From *The Innovators*, by Walter Isaacson, lol 474-491:

Babbage knew of the devices of Pascal and Leibniz, but he was trying to do something more complex. He wanted to construct a mechanical method for tabulating logarithms, sines, cosines, and tangents. To do so, he adapted an idea that the French mathematician Gaspard de Prony came up with in the 1790s. In order to create logarithm and trigonometry tables, de Prony broke down the operations into very simple steps that involved only addition and subtraction. Then he provided easy instructions so that scores of human laborers, who knew little math, could perform these simple tasks and pass along their answers to the next set of laborers. In other words, he created an assembly line, the great industrial- age innovation that was memorably analyzed by Adam Smith in his description of the division of labor in a pin- making factory. After a trip to Paris in which he heard of de Prony’s method, Babbage wrote, “I conceived all of a sudden the idea of applying the same method to the immense work with which I had been burdened, and to manufacture logarithms as one manufactures pins.”

Even complex mathematical tasks, Babbage realized, could be broken into steps that came down to calculating “finite differences” through simple adding and subtracting. For example, in order to make a table of squares— 1 2 , 2 2 , 3 2 , 4 2 , and so on— you could list the initial numbers in such a sequence: 1, 4, 9, 16. . . . This would be column A. Beside it, in column B, you could figure out the differences between each of these numbers, in this case 3, 5, 7, 9. . . . Column C would list the difference between each of column B’s numbers, which is 2, 2, 2, 2. . . . Once the process was thus simplified, it could be reversed and the tasks parceled out to untutored laborers. One would be in charge of adding 2 to the last number in column B, and then would hand that result to another person, who would add that result to the last number in column A, thus generating the next number in the sequence of squares.

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