The Philosophical Breakfast Club

by Laura J. Snyder

  In 1839, Ada, now Lady Lovelace, desired to return to her mathematical studies; she approached Babbage and asked him to recommend a tutor for her, perhaps hoping that he would take on the job (he would not).73 By the summer of 1840 she had resumed her studies after a four-year hiatus.74 Lovelace’s husband was encouraging, and seemed to agree with her mother that studying math would provide a kind of tranquilizer for her manic tendencies.75

  Lady Byron had the idea of asking Augustus De Morgan—a friend of Whewell’s since De Morgan’s undergraduate years at Trinity College—to tutor her daughter; in a sense it was all in the family, as De Morgan was married to Sophia Frend, the daughter of Lady Byron’s old tutor William Frend. Sophia Frend and Lady Byron had become close friends in childhood. Lady Byron had lent the De Morgans her house, Fordhook, near Acton, for ten weeks in 1838, so De Morgan could finish his Essay on Probabilities without distraction.76

  De Morgan was a first-rate mathematician who had graduated from Cambridge as fourth wrangler. Today he is known as one of the founders of symbolic logic, and the one who formalized rules known as “De Morgan’s laws”: namely, that negating an AND results in an OR and vice versa [that is, not (A and B) = (not A) or (not B), and not (A or B) = (not A) and (not B)]. These laws are widely used today in computer programming. De Morgan is also known, less academically, for composing “The Astronomer’s Drinking Song,” sung at the dinners of the old Mathematical Society, one stanza of which is:

  When Ptolemy, now long ago,

  Believed the earth stood still, sir,

  He never would have blundered so,

  Had he but drunk his fill, sir;

  He’d then have felt it circulate,

  And would have learnt to say, sir,

  The true way to investigate

  Is to drink your bottle a day, sir!

  De Morgan added a footnote to this stanza, explaining that “Dr. Whewell, when I communicated this song to him,” stated his opinion that drinking a bottle of wine a day “was a very good idea, of which too little was made.”77

  De Morgan assigned Lovelace work from textbooks, and met with her about every two or four weeks. She quickly mastered differential and integral calculus (on which topics De Morgan was in the midst of writing a textbook). Lovelace would send him letters when she was having trouble working through problem sets, and needed his assistance.78 The two got on exceedingly well; Lovelace told her mother that “no two people ever suited better,” and that she could never repay De Morgan’s kindness and patience.79 Although De Morgan did occasionally take private pupils because he needed the extra income, it appears that he tutored Lovelace for free; her husband would, on occasion, send De Morgan a gift of game from his estate, which was a sign of social parity and so not embarrassing to either party.80

  Once Lovelace resumed her mathematical studies, she conceived a plan to help bring about the result that Babbage had failed to manage: getting the government to commit to providing the funds for building the Analytical Engine. She wrote to Babbage:

  “I am very anxious to talk to you. I will give you a hint on what. It strikes me that at some future time … my head may be made by you subservient to some of your purposes and plans. If so, if ever I could be worthy or capable of being used by you, my head will be yours. And it is on this that I wish to speak most seriously to you. You have always been a kind and real and most invaluable friend to me; and I would that I could in any way repay it, though I scarcely dare to exalt myself as to hope however humbly, that I can ever be intellectually worthy to attempt serving you.”81

  With her intoxicating blend of flattery and self-regard, Lovelace could not help but be appealing to Babbage—who, after all, had been completely unsuccessful in getting what he wanted for his engines, and so was willing to entertain the grand visions of a young woman. She told him, “I am now studying attentively the Finite Differences … and in this I have more particular interest, because I know it bears directly on some of your business.”82 Lovelace’s plan for how, exactly, to help Babbage was vague. It was only when Menabrea’s article finally appeared in October of 1842 that she had her chance.

  The idea was suggested to her by Charles Wheatstone, a mutual friend of Lovelace’s and Babbage’s. Wheatstone was one of the inventors of the electric telegraph, the electromagnetic clock, the stereoscope (by which two photographs of the same object taken from different points of view are combined to make the object appear to “stand out” in a three-dimensional aspect), and numerous other ingenious devices. Wheatstone recommended that Lovelace turn her talents toward translating the article into English, so that British readers could be introduced to Babbage’s remarkable invention. A whole journal, Scientific Memoirs, was devoted to the publication of translations of foreign scientific papers; her translation would find a natural home there. Lovelace was delighted with the idea, and began work immediately. When she finished the translation, she presented it as a gift to Babbage. He was pleased that the paper would appear in English, but he asked why she had not written an original paper about the engine. “To this Lady Lovelace replied that the thought had not occurred to her,” Babbage recalled later. “I then suggested that she should add some notes to Menabrea’s memoir; an idea which was immediately adopted.”83 Finally, Babbage had a staunch supporter who was willing to do what he himself ought to have done: give the British scientific and political elite a detailed explanation of the workings and the advantages of his invention.

  Between this suggestion and the eventual appearance of the translation, in August 1843, Babbage and Lovelace sent countless letters back and forth between her country estate and Babbage’s house in London. In her letters Lovelace is at times coquettish, at others demanding, at some points lecturing the machine’s inventor about how much better she understands it than does he. Babbage for the most part acquiesces in this treatment from his young friend, calling her “my dear and much admired Interpretress.” She in turn refers to herself as his “Fairy for ever.” Ultimately, Lovelace would think of herself as the “High-Priestess of Babbage’s Engine.”84

  Lovelace added seven “translator’s notes,” from A to G, which together ran three times the length of Menabrea’s original discussion. In these notes Lovelace discussed the working and meaning of the Analytical Engine, in language meant to excite the reader to its potential. Beautifully describing the workings of the punched cards, she wrote that “the Analytical Engine weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves.”85

  There has been vehement debate about Lovelace’s notes, some biographers of Lovelace exalting her to the position of the “first computer programmer” (the U.S. Department of Defense has named its programming language in her honor), some biographers of Babbage considering her little more than Babbage’s secretary, who merely took down his dictation, and who was, to boot, “mad as a hatter.” It is certainly the case that Lovelace had a vastly inflated view of her own abilities. In February 1841 she wrote to her mother about her “scientific Trinity,” her three great gifts that distinguished her from all other mathematicians: intuition, “immense reasoning faculties,” and a “concentrative faculty.” Describing herself almost as a kind of calculating engine, Lovelace wrote, “Now these three powers … are a vast apparatus put into my power by Providence; and it rests with me by a proper course during the next 20 years to make the engine what I please.”86 She confided to Mary Somerville’s son, “I confess to you … that I have on my mind most strongly the impression that Heaven has allotted me some peculiar Intellectual-moral mission to perform.”87

  Yet Lovelace did seem to possess mathematical skills beyond what nearly any woman, and many men, of her day possessed. De Morgan expressed candidly his views of Lovelace’s abilities to her mother: her aptitude for mathematics was “so utterly out of the common way for any beginner, man or woman,” he noted. Any young man about to go to Cambridge, having shown such talent, would have been prophesied by De Morgan to be “an original mathematical investi
gator, perhaps of first-rate eminence.” He even compared her natural talents favorably to those of Mary Somerville, thirty-five years her elder, whose acclaimed book on Laplace’s mathematics and mechanics was already a classic.88

  Whatever Lovelace’s mathematical talents, her translation and notes did mark an important moment in the history of computing. Besides introducing English readers, for the only time during Babbage’s life, to the workings and importance of the Analytical Engine, Lovelace indisputably made two important contributions to computer science. In the last note, Lovelace included a method for calculating Bernoulli numbers with the engine—the first computer program, as we would call it. Bernoulli numbers are a sequence of numbers in which each is determined by the numbers that come before. The sequence of Bernoulli numbers can be calculated recursively, in the sense that a number in the sequence can be calculated using the ones that come before it. However, unlike other types of number sequences that can be recursively calculated, the Bernoulli numbers require that all the preceding numbers be used in order to obtain the value of the next one. So, for example, to get the 1,000th number in the sequence, one needs to perform a calculation using the previous 999 numbers. (This is unlike, say, the Fibonacci numbers, where only the two preceding numbers are needed.)

  A human computer can make this calculation, but obviously he or she would require a great deal of time to do so. Babbage’s Analytical Engine, with its capacity to store so many numbers, and its ability to make recursive calculations, would be able to compute even the 1,000th number in the Bernoulli sequence with relative ease. Indeed, this ability is precisely what distinguished the Analytical Engine from the Difference Engine. Lovelace, who suggested to Babbage that she include a method for calculating the Bernoulli numbers in her notes, was right that it was an excellent example for illustrating the power and novelty of the Analytical Engine.89 On Lovelace’s direction, Babbage wrote the method for “programming” the machine to perform this calculation. Lovelace found an error in his first attempt, and sent it back to him for revision. While there is some exaggeration in calling Ada Lovelace the first computer programmer, it is fair to say she was responsible for the creation of the program and its inclusion in her notes.

  Even more important, Lovelace recognized that the machine was capable of manipulating symbols of all kinds, not only numbers. In some ways this recognition can be said to mark the shift from understanding computing machines as calculators to seeing them as truly modern computers. As even Babbage had not done, Lovelace realized that in the future a machine like the Analytical Engine could have the capability to write music, with musical notes being another kind of symbol that could be manipulated by the mechanism:

  “Many persons … imagine that because the business of the Engine is to give its results in numerical notation the nature of its processes must consequently be arithmetical and numerical, rather than algebraic and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraic notation, were provisions made accordingly.”90

  Babbage himself never expressed the workings of his Analytical Engine in such a way. It was Lovelace’s vision of a computer, rather than Babbage’s, that would be formalized by Alan Turing in the 1930s: the notion of a computer as a general-purpose symbol manipulator rather than as a number cruncher.91

  Lovelace appended only her initials, AAL, to the notes, because it was unseemly for a lady of her social rank to have written something scientific. But word soon got out that this work was by a woman, and this undoubtedly influenced the reception of it. The next year, when a work endorsing evolution called Vestiges on the Natural History of Creation was published anonymously, Whewell’s friend Sedgwick would review the “beastly book” harshly, sneering that “it seems to have been written with the science gleaned at a ladies’ boarding school.” Although Sedgwick was a great favorite with the ladies, he still felt that the greatest insult he could make of the book was to suggest it was written by a woman. Indeed, he thought that Ada Lovelace might have written it. Babbage wondered as well; he recommended to Lord Lovelace that his wife read the Vestiges, “if she had not written it!”92

  Whewell’s friend Richard Sheepshanks scoffed that Babbage was too lazy to write about his own machine and had left it to a foreign mathematician and an English countess to do it for him.93 Babbage had been feuding with Sheepshanks for decades over an observatory that had been built for Babbage and Herschel’s friend Sir James South—the expenses had overrun the original estimate, and South refused to pay the difference to the instrument maker, who was a good friend of Sheepshanks. So Sheepshanks was inclined to denigrate Babbage at any opportunity. But his comment does raise a crucial question: Why did Babbage himself refuse to publish anything on the Analytical Engine? Babbage gave an answer to this question in a letter to one of his Italian colleagues. “The discovery of the Analytical Engine is so much in advance of my own country, and I fear even of the age,” Babbage explained, “that it is very important for its success that the fact should not rest upon my unsupported testimony.”94

  BY THE TIME Ada Lovelace’s translation of and notes to Menabrea’s report appeared, it was effectively too late—all hopes of building the Analytical Engine with support from the British government had already been definitively squelched. Babbage had suspected as much already in 1839, when he wrote (in a draft of a letter to Arago), “It is very improbable that I shall ever possess the pecuniary means to undertake [the engine’s] execution. I have spent many thousands of my private fortune on this pursuit, and when the drawings are completed, the invention can never be lost.”95

  Babbage was prepared to give Britain another chance. In January of 1842, while nervously awaiting the report of the Turin meeting, Babbage wrote to Robert Peel to reopen the question of funding for the Difference Engine, which he had ceased working on nine years earlier. Did he have any continued obligation to the project? he asked the Prime Minister. Peel ignored the letter, and three more sent from Babbage by October. Finally, Peel realized he would have to deal with this issue. He sought advice from the geologist William Buckland, who sometimes counseled him on scientific issues. “What shall we do to get rid of Mr. Babbage and his calculating machine?” Peel asked him plaintively.96

  Buckland’s response no longer exists. Finally, Peel deputed his chancellor of the exchequer, Henry Goulburn, to find out what the scientific community really thought of the invention. Goulburn wanted the opinion of Herschel, still considered one of the leading men of science in Britain; however, perhaps knowing of the close relationship between Herschel and Babbage, Goulburn asked G. B. Airy to act as an intermediary, telling him he could give his own opinion of the machine as well.

  Herschel’s response is not surprising. He wrote a long, detailed document, stating the benefits of the machine, while at the same time expressing concerns about the vast sums of money that had already been spent. Airy, on the other hand, offered a very damning assessment of Babbage’s invention. He pointed out that nepotism had besmirched the previous Royal Society committees. And he concluded by stating “without the least hesitation that I believe the machine to be useless, and that the sooner it is abandoned, the better it will be for all parties.”97

  Airy had been against the engine all along; now was his chance to scuttle it, and he succeeded. On November 3, 1842, just weeks after the appearance of Menabrea’s report, Goulburn wrote to Babbage, killing the project, telling him (a bit cruelly) that he could keep the demonstration model and the parts in exchange for his labors. Babbage refused to keep the demonstration model; it was later displayed at the gallery of scientific instruments at King’s College on the Strand, and eventually ended up at the Science Museum in Kensington.98 Babbage sent a reply to Peel asking if, instead, the government would like to fund his Analytical Engine. “I infer however both from the regret with which you have arrived at the conclusion … that you
would much more willingly assist at the creation of the Analytical Engine,” Babbage concluded, oddly optimistically. He was certain—he added with the hint of a threat—that Peel would not like to be the “cause of its total suppression or possibly of its first appearance in a foreign land.”99 Babbage asked for a personal meeting with the prime minister, which was offered on the following week.

  On November 11, 1842, Babbage strode into the prime minister’s office with a vengeance. He launched into a tale of woe: he had given up following his father into a lucrative banking career to devote himself to science, for the sake of his country. He had devoted twelve years of his life to an invention that could revolutionize science; building the Difference Engine ceased because of its machinist, not through any fault of Babbage’s own. He was then forced to rethink his design, and in the process invented an even more revolutionary machine. If the government refused to build this one, they should at least reward Babbage with money or honors like those that other men of science had received.

  We can almost imagine Babbage in high dudgeon, going over his prepared speech. Herschel had been knighted and created a baronet. Whewell had an income of £2,000 in his new position as Master of Trinity College. Airy, as Astronomer Royal, had a house and £1,500. Peacock, as Dean of Ely, had £1,800 a year; Sedgwick, as Dean of Norwich, had £1,000. Only Babbage, who had devoted his entire life to the scientific welfare of the nation, had received nothing. “I then concluded with stating that on those grounds I had some claim to the consideration of the government,” Babbage later recalled. “Sir R.P. denied altogether that either of these claims entitled me to any thing. He observed that I had rendered the Difference Engine useless by inventing a better.… I said that the general fact of machinery being superseded in several of our great branches of manufacturers after a few years was perfectly well known.”