Lovelace & Babbage and the Creation of the 1843 ‘Notes’

John Fuegi and Jo Francis Flare/MITH Augusta Ada Lovelace worked with Charles Babbage to create a description of Babbage’s unbuilt invention, the Analytical Engine, a highly advanced mechanical calculator often considered a forerunner of the electronic calculating computers of the 20th century. Ada Lovelace’s “Notes,” describing the Analytical Engine, published in Taylor’s Scientific Memoirs in 1843, contained a ground-breaking description of the possibilities of programming the machine to go beyond number-crunching to “computing” in the wider sense in which we understand the term today. This article expands on research first presented by the authors in their documentary film, To Dream Tomorrow.

What shall we do to get rid of Mr. Babbage and known to have crossed the intellectual thresh- his calculating Machine? Surely if completed it old between conceptualizing computing as would be worthless as far as science is con- only for calculation on the one hand, and on cerned? the other hand, computing as we know it —British Prime Minister Sir Robert Peel, 18421 today: with wider applications made possible by symbolic substitution. The Analytical Engine does not occupy common In an early background interview at the ground with mere ‘calculating machines.’ … In Science Museum (London) for the historical enabling mechanism to combine together gen- documentary film about collaboration between eral symbols, in successions of unlimited variety Lovelace and Babbage, To Dream Tomorrow,3 and extent, a uniting link is established between Babbage authority Doron Swade mentioned the operations of matter and the abstract mental that he thought Babbage and Lovelace had processes of the most abstract branch of mathe- “very different qualities of mind.” Swade’s matical science. A new, a vast and powerful lan- observation proved to be of enormous value for guage is developed for the future use of analysis our subsequent research. … An examination of the original Lovelace and —A.A. Lovelace, “Notes by A.A.L.,” 18432 Babbage documents shows that, whereas Bab- bage concentrated on the number-crunching Charles Babbage’s Difference Engine and possibilities of his new designs, Lovelace went Analytical Engine, conceived in the first half of beyond number-crunching to see possibilities for the 19th century, are often seen as anticipating wider applications. She wrote: key design features used in modern computing, even though none of Babbage’s extraordinary Supposing, for instance, that the fundamental devices was fully built in his lifetime. Augusta relations of pitched sounds in the science of har- Ada Lovelace, née Byron, who worked against mony and of musical composition were suscep- the restrictions on women of her day to suc- tible of such expression and adaptations, the cessfully train as a mathematician, worked engine might compose elaborate and scientific closely with Babbage to describe the more pieces of music of any degree of complexity or advanced of his Engines, the Analytical Engine, extent.4 in a collection of “Notes” published in Taylor’s Scientific Memoirs in 1843. Lovelace’s vision of Aware that the punched card mechanism the Engines’ potential for the future of compu- guiding the decision list of the Analytical Engine tation may now be seen as having exceeded was taken by Babbage from the Jacquard loom Babbage’s own vision for his machines in sev- and that Jacquard had created pictures of great eral key ways. She became the first person complexity by this means, she noted: “We may

16 IEEE Annals of the History of Computing Published by the IEEE Computer Society 1058-6180/03/$17.00 © 2003 IEEE say most aptly, that the Analytical Engine weaves Over the last four years, to gain access to algebraical patterns just as the Jacquard-loom and to use Augusta Ada Lovelace materials, we 5 weaves flowers and leaves.” Making her own needed to obtain the permission of Ada’s great- independence of thought clear within the great-grandson, the current Earl of Lytton. Lord “Notes,” she wrote: Lytton was pleased at, among other things, the idea of taking a fresh look at the role in Ada’s Whether the inventor of this engine had any education of his great-great-great-grandmoth- such views in his mind while working on the er, Lady Byron. Ada grew up essentially in a sin- invention, or whether he may subsequently ever gle-parent home; Lady Byron left the abusive have regarded it under this phase, we do not household of the famous poet Lord Byron know; but it is one that forcibly occurred to our- when Ada was five weeks old. Lady Byron (who selves6 on becoming acquainted with the means had herself received some training in mathe- through which analytical combinations are actu- matics) was primarily responsible for Ada’s edu- ally attained by the mechanism.4 cation up to and including the time Ada met Charles Babbage when she was 17 and he 42, In order for us to look closely at the original and she first saw Babbage’s prototype Lovelace and Babbage documents written at Difference Engine, a mechanical calculator. the time the “Notes” were being created, we It is important to note what happens both had to go to a number of different archives. We for Ada and Charles Babbage in the 10 years also had to take care when examining most that lie between Ada Byron’s first view of the published accounts. Most extant books tended prototype Difference Engine in 1833 and the to be either primarily accounts of Lovelace with creation of the “Notes” in 1843. In this period, Babbage as an important but subsidiary figure, the ideas of Babbage undergirding the more or accounts of Babbage with Lovelace often advanced calculating device, the Analytical reduced to a largely marginal figure. In con- Engine, emerged. Ada was present as the key trast, it was our intention in making To Dream new ideas were discussed between Charles Tomorrow to examine and acknowledge what Babbage and the great science expositor, Mary each one did as an individual, as well as what Somerville. By 1834, both Somerville and the two achieved working together. Babbage were mentors for the then 18-year-old Since the “Notes” are the single most compre- Ada, and Babbage supplied Ada with a number hensive description of the more advanced capa- of engineering drawings so she could better bilities of the Analytical Engine and since a understand his newest designs. full-scale Analytical Engine was never built, the Though Ada Byron (like her mother before “Notes” constitute the main conduit through her) was barred, as a woman, from attending which Babbage’s extraordinarily advanced engi- university in England at that time, she worked neering ideas influenced future generations. with a series of tutors in mathematics. After Consequently, the “Notes” and Lovelace’s role in meeting Babbage, her mathematical studies creating them, and the question of the extent to began to focus on what she needed to know to which she went beyond the ideas of Babbage are advance her understanding of the principles of historical significance. behind Babbage’s Difference and Analytical Lovelace’s letters to Babbage, with a large array Engines. Her study advanced even after she of other vital Babbage materials, are held at the married William, soon-to-be named Earl of British Library in London. A large number of Lovelace, and had three children in a little over Babbage’s drawings and notes, used by Doron three years; the last born in July 1839. In 1840 Swade and the late Allan Bromley to reconstruct she began a series of tutorials with Augustus De plans for Babbage’s various “Engines” (some of the Morgan, professor of mathematics at University plans of which have been published in the IEEE College, London. Annals), are at London’s Science Museum. A num- Babbage had first received a grant from the ber of Babbage’s letters to Lovelace are in the British government in 1823 to begin to build a Byron/Lovelace collection at Oxford’s Bodleian Difference Engine. Yet, despite expending large Library. Lovelace Estate Records (the documents sums of public funds and a great deal of his showing the financial and other material condi- own money, by 1833 he had failed to complete tions under which Ada worked after she married more than the small prototype Difference in 1835), are held at the County Historical Archive Engine. This prototype is a fully functioning in Woking, UK. As these historic materials have device that can be seen today at the Science never been published in their entirety, their inter- Museum in London. By 1834, however, relationship has often remained almost entirely Babbage began talking about having an even unexamined. more complex undertaking to displace the ear-

October–December 2003 17 Lovelace & Babbage and the 1843 ‘Notes’

lier one. As Ada, over a span of a decade, successful advertising campaign promoting the extended her capacities for understanding device. Wheatstone had also worked on designs Babbage’s Engines, in the same period, Babbage for calculating by machinery as we know from himself felt frustrated by being unable to con- an 18 May 1839 entry in Babbage’s Notebook: vince British authorities of the importance of “Yesterday saw Wheatstone’s model for telegraph his latest design, a proposal for an Analytical and his drawings for Multiplication Engine.” Engine of vastly greater scope than his earlier According to Anthony Hyman who cites the Difference Engine. But, by now, the British gov- Babbage Notebook, “Wheatstone’s apparatus ernment was frustrated by almost two decades gave Babbage the idea that he might use electro- of dealings with Babbage. On 11 November mechanical switching instead of mechanical 1842 the inventor had a meeting with the techniques for the Calculating Engines.”9 Prime Minister, Sir Robert Peel. Babbage (as we Considering the date, 1839, the idea is know from his own notes7) spent more time breathtaking, coming almost a century ahead attacking the government than describing the of Howard Aiken making his first advanced cal- new Engine. Peel, for his part, had, prior to the culator proposals to IBM.10 Even though meeting, solicited support to call Babbage’s Babbage had not adopted Wheatstone’s electro- work officially worthless. The meeting was a mechanical switching in 1839, in 1937 Aiken disaster. Both men talked past one another. On directly mentioned Babbage’s engine designs as January 5, 1843, Babbage was informed that a precursor and joked, “If Babbage had lived 75 the government had sent the prototype of the years later I would have been out of a job.”11 Difference Engine to the King’s College Descriptions of Babbage’s designs were also Museum.8 In March, Peel formally withdrew turned up by Konrad Zuse in Berlin as part of support for the project, and only a single voice his “prior art” patent search in 1937, and simi- in Parliament was raised on Babbage’s behalf. lar references crop up as well in accounts of the By 1843 it was clear that Babbage, for all his work of John von Neumann. H.J. Gray notes: technical brilliance, had been rejected in “John von Neumann urged that all the England for further government funding for machine units be connected … so that the completing either the older Difference Engine machine could be used as a computer of the or the newer Analytical Engine. Babbage type ... This was done and ENIAC was Before the formal rejection by Peel in operated in this fashion until it retired.”12 A 1842–1843, Babbage had gone to Turin in the further link is a reported conversation of John fall of 1840 hoping to line up foreign support von Neumann with S. Frankel cited by Andrew for his plans. Before going to Turin he had had Hodges.13 Hodges also notes that Turing was printed the 24-in. by 36-in. “Plan, #25,” one aware both of Babbage and Lovelace.14 Thus version of the ever-changing Analytical Engine some links can be shown between key 20th- design. In Turin, a young engineer, Luigi century figures in computer history (Turing, Menabrea, took notes on Babbage’s talks and Aiken, von Neumann), and the work done in began to prepare an article based on what England in the early 1840s, but dismissed by Babbage presented. Menabrea’s article, the British government then as worthless. “Notions sur la machine analytique,” was pub- In the fall of 1842, aware of what had happened lished in the journal Bibliothèque Universelle de between Babbage and Peel, Wheatstone and Genève, in October 1842. Lovelace, not yet mentioning the idea to Babbage When copies of the Menabrea article reached as he was ill after his meeting with Peel, thought it England in the fall of 1842 and Babbage had had could help the cause of advancing Babbage’s work his disastrous meeting with Peel, the French lan- in England if Ada would translate the Menabrea guage article was discussed by Ada Lovelace and article into English. She was skilled in French, as her the inventor, Charles Wheatstone. Both Lovelace mother had arranged for her to study languages and Wheatstone were probably better informed from childhood on and encouraged her to polish about the Difference and Analytical Engines her skills during a 15-month period they had spent than anyone other than Babbage himself and abroad. Lovelace went ahead with the translation possibly Somerville, and they had more knowl- over the winter of 1842–1843. As she was far more edge than Menabrea, who had met Babbage only knowledgeable than Menabrea about Babbage’s briefly in Turin. Wheatstone, a close friend of designs, she provided footnotes as she went along, Babbage and Lovelace, was one of the best tactfully correcting a number of Menabrea’s errors. informed people in Britain on developing and In early 1843, Lovelace showed Babbage marketing new technologies. By 1837, the what she had been working on over the winter. Cooke/Wheatstone Telegraph had been patent- Babbage’s response shows the high regard in ed, financed, built and marketed with a highly which he held Lovelace’s intellect and her

18 IEEE Annals of the History of Computing understanding of his work. Babbage recollect- will endeavour to find a complete set and bring ed 20 years later: them with me on Monday.”16

Some time after the appearance of [Menabrea’s] To create a comprehensive description of memoir the late Countess of Lovelace informed the Analytical Engine that did not (and indeed me that she had translated the memoir of does not) exist, a machine that was in a con- Menabrea. I asked why she had not herself writ- stant state of flux in Lovelace’s and Babbage’s ten an original paper on a subject with which she lifetime and for which Babbage had difficulty was so intimately acquainted? To this Lady turning up a full, internally consistent set of Lovelace replied that the thought had not drawings—was to attempt something of almost occurred to her. I then suggested that she should inconceivable difficulty. Swade reports in The add some notes to Menabrea’s memoir; an idea Cogwheel Brain how immensely difficult it was which was immediately adopted.15 for him and Allan Bromley, even over a period of several years, to work through thousands of The resulting “Notes” are three times the length pages of Babbage’s “Notes” in order to under- of Menabrea’s essay and contain the most stand a vast, unbuilt, constantly changing enti- influential insights. ty. Groping to arrive at correct formulations Lovelace (as we can confirm from her letters during a single intense summer of work in held at the British Library), wrote the “Notes” 1843, Lovelace and Babbage exchanged letters mainly at Ockham Park, an hour south of that are startlingly modern, almost email-like: London. Babbage wrote back to her from his abrupt, often informal, dashed off, and sent Dorset Street house in London, adjacent to his with uncorrected errors. custom-built, fireproof workshop. They met Lovelace in the summer of 1843 was 27 together to discuss problems and to do proof- years old and saw herself, as she noted in a let- reading at Ada’s London house, 12 St. James’s ter to a relative, as “a fully professional per- Square. Records in Lovelace’s, Babbage’s, and son.”17 Her letters to Babbage mix respect with Wheatstone’s handwriting at the British Library banter, and sometimes the bluntest frankness and at the Bodleian Library allow us to follow when he loses papers or fails to remain focused in an almost hourly way how the “Notes” came on the task at hand. Tellingly, she often wrote into being over the summer of 1843. With mul- “My Dear Babbage,” using the form of male-to- tiple mail deliveries each day, and with more male, colleague-to-colleague address of the missives delivered by personal messenger, one Victorian era. Babbage, who was in 1843 in his gets a sense of the mutual excitement, colle- early fifties, addressed her as “My Dear Lady giality, but sometimes fierce frustration on both Lovelace.” sides of the exchange. The letters crossed and The following letters give us a sense from recrossed as Lovelace’s working days sometimes Babbage’s perspective of how the work was pro- stretched to 18 hours. ceeding. Babbage, from Dorset St. 30 June One remarkable feature of Lovelace’s 1843, writes to Lovelace at Ockham Park in “Notes” is that they describe not the physical such a hurry that not enough postage was put reality of a single existing Analytical Engine on the letter, so it is marked on the envelope but what historian of technology Sadie Plant “More To Pay.” has called “a virtual machine.” “It is virtual on two levels,” said Plant when interviewed for My Dear Lady Lovelace To Dream Tomorrow. “She is,” notes Plant, “writing the program for a virtual machine, I am delighted with Note D. It is in your usual for a future machine in effect.” Most of the clear style and requires only one triffling [sic] mechanical parts for the Engine did not yet alteration which I will make. This arises from our exist, and the drawings, even when they did not having yet had time to examine the outline exist and Babbage could put his hands on of the mechanical part. … them, were incompatible as they reflected dif- I enclose a copy of the integration. I am still ferent stages of design over a nine-year period. working at some most entangled notations of We know that, even at the last stage, as the Division but see my way through them at the “Notes” were in press, Babbage told Lovelace expense of heavy labour, from which I shall not on 18 August 1843: shrink as long as my head can bear it. I have been somewhat impeded for the last few days. My Dear Lady Lovelace I much fear the drawings Your latest information was the most agreeable. will not be very intelligible. They were never Ever my dear Lady Lovelace Sincerely yours C. published and only a few proofs were taken. I Babbage.18

October–December 2003 19 Lovelace & Babbage and the 1843 ‘Notes’

On Sunday, 2 July 1843, Babbage wrote: There never was a note C. I do not know why I chose H instead of C and thus insulted the lat- I am very reluctant to return the admirable and ter worthy letter. philosophic view of the Abral. [sic] Engine con- I cannot imagine what you mean about the tained in Note A. Pray do not alter it and do let me Variable-Cards; since I never either supposed in have it returned on Monday. I send also the rest my own mind that one Variable-card could give of Note D. There is still one triffling (sic) misap- off more than one Variable at a time; nor have (as prehension about the Variable cards—A Variable far as I can make out) expressed such an idea in card may order any number of Variables to receive any passage whatsoever … 20 the same number upon theirs at the same instant of time—But a Variable card never can be direct- Having met with Babbage in London to ed to order more than one Variable to be given off work through the observations each had made, at once because the mill could not receive it and Lovelace wrote to him, both to clarify the issue the mechanism would not permit it. All this was of the variable cards and to convey her decision impossible for you to know by intuition and the to assert her authorship of the “Notes” in a let- more I read your Notes the more surprised I am at ter dated 4 July 1843: them and regret not having earlier explored so rich a vein of the noblest metal. Ockham, Tuesday Morning … Lord L. suggests my signing the translation and the Notes, by The account of them stands thus which he means simply putting … “translated by A.A.L;” & adding to each Note the initials A.A.L. It is not my wish to proclaim who has written it; A Sent to Lady L. F Retained by Lady L at the same time that I rather wish to appear any- thing that may tend hereafter to individualize and B With CB G Where is it gone?? identify it with other productions of the said A.A.L. My third topic, tho’ my last is my most anx- C Ditto H With CB ious and important. I have yesterday evening and this morning very amply analyzed the ques- D Sent to Lady L tion of the number of Variable Cards, as men- tioned in the final Note H (or G?). And I find that E With CB you and I between us have made a mess of it; (for which I can perfectly account in a very natural I have not seen Mr. Wheatstone and am manner). I enclose what I wish to inscribe instead ashamed to write until I can positively put the of that which is now there. I think the present whole of the Notes into his hands. wrong passage is only about eight or ten lines, & I will attend your commands tomorrow And is I believe on the second of the three great sheets am ever most truly yours C. Babbage19 which are to follow the diagram. The fact is that if my own composition about Lovelace wrote back at once to Babbage, her the Variable Cards in Note D had been strictly fol- second letter to him that day. She had decided lowed by myself in Note H this error would not that, since Babbage had made a mistake about have occurred. The confusion has arisen simply how she viewed the variable cards, she would from the circumstance of applying to the Variable need to see him the next day in London to get Cards, facts which relate to the Operation-Cards. several points clarified. She playfully and tact- In Note D it is very well and lucidly demonstrat- fully points out that in fact no Note C had ever ed that every simple operation demands the use existed. of at least those Variable Cards. It does not signi- fy whether the operations be in cycles or not. A Ockham, Sunday 6 o’clock. I have worked inces- million successive additions would each demand santly and most successfully all day. You will the use of these new Variable Cards under ordi- admire the Table and Diagram extremely. nary circumstances. In Note H, the erroneous They have been made out with extreme care lines are founded on the hasty supposition that and all the indices most minutely and scrupu- the cycle or recurring group of Operation-Cards lously attended to. Lord L[ovelace] is at this (13 . . . . . 23) will be fed by a cycle or recurring moment kindly inking it all over for me. I had to group of Variable-Cards. do it in pencil. I enclose what I believe it ought to be. If already You must bring all the Notes with you tomor- gone to the printer we must alter that passage in row as I have observations to make on each one the proofs unless you could call at the printers and especially on this final one H. and there paste over the amendment.21

20 IEEE Annals of the History of Computing She commented further on the technical Wednesday, July 1843, presumably of 5 July: issues in another letter to Babbage, probably also “Return sheet with two corrections. Right of 4 July. This letter is dated only “Tuesday about Card requiring new Variable.”25 1843,” but the context makes plain that it was This was typical of a staccato to and fro. Ada, written near the time of the 4 July letter: writing the “Notes,” queried Babbage, as the inventor of the yet unbuilt Engine, as to My Dear Babbage. whether or not he anticipated his Engine could I hope you will approve of what I send. I have do something and do it as she understood it. taken much pains with it. I have explained that Babbage’s replies suggest that he had learned there would be, in his instance & in many others, something new about his own machine from a recurring group or cycle of Variable as well as of Lovelace’s queries and speculations. For Operation Cards; and I have (I think very judi- instance, a letter headed “Ockham Thurs. Morn. ciously and easily) touched on the only departures 1843” reminds us that Lovelace was attempting from perfect identity which could exist during the a description of what Babbage himself was still repetitions of (13 . . . . . 23); and yet have not com- in the process of clarifying. She wrote: mitted myself by saying if the departures would require to be met by the introduction of one or My Dear Babbage. I have read your papers over more new cards or not; but have simply indicated with great attention. But I want you to answer me that as the associations follow a regular rule, they the following question by return post. The day I would be easily provided for. I think I have done it called on you, you wrote off on a scrap of paper admirably and diplomatically (Here comes in the (which I have unluckily lost); that the Difference intrigante and politician!) Ever yours A.L.22 Engine would do [Authors’ note: Lovelace draws a small triangle here] (something or other) Lovelace’s Note F describes how the [Authors’ note: The parentheses are hers] but that Analytical Engine could be used to calculate the the Analytical Engine would do [Authors’ note: values of the Bernoulli numbers. Lovelace, Lovelace again draws a triangle here] (something knowing that Babbage believed the Engine else that is absolutely general). Be kind enough to could have the capacity to handle Bernoulli write this out properly for me; and then I think I numbers, as he had discussed in a letter circa can make some very good Notes. … 26 January 1841 to the German savant Alexander von Humboldt,23 took it upon herself to make On 10 July 1843, Lovelace wrote: sure there was a written description and demon- stration of how this could be done. She writes My Dear Babbage. … I want to put in something from Ockham Park on Wednesday, 5 July 1843: about Bernouilli’s Numbers in one of my Notes as an example of how an implicit function may I do not go to town until Monday. Keep yourself be worked out by the engine without having open if you can for that day in case there is any- been worked out by human head or hands first. thing I wish to see you about which is very like- Give me the necessary data and formulae. Yours ly. But the evening I think is most likely to be my ever AAL 27 time for you, as I rather expect to be engaged incessantly until after 6 o’clock. I shall sleep in The correspondence brings to life the actual town that night. process of editing and proofreading: I am doggedly attacking and sifting to the very bottom all the ways of deducing the Bernoulli July 1843 Ockham Tuesday Morning. My Dear Numbers. In the manner I am grappling with Babbage. … What I want to know is this: can this subject; and connecting it with the others, I you be with me in town at 4 o’ clock. This is in shall be some days upon it. … order that I may read over aloud with you all the “Labore ipse voluptas” [Labor Is Its Own Notes. ...28 Reward] is in very deed my motto! And (as I hint- ed just now), it is perhaps well for this world that The fact Lovelace wanted to go through the my line and inclination is more the spiritual; and “Notes” with Babbage, and had previously sent that I have not taken it into my head or lived in him her translation of Menabrea to check times or circumstances calculated to put into my makes it clear that proofreading was a joint head to deal with the sword, poison, and intrigue undertaking, supplemented in the customary in the place of x, y, & z. … 24 way by the printers. Given this fact, it seems odd to dismiss (as one severe critic has done)29 In the archive, this letter is followed in folio only Lovelace for failing to catch an error made 354 by a very brief note from Babbage dated by the Swiss printer (an error of “cas” for “cos.”

October–December 2003 21 Lovelace & Babbage and the 1843 ‘Notes’

uncaught by Menabrea), and then using this to add to my trouble not infrequently and there is at claim Lovelace knew little about mathematics. any rate always the anxiety of doubting if you will By the end of July, Lovelace and Babbage not get me into a scrape even when you don’t. appeared to be on the final lap. Lovelace, the By the way, I hope you do not take upon your- mother of three children with the Earl of self to alter any of my corrections. I must beg you Lovelace, jokingly wrote about the “Notes” as not. They all have some very sufficient reason. though they were her first child: And you have made a pretty mess and confusion in one or two places (which I will show you Ockham Thursday morning July 27, 1843: My sometime) where you have ventured on my Dear Babbage. … To say the truth I am rather M.S.’s to insert or alter a phrase or word and have amazed at them [the Notes] & I have made Lord utterly muddled the sense …32 Lovelace laugh much by the dryness with which I remarked “Well. I am very much satisfied with From Lovelace’s letters, it is clear that she this first child of mine. He is an enormously fine thought the intense working period was yielding baby and will grow to be a man of the first mag- the desired result: a strong, persuasive article, nitude and power.”30 describing the capabilities and functioning of the Analytical Engine, to generate interest and sup- A meticulous worker, Lovelace struggled not port for its construction. But, by early August the only with the difficulty of the material but also tone of exchanges is increasingly acerbic as with the errors of the printers and Babbage Lovelace realizes that Babbage is trying to con- himself. On 28 July 1843, Lovelace wrote to vince the printer to include one of his diatribes Babbage from St James’s Square: (which he was, however, unwilling to sign). Babbage wanted, at the last minute, to prevent The beginning of Note G (by which I mean the the publication of the article unless he could Table & all that precedes it) never has been fulminate at length in the same issue about the returned into my hands; a small part of the way he had been and was being treated by the remainder was, but that I speedily gave you back, government. But Lovelace overrode him and had & there it is, now printed.— the printer proceed as originally planned. A key The missing part must be either at your house Babbage letter does not appear to have survived or at the printer’s; & it seems to me very unlikely as it is not at the Bodleian in the Lovelace/Byron that you should have retained it. So altogether I Collection. His letter must have been written would wager almost anything that it is at the around the beginning of August 1843 because office; or that if lost, it has been lost there. Ada Lovelace’s letter of 5 August 1843 is clearly At the same time, I have also fancied you were in response to something from him about her a little harum-scarum & inaccurate now & then overruling him on going ahead with the article. about the exact order & arrangement of sheets, She made her views clear in a letter to Babbage pages, & paragraphs & c. (witness that paragraph from Ockham on Sunday, 6 August 1843: which you so carelessly pasted over!) I suppose I must set to work to write some- My Dear Babbage … On the one point of not with- thing better, if I can, as a substitute. The same pre- drawing the translation & Notes from the cisely I could not recall. I think I should be able Memoir, or consenting to its separate publication, in a couple of days to do something. However I I was entirely and finally decided; as I think nei- should be deucedly inclined to swear at you, I will ther for your advantage nor my own, to do so; allow. added to my opinion that it would under the cir- I desire my messenger to wait; as it possible cumstances be dishonorable and unjustifiable … you may have something to communicate more Be assured that I am your best friend; but that I agreeable. never can or will support you in acting on prin- I go soon after seven. I believe I shall not be in ciples which I conceive to be not only wrong in Town myself on Monday as I expected. Yours themselves, but suicidal.33 A.L.31 In his reply of Tuesday, 8 August 1843, “Ockham Sunday Afternoon August 1, Babbage protested her decision, yet seemed to 1843,” Lovelace writes: acknowledge her authority to make it:

I am half beside myself with hurry and work. … I My Dear Lady Lovelace wish you were as accurate and as much to be I leave the Ms and also the proofs of the Notes relied on as I am myself. You might often save me I recd. last night and promised to send this much trouble if you were; whereas you in reality evening.

22 IEEE Annals of the History of Computing I will write to Printer to say you will send them to pursue the building of the Analytical Engine, up by post direct to them. provided he himself would stick to the techni- This direct communication will save time and cal aspects of the project. From Ockham Park there is very little to spare for this Number ought on Monday, 14 August 1843, Lovelace wrote to to be out in the course of a very few days. Babbage: I have nothing to add at present except that you do me injustice in supposing I wished you to I have now touched on all the grounds which break any engagement with the Editor. I wished can be taken on the supposition of its really being you to ask him to allow you to withdraw from it. pernicious to your interests that I have thus allowed Had the Editor been in England I believe he the article to appear ... My moral standard, such would at my request have inserted my defense or as it is, I must stick to; as long as it is my moral forborn to have printed the paper—As it stands standard. … I have a right to expect from you the I have done all I can at present to defend myself belief that I do sincerely and honestly take this and having failed in the most important part view. [I]f your knowledge of me does not furnish shall make the best I can of the rest. Ever truly sufficient grounds for doing so, then I can only yours C. Babbage34 say that no natural knowledge of any two human beings in this life can give fixed and sta- Babbage’s supposition about the editor’s ble grounds for faith and confidence then Adieu wishes did not turn out to be true. The editor to all truth and to everything most generous in backed Lovelace, not Babbage. Opposition to this world! Babbage’s diatribe idea was unanimous. Neither I must now come to a practical question Wheatstone nor Charles Lyell, the eminent respecting the future. … geologist and mutual friend of Lovelace and If I am able to lay before you in the course of Babbage, thought Babbage’s interests would be a year or two explicit and honourable proposi- served by yet another attack. Despite the advice tions for executing your engine (such as are of his closest friends, Babbage published his approved by persons whom you may now name diatribe separately, in a different magazine, a to be referred to for their approbation) would few weeks later.35 there be any chance of you allowing myself and Whatever Babbage might decide to do, such parties to conduct the business for you; Lovelace keenly felt her own responsibility for your own undivided energies being devoted to the this project. On Tuesday, 8 August 1843, she execution of the work; all these matters being wrote to her mother: arranged for you on terms which your own friends should approve? I have been harassed and puzzled in a most per- You will wonder over this last query. But I plexing manner by the conduct of Mr. Babbage strongly advise you not to reject it as chimerical. … I am sorry to come to the conclusion that he You do not know the grounds I have for believ- is one of the most impracticable, selfish, and ing that such a contingency may come within intemperate persons one can have to do with … my power and I wish to know before I allow my But I am happy to find that W. [Authors’ note: mind to employ its energies any further on the “W.” indicated William, her husband.] & subject, that I shall not be wasting thought and Wheatstone entirely approves my conduct and power for no purpose or result … Yours ever most means. I declared at once to Babbage that no sincerely A.A.L.37 power should induce me to lend myself to any of his quarrels … and that I should myself commu- A letter she wrote to her mother the next nicate in a direct manner with the editors … He day confirms that the printers were recognizing was furious. I imperturbable … I only want you her as author of the “Notes.” Tuesday, 15 to understand that all my time and my energy August 1843: have been miserably absorbed the last few days; for what between Babbage and the editors both … I was unexpectedly summoned by the print- pressing hard in different directions, I have been ers who needed a further supervision and as it is torn to pieces … 36 actually to be out I understand tomorrow, there was no time for post communications. No one Angry or not, Lovelace remained focused on can estimate the trouble of interminable labour of the central issue that the specific purpose of the having to revise the printing of mathematical for- translation and “Notes” was to advance the mulae. You will receive a few copies (amongst a actual building of a machine, rather than again hundred that are printed separately for me). … to attack the government. In a candid letter to If he [Babbage] does consent to what I pro- Babbage, she offered her talents and resources pose, I shall probably be enabled to keep him out

October–December 2003 23 Lovelace & Babbage and the 1843 ‘Notes’

of much hot water; and to bring his engine to examined the extensive exchange of letters and consummation (which all I have seen of him and the resulting “Notes”), when interviewed for To his habits the last 3 months, makes me scarcely Dream Tomorrow, commented: anticipate it ever will be, unless someone really exercises a strong co-ercive influence over him). Ada saw something that Babbage in some sense He is beyond measure careless and desultory at failed to see. In Babbage’s world his engines were times. … 38 bound by number. He saw that the machines could do algebra in the narrow sense that they With the final material delivered to the could manipulate plus and minus signs. But all printer and with most of the errors corrected, his calculating engines, his Difference Engine and after months of 18-hour days spent and his Analytical Engine, which is the pro- describing the possibilities of an extraordinari- grammable general-purpose machine, were all ly complex virtual machine, Lovelace now con- bound by number: They manipulated number as fessed herself often very tired. Lovelace came a manifestation of quantity, as a measure of up to London around 18 August to meet quantity. What Lovelace saw—what Ada Byron Babbage. He was still furious about not having saw—was that number could represent entities had his own way on the idea of appending a other than quantity. So once you had a machine diatribe to the “Notes.” He scribbled a curt for manipulating numbers, if those numbers rep- memo in the margin of Lovelace’s letter of 14 resented other things, letters, musical notes, then August: “Saw AAL this morning and refused all the machine could manipulate symbols of which the conditions.” Instead of using publication of number was one instance, according to rules. It the Memoir with the “Notes” as a descriptive is this fundamental transition from a machine model of a strategy for gaining public under- which is a number cruncher to a machine for standing and support to get the Engine manipulating symbols according to rules that is financed and constructed, Babbage would con- the fundamental transition from calculation to tinue until his death in 1871 to go his own, computation—to general-purpose computa- often irascible, way. tion—and looking back from the present high By 24 August 1843, the volume of Taylor’s ground of modern computing, if we are looking Scientific Memoirs with the translation of and sifting history for that transition, then that Menabrea’s “Memoir” and the “Notes” transition was made explicitly by Ada in that appeared. Lovelace wrote to her mother: “We 1843 paper. are by no means desirous of making it [Authors’ note: authorship of the “Notes”] a As Swade is fully aware, “[T]he Analytical secret although I do not wish the importance Engine,” as A.A.L. so clearly stressed, “does not of the thing to be exaggerated and over- occupy common ground with mere ‘calculating rated.”39 Charles Wheatstone wrote on 25 machines’.” This formulation, based on what August 1843: only existed as a virtual machine in 1843, went beyond any known statement of Babbage, and My Dear Lady Lovelace, I called yesterday at the beyond distinguished predecessors in mechan- printer’s and was informed that a separate copy ical calculation such as Blaise Pascal and of your paper had been forwarded by post to Gottfried Wilhelm Leibniz. A.A.L. anticipated Ockham, and the new number of the Scientific advanced work in the next century of Alan Memoirs sent to St. James’ Square … Yours very Turing, Konrad Zuse, Howard Aiken, Grace truly C. Wheatstone.40 Hopper, and John von Neumann. Looking far ahead to that time when a general-purpose Reaction to the work was swift and positive. The machine would no longer be declared worthless paper, so Michael Faraday, famous for his but would in fact be built, Lovelace argued that chemical and electrical experiments, declared to such a machine would serve as a springboard Babbage on 1 September, was so complex it was for an ever-increasing number of discoveries, well over his own head.41 Menabrea asked many of which would remain unimaginable Babbage to pass along his congratulations “à until such time as the machine was built and cette noble Dame, A.A.L.”42 With could be run. She wrote in Note A: congratulations pouring in, even Babbage was pleased, and he swiftly reconciled with Lovelace, [V]ery valuable practical results would be devel- concluding a letter to her of 12 September 1843, oped by the extended powers of the Analytical with the extravagant: “Ever my fair Interpretess Engine, some of which would be brought forth Your faithful slave C. Babbage”43 by the daily increasing requirements of science Babbage expert, Doron Swade (having and by a more intimate practical acquaintance

24 IEEE Annals of the History of Computing with the powers of the engine, were it in actual existence.44 Bibliography B.V. Bowden, ed., Faster Than Thought, Sir Isaac Pitman & Sons, Ltd., Lovelace was to be proven right, but it 1953. Includes the text of Lovelace’s translation of Menabrea and would take over 100 years. Only after the early the full text of her “Notes.” ENIAC (“a computer of the Babbage type,” as M. Campbell-Kelly and W. Aspray, Computer, Basic Books, 1996. H.J. Gray described it) was built to run rapid I.B. Cohen, Howard Aiken: Portrait of a Computer Pioneer, MIT Press, 1999. calculations for ballistics tables did engineers J. Fuegi and J. Francis, To Dream Tomorrow, 2003, documentary film and programmers, such as John von Neumann with Doron Swade, Sadie Plant, Miranda Seymour, David Herbert, and Grace Hopper, begin to move beyond what Michael Lindgren, and direct Lovelace descendant, the Earl of Lovelace had called “mere calculating Lytton; http://www.mith.umd.edu/flare. Also see http://www. machines” and begin, in Swade’s words, “to computer.org/annals/an2002/extras/a405602x.htm. manipulate symbols according to rules.” With D. Herbert, Lady Byron and Earl Shilton, Hinckley and District Museum, these developments in the mid-20th century, Leicestershire, 1997. the paradigm shift Lovelace had made in 1843 A. Hodges, Alan Turing: The Enigma, Vintage, 1992. would start to become our everyday reality. A. Hyman, Charles Babbage, Pioneer of the Computer, Princeton Univ. Press, 1982. References and notes M. Lindgren, Glory and Failure: The Difference Engines of Johann Müller, 1. British Library, London, additional manuscript Charles Babbage, and Georg and Edvard Scheutz, translated from (hereafter “add’l ms.”) 40,514, folio 223. Swedish by C.G. McKay, Linköping, 1987. 2. A.A. Lovelace, “Notes by A.A.L. [August Ada A.A. Lovelace’s Translation of Menabrea together with her “Notes” are Lovelace],” Taylor’s Scientific Memoirs, London, on the Web: http://www.fourmilab.ch/babbage/sketch.html. vol. III, 1843, pp. 666-731. These notes were P. Morrison and E. Morrison, eds., Charles Babbage and His Calculating originally printed in both Charles Babbage and His Engines: Selected Writings by Charles Babbage and Others, Dover Calculating Engines: Selected Writings by Charles Publications, 1961. Includes the full text of the Menabrea Babbage and Others, P. Morrison and E. Morrison, translation and the 1843 Notes. eds., Dover Publications, 1961 (which includes S. Plant, zeros + ones: Digital Women + the New Technoculture, the full text of the Menabrea translation and the Doubleday, 1997. 1843 Notes, pp. 225-297), and in Faster Than B. Randell, ed., The Origins of Digital Computers, Springer Verlag, 1973. Thought, B.V. Bowden, ed., Sir Isaac Pitman & Contains a number of vital historical papers and a lengthy, superbly Sons, Ltd., 1953, pp. 341-408. A.A. Lovelace’s annotated bibliography. translation of Menabrea together with her J. Shurkin, Engines of the Mind, W.W. Norton & Co., 1984. “Notes” are also on the Web: http://www. D. Swade, The Cogwheel Brain, Little, Brown and Co., 2000. The US edi- fourmilab.ch/babbage/sketch.html. tion of the same book: The Difference Engine: Charles Babbage and the 3. For information about the film, see Quest to Build the First Computer, Viking, 2001. http://www.mith.umd.edu/flare and B.A. Toole, Ada, The Enchantress of Numbers, Strawberry Press, 1992. Has http://www.computer.org/annals/an2002/extras the best collection of Ada Byron Lovelace letters now in print. /a405602x.htm. 4. P. Morrison and E. Morrison, eds., Charles Babbage and His Calculating Engines …, p. 249. 14. Ibid., p. 297 and pp. 357-358. 5. Ibid., p. 252. 15. Cited by D. Swade, The Cogwheel Brain, pp. 160- 6. She is, of course using the customary plural of 161. scholarly writers of the time. 16. Byron/Lovelace Collection, Bodleian Library, 7. British Library, add’l ms. 37,192, folios 189-194. Oxford, UK, box 168, folio 47, recto and verso. 8. British Library, add’l ms. 37,192, folio 326. 17. Cited by B.A. Toole, Ada, the Enchantress of Num- 9. A. Hyman, Charles Babbage, Pioneer of the Com- bers, p. 225. We might note that as we did our puter, Princeton Univ. Press, 1982, p. 227. own transcriptions of letters, in a number of cases 10. I.B. Cohen, Howard Aiken: Portrait of a Computer our reading and dating differs from Toole’s. Ideal- Pioneer, MIT Press, p. 63. ly, all these documents should be put directly on 11. Cited by D. Swade, Charles Babbage and His Cal- the Web so that various people can do their own culating Engines, Science Museum, 1991, p. 34. decipherments of texts that are often extremely 12. Cited from H.J. Gray’s Digital Computer Engineer- hard to read. In some cases, Toole has very use- ing, Prentice-Hall, 1963, in the annoted bibliog- fully included facsimiles of some of the handwrit- raphy given by B. Randell, ed., The Origins of ten documents, an excellent practice. Digital Computers: Selected Papers, Springer Ver- 18. Byron/Lovelace Collection, Bodleian Library, box lag, 1973, p. 420. 168, folio 43, recto and verso. 13. A. Hodges, Alan Turing: The Enigma, Vintage, p. 19. Byron/Lovelace Collection, Bodleian Library, box 304. 168, folio 45, recto and verso, and folio 46, recto.

October–December 2003 25 Lovelace & Babbage and the 1843 ‘Notes’

20. British Library, add’l ms. 37,192, folio 337. 39. Byron/Lovelace Collection, Bodleian Library, box 21. British Library, add’l ms. 37,192, folio 344. 42, folios 101-102. 22. British Library, add’l ms. 37,192, folio 348. 40. British Library, add’l ms. 54,089, folio 37. 23. British Library, add’l ms. 37,191, folio 638. 41. British Library, add’l ms. 37,192, folio 445. 24. British Library, add’l ms. 37,192, folios 351-352. 42. British Library, add’l ms. 37,192, folio 46. 25. British Library, add’l ms. 37,192, folio 354. 43. British Library, add’l ms. 54,089, folio 54. 26. British Library, add’l ms. 37,192, folios 357-358. 44. P. Morrison and E. Morrison, eds., Charles 27. British Library, add’l ms. 37,192, folio 362. Babbage and His Calculating Engines …, p. 256. 28. British Library, add’l ms. 37,192, folios 386-725. 29. See D.A. Stein, Ada, A Life and a Legacy, MIT Press, 1985, p. xi, where much is made of “her John Fuegi is currently a Mary- [emphasis added] curiously ignored translation of land Institute for Technology in a printer’s error.” Stein claimed that if Lovelace the Humanities (MITH) Fellow missed a proofreading error, she must have been and the Clara and Robert Vam- unsound in mathematics. Stein then argues we bery Distinguished Professor of must see Babbage as the primary author of the Comparative Studies at the “Notes” (though he, too, missed the printer’s University of Maryland, Col- error) and see Lovelace’s centrality as what Stein lege Park. He has taught at Har- calls a “mythology” (p. ix). However, from the vard University, the Freie Universität, Berlin, and has surviving letters of Babbage, Lovelace, held American Council of Learned Societies, Guggen- Wheatstone, Lyell, Faraday, Menabrea, and the heim, and Rockefeller Awards. He founded and cur- editors of Taylor’s Scientific Memoirs, it is clear that rently chairs Flare Productions. proofreading was done with Babbage, and that the original typesetting error was missed by Menabrea. The original documentation shows Jo Francis taught for many years that all contemporaries of Lovelace and Babbage, in Thailand and the US before having first-hand knowledge of how the “Notes” joining Flare Productions, a not- came into being, acknowledged Lovelace at the for-profit educational filmmak- time as the primary author. ing organization affiliated with 30. British Library, add’l ms. 37,192, folios 393-394. the Maryland Institute for 31. British Library, add’l ms. 37,192, folios 398-399. Technology in the Humanities 32. British Library, add’l ms. 37,192, folios 414-415. (MITH). She is a MITH Fellow 33. Letter is given in full in B.A. Toole, Ada, pp. 219- and has received national and international recogni- 222. tion for her teaching and her work in film. 34. Byron/Lovelace Collection, Bodleian Library, box 168, folios 41 and 42. Readers may contact John Fuegi and Jo Francis at 35. D. Swade, Cogwheel, p. 163. jf@flarefilms.org. 36. Byron/Lovelace Collection, Bodleian Library, box 42, folio 76. 37. British Library, add’l ms. 37,192, folios 425-426. For further information on this or any other com- 38. Byron/Lovelace Collection, Bodleian Library, box puting topic, please visit our Digital Library at 42, folios 86-88. http://computer.org/publications/dlib.

26 IEEE Annals of the History of Computing