Ada's Algorithm

by James Essinger

  I do not go to Town until Monday. Keep yourself open if you can for that day; in case there should be anything I wish to see you about, which is very likely. But the evening I think is most likely to be my time for you, as I rather expect to be engaged incessantly until after 6 o’clock.

  I shall sleep in Town that night.

  I am doggedly attacking & sifting to the very bottom, all the ways of deducing the Bernoulli Numbers. In the manner I am grappling with this subject, & connecting it with others, I shall be some days upon it.

  I shall then take in succession the other subjects that have been suggested to me during my late labours, & treat them similarly. –

  ‘Labor ipse voluptas’ is in very deed my motto! – And, (as I hinted just now), it is perhaps well for the world that my line & ambition is over the spiritual; & that I have not taken it into my head, or lived in times & circumstances calculated to put it into my head, to deal with the sword, poison, & intrigue, in the place of x, y, & z.

  By the way I shall set to work upon Ohm tomorrow, & continue it daily until I finish it.

  Your Fairy for ever

  A.A.L.

  During the summer of 1843, the friendship between Ada and Babbage unquestionably became very close and indeed seems to me to have acquired a romantic dimension, though it is important to emphasise that there is no documentary evidence that it ever became sexual.

  Ada, while a married woman, was highly flirtatious and William was often far from her. It is likely that she did have an affair with someone else later in her life; it seems she would have been capable of having had an affair with Babbage if he had set out to woo her. But Babbage seems to have wished to stay faithful to his beloved wife Georgiana long after her death. There is no evidence he ever had any relations with any woman after Georgiana died, and studying not just the documentary evidence relating to his life but also allowing oneself to get to know Babbage as a man tends to convince me that he really had no interest in having a sexual relationship with any woman once he became a widower. However, he certainly often felt lonely, despite his extensive and busy social life (indeed, that was doubtless at one level a defence against his loneliness) and his close friendship with Ada must have helped to some extent to relieve his loneliness. And Ada was certainly very familiar with him. For example, at the end of a letter she wrote to him on Thursday, July 6, 1843, Ada, writing about a male friend of hers, observes to Babbage:

  I see I am more his ladye-love [sic] than ever. He is an excellent creature, & deserves to have a ladye-love of his own.

  But of course Ada’s close friendship with Babbage was about business as well as pleasure. Ada’s profound insights into Babbage’s work were not only confined to her understanding of what the Analytical Engine really was. She also understood Babbage and, for all her affection and admiration for him, she knew that if his dreams were to come true, he needed help. And that was why, on August 15, 1843, she wrote one of the most poignant letters in the history of the computer. It is also one of the longest. Covering sixteen pages of her close handwriting, it runs to more than 2,000 words.

  If there is a moment in Ada’s story when we reach a crossroads where the future of the computer was at stake, this letter provides that moment. Ada’s letter to Babbage constituted an offer to handle, henceforth, what would be regarded today as the management, political and public relations aspects of Babbage’s work on the Analytical Engine. Ada admired Babbage but she was certain that the ornery and undiplomatic aspects of his personality greatly handicapped him when it came to advancing the cause of his engines.

  Ada was perceptive enough to understand something that Babbage never saw: that advancing his project required not only technical wizardry but also needed a velvet yet driven skill at dealing with influential and skeptical people.

  He and Ada sometimes had rifts with each other, and this letter shows Ada trying to mend one.

  My Dear Babbage

  You would have heard from me several days ago, but for the hot work that has been going on between me & the printers. This is now happily concluded. I have endeavoured to work up everything to the utmost perfection, as far as it goes; & I am now well satisfied on the whole, since I think that within the sphere of views I set out with, & in accordance with which the whole contents & arrangement of the Notes are shaped, they are very complete, & even admirable. I could now do the thing far better; but this would be from setting out upon a wholly different basis.

  I say you would have heard from me before. Your note (enclosed on Monday with my papers & c), is such as demands a very full reply from me, the writer being so old & so esteemed a friend, & one whose genius I not only so highly appreciate myself, but wish to see fairly appreciated by others.

  Were it not for this desire (which both Lord L – & myself have more warmly at heart than you are as yet at all aware of), coupled with our long-established regard & intercourse, I should say that the less notice taken by me of that note – the better; & it was only worthy to be thrown aside with a smile of contempt. The tone of it, it is impossible to misunderstand; & as I am myself always a very ‘explicit function of x,’ I shall not pretend to do so; & shall leave to you (if you please it) to continue the ‘implicit’ style which is exceedingly marked in the said note.

  As I know you will not be explicit enough to state the real state of your feelings respecting me at this time, I shall do so for you. You feel, my dear Babbage, that I have (tho’ in a negative manner) added to the list of injuries & of disappointments & mis-comprehensions that you have already experienced in a life by no means smooth or fortunate. You know this is your feeling; & that you are deeply hurt about it; & you endeavour to derive a poor & sorry consolation from such sentiments as ‘Well, she didn’t know or intend the injury & mischief if she has done’ &c. …

  I must now come to a practical question respecting the future. Your affairs have been, & are, deeply occupying both myself & Lord Lovelace. Our thoughts as well as our conversation have been earnest upon them. And the result is that I have plans for you, which I do not think fit at present to communicate to you; but which I shall either develop, or else throw my energies, my time & pen into the service of some other department of truth & science, according to the reply I receive from you to what I am now going to state. I do beseech you therefore deeply & seriously to ponder over the question how far you can subscribe to my conditions or not. I give to you the first choice & offer of my services & my intellect. Do not lightly reject them. I say this entirely for your own sake, believe me.

  My channels for developping [sic] & training my scientific & literary powers, are various, & some of them very attractive. But I wish my old friend to have the refusal.

  Firstly: I want to know whether if I continue to work on & about your own great subject, you will undertake to abide wholly by the judgement of myself (or of any persons whom you may now please to name as referees, whenever we may differ), on all practical matters relating to whatever can involve relations with any fellow-creature or fellow-creatures.

  Secondly: can you undertake to give your mind wholly & undividedly, as a primary object that no engagement is to interfere with, to the consideration of all those matters in which I shall at times require your intellectual assistance & supervision; & can you promise not to slur & hurry things over; or to mislay, & allow confusion & mistakes to enter into documents, &c.?

  Thirdly: If I am able to lay before you in the course of a year or two, explicit & honorable propositions for executing your engine, (such as are approved by persons whom you may now name to be referred to for their approbation), would there be any chance of your allowing myself & such parties to conduct the business for you; your own undivided energies being devoted to the execution of the work; & all other matters being arranged for you on terms which your own friends should approve?

  You will wonder over this last query. But, I strongly advise you not to reject it as chimerical. You do not know the grounds I have for believing that such a contingency
may come within my power, & I wish to know before I allow my mind to employ its energies any further on the subject, that I shall not be wasting thought & power for no purpose or result …

  Yours is to love truth & God (yes, deeply & constantly); but to love fame, glory, honors, yet more. You will deny this; but in all your intercourse with every human being (as far as I know & see of it), it is a practically paramount sentiment. Mind, I am not blaming it. I simply state my belief in the fact. The fact may be a very noble & beautiful fact. That is another question.

  Will you come here for some days on Monday. I hope so. Lord L – is very anxious to see & converse with you; & was vexed that the Rail called him away on Tuesday before he had heard from yourself your own views about the recent affair.

  I sadly want your Calculus of Functions. So Pray get it for me. I cannot understand the Examples.

  I have ventured inserting to one passage of Note G a small Foot-Note, which I am sure is quite tenable. I say in it that the engine is remarkably well adapted to include the whole Calculus of Finite Differences, & I allude to the computation of the Bernoullian Numbers by means of the difference of Nothing, as a beautiful example for its processes. I hope it is correctly the case.

  This letter is sadly blotted & corrected. Never mind that however.

  I wonder if you will choose to retain the lady-fairy in your service or not.

  Yours ever most sincerely.

  A.A.L

  Babbage didn’t accept the offer. He didn’t realise just how brilliant her understanding of his work really was, still less how deep her understanding of his personality was. One wonders how intently he had even read the discursive part of her Notes. If he had read them properly, wouldn’t he have realised just how useful her insights were into the advancement of the Analytical Engine?

  There is no written evidence surviving that Babbage truly understood what Ada had written about the Analytical Engine. In reading her Notes, he may have focused merely on the complex mathematical material (and attributed – or blamed – what he saw as its more discursive ideas on her ‘fairy’ imagination).

  All we know is that the day after Ada wrote this letter, Babbage said no to her without much consideration. At the top of the long letter that Ada sent him on August 14 and which is to be found in the Babbage papers, there appears a pencilled note in Babbage’s hand stating, simply:

  Tuesday 15 saw AAL this morning and refused all the conditions.

  Babbage could on occasion be selfish, stubborn and ungenerous of spirit where his work was concerned. In that short note he combines all three vices. Despite his respect for Ada’s ability to articulate and popularise the most important project of his life, he could never see her as anything more than an ‘interpreter.’ Ada’s reaction to what he told her on Tuesday or, indeed, how exactly he told her what he had decided is not recorded.

  Ada’s translation of Menabrea’s paper on the Analytical Engine was published a few days later in September 1843 in the third number of Scientific Memoirs. Entitled Sketch of the Analytical Engine invented by Charles Babbage, Esq., it was respectfully received by the scientific and mathematical community, but did not cause the sensation Babbage no doubt hoped for, nor did it prove to be the springboard to a literary and scientific career for Ada.

  One of the big problems was that Ada was a woman, and although she had signed her Notes only with the initials A.A.L., her authorship soon became generally known. The very fact that she was a woman ended up working against her, because the scientific community did not take her work seriously, as it would have done if she had been a man.

  16

  The Enchantress of Number

  If Ada was upset with Babbage, and surely she must have felt some disappointment that her idea had been dismissed, this is not apparent from her or his letters that survive from after her proposal to him.

  Nonetheless, there are no surviving letters from Ada to Babbage between the long one she wrote on August 14, 1843, and a short one she wrote to him on March 4, 1845. Instead, we have a letter from Babbage to her, which he wrote on Saturday, September 9, 1843, that opens a casual window on the nature of their relationship.

  This is not the first surviving letter after August 14, 1843; there is another, shorter letter on August 18, 1843, about some drawings he had sent her and concerning some mathematical papers that she had apparently asked him about, though it’s not clear whether she asked him verbally or in a letter.

  That day was clearly a day when Babbage was desperately frustrated with his life and with the difficulties he was facing in his work. He decided to put all the miseries of London behind him and went to see Ada and her husband – though it was clearly Ada he most wanted to see – at their home at Ashley Combe. Rather than hunting, riding, shooting or other leisurely country house pursuits, he was planning to take the train up to Ashley Combe to tackle with Ada topics of cutting-edge mathematics that had recently been discovered. As Babbage writes on September 9, 1843:

  My Dear Lady Lovelace

  I find it quite in vain to wait until I have leisure so I have resolved that I will leave all other things undone and set out for Ashley taking with me papers enough to enable me to forget this world and all its troubles and if possible its multitudinous Charlatans – everything in short but the Enchantress of Number.

  My only impediment would be my mother’s health which is not at this moment quite so good as I could wish.

  Are you at Ashley? And is it still consistent with all your other arrangements that I should join you there? – and will next Wednesday or next Thursday or any other day suit you: and shall I leave the iron-shod road at Thornton or at Bridgewater and have you got Arbogast Du Calcul des derivations with you there (i.e. at Ashley). I shall bring some books about that horrible problem – the three bodies which is almost as obscure as the existence of the celebrated book De Tribu Impostoribus so if you have Arbogast I will bring something else.

  Farewell my dear and much admired Interpreter.

  Evermost Truly Yours

  Charles Babbage

  Louis Arbogast’s Du Calcul des derivations was published in 1800 and contains the statement of a formula that would only receive widespread recognition fifty-five years later when it was named after an Italian mathematician, Faà di Bruno, who published two versions of the formula in an Italian academic journal. Not surprisingly, in 1834 the mathematical problem was still so new and difficult that Babbage refers to it jokingly as De Tribus Impostoribus. The educated would recognise the name as the mythical book that denied all three Abrahamic religions: Christianity, Judaism and Islam. It was a common rumour from the eleventh century to the eighteenth century that there was a heretical text by this name, but it never existed.

  Arbogast’s book developed an idea that was crucial to the success of the engine. Arbogast writes in the prelims to his book, ‘The secret power of Analysis consists in the happy choice and application of signs, which are simple and characteristic of the things they represent.’ Thus the light-hearted circumlocution for an engine that would handle infinite fractions and formulas accurately became the ‘enchantress’: not of numbers in plural, but of the analytical concept itself.

  Notice how Babbage, ever the analyst, refers to the railway as the ‘iron-shod’ road. This is, one might justly think, very typical of him and how he saw the world.

  Maybe, too, by this stage in his life, he had some iron in his heart as well. After all, something had made him reject Ada’s offer so brusquely, briefly and finally.

  Did he maybe suspect that she might be right, that indeed he needed help with dealing with ‘all practical matters relating to whatever can involve relations with any fellow-creature or fellow-creatures’?

  What is, furthermore, curious about this letter is the use of the phrase ‘Enchantress of Number’ for Ada. Babbage wrote ‘Number’ in the singular. This point needs making because there is a comprehensive misconception that he wrote ‘Enchantress of Numbers’ in the plural. A search for th
e phrase ‘Enchantress of Numbers’ on Google reveals 390,000 references, all wrong.

  The word ‘Number’ in the singular is unmistakably there at the end of the page of the manuscript of the letter. The mark to the right of the word is clearly a full stop. Of course, he might have misspelled the word and had meant to write ‘numbers.’ But whether he wanted to write ‘Enchantress of Number’ of ‘Enchantress of Numbers,’ what did he mean?

  Well, it’s at least inconceivable he meant the Analytical Engine. Perhaps ‘Enchantress of Number/s’ was a phrase he and Ada used in their private conversations together to mean the Analytical Engine. This is speculative; there is no evidence one way or another.

  The other obvious suggestion, and certainly the most romantic interpretation of the phrase, is that he was talking about Ada. There is sense in this as Dr Johnson defines a fairy in his 1755 Dictionary as an ‘enchantress, an elf, a fay,’ and to Babbage Ada described herself as a fairy during this period. Dr Johnson defines the word ‘enchantress’ itself less innocently as ‘a sorceress; a woman of extreme beauty or excellence,’ and a ‘sorceress’ as a ‘female magician or enchantress.’ Ada had never been encouraged to believe she was exceptionally gifted, let alone think of herself as an exceptional beauty.

  Whatever she may have felt deep inside, these views hadn’t changed in the August letter she had written to Babbage. The almost camp hyperbole of the word enchantress as a way of describing her powers might have made someone like Ada ill at ease, if indeed Babbage had meant to flatter her by way of a joke.

  My own reasons for nowadays believing that Babbage did mean Ada by ‘Enchantress of Number’ are, firstly, that the gallantry and flirtatiousness of the phrase ‘Enchantress of Number’ tallies with the warm sign-off (‘Farewell my dear and much admired Interpreter’).