When Computers Were Human (39 page)

On February 1, the WPA began to send workers to the Mathematical Tables Project office. Those who took WPA jobs were desperate for work. They lived at the edge of poverty and usually had held no stable job for a long time. The WPA's figures suggested that 90 percent of them lacked the skills that would gain them employment with a private firm.
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Gertrude Blanch, who had a tendency to see the best in anyone, recalled that “among them we found some very good material. Most of them were willing to learn, but we knew that we couldn't expect too much.”
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Though such native grace made her job a little easier, it did not allow her to be complacent or to feel sorry for her workers. She had less than five months to turn these workers into human computers. The WPA had authorized funds for the Mathematical Tables Project only through June 30. By then, if she could not demonstrate that her computers were producing useful public works, funds would be terminated and the project ended.

The most detailed picture of the computing floor in its first year comes from Blanch's closest friend at the project, Ida Rhodes (1901–1986). Rhodes did not join the project until 1940, but she would be Blanch's confidant for nearly forty years. She was outgoing while Blanch was retiring, flamboyant when Blanch was reserved, and critical when Blanch might have been gentle. Blanch generally approved Rhodes's accounts of the Mathematical Tables Project. “She had a way of getting across a point,” Blanch recalled, “in a way that no one else could, all with a sense of humor.”
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Some of Rhodes's stories contradict the administrative record of the WPA, but those that agree with other accounts of the project offer a bleak portrait of that first winter. “Many of our workers were physically ill,” Rhodes reported; “arrested TB cases, epileptics, malnourished persons abounded.” She seemed to delight in remembering that some of the computers had engaged in “several types of perversion and vice.” Those who were hardest to engage, those who were “most pitiful,” in her words, were the workers who had “lost their self respect in that horrible year.”
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By early spring, Blanch was working with a computing staff of one hundred and twenty-five, a number far short of the thousand Morrow had promised, but it was as large a computing force as had ever been assembled. The operations of the Mathematical Tables Project were overseen by a planning committee, a group of six mathematicians who prepared the computing plans. In theory, the planning committee was chaired by Lowan, but Blanch generally ran the group. Each member of the committee would take responsibility for one computation, researching
the background for the table, recommending a certain mathematical approach, preparing worksheets for the computers, and checking the final results. One committee member oversaw the operation of the “computing floor,” as the bulk of the computers came to be called. In addition, the planning committee worked with two smaller computing groups, the special group and the checking group. The special group tested methods, calculated initial values, and did other work for the planning committee. The checking group worked with the finished worksheets and with the final proofs for the tables. In 1938, the computers of these last two groups were the only ones who had access to the project's three adding machines.
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32. Computing floor of the Mathematical Tables Project

Blanch divided the computing floor into four groups, one for each of the arithmetical operations. The largest group, identified as group 1, did addition only. A slightly smaller group, group 2, did subtraction. Group 3, which had about twenty computers, multiplied numbers by a single digit. The elite of the computing floor was the tiny group 4. Its members did long division. She isolated each group within the Mathematical Tables Project office. She placed group members at long tables facing a wall. On the wall she put a poster to remind the computers of the basic rules of arithmetic. Few of them had completed high school, and fewer still could be trusted to work without direction. Since most did not know how to manipulate negative numbers, she devised a scheme that used black pencils to record positive quantities and red pencils to record the
negatives. The wall posters described how to handle numbers of different colors. The poster for the addition group read:

The worksheets had been duplicated on a mimeograph machine. “They generally had 100 lines and were on graph paper,” explained a veteran of the project.
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Whenever possible, Blanch tried to replace complicated operations with repeated additions. It was an approach that mimicked her driving habits. Family members remarked that she would go to great lengths to substitute three right turns for a single left-hand turn across traffic.
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Because the computing floor had one section for each operation, she could leave some multiplications and divisions on the worksheets. The sheets circulated through all four groups on the floor, often wandering through each section several times before the work was complete. For example, a sheet might start in the addition group and then move to the multiplication group after all the initial additions were done. “The human computers who liked boring work, did calculations vertically,” observed a planning committee member. “They did 100 operations before they moved to the next column.”
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When the worksheets returned to the planning committee, they were checked for errors. Blanch and Lowan went to extraordinary lengths to find every possible mistake, including errors created in transcribing the values to the final table. Behind their efforts was the knowledge, rarely mentioned, that one poorly computed table could permanently damage their reputation and limit their acceptance within the scientific community. “We had very little equipment,” reported Gertrude Blanch, “and a lot of supervisors who thought that this was another boondoggle project.”
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The first defense against errors was found within the worksheets. Blanch designed them in such a way that elementary mistakes in calculation could be quickly identified. The computers filled in a grid of numbers. The last column of this grid had to match a set of predetermined values, numbers that had been computed by the planning committee or one of the special computing groups. If they did not match, the sheet contained a mistake in calculation.

Some computers attempted to avoid the discipline imposed by the worksheets. Recognizing the structure of the sheet, a worker could put the predetermined values in the last column and then fill the remaining blanks with any values that seemed appropriate. This did not happen often, given the quality of the final tables, but each member of the planning committee could recall at least one incident of cheating. Blanch remembered two women who submitted falsified worksheets. “You can't
cheat in those things,” she said flatly. “It comes out almost immediately. Well, these girls were fired immediately.”
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The other examples of cheating or carelessness also ended in dismissals. One resulted in the departure of a planning committee member.
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Blanch checked each calculation with six or eight different procedures. Some of the procedures were based upon the mathematical properties of the function they were tabulating. All tables were checked with the technique known as differencing. Differencing had been used by the computers of de Prony and Maskelyne, but it reached a new level of sophistication in the hands of Gertrude Blanch. It reversed the method on which Charles Babbage based his difference engine. Babbage had shown that many functions could be reduced, through the method of finite differences, to a series of repeated additions of constant terms. Blanch used this technique to check tables by repeatedly taking the differences of adjoining terms. In a table of cubes, the first five values are the numbers 1, 8, 27, 64, and 125. The first differences are 8 − 1, 27 − 8, 64 − 27, and 125 − 64, or 7, 19, 37, and 61. If we repeat the process and take adjoining differences of these values, we get 19 − 7, 37 − 19, and 61 − 37, or 12, 18, and 24. In one final set of differences we get 18 − 12 and 24 − 18, or the numbers 6 and 6. If one of these third differences were not 6, then one of the original values in the table would be in error. For most functions tabulated by the Mathematical Tables Project, the sixth or seventh repeated difference would produce a list of nearly constant numbers. Any significant variation would indicate an error in the calculations.

By WPA regulation, the human computers worked thirty-two hours a week. They were supposed to spend the remaining time looking for permanent employment. This limitation on the program gave Blanch the opportunity to study the worksheets when the computing floor was silent. She spent many an evening hour checking calculations and preparing new worksheets for the next day. She seemed to enjoy the quiet time after the computers left for the day, when there were no workers to encourage, no questions to answer, no formulas to explain. The office was quiet, and she could concentrate on mathematics.

The Mathematical Tables Project finished the table of powers in early April 1938, printed the manuscript with a mimeograph stencil on rough sheets of paper, and bound the pages with a cardboard cover. A few of the numbers were a little difficult to read. Prominently displayed on the face of the book was a WPA seal, a small rectangle that identified it as the product of a relief effort. Lowan and Blanch claimed that there were no errors in the table, a claim that was tested when a copy reached the desk of L. J. Comrie in England. Comrie reviewed the entire work, checked every value with a difference test, and concurred that the table was entirely free of errors.
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Finishing the first table was a relief to the entire group and created what Blanch called a sense of “heartwarming camaraderie” among the staff.
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It steeled their courage for their second project, creating tables of the exponential function,
e
^x
. The exponential function is harder to compute than a simple power of an integer. It is the inverse of the logarithm and can be expressed as the sum of an infinite number of terms,
e
^x
=
x
/1 +
x
²
/2 +
x
³
/6 +
x
⁴
/24 and so on, continuing in the same pattern. In practice, a computer does not need to deal with an infinite number of operations, as the terms eventually become so small that they can be safely ignored.

The computers began working on the exponential calculations in the early spring, while they were still working on the powers of integers. It seemed important that this project be under way when the WPA reviewed the progress of the group in June. For all the anxiety among the planning staff, the review proved to be quick and perfunctory. The WPA officials reported that they were satisfied with the accomplishments of Blanch, Lowan, and the human computers and approved another six months of budget for the group.
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With the future of the project on a stronger financial foundation, Lowan was able to arrange for Columbia University Press to publish the tables from the project.

While Blanch was preparing computing plans and directing the daily operations of the human computers, Lowan was attempting to bring the Mathematical Tables Project to the attention of American scientists and engineers. His first problem was to overcome the stigma of the WPA. His second was to show that his group could equal the accomplishments of the two other scientific computing organizations in New York City. Thornton Fry, Clara Froelich, and the other Bell Telephone Laboratory computers worked two miles south of the Mathematical Tables Project office. Wallace Eckert and the Columbia University Astronomical Computing Bureau sat a slightly greater distance to the north. Both had reputations that Lowan would have liked to equal.

Beginning in the fall of 1938, Lowan began to promote his project as a general-purpose computing office for the nation's engineers and scientists. He prepared mimeographed circulars, using the same machines that reproduced his computing sheets, and mailed them to universities, government offices, manufacturers, and every scientist he could name.
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In general, these efforts at self-promotion were frustrating affairs, as he might have learned from anyone who dealt with direct mail advertisement. He often posted one hundred or two hundred letters in a month and received not a single reply. When he did receive a reply, he was usually disappointed. Lowan received requests to prepare salary tables, to tabulate data, and to do simple calculations for other WPA projects. In general,
he tried to decline such work by citing the WPA requirement that all products needed to be “widely usable.”
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However, he quickly learned that he was part of a government organization that could be subject to political pressure. More than once, a rejected request returned to his office in the form of a letter from Lyman Briggs. These letters reminded Lowan that the Mathematical Tables Project received government funds and that it would be well advised to honor the request, no matter how uninteresting it might be.
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