When Computers Were Human (23 page)

CHAPTER NINE

Captains of Academe

D
URING THE LAST DAYS
of July 1914, in the final hours of peace, the European powers positioned themselves for the impending conflict. Germany prepared to march its army through the supposedly neutral country of Belgium. The French hurried to throw their military might between the advancing troops and Paris. The English, perceiving that they had interests on the Continent, organized an expeditionary force to send into the fray. Karl Pearson, the great admirer of German culture, found himself caught on the European side of the English Channel. He hurried home to London on the first day of the conflict and declared that the needs of his country were more important than his personal ambition or his love of science. “On August 3, 1914,” he wrote, “I at once put the whole Laboratory staff at the service of any [British] Government department that was in need of computing or statistical aid.”
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In 1914, the Biometrics Laboratory employed a staff of ten computers, four men and six women. The military could have utilized all ten. They would have enlisted the men qualified for service and made them navigators and surveyors. The women, and those men who were unfit for military duty, would have been given jobs as clerks or engineering assistants. Pearson argued that the group should remain intact and under his control. “The Laboratory can do far better work nationally as a whole than scattered, as it is trained to work together.”
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At first, he was willing to accept relatively menial assignments for his computers. Beginning that fall, the Biometrics Laboratory “provided weekly some 500 or more graphs showing the state of unemployment of insured and of uninsured trade men and women.” The work required no advanced mathematics and was relatively straightforward, even though it kept the computers on a strict production schedule. “Six and sometimes eight series of these graphs were kept running and carried to date each week,” Pearson reported. The staff worked “without a break through all
the vacations up to July [1915],” balancing the requirements of the statistical reports with the demands of Pearson's biometrical research.
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When the laboratory staff returned from the summer vacation of 1915, Pearson learned that half of his workers were not satisfied with the role that they were playing in the war effort. The conflict still retained its heroic potential, its romantic promise of bold actions and daring deeds. On those days when the wind blew from the southeast, the more alert residents of London could hear the report of cannon and the muffled thud of exploding shells. Three of the male computers had tried to enlist in the army with the hope of serving on the front. All three were rejected by the recruiting office, but each had found a position in industries that were supplying the military. An equal number of female computers had also left the lab, one to serve in a hospital, one to teach, and one to rejoin her family.
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Pearson, conscious that he would have to train and recruit a new staff, decided to temporarily withdraw from war work.

On September 9, the war reached the Biometrics Laboratory. “We are all congratulating ourselves that we have seen a Zeppelin at last,” wrote one of the female computers. The Zeppelin had crossed the sea from Germany and followed railroad tracks into London. “I was coming home in a tram just before 11 PM,” she added, “when the driver called out that there was a Zep.” She got out of the tram and began walking home, keeping an eye on the big, hulking shape in the night sky. “Nobody obeyed the Instructions to seek shelter. We could see the flashes from the anti-aircraft guns but they all went very wide of the mark.” The airship was looking for the Charing Cross railroad station, which was situated on the river Thames, but it dropped a bomb near the university “and nearly every window is smashed and numerous shops were destroyed.” The computer reported that the population seemed to regard the event as an adventure rather than as a threat, claiming that the “whole of London is in a state of subdued excitement.”
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Pearson claimed that he was able to face the bombings with resolution. “I just went about my usual tasks,” he wrote after the war: “I made belief that it was nothing.”
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By December, he felt that his computers were ready to resume war work. This time they created shipping reports, “preparing graphs dealing with the tonnage required for various imports for the use of committees controlling these matters.”
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He reported that the work occupied all of the computers' time, but at least one of his computers was still doing biometric computations. Pearson continued with his statistical research but spent increasing amounts of his time doing analyses for aircraft factories. The aviation industry was only a decade old, and its engineers had much to learn about structure, motion, lift, and drag. Most of the problems undertaken by Pearson involved the flexing of structural parts: propellers, wing struts, airframes. The mathematics of
this analysis was somewhat tricky, but Pearson had studied the subject before he had become interested in mathematical statistics. The work brought him into direct contact with the military and introduced him to the big mathematical problem of the war: the calculation of bomb and shell trajectories, a subject known as mathematical ballistics.
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Mathematical ballistics lay behind the most brutal weapons of the war. It allowed artillery crews to aim their guns at distant targets, mortar crews to lob gas-filled shells from behind the protection of a hill, moving Zeppelins to bomb stationary structures, and defense gunners to destroy invading aircraft. It had a history as old and venerated as the history of mathematical astronomy, and it had a problem every bit as difficult as the three-body problem of Halley's comet: the problem of modeling the atmospheric drag on the flying shell. This problem had been first encountered in the fifteenth-century cannonball experiments of Galileo Galilei (1564–1642). Galileo argued that the air had no effect upon the motion of the balls and concluded that trajectories were graceful parabolas through the sky.
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Newton placed Galileo's analysis on a more formal foundation, but like his predecessor, he assumed that the cannonball was moving
in vacuo
. By the early eighteenth century, scientists had discovered that air resistance had a substantial impact upon ballistics trajectories, and they had also found it to be a complicated phenomenon. As a projectile neared the speed of sound, it created shock waves that dissipated energy and greatly increased the drag. For extremely high velocities, such as those achieved by projectiles as they left the barrel of a gun, the nature of the drag changed again. These variations thwarted any attempt to make a simple calculation of a trajectory. Scientists of the mid-nineteenth century could compute a trajectory only by using methods similar to those that had been used by Alexis Clairaut for Halley's comet. They would track a projectile along an idealized path and adjust its position to account for the drag.
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A clearer understanding of air resistance began to emerge in the 1860s, as military engineers began to amass a large collection of data. The first of this data came from pendulum tests. Gunnery crews would fire a shell at a large pendulum and measure the displacement of the bob. From these measurements, the engineers could determine the velocity of the shells and, ultimately, the atmospheric drag. By 1870, the armies of Prussia, Great Britain, France, Russia, and Italy had all estimated the nature of drag. These estimates took the form of graphs rather than mathematical expressions. No simple expression described the relationship between the velocity of a shell and the drag. The French estimate, usually called the Gâvre function, after the French proving ground, was generally considered to be the most reliable of the time. It was used by an Italian professor,
Francesco Siacci (1839–1907), to create a simple means of computing trajectories.

Siacci was a teacher at the Turin Military Academy and had served briefly as an artillery commander with the army during a brief conflict with Austria.
¹¹
Rather than calculating the entire flight of a shell, he concentrated on four factors: the range of the trajectory, the time of flight, the maximum height of the shell, and the velocity at impact. Each of these quantities could be used by an artillery officer to plan and direct artillery. The time of flight was used for setting fuses so that the shells would explode over the heads of enemy troops rather than in the ground. The maximum height was used for mortar fire over hills and tall buildings. The terminal velocity gave the amount of energy in a shell and suggested the extent of damage it could produce. Rather than compute these values for all guns and all shells, Siacci chose a strategy that resembled Nevil Maskelyne's approach to the lunar distance method of navigation. He prepared a set of mathematical tables that described idealized trajectories and then gave rules for transforming values from these tables into the motion of a real shell. The final results were only approximations of the real trajectory, but they were sufficiently accurate for the cannon of the day, including the old smoothbore cannon that had been used in the American Civil War and the new rifled steel barrels that were being produced by Krupp Industries in Prussia.
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Siacci's ballistics tables were quickly adopted by the armies of the industrialized countries. American officers translated Siacci's original paper into English less than a year after it appeared in Italian.
¹³

Had the First World War been only a duel of large guns across the fields of Flanders, then Siacci's method would have sufficed for most of the ballistics calculations. This method had its flaws, but most of them could be fixed with only a little effort. The biggest corrections would have included a refinement of the atmosphere drag function and the introduction of more detail into the mathematical equations. Ballistics officers were now able to measure the velocity of shells with electrical instruments. Their experiments had shown the need to incorporate new factors into the equations, including the density of the atmosphere and the direction of high-level winds. These changes could be handled without a large, permanent computing staff.
¹⁴
Computers were needed to help with artillery problems that came from the growing use of aircraft. Since Siacci's tables presented only a few points of the trajectory, they could not be used for antiaircraft artillery, for bombing, or for aerial combat. Anti-aircraft defense, a problem that became increasingly important during the war, was like duck hunting. The gunnery crew would fire an explosive shell into the air, hoping that it would explode near an oncoming plane.
To place that shot close to the plane, the gunners needed to know how fast a shell travels along the upward slope of its trajectory, information that was not easily gleaned from Siacci's theory.
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The British army first turned to a Cambridge professor, John Littlewood (1885–1977), for help with ballistics analyses. They gave him a lieutenant's commission and assigned him to work at the Woolwich Arsenal, a military facility located to the east of Greenwich.
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Littlewood was an expert with differential equations and could quickly produce rough approximations of “vertical fire,” the term used by the army for antiaircraft trajectories. When he needed more detailed calculations, he asked for assistance from the faculty and students at Cambridge. Often, he turned to Karl Pearson's former computer Frances Cave-Browne-Cave at Girton College. Professor Cave-Browne-Cave gladly offered to do calculations for Littlewood, but she had many responsibilities and occasionally needed help herself. “We had to ask my Girton sister to come home before she had finished her work on guns,” reported her sister Beatrice, “so I have been checking some of the most urgent of her work for her.”
¹⁷

The calculations for antiaircraft and anti-Zeppelin fire were substantially more complicated than those of the old Siacci theory. Computers needed to produce a complete trajectory, not just the endpoint and the time of flight. They calculated these trajectories using the method of mechanical quadratures, the same method that Andrew Crommelin had used to prepare the ephemeris of Halley's comet. They called their version of this technique “the method of small arcs,” for it divided the full trajectory of a shell into a series of tiny, curved steps. At each step of the calculation, they would advance the shell, estimate how much it had slowed in that interval, and recompute the drag. The process was simpler than computing the orbit of a comet, as the shell was influenced only by air resistance and earth's gravity rather than by the conflicting pulls of the planets. Even with this relative simplicity, the computation of a single trajectory by the method of small arcs still required at least a full day of effort.

By the spring of 1916, the computers of the Biometrics Laboratory, including Beatrice Cave-Browne-Cave, were accepting requests for trajectory calculations directly from the Ministry of Munitions. At first, they gave low priority to the ballistics work. “These [trajectories] you told me to leave till the last as you might not have them done,” Beatrice Cave-Browne-Cave wrote to Pearson; “shall I go on to this now?”
¹⁸
Pearson approved this request, but he was still trying to devote as much time as possible to his statistical research. He asked the computers to clean and measure a collection of skulls that spring, a task that uncovered an infestation of insects.
¹⁹
He also kept at least one of the computers away from
the ballistics calculations. This computer, a Norwegian student, did most of her work outside of the Biometrics Laboratory.
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