A Female Genius: How Ada Lovelace Started the Computer Age (10 page)

The friendship between Babbage and Herschel was the first serious intellectual friendship either had. They were touchingly good companions, and Babbage was to name his oldest son Benjamin, after his father, and Herschel. They addressed each other as ‘Dear Herschel’ or ‘Dear Babbage’ in letters: an extremely intimate salutation by the formal standards of the time. The informality of their letters (which usually contained abundant mathematical formulae as well as personal material) is neatly explained by a comment Herschel made at the start of a letter he wrote to Babbage on February 25 1813:

When men with common pursuits in which they are deeply interested, correspond on the subject of those pursuits, the trifling ceremonials of an ordinary correspondence may in great measure be waived.

Babbage’s friendship with Herschel frequently sustained and supported Babbage during a life with many setbacks.

While his father was still alive, Babbage pretended to have an interest in earning a living. But he never found any jobs that he either wanted to do, or was appointed to do. Despite moans and complaints, Benjamin gave the couple enough money to live on in reasonable comfort at 5 Devonshire Street, Portland Place, London.

At the same time, Babbage wasted no time in making his mark on the scientific scene. During 1815 – the year of Ada’s birth – he gave a series of lectures on astronomy to the Royal Institution. In the spring of 1816 he was elected a member of the Royal Society, a learned assembly of all the great scientists of the land. For the next few years Babbage’s work was mainly mathematical. He published more than a dozen mathematical papers, all of which were regarded as highly competent, though not of enormous importance.

Babbage, like Byron, doted on his children but after his wife Georgiana died in 1827 they were farmed out.

Herschel, his eldest son, stayed during the school holidays with Babbage’s mother Elizabeth who lived (until 1844) in London. Babbage’s beloved only daughter Georgiana (who was two years younger than Ada), also stayed with Babbage’s mother at her home at 5 Devonshire Street, a ten minute walk from Babbage’s house on Dorset Street.

Although he could easily afford to travel in style, Babbage was not the kind of man to idle time on a frivolous Grand Tour. Instead, Babbage and Herschel had made their first trip to France in 1819, the first of many such excursions they made to exchange information and ideas with French men of science. With Herschel’s father Sir William’s reputation opening doors for the two young men, they were able to meet several prominent French scientists, mathematicians and astronomers.

It was very likely during this first visit to Paris that Babbage first heard of an ambitious French project undertaken at the turn of the century to make a set of reliable mathematical tables for the French Ordnance Survey.

The project had been overseen by the eminent civil engineer Baron Gaspard de Prony. Despite often being in great jeopardy, he had managed to survive the French Revolution’s Reign of Terror mainly due to certain influential revolutionaries – chief among them Lazare Carnot himself,
L’Organisateur de la Victoire’
(‘the Organiser of the Victory’)– who admired his scientific talents.

The French Ordinance Survey required prodigious amounts of multi-digit multiplication and it needed accurate tables to simplify and speed up its work. Logarithms (a seventeenth century invention by John Napier) were the short-cut to such otherwise time-consuming multiplications. A logarithm converts each number into a calculation of the number 10. The great advantage of this is that if you look up the logarithms (logs) of the two numbers which you want to multiply, all you need to do is add their two logs together, note this total, and go back to the logarithm tables to see which number has the logarithm you end up with. That number is the product of the multiplication of the two original numbers.

While the principle appears simple, it is easier said than done. The purpose of De Prony’s undertaking was to calculate the logarithms of the numbers from 1 to 200,000, a massive undertaking even though 200,000 is not a particularly high number. For any numbers higher than 200,000, French surveyors would be obliged to do the laborious sums manually.

De Prony, not surprisingly, was terrified of failing as the Reign of Terror continued to claim the heads of its victims. It was only when De Prony came across a copy of Adam Smith’s
The Wealth of Nations
, published some two decades before in 1776, that he found his answer.

In a famous passage, Adam Smith relates how the productivity of a pin factory he had visited had been maximised by groups of workers specialising in different stages of the production of the pins. One group of workers had, for example, straightened the wire, another cut the wire, another sharpened the tips of the pins, and so on. In this way, Adam Smith explained, the total output of the pin factory would be many times greater than that which could have been produced if each individual worker had handled every stage of the pin-making process.

De Prony decided to use the same principle to make his vast set of tables with the greatest accuracy, and within a reasonable time-frame. After planning his approach carefully, he decided to divide his human calculators into three teams.

The first team would oversee the entire undertaking. This would involve investigating and furnishing the different formulae for each function to be calculated and setting down the simple steps of the calculation process. The team would be made up of half a dozen of the best mathematicians in France, including Carnot himself and Adrien-Marie Legendre (famous for important work on elliptic integrals, which provided basic analytic tools for mathematical physics).

The second team of seven or eight human calculators converted the formulae into key numbers which would be the basis for the actual calculations of the values to be set down in the tables.

The third team consisted of sixty to eighty clerks whose mathematical ability was largely limited to being able to add and subtract. By virtue of the way the huge project was organised, this was all they needed to do in order to perform their necessary calculations. Curiously enough, many of the clerks were former hairdressers to the aristocracy. These hairdressers found themselves unemployed after the Revolution’s thirst for decapitation.

The tables produced by De Prony’s pioneering technique occupied seventeen large folio volumes and had a reputation for being reliable. Their reliability was such that they were used by the French Army as late as 1940 to assist with calculations relating to surveys of terrain. The tables impressed Babbage enormously.

But even though De Prony’s tables were regarded by French mathematicians as an enormously useful asset for more than a century, they were never actually
printed
. Instead, they remained in manuscript form, apparently for cost reasons. Only surveyors at the French Ordinance Survey with access to the original volumes could actually use them.

De Prony’s mass-production approach to his enormous calculation assignment struck a chord deep within Babbage’s analytical mind. When Babbage developed his first cogwheel calculator, he decided to base his machine on the Method of Differences that would reduce the extremely complex business of tables calculation to its simplest essentials, much as De Prony had. Instead of 6 digits (200,000), he planned his tables to run to up to 30 digits, if ever completed.

Furthermore, Babbage knew about the problems De Prony had experienced with getting his tables printed. Babbage was determined to incorporate a printing mechanism within his machine. This would allow the machine to produce a printed output onto paper automatically, eliminating the possibility of human error. Babbage’s plan, in fact, was that the machine itself should make printing plates that could be used as many times as required.

Meeting this challenge, and grappling with the practical and conceptual difficulties it involved, took Babbage into a realm of almost inconceivably complex and original inventiveness, even if it never got further than the seventh part of the machine that Ada first saw in 1833. He started by planning his Difference Engine, he ended by designing what was nothing less than a calculator controlled by punched cards.

12

On Monday, December 19 1834, just five days after Ada turned nineteen, she spent a fascinating evening with Babbage, Lady Byron and Mary Somerville. Babbage was thrilled about the extraordinary new horizon that had opened up in his mind, and in his mad-scientist way, he communicated his excitement most successfully to his guests. We can get a good idea of just how excited he was from a journal entry Lady Byron made late that evening.

He spoke about his discovery in metaphorical terms rather than seeking to explain it in precise detail. The first glimpse of his discovery had aroused in his mind a sensation that was something like ‘throwing a bridge from the known to the unknown world’. According to Lady Byron’s journal, Babbage also said that the breakthrough made him feel that he was standing on a mountain peak and watching mist in a valley below start to disperse, revealing a glimpse of a river whose course he could not follow, but which he knew would be bound to leave the valley somewhere. Writing in her journal, Lady Byron later noted ‘I understand it to include means of solving equations that hitherto had been considered unsolvable.’

Babbage’s only daughter Georgiana had just died suddenly at the age of seventeen, just over three months earlier on September 26, and he had thrown himself into his work, solving an important mechanical issue of the Difference Machine.
4
Or else he had started on his next machine, the one on which he and Ada were to work together closely, the Analytical Engine.

The genesis of the device Babbage was to call the Analytical Engine – echoing the society he had founded with Herschel at Cambridge – can be traced back to a second paper on the Difference Engine that Babbage had read to the Royal Astronomical Society on December 13 1822, when Ada had just turned seven.

In this paper, he explained to his audience that useful as the Difference Engine was, it was always going to be handicapped by the need to reset the machine for each new set of calculations. The point was that the initial numbers that were entered on the cogwheels, had to be entered into the Difference Engine by hand. Once the Engine was set up, the handle could be turned to ensure that the calculation process went on automatically. In principle, the calculations would follow regularly without further intervention by whoever was operating it. But unfortunately, in some calculations, the results would start to become inaccurate as the table production progressed. The machine wasn’t to blame for this. It stemmed from the fact that the calculations were based on a mathematical formula which would not in every case be precisely accurate for every single desired numerical result due to the fact that certain numbers would need to be rounded off as they consisted of an infinite number of decimals (one third is a common division, for example, but as a number the Difference Engine could only approximate it as 0.3333 etc; the number of cogwheels limited the number of 3s and could in any case by definition never be infinite).

What was really needed was a machine that would not feature this continual slight reduction in accuracy; a machine, moreover, that could do far more than simply calculate mathematical tables. He named this new endeavour the Analytical Engine. It would soon supersede the Difference Engine into whose design the government had poured the equivalent of two frigates and Babbage himself more than a decade of his life.

Babbage pursued the notion of the Analytical Engine relentlessly during the months that followed his evening with Ada, Lady Byron and Mary Somerville.

The new machine Babbage envisaged would be enormous, about the size of a small steam locomotive in his day or a large van today. It would have contained perhaps as many as 20,000 cogwheels, some mounted in vertical columns like the Difference Engine but others used in a variety of other configurations. Thousands of gear-shafts, camshafts and power transmission rods would have enabled calculations carried out in one part of the machine to be mechanically relayed to other parts. In sketch-books containing his ideas, he made an enormous number of drawings and diagrams for the Analytical Engine, and completed some small working cogwheel components designed to be used in its mechanism.

Above all, the entire operation of the Analytical Engine would be controlled by a punched-card system. The punched-card system was not Babbage’s idea, but – as Babbage freely acknowledged (he was always generous with his credits) – based on the Jacquard loom. It was this part that was to provide an important catalyst for Ada’s understanding of what the Analytical Engine could really achieve – an understanding that even eluded Charles Babbage himself.

In the summer of 1834, Ada and Lady Byron had been on a tour of the industrial north of England and had visited many factories that were working at full tilt and saw with their own eyes the immense potential of machinery. They also visited the Midlands and saw printers and ribbon factories in Coventry, where Lady Byron drew a picture of a punched card used to instruct a Jacquard loom.

In the same year, Ada and Lady Byron’s friendship with Mary Somerville had begun to blossom in the early spring. 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 in mathematics the intellectual pursuit that satisfied her.

Babbage also became a fixture 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 that she hoped to meet Mary on Saturday evening at ‘Mr Babbage’s’. This appears to be a reference to Babbage’s Saturday evening soirees which had started in fact in the 1820s for his family but by the 1830s had become events for guests outside the family. As we shall see, the soirees 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 an 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 (and were to remain spinsters) than her, 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 something in himself that he had lost as a widower. It was not uncommon for young women of Ada’s age to marry older, wealthy men who had been married before. In many ways Ada was well suited for such a role, from Babbage’s perspective. Certainly as their friendship developed after Ada’s marriage their letters got increasingly light-hearted and self-confessional, as perhaps it had started more innocently at the beginning. Ada was slowly emerging from her chrysalis and was still physically frail and shy as she was preparing to enter London society. Through his interests Babbage had been able to get around her reserve, despite his gnomic utterances, and, with a fortune of £98,000 and four children who were younger than her, he might perhaps have thought that he had a chance. Immediately after Ada married, Lady Byron thus wrote to her ‘but has Babbage cut you since your marriage?’

12 St James Square.

But if Babbage was interested, he was not quite what Lady Byron had in mind. While some of her best friends were middle class, she was decidedly orthodox about blue blood. Others had the better measure. Woronzow Greig writes (well after the fact) ‘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 (Trinity 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 years 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 just bought 12 St James Square two years earlier, whose facade he had demolished a year after the marriage to be rebuilt by Cubitt in the style he had seen on his own Grand Tour: opulent, Italianate, with a glamorous staircase and enfilade of rooms that set it quite apart from its severe seventeenth original.

Nor was Ada indifferent to William, who was attractive as well as 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!’

… 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, after which Ada and William had a honeymoon at their stately home, Ashley Combe in Porlock, near Minehead in Somerset that 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, and a son, Byron (the heir), was born on May 12 1836; their daughter, Annabella, 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 that 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!’

Ashley Combe, Porlock, Somerset.