When Computers Were Human (5 page)

In the most charitable light, Clairaut had improved Halley's work by a factor of ten. By the time Halley had completed his research, he had recognized that the comet had a variation in its return of approximately two years, about 600 days. Clairaut's calculation missed the actual date of return by 33 days. As he might have undershot the date of perihelion by an equal amount, the rough accuracy of his calculations was twice 33, or 66 days. Beyond the simple accuracy of his result, Clairaut's more important innovation was the division of mathematical labor, the recognition that a long computation could be split into pieces that could be done in parallel by different individuals. In spite of d'Alembert's criticism, the astronomers of the mid-eighteenth century recognized that Clairaut's division of labor was an important contribution to astronomical practice.
⁴⁰
Clairaut never undertook another calculation of equal complexity, but his two assistants, Joseph Lalande and Nicole-Reine Lepaute, were involved with computation for the rest of their careers. In 1759, Lalande became the director of the
Connaissance des Temps
, an astronomical almanac published by the Académie des Sciences, and he appointed Nicole-Reine Lepaute as his assistant. The two of them prepared tables for the
Connaissance des Temps
that predicted the positions of the stars, the sun, the moon, and the planets. These tables were easier to calculate than the orbit of Halley's comet, as they were based on a long history of data and as they could be corrected from observations taken throughout the year. Likewise, the division of labor for these calculations was simpler than it had been for Halley's comet. Lalande prepared the computing plans and checked the results, while Lepaute calculated the values for the tables.

Lalande called Lepaute his “assistant without equal,”
⁴¹
but of course, she was anything but equal to him. Lalande was able to advance from his position and would eventually be appointed a professor of astronomy and director of the Paris Observatory. Lepaute had no such opportunities and would spend fifteen years as a computer for the
Connaissance des Temps
. However, even with its limitations, the appointment to the
Connaissance des Temps
had certain advantages for Lepaute. It gave her an official standing among French scientists, a rare accomplishment for a woman. During her fifteen-year career, she found that she could occasionally do some astronomical work outside of the
Connaissance des Temps
. In 1764, she published a map under her own name that predicted the extent and duration of an upcoming solar eclipse. She was apparently quite proud of that work, for she asked that it be included in a portrait that she gave to Lalande.
⁴²

“No scientific discovery is named after its original discoverer,” wrote
the historian Stephen Stigler.
⁴³
Even if Clairaut, Lalande, and Lepaute were the first astronomers to divide the labor of scientific calculation, their names did not travel with their contribution. Others would rediscover the idea without knowing of Halley's comet or the computations that were done at a table in the Palais Luxembourg. Still, the work of those three scientists during the summer and fall of 1757 identified a pattern that touched three or four generations of human computers, a pattern that divided calculations into independent pieces, assembled the results from each piece into a final product, and checked that result for errors.

CHAPTER TWO

The Children of Adam Smith

“T
HE SUPERIOR GENIUS
and sagacity of Sir Isaac Newton,” wrote the philosopher Adam Smith, “made the most happy, and, we may now say, the greatest and most admirable improvement that was ever made in philosophy.” Smith turned his generous praise on Newton's calculus and stated that new discoveries would come from “more laborious and accurate calculations from these principles.”
¹
At least one scholar has found Smith's praise insincere and has suggested that the philosopher distrusted any science that rested “primarily upon mathematics, rather than easily visualized phenomena, common to the mind of all men.”
²
Smith was more interested in things of earth than in things of heaven, the movement of goods and services rather than the cycles of planets and comets. At the time of the 1758 return, he was collecting the material that formed the basis for his book
An Inquiry into the Nature and Causes of the Wealth of Nations
. In this work, he sought a fixed principle that explained economic behavior as well as Newton's gravity explained celestial motion. He found this principle in the marketplace, “the propensity to truck, barter, and exchange one thing for another,” though he was not certain that the rules of the market equaled those of celestial motion. “Whether this propensity be one of those original principles in human nature,” he speculated, “or whether, as seems more probable, it be the necessary consequence of the faculties of reason and speech, it belongs not to our present subject to inquire. It is common to all men, and is to be found in no other race of animals.”
³

Smith claimed that the market encouraged people to specialize, to produce those goods that gained them the most profit. Butchers did not make shoes, nor did cobblers slaughter their own animals. This specialization was one part of a more general idea that Smith identified as the division of labor. “The greatest improvements in the productive powers of labour,” he wrote, “seem to have been the effects of the division of labour.” He claimed that there were three benefits to be gained from such division. First, it led to the “increase of dexterity in every particular
workman.” Laborers could focus on a small number of tasks and thus gain skill and efficiency. Second, divided labor made workers more productive by reducing “the time which is commonly lost in passing from one species of work to another.” Finally, the division of labor encouraged workers to improve their tools, to invent “a great number of machines which facilitate and abridge labour, and enable one man to do the work of many.”
⁴

Later generations would explore Smith's market principles and divided labor with the calculus of Isaac Newton. Smith was content to simply describe how his laws touched different aspects of economic behavior. He claimed that his ideas applied equally to manufacture and to “natural philosophy,” the term he used to describe scientific research. The “subdivision of employment in philosophy,” he wrote, “improves dexterity, and saves time.” Smith conceded that philosophers might not be motivated by the traditional economic forces of profit and loss, yet he argued that they desired to extract the greatest results from their limited resources, so that “more work is done upon the whole, and the quantity of science is considerably increased by it.”
⁵
The work of Alexis Clairaut, Nicole-Reine Lepaute, and Joseph Lalande was an early example of this observation. Without the division of labor, Clairaut could not have completed the calculations before the comet's reappearance and could not have devoted so much effort to checking the results.

At the time that Adam Smith was writing
The Wealth of Nations
, the British Admiralty, the executive office of the English navy, was organizing a new computing office and taking a further step in the division of labor. The Admiralty created this office in order to produce a nautical almanac, a volume of tables that gave the position of the sun and the moon, the planets and the stars. The founder of this office was the new Astronomer Royal, Nevil Maskelyne (1732–1811). Maskelyne was the successor, twice removed, of Edmund Halley, the fifth scientist to oversee the Royal Observatory at Greenwich. This appointment was not purely a scientific honor, as it carried a practical responsibility for the country's fleet of naval and merchant ships. Anyone who accepted the king's warrant for astronomy was required to develop methods of celestial navigation, particularly techniques for the “finding out of the longitude of places.”
⁶
As if to emphasize this charge, the Greenwich Observatory sat on the high bank of the River Thames in the midst of a royal estate. From his desk, Maskelyne could view the ocean traffic as it moved between the London docks and the open waters of the North Sea.

The
Nautical Almanac
was the outgrowth of a competition between two methods for finding longitude, one computational and the other mechanical. The two methods were nearly identical and differed only on a
single point: the means of determining the time at Greenwich. The time at Greenwich was important because it allowed a navigator to compare two observations of a single star. The first measurement would be taken by the navigator in the dim moments before dawn or in the dusky hour of twilight, when the thin line of the horizon was visible from the ship and at least a few bright stars could be seen in the violet sky. After determining the position of a star, the navigator would turn to a nautical almanac and find the position of the same star as it would be viewed at the identical moment from the observatory at Greenwich. The difference between these two positions, properly adjusted with a dozen steps of calculation, was the longitude of the ship.

In the 1760s, there were two possible ways of determining the time at Greenwich, both with advantages and drawbacks. The simpler way used a mechanical clock set to the time at Greenwich. This solution was problematic, as no common clock could guarantee sufficient precision under shipboard conditions. The roll of the waves disrupted pendulums. Variations in heat and humidity caused springs to expand and contract. A good clock might lose or gain four minutes a day, enough time to allow the earth to spin a full degree in its rotation. In the middle latitudes, a four-minute error could translate into a deviation of fifty miles. A navigator relying on such a clock could easily calculate a longitude that placed his ship at a safe distance from the shore when, in fact, the vessel was about to strike coastal rocks. In the early 1760s, English inventors strove to develop a precision clock that could record the time accurately under shipboard conditions. Of the timekeeping devices presented to the British Admiralty, one created by John Harrison (1693–1776) was the most promising.
⁷

The second approach to determining the time at Greenwich used the moon as a timekeeper. This technique was known as the lunar distance method. The moon moves twelve degrees across the sky each night, passing neighboring stars as if they were marks on a watch dial. That motion is enough to allow a skilled navigator to compute the time at Greenwich with sufficient accuracy, though the calculations are admittedly lengthy and require a special table that predicts the moon's position. The lunar distance method had been developed in the early eighteenth century but had been dismissed by most navigators because of the difficulties in predicting the position of the moon. Like the calculation of the perihelion for Halley's comet, the prediction of lunar position required the solution of a three-body problem. In this case, the three-body system involved the moon, the earth, and the sun. An acceptable solution to this particular system appeared only in the late 1750s, when the German astronomer Tobias Mayer (1723–1762) published a detailed table of lunar positions.
⁸
Astronomers praised Mayer's work as “the most admirable masterpiece
in theoretical astronomy,” and in 1761, the
Connaissance des Temps
published an article that showed how Mayer's tables could be used in navigation.
⁹

In popular accounts of the competition between Harrison's clock and the lunar distance method, Nevil Maskelyne has been portrayed as a villain, a powerful scientist who undercut a valid technology for personal reasons. His alleged villainy came when he was asked by the British Admiralty to compare Harrison's clock with the lunar distance method. Some writers have charged that Maskelyne was a prejudiced evaluator of the two techniques because he had publicly stated his admiration of Mayer's lunar tables before the trial began and was known to favor the techniques of astronomical calculation.
¹⁰
His conclusions from a test voyage certainly confirmed his opinion that the lunar distance method was a practicable means of determining longitude, and he dismissed Harrison's clock.
¹¹
From a modern perspective, precision clocks, now called chronometers, clearly provide the easiest way of determining the time at Greenwich, but such a conclusion may not have been so clear in the 1760s. The historian Mary Croarken has noted that Harrison's clock was an immature technology and was “much too expensive to be taken to sea by the majority of [English] navigators.”
¹²

On the trial voyage from England to Barbados and back, Maskelyne had required four hours to make a single computation of longitude with the lunar distance method.
¹³
“It is rather to be wished,” he wrote, “that such parts of the computations as conveniently can, were made previously at land by capable persons.”
¹⁴
Those parts of the computations that could be done in advance took the form of a set of tables that gave the distance from the moon to easily recognizable stars in a simplified form. These tables needed to be prepared and published annually, as the position of the moon varied from year to year. With such tables, a navigator could compute the time at Greenwich with a handful of operations and determine a ship's longitude with only thirty minutes of work.
¹⁵
Maskelyne wanted to include these tables as part of a general nautical almanac, as such values could be used for purposes beyond the problem of finding the time at Greenwich. They could even be used to check the settings of a chronometer in the middle of the ocean or guide a ship back to land should the chronometer fail.