For two centuries they were the blue collar workers of science, mental laborers who could grind out logarithms as efficiently as other factory workers turned out pins. A large percentage of them were women. Though male scientists deemed creative mathematics beyond feminine abilities, they saw women as perfect for this kind of numerical needlework. One even measured computing time in "girl hours": A complex calculation might even require "kilo-girl-hours."
In "When Computers Were Human," David Alan Grier tells the tale of these human drudges of mathematical calculation. They came in with the 18th-century Industrial Revolution and quickly disappeared in the mid-20th as electronic computers proved to be faster and, eventually, more reliable.
Most of the human computers left no record of their personal lives. They didn't think they were doing anything remarkable as they calculated using ink and paper and, later on, early mechanical computing machines like the Felt & Tarrant Comptometer or the Burroughs Arithometer.
One of the earliest human computers was Nicole-Reine Lepaute, the wife of France's royal clockmaker. In the 1750s, teamed with two male colleagues, she did some fancy figuring to predict the return of Halley's Comet in 1758 after a 76-year absence. The team's estimate was off by just over a month.
A few computers were innovators. In the early 20th century, Mary Clem, a woman with only a high school education working at the Iowa State Statistical Lab, developed her own system of "zero checks" for detecting errors in calculations.
Foreshadowing today's networked computers, human computers learned to divide up complex tasks. They cross-checked and doublechecked to winnow out errors.
A supervising computer, called the comparator, checked the work and searched for discrepancies.
By 1940, the Mathematical Tables Project, a giant effort funded by the Works Progress Administration, still employed more than 300 human computers, half of them using paper and pencil. But in 1952, IBM began selling its Model 701 electronic computer. By the 1960s, nearly all the number-crunching was being done by machines.
Grier has a knack for making elaborate scientific concepts understandable. His opening device, in which he tries to discover why his grandmother told him proudly that she took calculus in college in 1921, lends a human note.
Yet even a thorough historian like Grier somehow missed the amazing story of Henrietta Swan Leavitt. Fortunately, George Johnson has filled in the gap in his compelling "Miss Leavitt's Stars."
The daughter of a Congregational minister and a graduate of Radcliffe College, Leavitt took a job as a computer at the Harvard University Observatory in the 1880s. Her task was to compare glass photographic plates of the Magellanic Clouds to detect tiny differences in the brightness of the stars.
"We know them now as neighboring galaxies, companions to our Milky Way," Johnson writes. "Back then no one was quite sure what they were. Hunched over the plates in an observatory workroom, Miss Leavitt found the pattern that eventually led to the answer. She discovered a way to measure beyond the galaxy and begin to map the universe."
A star's brightness might be the function of its magnitude or its distance from earth: Stars that had similar apparent magnitudes could be vastly different distances away. But Leavitt had also noticed that "variable" stars gave off pulses of light and that a star's true brightness could be measured by the speed of its pulses. Brighter stars blinked more slowly. Compare that with the star's apparent brightness, and you could estimate how far away it was.
Male astronomers were impressed. "What a variable star 'fiend' Miss Leavitt is - One can't keep up with the roll of the new discoveries," a Princeton astronomer wrote in a letter to her boss.
Though she was commended for her good work, Miss Leavitt earned no promotion, no privilege to pursue her own research. She quietly continued computing, remaining single and living the life of a proper Bostonian. Her feelings about her important discovery remain a mystery, Johnson says. She left no journals or letters. Other women computers who did leave written accounts sometimes expressed frustration that they weren't allowed to explore the deeper implications of what they found.
Not all human computers were women, of course. Some were men, mostly young and in search of a steady job. The work was temporary; they were mathematical clerks, not scientists.
But a few, such as Miss Leavitt, looked up to the stars and made human computing into something much more.
• Gregory M. Lamb is on the Monitor staff.