intelligent, somewhat arrogant [and] assertive.” Aiken had supported his family since the age of fourteen, when he and his mother were abandoned by his father. As a high school student, he had taken night jobs while attending classes during the day. When he was an undergraduate at the University of Wisconsin, he had worked from four to midnight at the local electric and gas utility.39 His position at Harvard freed him from the need to seek outside employment and allowed him to search for someone who might be able to sponsor his computing research.
He first presented his ideas to an engineer at the Monroe Calculator Company, “a very, very scholarly gentleman,” Aiken recalled. The engineer quickly recognized what Aiken was attempting to do and “foresaw what I did not … the application to accounting.” The engineer gave a favorable review of the machine, but the management of Monroe decided that they were not interested in the project.40 Following this rejection, Aiken then turned to the computing staff of the Harvard Observatory. The observatory computing room operated much as it had in 1880 under Edward Pickering. A staff of computers and assistant astronomers, many of them women, measured photographs, interpreted data, and reduced the values recorded by the telescopes and sensors. The office had at least a few touches of modernity, such as mechanical adding machines, but it was more concerned with astronomy than with general methods of computation.41
35. Mark I mechanical computer at Harvard
The observatory director, through an indirect path, helped Aiken gain the attention of the senior managers at IBM. On a trip to New York, Aiken presented the IBM managers with a plan for a machine that would “be fully automatic in its operation once a process [was] established.”42 He visited the Columbia University Astronomical Computing Bureau, met Wallace Eckert, and studied the Orange Book. By the time his visit with IBM ended, Aiken had gained the attention of company president Thomas J. Watson. Watson was impressed with the proposal and offered to finance the project and build the machine in an IBM factory. Aiken would provide the general design and work with IBM engineers to develop the appropriate technology. Harvard would provide the computer center and operate the device.43 In a move that suggested that the two groups would not long cooperate on the project, IBM decided to call the machine the Automatic Sequence Controlled Calculator, while Harvard would name it the Mark I. By the time the project was finished, IBM had invested $100,000 in the construction of the machine and donated another $100,000 to cover operational costs, a combined sum that approached the annual budget for the Mathematical Tables Project.
Viewing the new computing machines, George Stibitz prophesied that “Human agents will [soon] be referred to as ‘operators’ to distinguish them from ‘computers’ (Machines).”44 Neither his machine nor that of John Atanasoff would take the title “computer” from human beings. The computers at Bell Telephone Laboratories may have operated the complex calculator, but they were more concerned with mathematics than with machinery. Atanasoff’s machine handled only one modestly complex step of a large process. Both inventions were intermediate devices that did not quite reach the era of stored programs and still looked back at the age of oil cans and orangewood sticks. Even Howard Aiken’s Mark I, the most sophisticated of the three machines, looked over its shoulder toward older technologies. One of Aiken’s assistants captured the traditional nature of the Harvard computing laboratory when he described the Mark I as emitting “a distinct sound, not unlike the clatter of steel-shod horse’s hooves clanging along a paved street.”45 Aiken generally employed his computing machine in work that could have been handled by the computing floor of the Mathematical Tables Project or the First World War computers of Aberdeen or even the Nautical Almanac computers of Charles Henry Davis. Shortly after the machine began operations, Aiken produced a set of mathematical tables. His volumes covered a different set of expressions from those being prepared by the computers of the Mathematical Tables Project, but the real difference between the two sets of computations was the difference between Harvard and the WPA, not the difference between machine calculation and handwork. The WPA reproduced its tables from mimeographed stencils. The Mark I tables were typeset and printed on fine paper. The WPA books were bound in a rough tan cloth and avoided references to work relief. Aiken used a fine blue cover and printed the university seal on the title page.46
CHAPTER FIFTEEN
Professional Ambition
I couldn’t find no job
So I went to the WPA.
WPA man told me:
You got to live here a year and a day.
Langston Hughes, “Out of Work” (1940)
LIKE THE ADDING MACHINES of the 1880s, the calculators of Stibitz, Atanasoff, and Aiken coincided with a world’s fair. This fair, which opened in the spring of 1939, was hosted by New York City. “It is arranged,” wrote the author H. G. Wells, “to assemble before us what can be done with human life today and what we shall almost certainly do with it … in the near future.” After pausing for a digression, he added, “It is a promotion show.”1 Like the World’s Columbian Exposition, now almost half a century in the past, the Long Island fair displayed the technologies that would be embraced by American culture. Visitors could examine television receivers, FM radios, prototypes of divided highways, and primitive fax machines. They could inspect the products of both Bell Telephone Laboratories and International Business Machines. IBM president Thomas Watson hosted a company conference at the fair and delivered a rousing speech on the future of punched card technology.2
In the midst of all the symbols of material progress stood the
WPA hall with its proud and slightly self-contradictory inscription, “This building shows the wealth created by the skill and artistry of America’s unemployed.” The presence of the WPA had been controversial and a little embarrassing to government leaders. The opening of the exhibit had been delayed by labor troubles, an ironic touch that delighted opponents of the New Deal.3 When the WPA finally allowed visitors into the building, more than three weeks had passed since the start of the fair. A signature book by the front door recorded the opinions of those who came into the exhibit during those first days. “The WPA must go,” signed former presidential candidate Alf Landon, but his comment was altered by a WPA supporter so that it read, “The WPA must go on.”4
“The exhibits cover every aspect of WPA activity,” wrote one reporter, “from art, music, and drama to the manufacture of clothing for the poor.” Above the displays, WPA employees had written slogans that portrayed the agency in a heroic light. “Work is the Right of every American,” read one panel, and “Work Builds Better Communities,” claimed another.5 Over the science projects was written, “Work Increases Knowledge,” a phrase that Gertrude Blanch and Arnold Lowan would have liked to claim for the Mathematical Tables Project. As far as we know, there were no calculations from the project on display.6 Only the powers of integers had been officially published. The second book, the volume on the exponential function, was still being printed.
During that first summer of the fair, Gertrude Blanch was still attempting to accumulate the information that she needed for her computing plans. Like others before her, she was learning that there was no single literature of computation. When she needed some mathematical theorem or technical analysis, she would send a junior member of the planning committee to the New York Engineering Societies Library with instructions to scan through some collection of journals, page by page if necessary. The fact that many on the planning committee were immigrants or the children of immigrants simplified such searches, as much useful material could be found in foreign language publications, such as the Archiv der Mathematik und Physik, the Mémoires couronnés et autres mémoires publiés par l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, and the Wissenschaftliche Schriften des Donetz-Tecknikums des Genossen Artjem zu Stalin.
The one organization that might have been able to assist the Mathematical Tables Project with its library searches, the Subcommittee on the Bibliography of Mathematical Tables and Other Aids to Computation of the National Research Council, was still moribund and unfocused. By the spring of 1939, the leaders of the National Research Council had lost all hope that A. A. Bennett would be an effective leader of the group. After the initial flurry of activity in 1935 and 1936, Bennett had all but abandoned MTAC. His communications with the National Research Council had became a litany of excuses. “Unexpected and extended interruptions have retarded the work in a way that was not anticipated,” he reported that April.7 Most of these “unexpected interruptions” had come from the Aberdeen Proving Ground, where Bennett served as a consultant. The proving ground had expanded its computing facility with a differential analyzer, the machine that had been invented to solve differential equations. “During the last part of the year,” wrote the base commander, “the analyzer has been used in the computation of two firing tables with gratifying results.”8 As gratifying as such results may have been, they did not suggest that the new computing machine would replace the human computers or eliminate all work for A. A. Bennett. The analyzer “saves a great amount of labor when a group of related trajectories are to be computed,” reported one of Bennett’s colleagues, but the device was sensitive and suffered from “mechanical inaccuracies.” The adjustment of the analyzer was “a delicate matter, requiring so much time that for a single trajectory [it was] more economical to compute in the usual way.”9
Sometime that spring, the leaders of the National Research Council quietly asked Bennett to resign his chairmanship. In his stead, they appointed Raymond Claire Archibald, who was, like Bennett, a professor of mathematics at Brown University. Archibald was a tall, imposing figure, filled with energy and topped by a head of hair that had retained its red color. He was a Canadian by birth and a distant cousin of Simon Newcomb, a connection that gave him great pride.10 He was also unmarried, a fact that he prominently displayed in his biographies and resumes.11 The council had twice passed over Archibald when it had sought a chair for MTAC, but in 1939, it was willing to accept anyone who might actually complete a bibliography. Archibald had already proven that he could be a leader of mathematicians, though not quite a leader with the stature of Veblen or even A. A. Bennett. During the First World War, Archibald had edited the American Mathematical Monthly, a prime job in ordinary times but one that seemed small compared to the experience of the Aberdeen veterans. Following the war, he had held several minor positions in the American Mathematical Society and, in the process, acquired the reputation of being difficult. He had once drawn a quarrel from Oswald Veblen over plans for financing the American Mathematical Society. “I gather from your letter,” Veblen had scolded, “that you have not understood my position in the matter. But on re-reading my [note to you], I don’t see how I can make it clearer. So I fear all I can do is to ask you to reread the last paragraph of that letter.”12
36. R. C. Archibald in his office at Brown University
When R. C. Archibald accepted the chair of MTAC, he put all of his considerable personality into the job. Within days of his appointment, he had written to the committee, asking members for “reactions, advice, comments and suggestions on various matters.” He explained that the committee would act as a “clearing-house of information about Tables,” that it would cooperate with England’s Mathematical Tables Committee in order “to avoid duplication of effort,” and that it might “take steps toward initiating the development of other tables which were thought to be desirable.”13 He proposed to establish a broad and inclusive committee that could direct any kind of computational work. Before the summer had ended, he had reorganized the group along lines that had been developed by the Mathematical Tables Committee of the British Association for the Advancement of Science, a structure that split the broad literature of mathematical tables into twenty-one different classes.
TYPOLOGY OF MATHEMATICAL TABLES
BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE
A.
Arithmetical Tables
B.
Tables of Powers
C.
Logarithms
D.
Circular Functions
E.
Hyperbolic and Exponential Functions
F.
Theory of Numbers
G.
Higher Algebra
H.
Tables for Numerical Solution of Equations
I.
Tables Connected with Finite Differences
J.
Summation of Series
K.
Statistical Tables
L.
Higher Mathematical Functions
M.
Integral Tables
N.
Interest and Investment
O.
Actuarial Tables
P.
Engineering Tables
Q.
Astronomical Tables
R.
Geodetic Tables
S.
Physical Tables
T.
Critical Tables of Chemistry
U.
Navigation Tables
Many of these categories had little in common. Integral tables (M) involved no calculation at all. Interest tables and actuarial tables (N and O) were prepared for businesses, not laboratories. Many engineering tables (P) contained collections of data that had been gathered from experiments. In addition to these categories, Archibald proposed one final division, Z, that would not deal with tables at all but would prepare the bibliography of calculating machines. For each division on the list, he inten
ded to create a small section of four or five members. The chairs of the sections plus Archibald would form an executive group.
The plan would create an unusually large committee for the National Research Council, and it did not take long for the organization’s staff to object to Archibald’s plans. “There is nothing in the by-laws or procedures of the Council to contravene what Professor Archibald proposes,” lamented the council secretary. “However, I cannot help feeling that making a difference between classes of membership in this way introduces a rather invidious distinction.”14 Grateful for any action within the committee, the council was willing to let Archibald proceed, even though one scientist on the council compared the new MTAC structure to the myriad agencies of Roosevelt’s New Deal and quipped that Archibald “apparently has caught the alphabet fever from the Government.”15
When Computers Were Human Page 30