The Philosophical Breakfast Club (38 page)

It is likely that when Clement stopped work on the Difference Engine, Babbage imagined he would hire another machinist and complete the machine. Babbage’s son Henry later estimated that to complete the Difference Engine—with most of its parts already manufactured—would have required only about another £500, which Babbage could have easily
afforded himself.
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But in the end it took over sixteen months to reach a settlement with Clement; only then were the drawings and pieces of the unassembled machine given to Babbage. When it was finally over, Babbage told a correspondent that “I am almost worn out with disgust and annoyance at the whole affair.”
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In the intervening time, he had the leisure to work on his argument against Whewell’s Bridgewater Treatise, and to start thinking of a new, more powerful engine. By the time all the parts and plans were in his possession, Babbage had moved on. Most of the pieces—handcrafted to such maddeningly high standards, at such a high cost—were eventually sold and melted down for scrap, besides some that were kept and assembled into small experimental models.

The feedback mechanism of his own demonstration model of the Difference Engine nudged Babbage’s thinking in a new direction. What if he could invent an engine that would be able to easily calculate these kinds of feedback functions, such as the sine function, in which the higher-order differences could be affected by the lower-order differences or the results column? He thought of this as “the Engine eating its own tail.”
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Could he create an engine that could tabulate any and all functions, using all four arithmetical operations, without needing to approximate them in the form of polynomials that could be calculated using only addition? What if the engine could, moreover, take the results from one calculation, and then “decide” between different further options based on the outcome? Babbage began to make sketches. Soon he would feel that “the whole of arithmetic … appeared within the grasp of mechanism.”
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At around this time, in July 1834, Babbage began a series of “Scribbling Books” that record his growing obsession with a new, more powerful engine. Between the summer of 1834 and the summer of 1836, Babbage invented the world’s first general-purpose computing machine. In the fall of 1834 he hired Charles Godfrey Jarvis, who had previously worked under Clement, as his new machinist, and most of the drawings and plans of the machine are in his hand. Babbage paid Jarvis’s high wages out of his own pocket. Their relationship was untouched by the kind of rancor and mistrust that had characterized Babbage’s dealings with Clement.

It has only been in the past few decades that scholars trying to piece together the progress of Babbage’s thought process have tackled the seven thousand large sheets of the Scribbling Books, some five hundred huge design drawings, each of which takes up a whole desk, and about one thousand miscellaneous sheets of paper covered with his
“notations”—symbolic descriptions of the mechanical flow of the machine’s elements—now held at the Science Museum of London’s storage site on an abandoned airfield in Swindon. But enough is known to say with confidence that Babbage’s Analytical Engine—really a series of engines, each a bit different as his thinking progressed—embodied all the features of today’s digital computers. It had a separate “memory” and a “central processor.” It was capable of “iteration,” the process of repeating a sequence of operations a programmable number of times. It performed conditional branching, in that it could take one action or another depending on the outcome of a prior calculation. It also allowed for the use of multiple processors to speed computation by splitting up the task (this is the basis for modern parallel computing). Babbage designed a number of possible output devices for the Analytical Engine, such as graph plotters and printers.
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Even Babbage, never one to underestimate his own intelligence, was impressed. He wrote to Quetelet, “I am myself astonished at the power I have been enabled to give this machine; a year ago I should not have believed this result possible.”
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Babbage’s first breakthrough was in separating two operations of the machine into two different physical locations: the “Mill,” where the mathematical operations were performed (analogous to today’s central processor), and the “Store,” where the numbers were kept before being brought to the Mill for processing, and where the results of computation would return afterwards (analogous to the memory of today’s computers). Babbage later explained that these terms were “an elegant metaphor from the textile industry, where yarns were brought from the store to the mill where they were woven into fabric, which was then sent back to the store.”
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Babbage had intensively studied the textile industry for the book on political economy he had published in 1832, and he brilliantly brought to bear what he had learned there when beginning to think of his new engine.

The Mill of Babbage’s new machine was a circular mechanism, containing the figure-wheel axes arrayed around a set of large central wheels. The Store was laid out in a straight line, with two rows of figure-wheel axes containing the numbers (each axis had forty figure wheels, in one of Babbage’s conceptions, so that numbers up to forty digits long could be saved there). The numbers from the store were conveyed to and from the Mill by a system of horizontal racks or toothed bars, what a modern expert on the Analytical Engine has called a “memory data bus.”
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The textile industry provided the next of Babbage’s innovations as well, perhaps the most revolutionary one of all. Babbage sought a method to instruct the engine what calculations to perform, on which numbers, and in what order. He first thought of a system of metal cylinders or drums, such as Jacques de Vaucanson had devised for the first automated loom in 1745 (previously, Vaucanson had created the famous “defecating duck,” with its four hundred moving parts). Before automated looms were invented, the creation of a patterned silk textile was extremely complicated. The warp—the lengthwise threads—were held in place on the loom. Two people were required to weave the patterned fabric: a skilled weaver who inserted the wefts—the filling, or side-to-side, threads—and a “draw boy” who had to manually select those warp threads that were to be raised for each pass of the wefts in order to create the desired pattern. In Vaucanson’s loom, a special control box above the loom used a metal cylinder with spokes, like those drums used in music boxes at the time, to raise and lower the warp yarns so that the wefts could be automatically drawn through the warp without the work of a skilled weaver. This could only produce regularly repeating patterns, however, as in damask fabric (in which a raised design appears on a lustrous background).
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In a momentous diary entry, on June 30, 1836, Babbage wrote, “Suggested Jacard’s [
sic
] loom as a substitute for the drums.” Babbage had realized that his purpose could best be served with the use of punch cards such as those devised for a later type of automatic loom by Joseph-Marie Jacquard in 1801—similar in form and function to those used by Herman Hollerith in 1884 for his electric punch-card tabulator, the first computing machine, developed for the company that would later be named the International Business Machines corporation, or IBM. In a sense, Babbage’s thought process, whether intentionally or not, recapitulated the evolution of the automatic loom, going from the metal drum mechanism to a system of punched cards. The Jacquard loom was the first machine to use punch cards to control a sequence of operations, and for this reason has a hallowed spot in the history of computing technology.

The Jacquard loom used a series of cards with tiny holes to dictate the raising and lowering of the warp threads. Rods were linked to wire hooks; each of these hooks could lift one of the threads strung vertically between the wooden frame. In sequence, the cards were pressed up against the end of the rods. If a rod coincided with a hole, then the rod passed through the hole and no action was taken with the thread. If no hole
coincided with the rod, then the card pressed against the rod and this activated a hook that lifted the thread attached to it, allowing the shuttle—which carried the cross-thread—to pass underneath. Series of cards were strung together with wire, ribbon, or tape, and folded into large stacks.

The arrangement of the holes determined the pattern of the weave. Jacquard looms could in this way weave extremely intricate designs fairly quickly, without the need for master artisans to perform the weaving operations (only a loom operator was required; he or she sat inside the frame sequencing the cards one at a time by a foot-pedal or hand-lever). This method could be used not only for repeating patterns, but also for complex and nonrepeating ones; such weavings could require over twenty thousand punched cards with one thousand hole positions per card.
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One famous Jacquard tapestry of the time mimicked a portrait of Jacquard himself; the image so closely resembled an engraving that viewers were shocked to discover it was an image in warp and weft rather than ink on paper. Babbage kept his copy of this tapestry portrait on his wall to remind himself of the origins of his Analytical Engine.
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(Ironically, modern Jacquard looms are controlled by digital computers instead of punch cards—so the circle has gone around: from loom to computer back to loom.)

Babbage devised a system for his Analytical Engine using four different types of cards, each the size of a small brick. Operation cards instructed the engine to add, subtract, multiply, or divide. Variable cards specified from where in the Store the number was to be retrieved, and to where in the Store the result should go. Combinatorial cards were used to get the engine to repeat a sequence of operations a predetermined number of times; to loop back and iterate a set of calculations. And, finally, number cards could be used if desired to save the results, like a kind of overflow memory.
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Babbage knew that slowness in calculation would be a major problem for his device. Once he had grasped the major elements of the Analytical Engine, much of Babbage’s time and energy was spent in trying to devise ways to speed up the calculating process. As he put it, “The whole history of the invention has been a struggle against time.”
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In his last description of the engine, written in 1864, Babbage estimated its speed of calculation as one addition or subtraction per second, and one minute per multiplication of two fifty-digit numbers or division of a one-hundred-digit number by a fifty-digit divisor—extremely fast compared to a human computer,
though extremely slow compared to a modern-day digital computer.
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(ENIAC, the first functional general-purpose digital computer—built in 1946—could perform up to five thousand simple subtractions and additions every second.)

At the start of his efforts, Babbage realized that the successive carry mechanism he had worked out for his Difference Engine, though ingenious in its own way, would be too slow for the very large numbers and long operations of multiplication and division envisioned for the new engine. In that mechanism, the carrying of tens was not performed until the addition of numbers was complete; only then would the arm sweep over the digits to catch on the latches in the warned position, indicating the need for a carry. But for numbers with many digits, that process of sweeping over the digits could take even longer than the addition itself.

In a marathon brainstorming session that took over eleven hours, Babbage worked out the details of what he would call the “anticipating carriage mechanism.” Just as he had argued that God could anticipate, at the moment of the world’s creation, the need for changes in natural laws in the future, Babbage’s new mechanism “anticipated” when a carriage would be needed, and executed all the carriages of all the digits in one operation—not like the successive carry, where the operation was carried out for each digit one at a time. With this mechanism, the time needed for the carriage was the same no matter how many digits were involved, because all the carries were effectuated together.
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The designs for the Analytical Engine called for an enormous machine. The Mill would have been fifteen feet tall and six feet in diameter. The length of the Store would depend on its capacity: to keep one hundred fifty-digit numbers would require a Store twenty feet in length—the size of a steam locomotive in those days! In his notebooks Babbage sometimes wrote of engines with storage capacity of one thousand numbers, which would have entailed a Store over one hundred feet long.
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(We should keep in mind that ENIAC was also huge, weighing thirty tons and taking up 680 square feet—it was eight and a half feet tall by three feet wide by eighty feet long.) Babbage was never afraid of thinking big.

A
S
B
ABBAGE WORKED
on the new machine, he was well aware of the pieces of the Difference Engine gathering dust in his new fireproof storage room. His heart was no longer with that engine; he was spending most of
his waking hours working on the new one. But Babbage felt duty-bound to alert the government to this new development. He wrote to the Duke of Wellington, then foreign secretary in the new Tory government, in December 1834. The tone of the letter is extraordinarily insolent. Babbage rehashed all his old grievances against how he and his invention had been mistreated over the years. He had spent thirteen years of his life on a project for the good of the nation, with nothing to show for it. He told the duke of his new engine, a “totally new engine possessing much more extensive powers.” He did not specifically ask for funding for the new engine, nor did he say whether he intended to continue working on the old one, so it is unclear what he hoped the letter would accomplish.

Babbage waited to hear back from the government. Meanwhile, in May 1835, a parliamentary debate was held on the Civil Contingencies fund, out of which Babbage was paid. As in modern congressional debates about “pork” in the budget, it was charged that some projects amounted to “unprincipled waste and squandering of public money.” Babbage’s project was specifically mentioned as one of those suspect projects. Thomas Spring Rice, the new chancellor of the exchequer (who would later be Whewell’s brother-in-law), defended the Difference Engine. Another member worried that Babbage’s desire to build the best machine with the most accuracy would lead him to successive improvements, on and on, forever, with no end.
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