Ada's Algorithm

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Ada's Algorithm Page 11

by James Essinger


  Suggested Jacard’s [sic] loom as a substitute for the drums.

  What exactly does the entry mean?

  It reveals that prior to seeing that the Jacquard cards were ideal for operating his Analytical Engine, Babbage toyed with the idea of programming his new machine by using a revolving drum featuring little raised studs as a mechanical means of inputting data and operating the machine. This type of drum was the basis for the control system of a loom invented by a Frenchman called Jacques de Vaucanson, who was essentially a predecessor of Jacquard.

  The notebook entry marks the decisive moment when Babbage abandoned that plan in favour of the Jacquard punched-card system.

  Certainly, it made very good sense for Babbage to focus on the Jacquard cards. For one thing, producing punched cards is easier and cheaper than manufacturing metal drums. Yet more important, the Jacquard control system offered the possibility of a potentially limitless programming system, whereas a revolving drum will, by definition, start to repeat itself before long.

  Babbage was a prolific writer on industry and machinery. It is perfectly possible that Babbage had known about the Jacquard loom since his university days, but in any event there can be no doubt that by 1836 he was entirely familiar with the machine and with the details of how it operated. By the mid-1830s, there were several hundred Jacquard looms in Britain, with many of the weavers who worked on them plying their trade in London’s Spitalfields district, where a silk-weaving industry had sprung up that offered more than token competition to the silk industry in Lyons. Babbage would have been well aware of this industry.

  Writing in his 1864 autobiography, Babbage makes explicit the enormous influence and importance of the Jacquard loom. As he says:

  It is known as a fact that the Jacquard loom is capable of weaving any design which the imagination of man may conceive. It is also the constant practice for skilled artists to be employed by manufacturers in designing patterns. These patterns are then sent to a peculiar artist, who, by means of a certain machine, punches holes in a set of pasteboard cards in such a manner that when the cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.

  Babbage went on:

  Now the manufacturer may use, for the warp and weft of his work, threads which are all of the same colour; let us suppose them to be unbleached or white threads. In this case the cloth will be woven all of one colour; but there will be a damask pattern upon it such as the artist designed.

  But the manufacturer might use the same cards, and put into the warp threads of any other colour. Every thread might even be of a different colour, or of a different shade of colour; but in all these cases the form of the pattern will be exactly the same – only the colours will differ.

  The day Babbage decided to make use of the Jacquard cards in his design for his Analytical Engine is one of the most momentous in Ada’s story, because her profound vision of the potential of the Analytical Engine was intimately linked with Babbage’s borrowing of the punched card.

  The late Bruce Collier, in his study of Babbage’s work, The Little Engines that Could’ve, is in my view wrong about Ada, but when it comes to Babbage’s work he is perceptive. He makes the important comment:

  The introduction of punched cards into the new engine was important not only as a more convenient form of control than the drums, or because programs could now be of unlimited extent, and could be stored and repeated without the danger of introducing errors in setting the machine by hand: it was important also because it served to crystallise Babbage’s feelings that he had invented something really new, something much more than a sophisticated calculating machine.

  Collier’s point here is of crucial importance. Furthermore, today our whole idea of how computers should be programmed can be traced directly back to the Jacquard loom and its punched cards. Indeed, the Jacquard card can even be said to constitute the invention of the binary digit or ‘bit.’

  A bit is a unit of information expressed as a choice between two equally probable alternatives. It’s the smallest and most fundamental element of computerised information. These alternatives can be boiled down to ‘0’ or ‘1,’ alternatives that can in turn conveniently be represented electronically within the actual physical structure of a computer’s circuitry by a tiny electronic switch that is either ‘off’ (for 0) or ‘on’ (for 1).

  At the most fundamental level, this is how computers work. And the whole idea was essentially Jacquard’s.

  Writing in his autobiography, Babbage explains how the Analytical Engine would operate. He states that the machine would consist of two parts. These are, firstly, the store containing ‘all the variables to be operated upon’ and, secondly, the mill ‘into which the quantities about to be operated upon are always brought.’ In his autobiography Babbage writes ‘qualities’ not ‘quantities’ but this is likely a misprint.

  Babbage’s use of the terms store and mill are brilliant and far-sighted anticipations of the modern computer features of memory and processor, respectively. In choosing the terms he did, Babbage was also alluding to the cloth industry of Totnes, the town where he spent much of his childhood and to which he often returned as an adult. As the distinguished computer historian Martin Campbell-Kelly observes in his introduction to the 1994 reprint of Babbage’s autobiography:

  This terminology was an elegant metaphor from the textile industry, where yarns were brought from the store to the mill where they were woven into fabric, which was then sent back to the store. In the Analytical Engine, numbers would be brought to the store from the arithmetic mill for processing, and the results of the computation returned to the store.

  In his 1864 autobiography, Babbage points out that every formula the Analytical Engine may be required to compute consists of certain algebraic operations to be performed upon given letters, and of certain other modifications depending on the numerical value assigned to those letters. By ‘letters,’ Babbage is referring to letters in algebraic formulae such as 2x = 1; 2y3 = 16, etc., although the machine was designed to handle far more complex formulae than this.

  Though his notes describe the machine’s two sets of cards, in practice Babbage used three types of cards, since there were also cards that contained the values to load into the machine. In other words, some cards (the Operation Cards) were to be used to control the actual operations of the machine, others (the Variable Cards) to specify from where in the store the number to be operated on was to be fetched, and still others (the Number Cards) were to specify the actual numbers on which the machine operates. A modern computer program works in an almost identical way.

  Babbage concludes by making the observation that the Analytical Engine is ‘a machine of the most general nature.’ He explains that whatever mathematical formula it is required to calculate, the details of the formula must be communicated to it by two sets of cards, and that once the machine has been programmed by the cards in this way, the engine will always operate according to that formula until a new program is fed into it.

  In the summer of 1834, Ada and Lady Byron had embarked on a tour of the industrial heartland of northern England, visiting many factories and seeing with their own eyes the immense potential of machinery. They saw a Jacquard loom in action, and Lady Byron even drew a picture of a punched card used to control the loom’s operation.

  In early spring of the same year, Ada and Lady Byron’s friendship with Mary Somerville had begun to blossom. It was an exciting friendship for Ada, because by now Mary Somerville was one of the best-known mathematicians in Britain, unlike the well-meaning Dr King whom she prodded for a proper study programme in mathematics. Finally, she had found intellectual pursuit that most satisfied her, and it was mathematics.

  Babbage also became a fixture in her life during these months; though we can’t be certain how often their meetings took place, but there are certainly clues: for example, on Thursday, March 19, 1834, Ada had written a brief letter to Mary Somerville saying t
hat she hoped to meet Mary on Saturday evening at ‘Mr Babbage’s.’ This appears to be a reference to Babbage’s Saturday evening soirées, which had started in fact in the 1820s for his family but by the 1830s had become events for outside guests. As we shall see, the soirées had their heyday in the 1840s but evidently they were already an important part of Babbage’s social life at this stage.

  Ada continued to write to Dr William King about mathematical matters at this time. She additionally wrote to Mary with whom her friendship was becoming increasingly intimate, reminding her on Monday, November 8, 1834, that she promised to make Mary a cap and would do so as soon as Ada finished her own bonnet.

  Ada even had two pupils of her own: Annabella and Olivia Acheson. Olivia and Annabella were the youngest daughters of one of Lady Byron’s friends, Lady Gosford, who went off on health cures with her and had evidently named her youngest daughter after Lady Byron. Ada decided to make the most of her time and teach Annabella and Olivia mathematics. They were, respectively, five and four years older than her (and were to remain spinsters), but this didn’t stop Ada, who wrote confidently:

  Remember above all things that you are not to hurry over anything. There is plenty of time, and if you lay a good & solid foundation, the superstructure will be easy, & delightful to build!

  Do not become afraid of my becoming too learned to teach you. The more I know myself, the more pleasure I shall take in going over with you the ground I have myself successfully transversed; I get so eager when I write Mathematics to you, that I forget all about handwriting and everything else. – Your progress is the only thing I desire.

  Believe me, Your affectionate & untenable Instructress

  Ada Byron

  By the end of 1834, the Analytical Engine was not the only thing on Ada’s mind. She had turned nineteen on December 10. Lady Byron was determined that the time had come for her daughter to find a husband. It appears that Babbage hovered on the radar. While Ada had rediscovered her passion for mathematics as a result of Babbage, it may well have been that bachelor of seven years Babbage also rediscovered a sense of vigour about his emotional life that he had lost as a lonely widower.

  Did he see himself as a potential suitor for Ada? It’s possible he did, and that Ada did too. Certainly, it wasn’t uncommon at the time for young women of Ada’s age to marry older, wealthy men who had been married before. Besides, Babbage would very likely have regarded Ada as well suited for such a role.

  But in any event, it is perfectly clear that, even if Ada had ever mentioned to her mother that perhaps she – Ada – might marry Babbage (there’s no evidence Ada did suggest this, but there’s also no evidence she didn’t), Lady Byron would have been implacably opposed to the idea. She was insistent that Ada would marry an aristocrat, and ideally one whose title was at least a century old, which was regarded as the minimum age of the title (though not of the aristocrat himself) for maximum eligibility for marriage. Thus there was a snobbery even about this among the British upper class at the time.

  So if Babbage was interested in Ada as a potential wife who would end his solitary – and indeed often lonely – life, he was doomed to disappointment in that respect. While some of her best friends were middle class, she was decidedly orthodox about blue blood.

  Some of her friends understood perfectly what suitability in a husband for Ada actually meant. At this crucial stage in our story, up pops that voyeuristic pedant Woronzow Greig again. Writing long after the fact, he recalls: ‘During the spring of 1835 I suggested to my friend Lord Lovelace, then Lord King, that she would suit him as a wife. He and I had been at college together [this was Trinity College, Cambridge, Byron’s and Babbage’s college] and have continued through life on the most intimate terms.’ Whether Greig was involved or not, the spring of 1835, Ada was introduced to William, Lord King, who was thirty years old, on a visit to the Warwickshire home of a Sir John Philips.

  William, in a word, was a catch. Even Lady Byron could hardly wish for much more. Lord King hailed from an influential political, social, intellectual and religious background. With a title created in 1725, his was just on the right side of Lady Byron’s hundred-year watershed. And he came with a number of substantial properties, including Ockham Park, Surrey, the Jacobean family seat (he was Lord King, Baron of Ockham) and Ashley Combe in Somerset. He had also bought 12 St James’s Square, London, two years earlier. Nor was Ada indifferent to William, who was good-looking in addition to being immensely wealthy. On June 28, 1835, less than a fortnight before their marriage, she enthused, ‘What a happiness it is to feel towards any one what I do towards you, & to feel too that it is reciprocal!’ And Ada went on:

  I do not think there can be any earthly pleasure equal to that of reposing perfect trust & confidence in another, more especially when that other is to be one’s husband.

  I hope, my dear William, that I shall make you a very affectionate and very conscientious wife, & shall fulfil all my duties towards you & towards your family in such a manner as to make you the only return I can make for all I owe you, & of which I am so sure that I shall never be reminded by you, that I must take care to keep the remembrance of it in my head.

  While that may still have been written at Annabella’s prompting, Ada did take to her marriage with relish. It took place on Wednesday, July 8, 1835, at Fordhook House, after which Ada and William had a honeymoon at their stately home, Ashley Combe (located in Porlock, near Minehead in Somerset), which William had set about renovating in a romantic style. In one letter to William, on Friday evening, October 9, 1835, when they were temporarily apart, she describes her pregnancy as ‘the commencement of the hatching,’ and refers to herself as a ‘hatch bird.’ She adds, ‘I want my Cock to keep me warm’ – William’s nickname, chosen by Ada, was ‘Cock’ – signing off, ‘My dearest mate, yours most affectionately.’

  In short succession Ada did what was expected: a son, Byron (the heir), was born on May 12, 1836; a daughter, Annabella, followed on September 22, 1837; and she gave birth to a second son, Ralph (the spare), their last child, on July 2, 1839. It helped no doubt that loveable, malleable William seems almost from the outset to have accepted that his wife was more intelligent than he was and to have been willing to adopt a fairly subservient position in the relationship. Later in their marriage he would say ‘what General you would make!’

  It didn’t take Ada too long to realise that William was a somewhat aimless man. He spent a great deal of time and money designing and ordering the construction of tunnels at their country houses. The precise purpose of all these tunnels was never clear and it is possible that there wasn’t any purpose of them other than to provide William with something to do with his time.

  When Princess Victoria became Queen Victoria in 1837, William was elevated in the peerage from Baron to Viscount of Ockham, and to the Earldom of Lovelace, an extinct title from Annabella’s family the Noels (upon the death of her uncle Lord Wentworth, she and her father had inserted ‘Noel’ before ‘Milbanke’). But rather than rewards for any particular achievements of William’s, they appear to have been political pleasantries from the new monarch prompted by one of her ministers. Ada herself would henceforth sign her name ‘Ada Lovelace,’ using her own family name. Paradoxically, Lady Byron never dropped her husband’s name, even when she eventually inherited her uncle’s title and became Baroness of Wentworth.

  After a few years of what appears to be genuine happiness, Ada began to find her husband’s lack of overall purpose intensely irritating. This was evidently a problem throughout their marriage; one of the letters discovered in the north of England and written by Ada on Christmas Day 1846, amounts to a ticking-off of Babbage for, as she saw it, obstructing the procurement of a possible appointment for William. ‘You can have no conception of what my husband is, when his home alone occupies his irritable energies,’ she wrote. She craved a husband who would do great things, stride to fame and illustriousness with her by his side and understand her own pressing needs for a
n intellectual life. But William was not that man.

  Her duty as wife having been dispensed with, Ada resumed her passion for mathematics despite the wealth that surrounded her. She became determined to find a distinguished mathematical and scientific tutor who would guide and accompany her on her intellectual quest. Who better to ask than Babbage?

  During the first few years of her marriage, the inventor of the Difference Engine and Analytical Engine was often a visitor to Ada and William at their home in Ockham in Surrey. Ada was certainly keen to see him. In one short letter written on March 24, almost certainly in 1839, she chastises Babbage playfully:

  Sat[ur]d[a]y next will suit us perfectly, but we hope you will stay on as far into the following week, as possible. Surely the machine allows you a holiday sometimes. –

  This note sets the tone for how their friendship would develop with Ada often describing herself as ‘a fairy.’ In November 1839, she writes to Babbage to ask if he could help her find someone to teach her mathematics:

  … quite made up my mind to have some instruction next year in Town, but the difficulty is to find the man. I have a peculiar way of learning, & I think it must be a peculiar man to teach me successfully. –

  Do not reckon me conceited, for I am sure I am the very last person to think over-highly of myself; but I believe I have the power of going just as far as I like in such pursuits, & where there is so very decided a taste, I should almost say a passion, as I have for them, I question if there is not always some portion of natural genius even. – At any rate the taste is such that it must be gratified. – I mention all this to you because I think you are or may be in the way of meeting with the right sort of person, & I am sure you have at any rate the will to give me any assistance in your power.

  Lord L [Lovelace] desires all sorts of reminiscences, & that I am to take care & remind you about coming to Ockham. –

 

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