Ada's Algorithm Read online

  In his autobiography, Babbage says:

  In 1840 I received from my friend M Plana a letter pressing me strongly to visit Turin at the then approaching meeting of Italian philosophers. M. Plana stated that he had enquired anxiously of many of my countrymen about the power and mechanism of the Analytical Engine. He remarked that from all the information he could collect the case seemed to stand thus: ‘Hitherto the legislative department of our analysis has been all-powerful – the executive all feeble. Your engine seems to give us the same control over the executive which we have hitherto only possessed over the legislative department.’

  Considering the exceedingly limited information which could have reached my friend respecting the Analytical Engine, I was equally surprised and delighted at this exact prevision of its powers.

  Plana’s comment in effect amounted to a recognition that the Analytical Engine might be able to solve the long-standing problem of the lack of processing power to evaluate complex mathematical formulae. It was an extraordinarily far-sighted observation, and it is hardly surprising that Babbage was so thrilled at Plana’s perceptiveness.

  The German Romantic poet and philosopher Novalis once remarked: ‘It is certain my conviction gains infinitely, the moment another soul will believe in it.’ This could be a motto for all of Babbage’s life; it explains much of his behaviour, especially during the long and often lonely years when he was working on his cogwheel computers. With no efficient working version of a Difference Engine or Analytical Engine to show the world, he was obliged to seek what seemed the next-best thing; the society of those who seemed to understand what he was trying to do. The fact that he was prepared to travel all the way to Italy – a far from easy journey in 1840, even for a man of Babbage’s financial resources and energy – suggests how cut off from empathy and support at home he perceived himself to be.

  Very possibly he was also influenced in his decision to make the journey by the fact that the journey to Turin offered Babbage an ideal opportunity to visit Lyons on the way, and find out more about Joseph-Marie Jacquard.

  Ada herself knew all about the Jacquard loom when she was still a young woman. As we’ve seen, Ada and Lady Byron saw the Jacquard loom in operation during their tour of the factories of the north of England in 1834.

  The idea of the Analytical Engine as a kind of Jacquard loom that wove calculations had a deep and persisting appeal for Ada. When we look carefully at Babbage’s writing style compared with Ada’s, we are driven to the conclusion that he saw the world, and mechanisms, in a much more literal, factual and – indeed – analytical way than she did. For Ada, inventing metaphors for understanding science was second nature. Babbage hardly ever did this.

  But the real point – and this explains why Ada’s contribution to the idea of the Analytical Engine is so important – is that the brilliance of the conception of the Analytical Engine requires both a scientific and emotive perception if it is to be fully understood and expressed. For Ada, Jacquard’s loom was a conceptual gateway for developing that emotional understanding.

  Babbage returned to Britain in September 1840. Temporarily exhilarated by his visit to Turin, where he had been received as an eminent international scientist and inventor, he had to confront the depressing truth that it was increasingly unlikely he would ever be able to afford to build the Analytical Engine. He knew that his own financial resources, considerable as they were, would be nowhere near enough for the task. Yet somehow he continued to apply himself with energy and dedication to his great object.

  He was sustained by two hopes.

  Firstly, he thought it reasonably likely that one of the Italian scientists whom he had recently visited might write a lengthy and detailed paper on the new project. Babbage hoped that such a paper would affirm the importance of the invention and give him leverage with the British Government who had so generously supported him with the construction of the Difference Engine. He had a curious habit of trying to win influence by these rather indirect means instead of honing his diplomatic skills and adopting a more direct, and possibly more successful, approach.

  His host in Turin, Giovanni Plana, had indicated that he himself was not in sufficiently good health enough to undertake the job, but Luigi Federico Menabrea, a talented young mathematician whom Plana had introduced to Babbage in Turin, appeared interested in carrying it out. Babbage remained in touch with Menabrea and supplied him with comprehensive information about the Analytical Engine. It was this connection with Menabrea that was soon to lead to the involvement of Ada Lovelace.

  Babbage’s second cause for optimism, however tenuous, was that the Government might, after all, have a spontaneous change of heart and make new funding available to him. This was something he intended to advance. It may well be that in his mind the idea had formed that Ada’s involvement could in some way help his indirect campaign to spread the word about his new engine.

  Babbage no longer had the portrait of Jacquard he had bought in Lyons, but he still had the portrait Arago had obtained for him, and Babbage made excellent use of it both as a fascinating object of scientific display, and also as a conversation piece.

  If you wanted to be part of the scientific and literary set in the London of the 1840s, you would have done just about anything to beg, steal or borrow an invitation to one of Babbage’s soirées.

  Babbage had moved to Dorset Street in 1828 after the death of his wife. For the first few years, his parties there were private functions for family and close friends. But in the early 1830s, as he needed influential allies, he broadened the list of guests to include many of the leading luminaries of British intellectual life.

  During the next decade his social gatherings became renowned throughout the capital. They frequently lasted until well after midnight, under the glow of thousands of candles. Three hundred guests, or even more, might attend. Invitations were so prized that even some of the most famous people in London used to write begging letters to Babbage to try to secure an invitation for themselves, their family or friends.

  By this time the soirées were becoming one of the great rendezvous points for liberal intellectuals in Victorian London. Charles Dickens, Charles Darwin, the actor William Macready, the scientist Henry Fitton and his wife, the geologist Charles Lyell, Mary Somerville and her family, the anatomist Richard Owen, the magistrate William Broderip, Sir John Herschel, and of course Ada – these are just a few of the ‘names’ who were often to be found at Babbage’s parties. George Ticknor, a man of letters from the United States, describes a visit to one of Babbage’s parties on May 26, 1838:

  About eleven o’clock we got away from Lord Fitzwilliam’s and went to Mr Babbage’s. It was very crowded tonight, and very brilliant; for among the people there were Hallam, Milman and his pretty wife; the Bishop of Norwich, Stanley, the Bishop of Hereford, Musgrave, both the Hellenists; Rogers, Sir J. Herschel and his beautiful wife, Sedgwick, Mrs Somerville and her daughters, Senior, the Taylors, Sir F. Chantrey, Jane Porter, Lady Morgan [the novelist], and I know not how many others. We seemed really to know as many people as we should in a party at home, which is a rare thing in a strange capital, and rarest of all in this vast overgrown London. Notwithstanding, therefore, our fatiguing day, we enjoyed it very much.

  The completed one-seventh portion of the Difference Engine was, ever since the portion was completed in the early 1830s and then installed by Babbage in the drawing-room of his home, the most prominent conversation piece at his glittering events. He also delighted in entertaining the guests who came to his soirées with ingenious devices and gimmicks.

  In the spring of 1840, Babbage started exhibiting something else: the almost miraculous woven portrait of Jacquard. The woven portrait shows the inventor sitting in a luxurious cushioned chair at his workbench. He is holding a pair of calipers against long strips of cardboard that have tiny holes punched in them. The bench also accommodates a model of a loom. Hanging up on a rack on a wall behind the inventor are chisels and other tools in a var
iety of shapes and sizes. Rolled-up plans are poking out of a drawer on a table beneath the rack.

  The portrait gives the impression of being an informal snapshot of the inventor as he momentarily turns away from his work and glances at the artist. He has a thoughtful, frowning air about him, and his well-cut coat and general air of prosperity suggest that this is an inventor who has enjoyed some success.

  Babbage enjoyed showing the portrait to his guests. He would then ask them how they thought it had been made. When they told him they thought it was an engraving, as they usually did, he gave a knowing smile.

  One evening in 1842, two of the most distinguished people in the realm had attended a Babbage soirée. They were the Duke of Wellington and Prince Albert, Queen Victoria’s husband. The ‘Iron Duke’ was, of course, the hero of Waterloo and a former Prime Minister. Prince Albert was famous for his intellect and the important, even essential, role he played in governing Britain. Officially he had no power, but in practice the Queen deferred to his judgement and opinion on almost every matter. She usually succeeded in persuading her ministers to do the same.

  Almost as soon as the Duke and the Prince arrived, Babbage showed them the portrait. The Prince asked Babbage why he thought the portrait so important. Babbage replied, in characteristically enigmatic fashion, ‘it will greatly assist in explaining the nature of my calculating machine the Analytical Engine.’

  Once the two guests had examined the portrait, Babbage asked them what they thought it was. The Duke of Wellington made the usual mistake of responding that it must be an engraving. But it turned out the Prince knew the truth, having apparently heard of the portrait before. He informed the Duke of Wellington that the portrait was not an engraving at all, but a woven piece of fabric.

  A few originals of the woven portrait still exist today. As we gaze into Jacquard’s stern features, it is difficult to believe that this faded, rather small picture (it only measures twenty inches by fourteen) could have had such a prodigious effect on Ada’s imagination, but it did. It’s no exaggeration to say that without this woven portrait, Ada would almost certainly have never had the insight she did – not only into Babbage’s Analytical Engine, but into her dream of what a computer could be.

  Ada often attended Babbage’s soirées as one of the many guests there, and his friendship with Ada was something he could also enjoy in a more public sense. Here, for example, is a letter she wrote to Babbage on Tuesday, January 12, 1841. She was very keen to be involved with his plans, and pressed him on this whenever she could.

  My Dear Babbage.

  If you will come by the Railway on Friday, we will send the carriage to meet you at Weybridge, for the Train that leaves Town about 4 o’clock & arrives at Weybridge a few minutes before 5 o’clock.

  Bring warm coats or cloaks, as the carriage will be probably an open one.

  If you are a Skater, pray bring Skates to Ockham; that being the fashionable occupation here now, & one I have much taken to.

  I am very anxious to talk to you. I will give you a hint on what. It strikes me that at some future time, (it might be even within 3 or 4 years, or it might be many years hence), my head may be made by you subservient to some of your purposes & 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 & most invaluable friend to me; & I would that I could in any way repay it, though I scarcely dare so exalt myself as to hope however humbly, that I can ever be intellectually worthy to attempt serving you.

  Yours most sincerely

  A.A. Lovelace

  You must stay some days with us. Now don’t contradict me.

  The tone of this letter is pretty typical of how Ada usually was when she wrote to Babbage: slightly flirtatious, a bit bossy and with some intellectual humility—though on occasion, she dispensed with the humility.

  There is no record of Babbage’s visit to Ockham for that particular weekend, let alone any account of the great analyst skating on the ice, which must have been quite a sight. Very likely Babbage declaimed about the phenomenon of friction (or lack of) while he was skating.

  But there is no reason to believe that he didn’t visit Ada and William that weekend, even if he didn’t, in the end, decide to skate.

  Six weeks later, after the weekend when skating may or may not have taken place, Ada returned to her fashionable, modern, Cubitt-designed house on St James’s Square where her husband William’s ambitious renovations had evidently already been completed. She urged Babbage to visit at once and mentioned with mounting excitement that they will embark on a project together.

  Monday, 22 February,

  Ockham Park

  My Dear Mr Babbage

  We are to move to Town on Thursday; & I hope to see you as soon afterwards as you like, – the sooner the better.

  Remember that one o’clock is the best hour for a call. –

  I believe I shall perhaps pass Sunday Evening with Mr & Mrs De Morgan [Augustus and Sophia (Frend)]; but this is not yet quite fixed, & if it should not take place, will you come & spend it in St James’ Sqre – You see I am determined to celebrate the Sabbath Mathematically, in one way or other.

  I have been at work very strenuously since I saw you, & quite as successfully as heretofore. 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. – Altogether I am going on well, & just as we might have anticipated.

  I think I am more determined than ever in my future plans; and I have quite made up my mind that nothing must be suffered to interfere with them. – I intend to make such arrangements in Town as will secure me a couple of hours daily (with very few exceptions), for my studies.

  I think much of the possible (I believe I may say the probable) future connection between us; and it is an anticipation I increasingly like to dwell on. I think great good may be the result to both of us; and I suspect that the idea, (which by the bye is one that I believe I have long entertained, in a vague and crude form), was one of those happy instincts which do occur to one sometimes so unaccountably & fortunately. At least, in my opinion, the results may ultimately prove it such.

  Believe me

  Yours most sincerely

  Ada Lovelace

  14

  A Mind with a View

  Luigi Federico Menabrea’s paper on the Analytical Engine might have stayed as obscure as the learned Swiss journal in which it was published had not Ada decided that translating it into English would neatly achieve two objects that she considered close to her heart.

  Firstly, it would give her the opportunity to publicise the important work being done by her close friend Babbage, of whom she was seeing a good deal more than ever before.

  Secondly, the translation work would allow her to advance her dream of having an intellectual career which would lift her above the demands of motherhood, running three homes and looking after a wealthy but ineffectual husband.

  Ada was conscious of the difficulty of her task, but was convinced that she was more than equal to the job. She launched into it with characteristic energy. Her French was excellent, and her best writing has a fluency, clarity of expression and mastery of metaphor and image that on occasion even recalls her father’s fluent and expressive prose. There is no reason to disbelieve Babbage’s account in his autobiography that it was Ada’s idea to produce the translation in the first place. Here is what Babbage says in Passages from the Life of a Philosopher. Babbage calls Menabrea’s article a ‘memoir,’ presumably after Scientific Memoirs in which Ada’s translation was published in 1843:

  Some time after the appearance of his memoir on the subject in the Bibliothèque Universelle de Genève, the late Countess of Lovelace informed me that she had translated the memoir of Menabrea. I asked why she had not herself written an original paper on a subject with which she was so intimately acquainted? To this L
ady Lovelace replied that the thought had not occurred to her. I then suggested that she should add some notes to Menabrea’s memoir: an idea which was immediately adopted.

  This passage is telling in many significant ways. It was written by a man who was convinced of his own abilities. From his early youth he had been coddled, encouraged, and told he was brilliant – which he undoubtedly was. Only months earlier to the events he describes he had, as we shall see, almost verbally assaulted a man he’d never met and whose views he didn’t know but whose support he nonetheless sought. Ada was undoubtedly gifted, but had been told from early youth to not think too much of herself – as was common for rich aristocratic girls surrounded by tutors and governesses – lest it encourage the wilful parts of her personality. She was highly intelligent and used to getting her way as she grew older and less timid. In science, her confidence melted away and she saw her role as that of the hand-maiden to others. Even her close friendship with the highly respected scientist Mary Somerville had made little difference on what Ada thought of herself. Babbage was surprised by her suggestion to translate Menabrea’s essay, and seems to have thought she knew enough about his invention to be able to write an article of her own. The confidence Babbage expressed in her abilities appears not to have convinced Ada, however. She decided to go ahead with a translation, aided by Babbage.