In the summer of 1838 – that same summer in which the King sisters and her mother were all out of the country – Ada lost this most cherished of all her connections. Mrs Somerville’s health had been impaired by fifteen years of living in a damp house near a smog-shrouded river. A shortage of money contributed to Dr Somerville’s decision, in 1838, to quit his medical post and exchange cold, expensive England for a warmer, more affordable life abroad. Martha and Mary accompanied their parents on the family’s journey to Italy, a country where Mrs Somerville’s gender offered less impediment than in Victorian England to her recognition as a woman of preeminent intellectual achievement. Mary made only a couple of brief returns to Britain, where her son Woronzow Greig, having married a charming and pious Scottish girl in 1837, continued to work as an attorney.
Mary had gone and Ada was bereft, not only of a woman who had become close to her as a second mother, but of a magnificent tutor, without whom she was lost. In 1839, she began to put pressure on Charles Babbage to come to her rescue.
In February 1840, at a time when Babbage was in especially low spirits about the future of his unbuilt Analytical Engine, Ada showed the first hint of her secret and immense ambitions. If Mr Babbage would only hurry up and find her a new teacher, the world might benefit from the results.
I hope you are bearing me in mind. I mean my mathematical interests. You know this is the greatest favour any one can do me. Perhaps, none of us can estimate how great. Who can calculate to what it might lead . . . Am I too imaginative for you? I think not . . .?
Babbage took his time in looking, but he did not let Lady Lovelace down. The wonder was only that it had occurred neither to Lady Byron nor to her daughter that Augustus De Morgan, the brilliant mathematical logician who had recently married Sophia Frend, might be able to take Mrs Somerville’s place.
By October 1840, the new arrangement had taken shape. De Morgan had not only rejected the idea of payment, but he had willingly taken this most unconventional student under his personal wing. The boost to Ada’s confidence and energy proved to be immense. Writing to her absent mother that month, she boasted that she felt ‘wonderfully altered as to courage’. Better than this: ‘I am absolutely afraid of nothing. I never was so bold & full of nerve at any time in my life.’
There’s no doubt that much of Ada’s new-found elation stemmed from her new connection to the witty, brilliant and empathetic Augustus De Morgan, the very teacher whom she craved. (‘Never was a better hit than that,’ she rejoiced to Lady Byron.)
It’s possible that some of Ada’s new-found confidence also derived from the fact that Lady Byron – that ‘merry old hen’ who had been clucking about nothing but educational reforms and Ada’s need to be more closely involved in the field of good works all summer long – was once again safely out of the country. For the present, the Hen’s relentless interest in reform, Ada and even her grandchildren had been unexpectedly cast in the shade by a new and enthralling link to Annabella’s own Byron-haunted past.
* * *
* Both of the Combe brothers, Andrew and George, were ardent phrenologists. George was by far the better known of the two, but Annabella preferred his gentler and more modest sibling.
* The choice of title (although taken from a valid claim through ancestry) must have caused Prime Minister Melbourne to smile a bit. It remains a mystery why the well-read and discreet Lady Byron should have chosen to attach to her own daughter and son-in-law the name of Samuel Richardson’s notorious libertine.
* Locke King, drawing up a peevish retrospective record of injuries done to him, his wife and his mother, identified 1838 as the year in which ‘my sisters were so ill natured to Louisa [his wife] that I could not go on & intended to speak to them but he [William] said oh no doubt but let me send for them & Ly King [Ada] will talk with them & they will make peace . . . I was not allowed to see them unless I would promise to say nothing of the past . . .’ (Peter Locke King, undated note in the Locke King family archive at Brooklands Museum.)
CHAPTER FIFTEEN
AMBITIONS AND DELUSIONS
(1840–1)
Charles Babbage, by 1840, was a disappointed man. His uncompleted Difference Engine had passed into the control of a government that showed no faith either in it or in its infinitely more complex and dynamic successor, the Analytical Engine, upon which Babbage had expended all of his considerable inventive genius. On the Continent, he was justly regarded as a genius; in England, his career had utterly stalled.
In Italy, the far-sighted Charles Albert, King of Sardinia (father of the future King of Italy, Victor Emmanuel II), encouraged the setting-up in the autumn of 1840 of a scientific conference in Turin. Babbage, formally invited by his elderly admirer and fellow mathematician, Count Giovanni di Plana (Mary Somerville, now settled in Italy, had acted as intermediary), would explain the significance of his revolutionary invention.
Bringing with him as interpreter Fortunato Prandi (one of the Young Italy group focussed around the exiled Giuseppe Mazzini in London), Babbage was treated with gratifying respect at that September conference.* The contrast to the indifference shown to the inventor in his own country was poignant. Charles Albert, a stickler for etiquette, permitted Babbage to remain seated in the royal presence. The king even – this was an unprecedented honour – allowed Mrs Somerville’s brilliant friend to present the queen with a portrait of the famous M. Jacquard, woven upon one of the industrialist’s own automated silk looms at Lyons. (Babbage had inspected the Lyons looms and had purchased the artefact en route to Italy, evidently intending to highlight the respects in which that successful invention resembled the projected activity of his own unbuilt machine.) Ill health marred the end of Babbage’s visit and forced him to cancel his plans to visit the Somerville family at their new home in Florence. Nevertheless, Babbage’s feathers, ruffled by English indifference, were smoothed by Italian courtesy. In 1842, King Charles Albert would present the British inventor with a commendatore’s order. It was the only award that the prickly Charles Babbage ever consented to accept.
Babbage pinned very high hopes upon the Turin conference. Writing to an Italian colleague, he explained why.
The discovery of the Analytical Engine is so much in advance of my own country, and I fear even of the age, that it is very important for its success that it should not rest upon my unsupported testimony. I therefore selected the meeting at Turin as the time of its publication, partly from the celebrity of its academy, and partly from my high estimate of Plana.
Babbage’s reasonable supposition was that his official host, Count di Plana, would write up a full and positive report before submitting his personal appreciation of the Analytical Engine to Britain’s Royal Society. Armed with this impartial endorsement, the inventor stood a far better chance of gaining the support from the British government that he required. Unfortunately, di Plana himself had grown too old and infirm for the demanding task of describing such a complex – and still unbuilt – machine. In 1841, encouraged by Mary Somerville and in the hope of further developments, Babbage again travelled out to Italy – this time for a conference at Florence. His reception was as enthusiastic as before but, apart from the pleasure of seeing the Somervilles, his hopes were once more crushed. Di Plana had done nothing.
By the summer of 1842, almost two years after the Turin conference, no report had yet been published upon Babbage’s wondrous invention.
In the autumn of 1840, as Babbage set off for Italy with such high hopes, his future interpreter embarked upon the most significant phase of her mathematical education. Following the recommendation of Babbage (and bowing to the unyielding persistence of Lady Lovelace herself), Augustus De Morgan had taken over the role of mathematics coach to a strong-willed young woman whose intelligence and determination still greatly outstripped her mathematical skills.
The challenge of tutoring Ada was considerable. Aged just under twenty-four, and still equipped with only a modest understanding of either algebra or trigonom
etry, Lady Lovelace wanted to launch straight into differential calculus. Mrs Somerville’s counsel about cautious progress was forgotten in Ada’s habitual impatience to rush ahead. ‘Festina lente,’ De Morgan reproved her on 15 September 1840: ‘ . . . it is no use trying to catch the horizon.’ A few days later, he was again obliged to rein back his ambitious pupil. Lady Lovelace might wish to bestride Parnassus, but the problems of calculus must wait until attention had been paid to the more basic skills which, as De Morgan bluntly stated, ‘you have left behind’.
It was not immediately pleasing to an impetuous young woman to be compelled to follow the sage advice that she herself, aping Mrs Somerville, had once been keen to dish out to Mary Gosford’s little daughter. ‘I work on very slowly,’ Ada sighed to her mother on 21 November 1840. ‘This Mr De Morgan does not wish otherwise.’ A month later, however, she was beginning to get the point. ‘I have materially altered my mind on this subject,’ she confessed to her tutor. ‘I often gain more from the discovery of a mistake of this sort [a simple oversight caused by hasty reading] than from 10 acquisitions made at once without any kind of difficulty . . .’ Ada’s impulse to swagger about her own cleverness remained strong, but how could De Morgan not be disarmed by the frankness with which his pupil expressed her gratitude? (‘I can only end by repeating what I have often said before,’ she wrote: ‘that I am very troublesome, & only wish I could do you any such service as you are doing me.’)
Ada was lucky. Thanks to Babbage and possibly to Mrs Somerville (still advising from afar), she had acquired her ideal teacher. Only ten years older than his pupil, De Morgan himself had been just fourteen when his gift for mathematics was first noticed. Educated at Trinity at the same time as Woronzow Greig and William King, he was soon moving at the same intellectual level as their brilliant tutors. One, William Whewell, became a lifelong friend. Another, George Peacock (who had helped his own fellow student, Charles Babbage, to found the Cambridge Analytical Society back in 1815), had written the study of differential and integral calculus from which Ada would first begin to learn about algebra. In 1828, De Morgan – still aged only twenty-two – became the new University of London’s first professor of mathematics. He taught there – with one gap of five years (due to a personal dispute) – for the next thirty years. Unremittingly industrious, he filled his spare time (when not composing his own celebrated study of differential calculus) with writing over 700 articles on mathematics for the general reader.
De Morgan’s readiness to help Ada was based in part upon a close family connection. His wife, Sophia Frend, was the daughter of Lady Byron’s own first tutor. In 1838, while Annabella visited Germany with the newly-wed Noels, the De Morgans were allowed to honeymoon for free at Fordhook for ten happy weeks. Early in 1841, they moved into the book-crammed house where Sophia’s late father had lived in Gower Street, near the British Museum. Here, more often than not, Ada went to a quick informal supper that was followed by a session of coaching by De Morgan. When his pupil was unwell – as was increasingly the case – De Morgan often accepted a ride in the Lovelace coach, in order to teach Ada at 10 St James’s Square. Invited to Ockham and beguiling Ashley Combe, however, De Morgan always refused. A college library held more charm for this modest and unworldly man than the social demands of life at a country house.
Lady Lovelace had adored and revered Mary Somerville, but De Morgan’s mischievous wit lent an unexpected bonus to her lessons. ‘I don’t quite hear you, but I beg to differ entirely with you,’ was one of De Morgan’s celebrated dry asides; another was that ‘it is easier to square the circle than to get round a mathematician’.
He meant it. Sophia, writing a tribute to her brilliant husband in the 1880s, described how little sympathy De Morgan had for Ada’s impulse to race towards any new goal, as soon as it was first glimpsed. ‘Show me,’ he would command wherever an error had occurred. Caution was De Morgan’s creed: no progress was permitted until he was shown the exact progress of thought from which the fault had risen, in order that all confusion could be resolved.
The correspondence between pupil and tutor, at its most intense during the period 1840–1, offers evidence of Ada’s potential to become a remarkable mathematician. What it also reveals is how – carefully coached towards this end by Mrs Somerville and held to that same course by De Morgan – Ada became willing to persist with a single point until her mastery of it was certain. What De Morgan evidently admired in her was the energy and perseverance with which, even during periods of the grave sickness that had periodically begun to afflict her, his sweet-natured pupil bound herself to the task of her own mathematical improvement. Anything that she did not understand was instantly acknowledged. Writing to Mrs Somerville about her new telescope back in 1836, Ada had shown no qualms about admitting her absolute ignorance of how to use the instrument. So it was now when, writing to De Morgan on 13 September 1840, she freely admitted that she had no idea what was meant by an equation to a curve. Cock-a-hoop two months later when she thought she had spotted errors in George Peacock’s text-book on algebra, she readily accepted (10 November) that Peacock’s mistakes were in fact those arising from her own beginner’s mind, one ‘which long experience & practices are requisite to do away with’. Always eager to plunge into the mysteries of differential calculus, Lady Lovelace was beginning, nevertheless, to grasp (writing in this same letter) ‘the importance of not being in a hurry’.
Ada’s lessons with De Morgan took place approximately every fortnight. Frustratingly, no account survives of what was said during these sessions. Did Ada ever actually hear her teacher pronounce his well-known maxim, ‘The moving force of mathematical invention is not reasoning but imagination’? Or had Ada’s own faith in the power of imagination inspired De Morgan’s pronouncement? The connection is intriguing because, on 5 January 1841, during the time that Ada was closest to De Morgan, she wrote an essay about the potentially fruitful collaboration between the scientific faculties and the inventive aspects of the mind.
Imagination is the Discovering faculty, pre-eminently. It is that which penetrates into the unseen worlds around us, the world of Science. It is that which feels & discovers what is, the real which we see not . . .
Mathematical Science shows what is. It is the language of unseen relations between things. But to use & apply that language we must be able fully to appreciate, to feel, to seize, the unseen, the unconscious. Imagination too shows what is, the is that is beyond the senses. Hence she is or should be especially cultivated by the truly Scientific, – those who wish to enter into the worlds around us.
Writing the essay in which this intriguing passage appears, Ada laid particular emphasis upon what she described as ‘the Combining Faculty’: an ability to seize upon points in common, ‘between subjects having no very apparent connexion, & hence seldom or never brought into juxtaposition’. That analogical capacity was precisely the quick-witted, insightful approach that would glow out of the one piece of work for which Ada would later become famous.
It’s apparent that De Morgan respected what he recognised, more than any of his contemporaries, to be an extraordinary mind. Writing a long letter to Lady Byron in 1844 about the way it might develop, the logician expressed no doubt about what Ada had the potential to achieve. The worry – one upon which Annabella now sought his opinion – was the danger presented to a delicate constitution by an excess of mental strain. Caution was required. Nevertheless:
I feel bound to tell you that the power that Lady L[ovelace]’s thinking has always shewn, from the beginning of my correspondence with her, has been so utterly out of the common way for any beginner, man, or woman, that this power must be duly considered by her friends, with reference to the question whether they should urge or check her obvious determination to try not only to reach, but to get beyond the present bounds of knowledge.
If you or Lord L[ovelace] think it is a fancy for that particular kind of knowledge which, though unusual in its object, may compare in intensity with
the usual interests of a young lady, you do not know the whole . . . Mrs Somerville’s mind never led her into any other than the details of mathematical work. Lady Lovelace will take quite a different route.
De Morgan liked Lady Byron, regarding her (according to his wife’s memoir), as ‘impulsive and affectionate almost to a fault’. But his was not a letter that set out to flatter or please. He was simply stating what seemed to him to be the obvious fact. Ada Lovelace was a one-off, like no other, neither in her ambitions nor her abilities. She might go beyond them all. The question – one that troubled her mother as much as it did De Morgan himself – was whether it was safe to allow her to do so.
Back in the autumn of 1840, Ada Lovelace felt no such fears. Woronzow Greig heard only that she had never been so happy. Annabella, out in France, was told that Mr De Morgan was a wonderful teacher, the answer to her daughter’s prayers. No two people could suit each other better, Ada announced, blithely oblivious to the fact that Mr De Morgan had been happily married for just two years to one of Lady Byron’s most cherished friends. (Perhaps it is not surprising that Sophia De Morgan’s memoirs would later portray her husband’s protégée in a less than flattering light.)
It seemed, during that halcyon autumn of 1840, as though the nearly 25-year-old Ada had discovered a perfect balance. Down in Somerset, she broke away from her studies only to ride up the hills flanking Ashley Combe, in order to enjoy a long, wild gallop across the empty heathland of Exmoor. When at Ockham Park or St James’s Square, she cheerfully relinquished the children to the care of Hester and Charlotte. It was really so much better for them as well as herself, she explained:
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