When Computers Were Human (40 page)

The few letters from well-reputed scientists could be tantalizingly sad, like the gentleman caller who offers a moment of hope and happiness and promise before disappearing. In response to a circular, John von Neumann wrote, “Many thanks for the announcement of your project. I am much interested in your program and should like to get your material.” He ended the letter, “I may have some remarks and suggestions in connection with these things and will write to you concerning them before long.”
⁷⁷
As Lowan had known von Neumann at the Institute for Advanced Study, he had some reason to expect that the mathematician would act on his promise, but the weeks passed, and the Mathematical Tables Project received no further correspondence.

The one scientist who offered more than hope was Philip Morse (1903–1985), a professor of physics at the Massachusetts Institute of Technology. “I have been in charge of a number of similar projects,” he wrote, and felt “that I should get in touch with you.” With no more introduction or pleasantries, he then described a lengthy calculation, acknowledging at the end that “this calculation has no particular difficulties but requires considerable man-hours and if you are in a position to be of help, this help would be welcomed.” Such interest was well received by Lowan, Blanch, and the rest of the senior staff, but it was accompanied by an embarrassing query. Morse ended his letter by stating, “I will be very pleased to know just what sort of arrangements you make on calculating facilities and in general how you operate.”
⁷⁸

Lowan responded quickly, assuring Morse that his group would be happy to compute for anyone at the Massachusetts Institute of Technology. He gave a brief overview of the Mathematical Tables Project, telling Morse that “we are operating with a staff of 110 workers under the supervision of a planning section of which I am in charge.” He mentioned nothing about worksheets or relief workers. When he reached the topic of machinery, he equivocated. “Most of the work is, of course, done with the aid of calculating machines.”
⁷⁹
Strictly speaking, the statement was true, as the project's three adding machines contributed indirectly to everything that the staff did. However, the bulk of the calculations were done with only paper and pencil.

We do not know when Morse learned the true nature of the Mathematical
Tables Project computers. He was unusually well connected in the scientific community and may have known from the start that Lowan was stretching the truth. He never criticized Lowan, never suggested that there was anything wrong with the project. In fact, he seemed to grasp innately the nature of the group. In his second letter to Lowan, he said that he had “one or two other sets of calculations which I want to suggest to you in the next month or so” and that he would “consult with a number of the other members of the Physics and Mathematics Departments here and at Harvard in order to submit to you a program that is not a set of personal interest.”
⁸⁰

The last phrase in Morse's letter was important. Lowan had to establish that every calculation was of general interest and would benefit more than a single scientist or engineer. None of the tables could be copyrighted, as they had been prepared with public money. It was one of the WPA policies that governed his actions as long as he accepted their money. The WPA also required that he use labor-intensive methods, in order to employ the greatest number of people, and restricted the number of female employees to about 20 percent of his staff, an attempt to prevent one household from receiving two sets of benefits.
⁸¹
Every request for scientific calculation had to follow the WPA rules, even if that meant using methods that seemed archaic or unsuited to 1930s research.

Morse never seemed to be bothered by the WPA restrictions. He proved to be a tireless ally and a key link to the scientific community. He helped bring the group its first important scientific computation, a problem posed by the Cornell physicist Hans Bethe (1906–). Bethe was studying the processes that produce solar energy. In order to understand these reactions, he needed a table that would show the internal temperature of the sun, beginning at the outer edges and moving inward to the core. Since these measurements could not be taken directly, they had to be computed from a mathematical model.
⁸²
Bethe claimed that the calculations were not “prohibitively laborious” but were so difficult that no one had attempted the work without first substantially simplifying them.
⁸³

Lowan eagerly agreed to undertake the project, for the work would bring the Mathematical Tables Project to the attention of astrophysicists and might also show that the group was as capable as the Columbia Astronomical Computing Bureau. If he expected that the calculations would be done quickly, he was mistaken. After the planning committee reviewed the plan, they had a half dozen questions for Bethe. They asked Bethe to verify equations and check key values. The calculations involved a three-dimensional system of differential equations, the form of equations found in Richardson's weather model. Though the equations were simpler than those posed by Richardson, they still demanded a great deal of work. If the starting values were wrong, the effort would be wasted.
Not even Hans Bethe could adjust the sun and bring it into agreement with a mistaken calculation.

In the end, Gertrude Blanch decided to do all the computations herself. She concluded that she could calculate the tables in the time that it would take her to prepare worksheets for the computing floor.
⁸⁴
The calculations took about three weeks of effort. Bethe was impressed with the results, calling them the “first modern determination of the temperature of a star.”
⁸⁵
The table was published in the
Astrophysical Journal
, which must have pleased Lowan. It was the first major publication to come from the project. Perhaps more important, it brought attention from a major physics department. Bethe reported that his colleagues had taken a look at the group's first tables and that “the department has decided to order copies of them.”
⁸⁶

By this time, the project's second volume,
Tables of the Exponential Function
, had appeared in print. Compared to Karl Pearson's
Tracts for Computers
or H. T. Davis's
Tables of Higher Mathematical Functions
, this new volume received serious attention from the scientific press. Though book reviewers inevitably mentioned that the volume had been produced as a relief project, they generally treated it with respect. The review in the widely circulated
American Mathematical Monthly
was positive, though perhaps not as enthusiastic as Lowan might have liked. The reviewer, John Curtiss (1909–1977) of Northwestern University, noted that the book claimed to be “entirely free from error.” If he had been L. J. Comrie, he would have tested this assertion. As he was not, he was willing to concede that “the precautions taken seem to give considerable weight to this claim.”
⁸⁷

John Curtiss's review was an important milestone for Blanch and Lowan, evidence that they had done their job well, had met the requirements of the WPA, and had created an organization that could produce something of value to at least a few scientists. Nevertheless, the project was still a work relief effort. It still occupied a dirty industrial loft in an unattractive part of Manhattan. Each week, the members of the computing floor collected their wages hoping that by the next payday they would have a full-time job with some employer that was not the WPA.

CHAPTER FOURTEEN

Tools of the Trade: Machinery 1937

W
HEN
M
ATILDA
P
ERSILY
came to work at the Mathematical Tables Project, she followed a little ritual to prepare her tools for the day. She was part of the special computing group, one of the few who regularly used an adding machine. Her machine was a old Sunstrand, an inexpensive device that had ten keys on the top and a crank on the right side. She would first add a few meaningless numbers while sharing a moment of conversation with other members of the staff. As she talked, she would listen for the sound of grit in the gears and try to feel any catch or slip in the mechanism. She could apply some lubricating oil from a can that sat on a small shelf, but too much oil would attract the very dust she was trying to avoid. She had found that the machine was best cleaned with an orangewood stick; such sticks were sold at drugstores to groom fingernails and cuticles. Once convinced that the machine was ready, she would sit at her desk, take out her worksheets, and begin to compute.

Most of the computing machinery acquired by the Mathematical Tables Project during its first years of operation was scavenged from terminated WPA offices and other government agencies.
¹
Ida Rhodes described this equipment as “the most broken down, the most ancient of contraptions.”
²
The majority were inexpensive, hand-cranked Sunstrand calculators. They were not designed for the repetitious work of the computing floor, nor was their crank mechanism easy for project computers to pull. Rhodes would complain, “Oh, how my arm ached by the end of the day.”
³
Few of these machines were in operating condition when they arrived at the project's office. A couple of the senior computers had learned how to transplant gears and levers from one machine to another and were able to produce two or three working machines for every four that came to their door. Through 1938 and 1939, the group had no other way to acquire calculators. A new mechanical calculator cost $400, almost as much as the $560 annual salary paid to a WPA worker.

During the Great Depression, most computing laboratories had at least
one staff member with enough mechanical expertise to repair or modify their desk calculators. Even the smallest laboratory had to follow a maintenance regimen for its machines, oiling gears and adjusting levers. Observatories relied on the same technicians that kept telescopes in working order. The larger organizations, such as the Iowa State Statistical Laboratory, kept a mechanic on their staffs. The Iowa State laboratory, formerly known as George Snedecor's Mathematical and Statistical Service, had to maintain an unusually large number of machines, as the laboratory acted as a general computing facility for the campus. It not only did calculations for any college faculty member but also provided adding machines and calculators to campus laboratories and offices. Laboratory staff kept the machines in good repair and trained the people who would use them.
⁴
With such a responsibility, it is perhaps not surprising that the laboratory director in 1938, Alva E. Brandt (1898–1975?), was a trained mechanical engineer and had once served as a professor of farm machinery at Oregon State University.
⁵

The computing office at Bell Telephone Laboratories probably had the greatest access to trained engineers and inventors. Regularly, laboratory scientists turned their gaze on the computing staff of Clara Froelich and saw them as a model for some new calculating device. “In these laboratories,” observed the staff scientist George Stibitz (1904–1995), “we have 10 or more girls, including at least one Hunter graduate, who spend most of their time dealing with [complex numbers].” Stibitz, a physicist, was a new addition to the mathematical division. In spite of his patronizing language toward the women, who were often a decade or more older than himself, he was one of those rare scientists who treated the computers as individuals. He seems to have been friendly with them, pausing over their desks to share a bit of conversation, comment on the upcoming weekend, and learn how they handled their calculations. He rarely described his early research without mentioning them.

By 1937, Stibitz had begun to think about building a machine that could perform complex arithmetic. Unlike L. J. Comrie in England, he was not inclined to adopt existing computing machines. “Although there are well-known rules for the use of ordinary computing machines to handle complex numbers,” he observed, “the work is tedious and likely to lead to errors on the part of the operator.”
⁶
Others at Bell Telephone Laboratories had already designed calculators for complex arithmetic, but they had met with mixed success. One laboratory engineer had created a special slide rule that could multiply complex numbers. Unlike an ordinary rule, this device could account for the two parts of a complex number, the value identified as the real part and the value identified as the imaginary part. In spite of its ingenuity, the new slide rule was never adopted by the human computers. In all likelihood, they
found the device too cumbersome and judged that it was faster to do the work by hand.
⁷

A second computing machine for complex arithmetic had been created by Thornton Fry, but this machine was a specialized instrument. Fry's machine, which he called an isograph, could be used to find the zeros of a polynomial. The zero of a polynomial is a value that makes the expression equal zero. These values are often called “roots,” a term that suggests the part of a plant that is underground; hence roots are the values for which an expression vanishes to nothing. For the polynomial
x
²
− 5
x
+ 6, one of the roots is the value 3, because for
x
= 3, the value of the polynomial
x
²
− 5
x
+ 6 equals 3
²
− 5 × 3 + 6 or 9 − 15 + 6, which is 0. All polynomials have roots, but they can be complex numbers and are often quite hard to find.

The isograph is best understood as an oracle for polynomials. It was not a true calculator but a device that could provide computers with information about their work. The idea had come from an analysis of gears that had been done jointly by Fry and Stibitz. The two had shown that the action of a certain combination of gears was best modeled by complex numbers. Fry took a similar set of gears and used it as the basis for the isograph. The device was big, about twelve feet in length, and was driven by an electric motor. A wheel on the left side of the machine could be used to advance the machine should the motor jam. Froelich, or one of the other computers, operated the isograph by setting a row of knobs that protruded from the base of the machine. They started their work by guessing a value that might make their polynomial equal zero. The isograph would process this guess, grinding its gears and producing a graph of circles on a plotting table. The computer would have to interpret these circles and determine whether the guess was too little or too big. The computer would then adjust the guess and ask for a second response from the machine. Continuing in this manner, with a little bit of strategy and a fair amount of patience, the computer could eventually find the values that made a polynomial equal zero.
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