Calculating Women

NASA Langley Research Center
Katherine Johnson, the NASA mathematician who calculated the reentry trajectory for John Glenn’s Mercury Friendship 7 mission as he returned from orbiting the earth, 1962

After a precisely calculated and perfectly executed voyage, the Mars Orbiter Mission reached its destination on September 24, 2014. The Indian Space Research Organisation, which oversaw the mission, had succeeded in doing what Russia, the United States, China, and Japan had failed to do: send an unmanned probe into orbit around Mars on the first attempt. The project’s success captured headlines worldwide, and a photograph of the cheering women on the administrative staff in the operations control room went viral on the Internet. Subsequently, articles about the female scientists and engineers who were central to the success of the project were widely published.

Perhaps never before had the participation of women in a space mission been so visible, even though women had been making fundamental computational contributions to astronomy and aeronautics for well over a century. Three recent books—Dava Sobel’s The Glass Universe, Margot Lee Shetterly’s Hidden Figures (which has also been turned into an Oscar-nominated film), and Nathalia Holt’s The Rise of the Rocket Girls—show some of what they accomplished.

In the late nineteenth century, the term “computer” referred not to a machine but to a person who took measurements, graphed data, and made calculations that helped interpret information and predict results. Although computing was considered mechanical and menial, it was a necessary task that required precision and patience. Before the invention of the modern digital computer, it was crucial to the advance of science and technology. Computers were often women, who could be paid less than men and could work during wartime. Despite the integral part they played in establishing the US as a leader in modern astrophysics and space exploration, their work has remained largely unknown.

Although advances in science and technology are often portrayed as the work of solitary men—for example, Isaac Newton, Thomas Edison, and Albert Einstein—science has always been a collective enterprise, dependent on many individuals who work behind the scenes. This has become increasingly true as more scientists work on large research projects funded by governments and staffed by hundreds of technicians. Yet despite the collaborative nature of science, for too much of its history the work of women and scientists of color was exploited, deemed rudimentary, and unacknowledged. Taken together, the books by Shetterly, Sobel, and Holt provide important insights into how they contributed to the emergence of Big Science.

Sobel’s book recounts the history of female computers whose work at the Harvard College Observatory in the late nineteenth and early twentieth centuries was crucial to discoveries in modern astrophysics. Edward Pickering, the director of the observatory from 1877 to 1919, sensed, as Sobel writes, that “the stars…were telegraphing important behavioral clues.” It was unclear, however, just what the stars were communicating.

Much of the work Pickering oversaw at the observatory involved analysis of the chemical composition of stars. Earlier in the nineteenth century, scientists had discovered that every chemical element, when heated to the point of incandescence, emits light of a distinct and identifiable frequency. At the base of their telescopes, Pickering and the other observers affixed a device called a spectroscope, which contains a prism. When light is passed through a prism, it is dispersed into a faint strip of rainbow colors, from red to orange to yellow and on to violet. A person looking through a spectroscope will see not only the rainbow strip but also black lines of varying thickness that reveal the individual elements of which the light is composed.

Owing to advances in photography, images of the lines created by starlight and passed through a spectroscope could be recorded directly onto glass plates. By measuring the thickness of the lines and their placement along the spectrum of visible light, the Harvard Observatory workers were able to discern the chemical composition of stars. This brought about a revolution in astronomy, which shifted from subjective descriptions and handmade drawings to objective photographic records of the cosmos. In 1882, Pickering began compiling the Henry Draper Catalogue of Stellar Spectra, with the intention of recording the brightness and chemical composition of stars in both the northern and southern hemispheres. The catalog was funded by Anna Palmer Draper in memory of her late husband, himself a renowned scientist who was the first to photograph the spectra of stars.

By 1893, Harvard had produced 30,000 glass plates. Analyzing them was tedious, painstaking work that required an acute analytical mind. Recognizing that they were just as capable as men and would work for lower wages, Pickering hired women who were good at math or devoted stargazers to examine the plates, analyze the spectra of stars and the distance between them, and devise systems to classify this vast stellar landscape.

Sobel follows the lives and work of several of the observatory’s female computers, including Williamina Fleming, who had been Pickering’s maid; Antonia Maury, Henry Draper’s niece and a former student of the Vassar astronomer Maria Mitchell; and Annie Jump Cannon, who had studied physics at Wellesley and astronomy at Radcliffe. Although the women at the observatory were disparagingly known as “Pickering’s harem,” the director persistently supported them and tried to get them wider recognition for their contributions to what was then the cutting edge of astronomy.

Plate by plate, Fleming and Maury analyzed the brightness of stars, applied formulas to compute their sizes, and measured the dark lines and the spaces between them that appeared in the spectra. Maury and Cannon later revised the scheme that Fleming had created to organize stars into distinct spectral families based on other similarities. Together they classified well over 200,000 stars that were compiled in the Draper Catalogue. Cannon, who was the first female researcher to do nighttime observations, acquired her own data using the observatory’s six-inch telescope. Having examined the spectra of about 220,000 stars, Cannon set the standard for classifying them.

Pickering instructed his computers to photograph the same patch of sky repeatedly and to note the exact time the glass plates were exposed. He suspected that the brightness of stars varied over time, and he wanted to capture their fluctuations. Indeed, these successive time-lapse images revealed stars whose brightness changed measurably from frame to frame. This discovery was both exciting and puzzling, especially since it was unclear what caused stars to glow in the first place.

It was also uncertain how far away these stars were. In the night sky, stars merely appear as shining dots and shimmering points of light. Measuring the distances between them was a major challenge to astronomy. Stars are born with a wide range of brightnesses, and the image of a star can appear dim either because it is intrinsically faint and nearby or because it is extremely bright but distant. It is impossible to understand a star’s properties without knowing how far away it is.

Henrietta Swan Leavitt, another computer at the observatory, found an unusually large number of variable stars clumped close together in the Small Magellanic Cloud, a nearby galaxy, a bound satellite of our own Milky Way. These stars, called Cepheids, appeared to flicker from maximum to minimum brightness almost daily. Leavitt assumed correctly that all the Cepheids were at the same distance from earth. She discovered a law for computing their intrinsic brightness, derived from how their observable brightness varied and from their distance. Leavitt’s law continues to serve as the method by which cosmic distances are calculated.

Leavitt’s formulation was foundational to modern astronomy and cosmology, allowing scientists to accurately determine how far stars and galaxies are from earth. Many aspects of our current view of the cosmos, such as Edwin Hubble’s findings, in the 1920s, of the expanding universe, rely on Leavitt’s discovery.

The Harvard Observatory also launched the career of Cecilia Payne- Gaposchkin, the first woman to break into academic astronomy. Her remarkable Ph.D. thesis showed that while all stars are nearly identical in their chemical composition, their temperatures vary, and their spectral classification is related to this variation. Her research formed the basis of the theory of stellar evolution, which explains how nuclear reactions in the centers of stars power them and cause them to evolve, producing changes in their color and composition as they age.

The remarkable story Shetterly tells in Hidden Figures, which takes place during World War II, the cold war, the civil rights movement, and the space race, centers on the work of AfricanAmerican female mathematicians at the Langley Memorial Aeronautical Laboratory (now part of NASA). Shetterly’s father had worked at Langley, in Hampton, Virginia, between 1964 and 2004. As a child she knew some of the remarkable women she writes about, but at the time she was not aware of their essential contributions to aerospace science and the American space program. Their work was hidden, partly because it was top secret, and partly because no one bothered to tell their story.

Hastings Historical Society, New York
Antonia Maury, an astronomer who made significant contributions to the classification of stars at the Harvard College Observatory, with a six-inch telescope that she installed in Draper Park, Hastings-on-Hudson, New York, 1920s

White women computers, begrudgingly accepted by male engineers who felt that they weren’t suited to mathematical computation, began working at Langley in 1935, processing data from tests of airflows, friction, and drag around the wings of aircraft in wind tunnels against predictions from models developed by engineers. The pace of this work accelerated rapidly during World War II, with Henry Reid, the head engineer of the National Advisory Committee for Aeronautics (NACA), declaring that the US could attain “victory through airpower.” Every manufacturer that was producing high-performance aircraft for the war sent a working prototype to Langley for rigorous testing.

During the war, Langley ran tests for three shifts a day, six days a week, and a large staff was required to help the engineers graph and analyze results. By the early 1940s, the supply of human computers could no longer keep pace with the urgent need for fast and accurate calculations to process data.

In response to pressure from civil rights activists, including A. Philip Randolph and Bayard Rustin, President Franklin D. Roosevelt issued two executive orders in 1941 to desegregate the military and defense industry as the nation prepared for war. At Langley, the orders helped personnel officer Melvin Butler expand recruiting efforts to include African-American math teachers educated at historically black colleges and universities. Yet these efforts remained constrained by Jim Crow prejudice, and the corps of new computers remained segregated from their white women colleagues.

These talented number-crunchers, who had been given a crash course in engineering physics and the theory of airflows, processed the data produced by the around-the-clock flight simulations. Using slide rules and calculating machines, they modeled results using equations that the engineers supplied. By the war’s end, they had become a vital part of the burgeoning high-technology aircraft industry that would help the US win the space race. Their work helped break the sound barrier, which was once thought impossible, and their calculation of the trajectories of satellites eventually helped propel Americans into space.

Shetterly follows the extraordinary careers of Dorothy Vaughan, Mary Jackson, Katherine Johnson, and Christine Darden. Starting as a computer, Jackson went on to conduct wind tunnel experiments alongside the engineers. Encouraged by her boss, Kaz Czarnecki, she fought for permission to take classes at Hampton High School that were otherwise accessible only to her white counterparts. Having finished her training successfully, Jackson became the first female African- American engineer to work for NACA.

Although Vaughan ran the segregated unit of female African-American mathematicians known as the West Area Computing Pool, she was only given the official title of supervisor after eight years on the job. Brilliant, strategic, and resourceful, Vaughan realized that the computers’ jobs might be threatened by the arrival of the first digital computer at NACA in 1947, and she was one of the first of them to teach herself programming. Vaughan, Jackson, Johnson, and Darden worked hard, supported one another, and forged alliances with open-minded colleagues and superiors. They managed, in Shetterly’s words, to exile “the demons [of discrimination] to a place where they could do no harm.”

The early space missions carried out by NASA, which was founded in 1958, were extremely risky; one major obstacle was that the shape required for spacecraft to attain escape velocity after liftoff made them likely to overheat when they reentered earth’s atmosphere. The success and safety of these missions depended on extremely accurate calculations of a reentry trajectory that would avoid this danger. When the Mercury Friendship 7 mission, piloted by John Glenn in 1962 was returning to earth, its automatic control system failed, forcing him to manually navigate the capsule to touchdown.

It has been little known that Katherine Johnson calculated and graphed Glenn’s reentry trajectory in real time. With her superb grasp of analytic geometry, she accounted for all possible complications and traced the exact path that Glenn needed to follow in order to splash down safely in the Atlantic. It was only after this incredible success that Johnson was allowed to be a coauthor on the reports of her trajectory calculations and her computation of launch windows (the period during which a rocket must be launched in order to reach a specific destination, such as a space station). By the time Darden joined Langley, now part of NASA, in 1962 as a data analyst, she had already been a mathematics professor at Virginia State. Today she is recognized as one of NASA’s preeminent experts on supersonic flight and sonic booms, and she became the first African-American at Langley to be promoted to its senior executive ranks.

Rise of the Rocket Girls by Nathalia Holt examines the professional lives of another group of human computers, the mostly white women who worked at the Jet Propulsion Laboratory (JPL) in Pasadena during World War II. They calculated the mathematical elements of rocket design and launch systems for the first American ballistic missiles. While race was not an obstacle for these women, their skills were recognized only because of the acute labor shortage and their willingness to work for lower wages. In 1958, the JPL came under NASA’s control, and its women computers turned to space exploration, making calculations for the first space probes to the moon and other planets. These women learned to operate the new technology of digital computers, and, unlike most of the members of the West Area Computing Pool at NACA, many were retained as computer programmers and engineers at the JPL.

Accounts of the histories of scientific discovery often center on the epiphanies of brilliant individuals, such as August Kekulé, who saw the structure of benzene in a dream, or James Watson and Francis Crick, who discovered the structure of DNA. The work of these individuals was not isolated and was often built on the labor of many others. For instance, though Watson and Crick could not have solved the structure of DNA had they not seen Rosalind Franklin’s X-ray image of it—the famous “Photo 51”—she did not share their 1962 Nobel Prize for Medicine for this discovery.

Women scholars and feminists such as Evelyn Fox Keller, Sandra Harding, Anne Fausto-Sterling, Ruth Hubbard, Emily Martin, and Londa Schiebinger have criticized such scientific histories and called attention to the important, overlooked work female scientists have done. Their criticisms have also raised more fundamental challenges to our assumptions about how scientific progress works. They suggest that science is advanced less by individuals working in isolation than by many enablers whose contributions often go unrecognized.

Making science more inclusive and equitable requires a sharper understanding of the ways its practice is shaped by assumptions about the capabilities of men and women. We might usefully ask, for instance, whether human computers happened to be women because computing was seen at the time as a skill that didn’t require originality, or because women had lower social status and were willing to be paid lower wages to perform the work. While the books reviewed here emphasize work done by women and scientists of color, they do not directly ask deeper questions about how science is done, who does it, and who reports its achievements.

Thomas Kuhn’s influential book The Structure of Scientific Revolutions (1962) challenged the view of scientific discovery in which progress is generated and accelerated by a particular great scientist. Instead Kuhn argued that new discoveries depend on the shared theoretical beliefs, values, instruments, and techniques of the larger scientific community—what he termed the entire “disciplinary matrix” or “paradigm.”

Kuhn mentions only in passing that social and political circumstances also inform the outcome of scientific debates, but later historians took up his suggestion to reconsider how scientific progress occurs. Feminist scholars like Evelyn Fox Keller identified attitudes toward gender and race as part of these shared values and beliefs in her book Reflections on Gender and Science (1985). She argued that we need to question the way in which histories of science recount who does what, what counts as intellectual activity, and who gets credit for discoveries. “Just as science is not the purely cognitive endeavor we once thought it,” she writes, “neither is it as impersonal as we thought: science is a deeply personal as well as a social activity.”

Although the books by Sobel, Shetterly, and Holt are not polemical, they have an argument: science is not about singular discovery and invention. It is not an activity reserved for male geniuses working on their own. Discovery in almost every scientific field occurs through the collaboration of a large number of experts. This has been the case in genetics (the Human Genome Project), high-energy physics (the discovery of the Higgs boson at the Large Hadron Collider), and space science (the many NASA missions to distant planets).

These books unfold the complex ways in which scientific work in astronomy and space science has been shaped by inclusion and exclusion, power and privilege. They also suggest how the development of those fields between the second half of the nineteenth century and World War II provided new circumstances in which women could participate in research and analysis. Such stories may not seem radical, but that may be their hidden power. These treatments of the past encourage us to create a future in which more and different people—regardless of gender, race, class, or sexual identity—can imagine themselves as participants in new discoveries.