Ada's Algorithm

by James Essinger

  We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

  To ascertain what Babbage means by the ‘grave mistake’ we need to look closely at some of the correspondence between Ada and Babbage during the summer of 1843, when Ada was working on her own material about the Analytical Engine, and seeking advice from Babbage when she felt she needed it.

  However, her work was her own and indeed she very clearly, and correctly, insisted on being in charge of the project to produce her material.*

  On Sunday, July 2, 1843, Babbage wrote a letter to Ada that included the following comment on a draft he had seen of part of her work:

  There is still one trifling [sic] misapprehension about the Variable cards – a variable card may order any number of Variables to receive the same number upon theirs at the same instant of time – But a Variable card never can be directed to order more than one Variable to be given off at once because the mill could not receive it and the mechanism would not permit it. All this was impossible for you to know by in intuition and the more I read your Notes the more surprised I am at them and regret not having earlier explored so rich a vein of the noblest metal.

  Babbage appears to be intending a compliment here to Ada’s insights into the Analytical Engine. The way Babbage signs off this letter a little later does indeed make clear his deference to Ada, his respect for her perspicacity and his acknowledgement that she is heading the creation of the Notes. As Babbage writes:

  I will attend your commands tomorrow and am ever most truly yours. C. Babbage

  Babbage had, however, misconstrued how Ada saw the variable cards. She wrote back at once to Babbage and made arrangements to go to see him in London from Ockham to clarify several points, including that she did have an accurate understanding of the role of the variable cards. As Ada wrote in her letter:

  I cannot imagine what you mean about the Variable-Cards; since I never supposed in my own mind that one Variable-card could give off more than one Variable at a time; nor have (as far as I can make out) [I] expressed such an idea in any passage whatsoever.

  This misconception by Babbage appears to be the grave mistake to which he refers.

  Here, as indeed throughout the correspondence between Ada and Babbage over her creation of the Notes, reading the correspondence makes it completely clear (only too clear, Babbage might have thought) that Ada was running the show and that Babbage was helping, but only when she wanted him to do so.

  When the Notes were on the verge of being ready for publication, there arose an obstacle. Babbage, who was convinced that the British Government had a grudge against him and that the British Government constantly denied him preferment and various academic posts to which he felt himself entitled, wanted to include in the same issue of the journal that was going to publish Ada’s Notes a diatribe (which he was, however, unwilling to sign) that fulminated about the way he believed he was and had been treated by the British Government.

  Ada, however, was adamant that the diatribe not be included and she asked the printer to proceed without publishing Babbage’s own hectoring article. As she wrote to Babbage on Sunday, August 6, sugaring the pill but making her own position perfectly clear:

  Be assured that I am your best friend; but that I never can or will support you in acting on principles which I conceive to be not only wrong in themselves, but suicidal.

  The truth of the matter is that the correspondence between Ada and Babbage during the period when Ada writing her Notes makes clear both implicitly and explicitly that Ada was thoroughly in charge of the creation of the Notes. Even leaving aside the abundant evidence in the text of the Notes that they were Ada’s creation rather than Babbage’s, only someone who has not read the accompanying correspondence could seriously doubt that the Notes were Ada’s.

  So Ada had indeed decided to go along with Babbage’s suggestion that she write some additional material of her own about the Analytical Engine. Indeed, the material of hers that she appended to her translation of Menabrea’s exceeded the length of the translation several times over. As Babbage accurately pointed out, also in his autobiography:

  The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject.

  Ada’s additions to her translation of Menabrea’s article on the Analytical Engine constitute the core of her life’s intellectual work, the essence of the reason why (in my view) it is abundantly reasonable to describe her as a genius. Her additions to the translation also constitute the intellectual heritage she offered posterity. She offered this unwittingly; she had no idea her thinking would be so highly regarded in the future. Because we live surrounded by computers and personal digital tools, it is too easy to forget that when Ada slipped into the pain-ridden unconscious that was the start of her death, she had no idea whatsoever that one day her vision of what a computer could do and could be would come so completely true.

  Later in this chapter I look at Ada’s Notes, and that nature of that intellectual heritage, in detail, while in the next chapter we consider Babbage’s reaction to them.

  It has been suggested by some modern – mostly male – writers that the translation and notes were really the work of Babbage. Certainly he stood to gain from an extended article as the two parts together showed the entire operation of the machine. As Babbage wrote in his autobiography (by ‘two memoirs’ he means Ada’s translation of Menabrea’s article and her Notes):

  The two memoirs taken together furnish, to those who are capable of understanding the reasoning, a complete demonstration – That the whole of developments and operations of analysis are now capable of being executed by machinery. [Babbage’s italics]

  As Babbage, who knew Ada and worked with her, very willingly reports to posterity that Ada’s translation and Notes were her own work, what right has anyone from posterity, who didn’t know Ada and never worked with her, to gainsay Babbage and contradict him retrospectively? Babbage was all his life a believer in a sense of justice. Like all of us, he had faults, but telling lies was not one of them. Moreover, if he had concocted an elaborate lie about the extent of Ada’s authorship of her Notes then why exclude the ‘working out of … the numbers of Bernoulli.’ This is quite apart from the ample linguistic and epistolary evidence (which I examine later in this book) proving beyond reasonable doubt, in my opinion, that her writings on the machine were her own. There seems little doubt that he was closely involved with her work and no doubt read her work as it progressed, but peer-review is common in scientific writing.

  As The Ada Initiative – mentioned in the Preface to this book – states pertinently on its website, some have argued that when Babbage refers in his autobiography to ‘the algebraic working-out’ of the numbers of Bernoulli, this means that Babbage himself wrote the ‘program’ (if strictly speaking it was a program) which would be designed to calculate the numbers of Bernoulli in a completed Analytical Engine. But The Ada Initiative website argues that Ada’s Notes contain

  an actual algebraic equation for calculating the numbers of Bernoulli – separate from the computer program – which would seem more likely to be what Babbage was referring to.

  And The Ada Initiative website continues by arguing that there is today evidence that includes Ada’s extrapolations of what a general-purpose computer could do, which stretched far beyond Babbage’s ideas for its use.

  That is exactly right, and below I look at the specific evidence that justifies this accurate claim.

  Babbage’s own attempts to advance the interests of the Analytical Engine had encountered a m
ajor disaster. A particularly unfortunate example of this was his meeting, on Friday, November 11, 1842, with the Prime Minister, Sir Robert Peel. Babbage was trying to obtain government funds to complete the machine. The meeting took place not long after Prince Albert’s visit and perhaps his intercession had helped Babbage to secure a meeting with the most powerful man in Britain at that moment.

  The interview was an unmitigated catastrophe for Babbage. It is possible to reconstruct it almost on a minute-by-minute basis from a detailed account Babbage wrote of the interview. The word ‘wrote’ is in fact not really adequate to describe how it came to be composed. Immediately after the interview, in a hot fury of anger and disappointment, Babbage rushed back into his house, dashed into his study and – as if aware this was the only way he could obtain any relief – gouged onto paper a blow-by-blow account of what he must even at the time have realised was a meeting that pretty well killed his twenty-year vision of cogwheel computing stone dead.

  The document containing the account is lodged in the British Library in London. It is both deeply moving and profoundly troubling.

  What Babbage wrote is how what might have been never was. Had the meeting been successful, the seeds would have been sown for the start of an information technology revolution in Victorian Britain. The ways in which technology might have accelerated, and history run differently, over the course of almost two centuries are too enormous to contemplate.

  Babbage’s vivid account of the meeting includes much of the verbatim dialogue between the two men. His pain and upset are even apparent in the appearance of the writing itself, which is hastily scrawled out and not easy to decipher, and in its syntax. Uncharacteristically for him, in his haste and anger his description of the meeting leaves out much of the punctuation and even some of the words. But he does provide a verbatim account of some of the conversation, so here we have some actual dialogue that can be set down.

  The timing of the meeting was, from any perspective, extremely unfortunate. The year 1842 had been a truly tough one for Peel. Shortly before the day when he met Babbage, Peel had written to his wife Julia that he was ‘fagged to death,’ with the cares of office. Much of the population – whether working in towns or on the land – was permanently close to starvation. Hunger and rioting were widespread.

  Peel was in no mood to meet Babbage at all, let alone in the mood for a stressful confrontation with a mad scientist. Babbage would have done much better if he had handled the meeting in a radically different manner. He should have been to the point, pleasant and placatory, and done his utmost to explain his work to Peel in language that presented the practical function to Britain’s economy of his invention. As it was, and this is clear even from Babbage’s own notes, he conducted the meeting in a defensive, sullen, bad-tempered, querulous, self-centred and self-pitying manner that would only irritate and alienate Peel. As Babbage explains in his account of the interview he began somewhat irrelevantly telling Peel how his detractors might see him:

  I informed Sir RP that many circumstances had at last forced upon me the conviction, which I had long resisted, that there existed amongst men of science great jealousy of me. I said that I had been reluctantly forced to this conclusion of which I now had ample evidence, which however I should not state unless he asked me. In reply to some observation of Sir RP in a subsequent part of the conversation I mentioned one circumstance that within a few days the Secretary of one of the foreign embassies in London has incidentally remarked to me that he had long observed a great jealousy of me in certain classes of English Society.

  Babbage went on to explain why he was mentioning all this. He told Peel of his fears that some of those who had advised the Government over the worth of the engines might have based their decision on personal malice rather than on an objective assessment. Peel evidently made no direct reply to this.

  Then, finally, Babbage got down to what really mattered:

  I turned to the next subject, the importance of the Analytical Engine. I stated my own opinion that in the future scientific history of the present day it would probably form a marked epoch and that much depended upon the result of this interview. I added that the Difference Engine was only capable [of] applications to one limited part of science (although that part was certainly of great importance and capable of more immediate practical applications than any other) but the Analytical Engine embraced the whole science.

  I stated that it was in fact already invented and that it exceeded any anticipations I had ever entertained respecting the powers of applying machinery to science.

  The brilliance of Babbage’s anticipation how posterity would see the Analytical Engine uncannily reflects the view of him currently, a time when even the smallest computer has a digital version of what he proposed.

  Yet as far as his dealings with the pragmatist Peel were concerned, the problem was that Peel had no real idea what the difference was between the Difference Engine and the Analytical Engine. Peel had no doubt been clearly briefed that the Difference Engine had swallowed up funding equal to two frigates and that it was a technological boat whose inventor himself had decided would never sail. Babbage would surely have done better to have given Peel a clear indication of the practical benefits of his machines, accompanied by a realistic plan of action and a date when the Government could expect that something of definite practical usefulness would be completed, and how completing the Difference Engine would cost more than completing the Analytical Engine – or something to that effect.

  But Babbage, in his bitterness and haste to justify himself, tried quoting to Peel the comment Plana had made that the invention of the Analytical Engine would provide ‘the same control over the executive [department of analysis] as we have hitherto had over the legislative.’ Again, it is difficult to imagine that Peel had the faintest idea what Babbage was talking about. And even if Peel had been carefully briefed, why the British taxpayer should invest a substantial amount of money in furtherance of an obscure statement by an obscure Italian mathematician.

  After another bad-tempered, irrelevant and unpleasant discussion, initiated by Babbage, about the different pensions and grants given to scientists by the Government, Peel finally decided to interrupt the endless stream of complaints and grievances and call Babbage to order with a hard fact: ‘Mr Babbage, by your own admission you have rendered the Difference Engine useless by inventing a better machine.’ Babbage took the bait and glared at Peel. ‘But if I finish the Difference Engine it will do even more than I promised. It is true that it has been superseded by better machinery, but it is very far from being “useless.” The general fact of machinery being superseded in several of our great branches of manufacture after a few years is perfectly well known.’

  Only briefly diverted from his spilling his spleen, Babbage again went on to complain of all the vexation and loss of reputation he considered that he had suffered from those members of the public who believed him to have profited personally from the money the Government had granted towards the development of the Difference Engine. ‘This belief is so prevalent that several of my intimate friends have asked if it were not true,’ Babbage said. ‘I have even met with it at the hustings at Finsbury.’

  Peel was on home territory now. ‘You are too sensitive to such attacks, Mr Babbage,’ he replied. ‘Men of sense never care for them.’

  Fixing the Prime Minister with another hard stare, Babbage finally showed the wit that his friends loved and might have got Peel on his side if by now a river of bile didn’t flow between them:

  Sir Robert, in your own experience of public life you must have frequently observed that the best heads and highest minds are often the most susceptible of annoyance from the injustice or the ingratitude of the public.

  Peel was exhausted and irritated with Babbage. Babbage felt hurt, betrayed and angry that the Prime Minister could be so reluctant to support the continued development of machines whose worth seemed to Babbage at any rate self-evident.

  One wonde
rs to an extent whether Babbage’s bluster might have been partly due to the fact that, unlike the Difference Engine which was directly inspired by De Prony’s work for the French Ordinance Survey, he found it less easy in his own mind to see the exact point of the far more open-ended Analytical Engine beyond its pure mathematical use.

  ‘I consider myself to have been treated with great injustice by the Government,’ was Babbage’s unhelpful parting comment, ‘But as you are of a different opinion, I cannot help myself.’

  Babbage got up from his chair, wished his Prime Minister good morning, and abruptly left the room.

  Presumably Ada very quickly heard from Babbage about Peel’s rejection. We can readily imagine Ada being sympathetic, but what happened when Babbage met Peel can only have reinforced Ada’s conviction that Babbage needed some significant help to advance the interests of the Analytical Engine in the circles of influential people Babbage needed on his side. We can see this clearly from the period from June to September 1843, which is the best documented one of Ada’s friendship with Babbage.

  After Menabrea’s article was published in the Swiss journal Bibliothèque Universelle de Genève in October 1842, Babbage is known to have scribbled a personal note in his own papers on February 7, 1843, stating that he had had a meeting with Ada ‘under new circumstances.’ While it seems likely that this was relating to Ada’s involvement in the Menabrea translation, we can’t know this for certain. It could also be his dashed hopes after the disastrous meeting with Peel. Ada did not start work on her own, additional, material until May or June, but it seems likely that by February 1843 she had drafted her translation of Menabrea’s article.

  Ada’s translation sets out clearly the background of Babbage’s new engine and explains how even the finest mathematical minds have been unable to translate even simple mathematics into a machine that executes in numbers what mathematicians describe on paper in mathematical symbols.