LITMIR.BIZ

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to the Continent, to “analysis” and the language of differentiation as invented by Newton’s rival and nemesis, Gottfried Wilhelm Leibniz. Fundamentally, there was only one calculus. Newton and Leibniz knew how similar their work was— enough that each accused the other of plagiarism. But they had devised incompatible systems of notation—different languages—and in practice these surface differences mattered more than the underlying sameness. Symbols and operators were what a mathematician had to work with, after all. Babbage, unlike most students, made himself fluent in both— “the dots of Newton, the d’s of Leibnitz”—and felt he had seen the light. “It is always difficult to think and reason in a new language.”

      Indeed, language itself struck him as a fit subject for philosophical study—a subject into which he found himself sidetracked from time to time. Thinking about language, while thinking in language, leads to puzzles and paradoxes. Babbage tried for a while to invent, or construct, a universal language, a symbol system that would be free of local idiosyncrasies and imperfections. He was not the first to try. Leibniz himself had claimed to be on the verge of a characteristica universalis that would give humanity “a new kind of an instrument increasing the powers of reason far more than any optical instrument has ever aided the power of vision.” As philosophers came face to face with the multiplicity of the world’s dialects, they so often saw language not as a perfect vessel for truth but as a leaky sieve. Confusion about the meanings of words led to contradictions. Ambiguities and false metaphors were surely not inherent in the nature of things, but arose from a poor choice of signs. If only one could find a proper mental technology, a true philosophical language! Its symbols, properly chosen, must be universal, transparent, and immutable, Babbage argued. Working systematically, he managed to create a grammar and began to write down a lexicon but ran aground on a problem of storage and retrieval—stopped “by the apparent impossibility of arranging signs in any consecutive order, so as to find, as in a dictionary, the meaning of each when wanted.” Nevertheless he felt that language was a thing a person could invent. Ideally, language should be rationalized, made predictable and mechanical. The gears should mesh.

      Still an undergraduate, he aimed at a new revival of English mathematics—a suitable cause for founding an advocacy group and launching a crusade. He joined with two other promising students, John Herschel and George Peacock, to form what they named the Analytical Society, “for the propagation of d ’s” and against “the heresy of dots,” or as Babbage said, “the Dot-age of the University.” (He was pleased with his own “wicked pun.”) In their campaign to free the calculus from English dotage, Babbage lamented “the cloud of dispute and national acrimony, which has been thrown over its origin.” Never mind if it seemed French. He declared, “We have now to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us.” They were rebels against Newton in the heart of Newton-land. They met over breakfast every Sunday after chapel.

      “Of course we were much ridiculed by the Dons,” Babbage recalled. “It was darkly hinted that we were young infidels, and that no good would come of us.” Yet their evangelism worked: the new methods spread from the bottom up, students learning faster than their teachers. “The brows of many a Cambridge moderator were elevated, half in ire, half in admiration, at the unusual answers which began to appear in examination papers,” wrote Herschel. The dots of Newton faded from the scene, his fluxions replaced by the notation and language of Leibniz.

      Meanwhile Babbage never lacked companions with whom he could quaff wine or play whist for six-penny points. With one set of friends he formed a Ghost Club, dedicated to collecting evidence for and against occult spirits. With another set he founded a club called the Extractors, meant to sort out issues of sanity and insanity according to a set of procedures:

      1 Every member shall communicate his address to the Secretary once in six months.

      2 If this communication is delayed beyond twelve months, it shall be taken for granted that his relatives had shut him up as insane.

      3 Every effort legal and illegal shall be made to get him out of the madhouse [hence the name “Extractors”].

      4 Every candidate for admission as a member shall produce six certificates. Three that he is sane and three others that he is insane.

      But the Analytical Society was serious. It was with no irony, all earnestness, that these mathematical friends, Babbage and Herschel and Peacock, resolved to “do their best to leave the world a wiser place than they found it.” They rented rooms and read papers to one another and published their “Transactions.” And in those rooms, as Babbage nodded over a book of logarithms, one of them interrupted: “Well, Babbage, what are you dreaming about?”

      “I am thinking that all these Tables might be calculated by machinery,” he replied.

      Anyway that was how Babbage reported the conversation fifty years later. Every good invention needs a eureka story, and he had another in reserve. He and Herschel were laboring together to produce a manuscript of logarithm tables for the Cambridge Astronomical Society. These very logarithms had been computed before; logarithms must always be computed and recomputed and compared and mistrusted. No wonder Babbage and Herschel, laboring over their own manuscript at Cambridge, found the work tedious. “I wish to God these calculations had been executed by steam,” cried Babbage, and Herschel replied simply, “It is quite possible.”

      Steam was the driver of all engines, the enabler of industry. If only for these few decades, the word stood for power and force and all that was vigorous and modern. Formerly, water or wind drove the mills, and most of the world’s work still depended on the brawn of people and horses and livestock. But hot steam, generated by burning coal and brought under control by ingenious inventors, had portability and versatility. It replaced muscles everywhere. It became a watchword: people on the go would now “steam up” or “get more steam on” or “blow off steam.” Benjamin Disraeli hailed “your moral steam which can work the world.” Steam became the most powerful transmitter of energy known to humanity.

      It was odd even so that Babbage thought to exert this potent force in a weightless realm—applying steam to thought and arithmetic. Numbers were the grist for his mill. Racks would slide, pinions would turn, and the mind’s work would be done.

It should be done automatically, Babbage declared. What did it mean to call a machine “automatic”? For him it was not just a matter of semantics but a principle for judging a machine’s usefulness. Calculating devices, such as they were, could be divided into two classes: the first requiring human intervention, the second truly self-acting. To decide whether a machine qualified as automatic, he needed to ask a question that would have been simpler if the words input and output had been invented: “Whether, when the numbers on which it is to operate are placed in the instrument, it is capable of arriving at its result by the mere motion of a spring, a descending weight, or any other constant force.” This was a farsighted standard. It eliminated virtually all the devices ever used or conceived as tools for arithmetic—and there had been many, from the beginning of recorded history. Pebbles in bags, knotted strings, and tally sticks of wood or bone served as short-term memory aids. Abacuses and slide rules applied more complex hardware to abstract reckoning. Then, in the seventeenth century, a few mathematicians conceived the first calculating devices worthy of the name machine, for adding and—through repetition of the adding—multiplying. Blaise Pascal made an adding machine in 1642 with a row of revolving disks, one for each decimal digit. Three decades later Leibniz improved on Pascal by using a cylindrical drum with protruding teeth to manage “carrying” from one digit to the next.¹ Fundamentally, however, the prototypes of Pascal and Leibniz remained closer to the abacus—a passive register of memory states—than to a kinetic machine. As Babbage saw, they were not automatic.

      It would not occur to him to use a device for a one-time calculation, no matter how difficult. Machinery excelled at repetition—“intolerable labour and fatiguing monotony.” The demand for computation, he foresaw, would grow as the uses of commerce, industry, and science came together. “I will yet venture to predict, that a time will arrive, when the accumulating labour which arises

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