David Alan Grier

“The structure of de Prony’s computing office cannot be easily seen in Smith’s example. His computing staff had two distinct classes of workers. The larger of these was a staff of nearly ninety computers. These workers were quite different from Smith’s pin makers or even from the computers at the British Nautical Almanac and the Connaissance des Temps. Many of de Prony’s computers were former servants or wig dressers, who had lost their jobs when the Revolution rendered the elegant styles of Louis XVI unfashionable or even treasonous.35 They were not trained in mathematics and held no special interest in science. De Prony reported that most of them “had no knowledge of arithmetic beyond the two first rules [of addition and subtraction].”36 They were little different from manual workers and could not discern whether they were computing trigonometric functions, logarithms, or the orbit of Halley’s comet. One labor historian has described them as intellectual machines, “grasping and releasing a single piece of ‘data’ over and over again.”37 The second class of workers prepared instructions for the computation and oversaw the actual calculations. De Prony had no special title for this group of workers, but subsequent computing organizations came to use the term “planning committee” or merely “planners,” as they were the ones who actually planned the calculations. There were eight planners in de Prony’s organization. Most of them were experienced computers who had worked for either the Bureau du Cadastre or the Paris Observatory. A few had made interesting contributions to mathematical theory, but the majority had dealt only with the problems of practical mathematics.38 They took the basic equations for the trigonometric functions and reduced them to the fundamental operations of addition and subtraction. From this reduction, they prepared worksheets for the computers. Unlike Nevil Maskelyne’s worksheets, which gave general equations to the computers, these sheets identified every operation of the calculation and left nothing for the workers to interpret. Each step of the calculation was followed by a blank space for the computers to fill with a number. Each table required hundreds of these sheets, all identical except for a single unique starting value at the top of the page. Once the computers had completed their sheets, they returned their results to the planners. The planners assembled the tables and checked the final values. The task of checking the results was a substantial burden in itself. The group did not double-compute, as that would have obviously doubled the workload. Instead the planners checked the final values by taking differences between adjacent values in order to identify miscalculated numbers. This procedure, known as “differencing,” was an important innovation for human computers. As one observer noted, differencing removed the “necessity of repeating, or even of examining, the whole of the work done by the [computing] section.”39 The entire operation was overseen by a handful of accomplished scientists, who “had little or nothing to do with the actual numerical work.” This group included some of France’s most accomplished mathematicians, such as Adrien-Marie Legendre (1752–1833) and Lazare-Nicolas-Marguerite Carnot (1753–1823).40 These scientists researched the appropriate formulas for the calculations and identified potential problems. Each formula was an approximation, as no trigonometric function can be written as an exact combination of additions and subtractions. The mathematicians analyzed the quality of the approximations and verified that all the formulas produced values adequately close to the true values of the trigonometric functions.”
― David Alan Grier, When Computers Were Human