I have numbered the holes in my drawing for the sake of convenience of reference. The real boards are not numbered. –
Do not forget that I am to have the “Stratagems of Chess.”
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; if we look on beyond this present condition especially? –
You know I am by nature a bit of a philosopher, & a very great speculator, – so that I look on through a very immeasurable vista, and though I see nothing but vague & cloudy uncertainty in the foreground of our being, yet I fancy I discern a very bright light a good way further on, and this makes me care much less about the cloudiness & indistinctness which is near. – Am I too imaginative for you? I think not. –. . .
To Charles Babbage
Saturday, 14 March [1840]
Ockham
My Dear Mr Babbage. …We want to ask him here for Satdy next, & cannot you add yourself? – Or if not that day, is the following Tuesday, the 17th, quite out of the question? –
I fear not withstanding the Eglintoun Tournament, that the real days of Chivalry are gone bye, or you would never resist a lady’s entreaties as you do. –
We shall not I think be in Town quite in time for your party the 21st; – probably a day or two later.
I am reading a book which is really well & lucidly explained, & to me very interesting; – Mosely’s Mechanics applied to the Arts, &c. Do you know anything of him? – If I can judge from a man’s writing, he is no common person. –
Should there seem no chance after I go to Town, of the much desired great Unknown being found for me, I have some idea of having instead for this season some German lessons. I know a little of it already, & have always intended to know more. Indirectly I think it would bear on some of my objects. . .
Yours most sincerely
A.A. Lovelace
Augustus De Morgan
Augustus De Morgan became Ada’s teacher. He was a friend of Charles Babbage’s, but a much closer friend (because of his wife Sophia Frend De Morgan) of Lady Byron’s. He was considered one of the greatest logicians of the nineteenth century and taught at the University of London. De Morgan assigned work for Ada to do from textbooks, and he met with her about every fortnight, sometimes only once a month. E-mail would certainly have been a great advantage since her instruction was primarily by correspondence.
The language of their mathematical correspondence was full of poetical allusions and metaphor. He talked of algebraic functions “sowing their wild oats”; such allusions were a perfect fit for Ada’s peculiar way of learning. Despite a very flimsy background of what today would be considered a minimum high school mathematics program, Ada quickly moved into differential and integral calculus.
Any conclusion about Ada’s mathematical expertise based on the remains of their correspondence is unwarranted. De Morgan was not paid a fee and as a result Ada most likely did not bother him unless she had a serious problem. Thus, these letters reflect what Ada did not understand, not what she did understand. They are, in statistical terms, a skewed sample—not the whole story. De Morgan knew the whole story and later assessed Ada’s expertise.
The importance of these letters is that they give us a glimpse of the kind of material she was studying and the questions and problems she had. Her questions very often came down to basic principles, as she stated in a letter written in 1842: “what does it mean, & how was it got?”
In one of her first letters to De Morgan she complains about studying many subjects at the same time: algebra, trigonometry, and differential calculus. I showed all of her letters to the late Dr Steven Deliberto, who was vice-chairman of the Mathematics Department at the University of California at Berkeley. He said Ada was studying material on the cutting edge of mathematics at the time. Despite complaints, Ada proceeded always asked questions to clarify what she did not know.
Lady Byron went off to France in the summer of 1840 to visit her cousin Edward Noel, who was married to Ada’s childhood friend Fanny Smith. They had just had a baby girl. Their permanent home was on the island of Euboea in Greece, where Edward acted as Lady Byron’s land agent. Land was cheap, 30 shillings an acre, and Lady Byron invested £1000. In addition, Edward, who had been trained at DeFellenberg’s school, instructed the local population about cooperation and agricultural techniques.
The focus of Lady Byron’s time in France turned to Ada’s cousin Elizabeth Medora Leigh, who lived in Tours. Medora, the daughter of Augusta Leigh, Lord Byron’s half sister, had fallen on bad times. She had gone to France to join her sister Georgiana (who had been Lord Byron’s favorite niece) and her husband, Henry Trevanion. Sixteen-year-old Medora, who was soon pregnant by her brother-in-law, was abandoned and sought help from her mother.
In 1838 Lady Byron had written that she was bored; now faced with Medora’s problems, she had found a situation that interested her. She gave Medora financial aid and invited Medora to join her in Paris. Lady Byron wrote to Ada that she was helping Medora, and Ada was impressed by her mother’s noble actions. Since Medora was Augusta’s daughter, Ada had seen very little of her. Ada expressed some concern over Medora, but Ada was fully occupied with her own problems.
This period of Ada’s life was happy—her letters were enthusiastic and hopeful. She continued to ride her horses, to ice skate, and to socialize with her many scientific friends. Even with all these activities, her mathematical studies proceeded full speed ahead. When her mother expressed concern that Ada was not paying attention to her studies, Ada replied that “Calculus was King.” She was interested in developing skills for a profession. De Morgan cautioned her to slow down, and Ada stepped back and continued to question basic mathematical assumptions, or first principles. To De Morgan she complained about her many errors, moaning about “time lost,” but she realized she gained more from making mistakes.
Ada was doing her best to bring up her children, but handling three children under the age of four was a difficult task. She relied on William’s sister Hester to help her. Lady Byron complained that the children were undisciplined and suggested that Ada consult her friend Mrs Barwell to help find suitable supervision. Taking her mother’s advice, Ada wrote to Mrs Barwell and received more criticism. Mrs Barwell suggested that Ada was “secretive” about how she handled her children.
In 1885, Annabella, later Lady Anne Blunt, recalled what life was like at St James’ Square. She described how they played steeplechase over their beds when the nursemaid thought they were asleep, and how she was constantly hungry. If Byron was eating a mutton chop, she would eye it until he relented and gave it to her. She recalled how she felt no guilt over their raucous behavior.
Ada wrote once again to Mrs Barwell and stated how she intended to handle her own children. She was forceful and clear and according to her perception had the situation under control. She then focused on her studies and made great progress. She began to feel confident and to think about ways that she might help Charles Babbage. It had been a long time since she had seen him, and she invited him for a visit. He was due to come on 10 January 1841.
Poetical Science
Games are a wonderful way to integrate imagination and science. Games not only entertain, but help us learn. Solitaire was a board game that originated in India and came to England in about 1830. You can find out more about the game by going to puzzlemuseum.com
The English Board is the smallest, gapless board, but Ada might have used a different version in 1840 than the one displayed. There are many books today that carry on Ada’s style of thinking about strategies to win a board game.
This web site http://home.comcast.net/gibell/pegsolitaire/#gaplesshht is an excellent source, as well as this book, Winning Ways for Your Mathematical Plays, Volume #4 which contains a peg solitaire chapter.
The best way to exercise your poetical science skill is to develop your own g
ame. Choose a problem, for example teaching a blind person basic skills or perhaps designing a simple game to go on the Internet.
9
In Due Time I Shall Be a Poet, A Scientific Trinity,
A Most Strange and Dreadful History
[1841]
Ada began the year 1841 with high hopes for the future. On 5 January 1841 she wrote at least seventeen pages ranging in content from the personal to the practical to the metaphysical.
She replied to Mrs Barwell’s persistent criticisms about the children by defending them and then wrote to Charles Babbage inviting him to come and tell her all about the latest developments with his Analytical Engine. Since 1834 when he first shared his vision for the Analytical Engine with Ada, he had toiled away on the designs and plans. He believed that no one in England, especially the English government, was interested in his idea, but Ada was interested, and several other people as well.
In the autumn of 1840 Babbage was invited to go to Turin to explain his idea for the Analytical Engine before a gathering of Italian philosophers. He took with him examples of how the engine would handle calculations. Today these iterations would be called “programs.” An engineer soldier in the audience, L. F. Menabrea, was particularly interested. He listened attentively and examined Babbage’s drawings and sample “programs.” The presentation was well received, and King Charles Albert gave Babbage a gold medal.
Babbage, pleased with everything that had transpired in Turin, left by mail coach for England. He recounted the day vividly, years later in his autobiography, and it is striking to compare the following account to the one he described to Ada in 1834, when he foreshadowed his pathway to a new discovery.
Before Babbage and an aide reached Annecy, they crossed a famous suspension bridge named in the King’s honor, the Pont Charles Albert. A third of a mile from the bridge, Babbage descended from the carriage, instructing the postillions to drive slowly across and wait on the far side. The gorge was deep and the bridge itself partly covered in clouds:
We were singularly favoured by circumstances. We saw the carriage which had left us apparently crossing the bridge, then penetrating into the clouds, and finally becoming lost to our view. At the same time the dissolving mist in our own immediate neighbourhood began to allow us to perceive the depth of the valley beneath and at last even the little wandering brook, which looked like a thread of silver at the bottom.
The sun now burst from behind a range of clouds, which had obscured it. Its warm rays speedily dissipated the mist, illuminated the dark gulf at our own side, and discovered to us the mail on terra firma on the opposite side of the chasm waiting to convey us to our destination.
Ada was as interested in the process of scientific discovery as she was in the result of the discovery. To Lady Byron and to many people, science meant and still means “the facts,” or digital, quantitative skills and analysis, based on observation and experimentation. Yet to Ada science meant much more, for it involved the integration of digital skills with what today we refer to as analog skills such as imagination and metaphor. She was her father’s, as well as her mother’s, daughter: the role of imagination was critical to her understanding of science. The romantic poets had discussed the role of imagination in the creation of poetry, and she pondered its connection to science and the process of scientific discovery.
Shelley, her father’s close friend, wrote in the Defense of Poetry that “imaginative language marks the before unapprehended relation of things.” Coleridge’s view of metaphysical poetry was that it was both intelligible and mysterious or imaginative. In her essay of 5 January Ada used what was almost a cliché about imagination to define mathematical language, only to fold this back on itself and claim that the two are indeed, if not identical, necessary for each other. Ada juxtaposed opposites, imagination and science, and saw their necessary connection just as her father did in his description: “I stood in Venice, on the Bridge of Sighs: A palace and a prison on each hand . . .”
Like Holmes’s description of Coleridge, “. . . fascinated by anything that promised poetical marvels or metaphysical peculiarities,” Ada saw in Babbage’s designs the opportunity for scientific miracles and metaphysical speculations. Once Ada saw this approach there was no stopping her.
To Charles Babbage
Tuesday, 5 January [1841]
Ockham
My Dear Mr Babbage. You have put me into a Dilemma, because I should naturally say- Come on Friday, & come again rather later.
If you come this week, you will I believe find us quite alone; if later, suppose about the 15th, there will probably be company. Now we like so much to have you in either circumstances; when alone the pleasure of monopolizing you is so great; when in company, you make the company so tenfold agreeable, that I cannot choose between them. I can only say we wish to see you at all times, & as much as possible
. . .
I much wish to have you here, & talk with you over some of my own doings &c. Today, I have been working much at Mathematics. It has been bad for outdoors, & therefore I have got a lift at in-doors pursuits. –
I must show you a certain book called my Mathematical Scrap-Book. . .
But pray do not think of coming for so very short a time as only 3 nights. It would be shameful! –
Some day or other, you will have to put me in possession of the main points relating to your engine. – I have more reasons than one for desiring this. –
Yours most sincerely
A.A. Lovelace
On Tuesday before Babbage arrived she pondered what scientific discovery was and came to the conclusion it was the combining of imagination and science. She wrote:
“Imagination is the Discovering Faculty, pre-eminently. It is that which penetrates into the unseen worlds around us, the worlds of Science. It is that which feels & discovers what is, the real which we see not, which exists not for our senses. Those who have learned to walk on the threshold of the unknown worlds, by means of what are commonly termed par excellence the exact sciences, may then with the fair white wings of Imagination hope to soar further into the unexplored amidst which we live.
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!”
On 10 January Ada sent De Morgan a fourteen–page letter (not included in this series) filled with differential calculus equations. She concluded that “I am much pleased to find how very well I stand work, & how my powers of attention & continued effort increase. I am never so happy as when I am really engaged in good earnest; & it makes me most wonderfully cheerful & merry at other times which is curious & very satisfactory.”
She reported to her mother she had a “mathematical week,” which she associated with the immense development of her imagination. She speculated that though it might seem strange “I shall in due time be a Poet.”
In response her mother complained about how Ada was bringing up her children. Ada came to her own defense and characterized Ralph, her youngest, as a “troublesome virago.” Years later Ada’s future son-in-law, Wilfrid Scawen Blunt, would have delighted in Ada’s description of Ralph. In his diaries that were not opened until fifty years after his death, and in his private correspondence that I consulted, Wilfrid described Ralph exactly as Ada did. In his diaries Blunt suggested that Ralph should be put in a laundry bag and thrown in the Thames for having made known the dirty family laundry in Astarte, his privately printed memoir of the family letters.
She shared her great enthusiasm for the future with Greig, who, knowing Ada’s personality, cautioned her to go slowly, like a mountaineer, taking it step by step. Ada repeated Greig’s criticism of her to De Morgan by stating that she would try to keep her metaphysical head in or
der.
To her mother she explained why she wanted to develop her mathematical skills along with her imagination. She wrote it was “never to be attained for my own glory, which should be a most subordinate consideration” but for the benefit of mankind. Ada would raise this point of view later with Babbage. At this time her main focus was to get him to come for a visit.
To Charles Babbage
Tuesday, 12 January, [1841]
Ockham
My Dear Babbage. If you will come by the Railway on Friday, we will send the carriage to meet you at Weybridge, for the Train that leaves Town about 4 o’clock & arrives at Weybridge a few minutes before 5 o’clock.
Bring warm coats or cloaks, as the carriage will be probably an open one.
If you are a Skater, pray bring Skates to Ockham; that being the fashionable occupation here now, & one I have much taken to. –
Ada, the Enchantress of Numbers:Poetical Science Page 7
