It was a bittersweet moment when I departed the offices—my task complete, my arms empty, my heart full. I could not wait for the translation to be published, and I dared to think that someday I might look back upon this moment as the beginning of a true mathematical career. I would be an author, I realized, and I could not suppress a smile at the thought. I wondered if my father had felt this same glow of expectation when he learned that his first poem would be published.
I stayed overnight at Saint James’s Square rather than returning immediately to Ockham Park—and what a blissful night it was, my first taste of peace and quiet and blessed solitude in years. The following afternoon I called on Mr. Babbage, after sending a servant to inquire if he would be receiving visitors. He had been ill, I had heard, but inconveniently rather than seriously, and so he had not hosted an evening soirée or gone out in Society for weeks. He had no idea that I had been working on the translation for Taylor’s Scientific Memoirs, and I was looking forward to surprising him with the news, and with a copy of Signor Menabrea’s treatise in English, written in my finest hand.
I found Mr. Babbage hoarse and a bit pale, but cheerful and very pleased to see me. He offered me tea in his drawing room, and we caught up on all the news since the previous autumn. Neither of us mentioned his unfortunate meeting with Sir Robert Peel.
“I have a surprise for you,” I told him, smiling as I handed him the paper-wrapped parcel I had brought along, and which until then he had politely pretended not to notice. “I have been a busy little mathematical fairy all winter, or perhaps I should say une petite fée très occupée, flitting about and making magic with my pen.”
“What is this?” he said, removing the manuscript from its wrappings. As he leafed through the pages, a smile of wonder and delight slowly lit up his face. “Why, Lady Lovelace, this is astonishing. But I must ask, did you write this up for me alone? It appears ready for publication.”
“It is not for you alone. It is for anyone wise enough to purchase the issue of Taylor’s Scientific Memoirs in which it shall appear.” I explained to him about Mr. Wheatstone’s assignment, modestly adding that I had been his first choice as translator.
“Of course you would be. Who better than yourself?” Then his brow furrowed in puzzlement. “But, Lady Lovelace, rather than translating Menabrea’s piece, why did you not instead write an original paper, since this is a subject with which you are so intimately acquainted?”
“Because—” I hesitated. “Because that is not what Mr. Wheatstone requested, and I confess the idea never occurred to me.”
“I see.” Mr. Babbage frowned, thoughtful. “Then perhaps you might consider adding some notes of your own to the work.”
“What sort of notes?”
“Your own observations, of course. Notes illuminating aspects of the Analytical Engine that Menabrea left obscure, as well as those details that have been supplanted by the alterations I’ve made to the design in the meantime.” He regarded me expectantly. “I think that would be a most welcome addition to the translation, don’t you?”
“I agree,” I managed to say, “but don’t you think—”
I broke off, embarrassed to give voice to my doubts. Except for Mary Somerville, who was an extraordinary exception, women almost never published papers in respected scientific journals. When women did write on scientific subjects, it was to make the discoveries and ideas of men of science understandable to ladies with an interest in science, but no expertise. Mr. Babbage was suggesting something entirely different—an original scientific paper written for an audience of scientific men.
It was unimaginable—and yet it was precisely the sort of original scientific work I had longed to do since I was a little girl dreaming of Flyology, the Great Work that would advance human understanding and enshrine my name among those of the greatest scientists, philosophers, and mathematicians of my generation.
“Lady Lovelace?” Mr. Babbage prompted.
“I think it’s a brilliant notion,” I declared, smiling, “and I believe I’m the ideal person to attempt it.”
Chapter Twenty-seven
What Is Writ, Is Writ
February–August 1843
My first task was to write to Mr. Wheatstone and inform him of the proposed changes to my manuscript. He and Mr. Taylor readily agreed to wait to publish the translation until I could compose my notes.
My second task was to obtain copies of Mr. Babbage’s notes and sketches for the Analytical Engine. I had examined them before, but he had altered the design in the meantime, and I would need to refer to them too often in the weeks ahead to rely upon memory alone. Mr. Babbage promptly supplied everything I requested, thousands of pages of drawings and descriptions. He seemed almost as eager as I was for the project to begin.
My third task was to set aside notes, sketches, plans, papers, and translation so that I could prepare for a very happy event—Hester’s marriage to Sir George Craufurd. I will not claim credit for persuading William to give the match his blessing, although I had staunchly taken George’s part whenever the question arose. Instead I think that George, by conducting himself with honor and integrity every day, convinced William that he would be a devoted, faithful, loving husband to Hester. A brother would have to have a heart of stone to forbid a marriage that seemed so certain to bring love, joy, and comfort to a cherished sister, and although William and I were not as close as we once had been, I knew better than anyone that he had a loving heart.
They were wed at Ockham Park on 15 February, a sunny, clear, and frigid day, but the bride was so radiant, the groom so jovial, and the company so merry that we scarcely noticed the cold. We kept warm with dancing, and by drinking spiced cider and mulled wine, and I confess I shed tears of joy when Byron, Annabella, and Ralph, adorably splendid in their wedding finery, kissed their auntie Hester good-bye just before her new husband assisted her into a gleaming black carriage and they set off for their honeymoon through a gentle fall of snow.
As soon as the wedding festivities concluded, I commenced work on my notes in earnest. From the moment I took up my pen, I knew that two challenges in particular confronted me: how to explain clearly the purpose and function of a machine as complex as the Analytical Engine, which frankly was rather difficult for even the most brilliant scientific minds to understand; and how to convince my readers that it mattered, that it was an even more important technological development than the railroad or the Jacquard loom.
I soon realized that I could not accomplish this by simply presenting facts and figures, straightforward and linear, because facts alone could never adequately explain something that had never before been imagined. To convey what a true marvel the Analytical Engine was, I would have to delve into the metaphysical—dare I say the poetical.
And so I threw myself into the work, beginning with what I considered the most essential and most difficult aspects to explain: how the Analytical Engine differed from the Difference Engine (as well as the simpler calculating machine Pascal had created years before), how the Analytical Engine functioned, and what it was capable of doing. It was capable not only of tabulating the results of one particular function, I emphasized, but of developing and tabulating any function whatsoever. In fact, this ingenious machine could act upon any information that could be represented symbolically, not only numbers. “Supposing that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations,” I wrote, drawing upon one of my favorite subjects, music, to illustrate this point. “The engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.”
I described the Analytical Engine in great detail, aiming for clarity and simplicity but also completeness, especially in a long section in which I explained how useful it would be, how it would offer untold practical benefits. My pragmatic readers might agree that the Analytical Engine was
a marvel of technology, but they would remain reluctant to pay for it if they thought it was no more than an object of curiosity. They would never support funding a project that would turn out to be no more than a very expensive and far less charming Silver Lady.
Well aware of how strange and unfamiliar the Analytical Engine would seem to readers who had never seen it, who had not spent years observing it and contemplating it as I had, I endeavored to compare the unknown to the familiar:
The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
There was much more to say on this opening subject, of course, and I said it. As I wrote, I found myself understanding the Analytical Engine even better than I had before, discovering new facets that had eluded my imagination until then. I realized that it could provide two types of results, numerical and symbolic, and thus would be capable of generating not only numbers, but entirely new operations. Wonder and excitement fueled my writing, and when at last the draft was complete to my satisfaction, I titled this portion “Note A,” sent it off to Mr. Babbage for review, and commenced with bolstered confidence and undiminished enthusiasm my work upon Note B.
The next day, the second of July, Mr. Babbage sent me a most gratifying reply. “If you are as fastidious about the acts of your friendship as you are about those of your pen, I much fear I shall equally lose your friendship and your Notes,” he wrote, a comic lamentation. “I am very reluctant to return your admirable and philosophic Note A. Pray do not alter it. All this was impossible for you to know by intuition and the more I read your notes the more surprised I am at them and regret not having earlier explored so rich a vein of the noblest metal.”
Warmed by his praise, and relieved to know that I was proceeding as I should, I toiled away diligently and contentedly, likening myself to a mathematical fairy weaving magic with numbers and words. Throughout July the work offered me respite and distraction from unpleasant developments elsewhere in my life, the bane of persistent illness and the worrisome news from France, where Medora continued to plague and harass us through the post. All this—or most of it, anyway—I was able to put aside as I worked through Notes B, C, D, E, and F, which described in minute detail the mechanical functions and processes of the Analytical Engine.
By that time it had become apparent that my Notes were going to be much longer than the translation of Signor Menabrea’s original treatise, perhaps more than twice as long. “Never mind that,” Mr. Babbage urged me in a brief letter. “You have not included a single extraneous phrase yet, in my opinion. Use precisely as many words as you need to do justice to your subject, no less and no more.”
Heartened, I wrote “Note G” at the top of a fresh sheet of paper and carried on.
In this Note, which I presumed would be the last, I wanted to offer several practical examples of how the Analytical Engine had transcended the bounds of arithmetic the moment punched cards were introduced to the design. Because of that feature, not only the mental and the material, but also the theoretical and the practical in mathematics could be brought into more intimate and effective connection than had ever been possible with any previous machine.
If my readers could understand this, they could not doubt that the Analytical Engine was too important, too revolutionary, to let it remain merely a brilliant but unrealized idea, merely ink on a page.
Of the examples I included, I was most satisfied with my explanation of how the Analytical Engine would generate Bernoulli numbers, an endless sequence of rational numbers that figure significantly in certain functions and formulae. I decided to create an algorithm that the Analytical Engine could employ to generate these numbers easily, quickly, and flawlessly as they tumbled off in an irregular fashion to infinity. This, I knew, would impress my scientific readers more than any other example, due to the complexity of the sequence of operations that must be performed. No other calculating machine in existence could accomplish this feat without human intervention throughout the process. This example would prove that the Analytical Engine was superior and unique.
Naturally, composing this algorithm was easier said than done. “I am doggedly attacking and sifting to the very bottom all the ways of deducing the Bernoulli numbers,” I wrote to Babbage one afternoon. “In the manner that I am grappling with this subject, and connecting it with others, I shall be some days upon it.” Then, reflecting upon how adept I had become at this subject I had studied so long, I quipped, “It is perhaps well for the world that my line and ambition is the mathematical, and that I have not taken it into my head, or lived in time and circumstances calculated to put it into my head, to deal with the sword, poison, and intrigue, in the place of x, y, or z.”
As I struggled with this complex and elusive algorithm, I confess there were moments when I doubted I would succeed. “I am in much dismay at having got into so amazing a quagmire and botheration with these numbers,” I lamented, setting the whole mess aside for a moment to vent my frustration in another letter to Mr. Babbage. But I did not despair, and eventually I was able to neatly resolve the last remaining puzzles.
How exhilarated I felt when the algorithm was complete! I was so thrilled with the accomplishment that I could almost forget my exhaustion, and yet, as I read over Note G, I realized that I must add a caveat or two, lest I raise expectations that the Analytical Engine in all its magnificence could not fulfill. Although I had promised nothing I was not absolutely certain the machine could do, I knew the more skeptical readers in my audience would assume I exaggerated its capabilities unless I also devoted a few lines to what it could not do.
And so I returned to the beginning of Note G and added a word of caution. “It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine,” I noted. “In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable.”
I could think of no more polite and cordial way to plead with my readers to keep an open mind. Then I remembered my mother’s reaction when she had observed the demonstration model of the Difference Engine, how she had referred to it as a “thinking machine.” It would be disingenuous of me, in my enthusiasm, to lead anyone to believe that the Analytical Engine could “think” any more than its predecessor could. And so another caveat: “The Analytical Engine has no pretensions whatever to originate any thing,” I emphasized. “It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths.”
With that Note G was complete.
But of course, I was far from finished. Throughout the spring and summer I had sent Mr. Babbage my work in progress, received his comments, and revised my Notes accordingly. Our exchange was humorous, delightful, illuminating, and occasionally infuriating. Sometimes he sent me praise and useful comments, and we bantered teasingly back and forth about how I was like a fairy using my magic in his service. Then, on other occasions, I confess I sent him snappish, indignant letters complaining about changes he had made to my writing. “I am much annoyed at your having altered my Note,” I wrote in mid-July. “You know I am always willing to make any required alterations myself, but that I cannot endure another person to meddle with my sentences.
”
Then, less than a week later, I became furious with him after he confessed that he had somehow misplaced several important pages of the manuscript, obliging me to redo work that had been tedious and difficult to create in the first place. “I have always fancied that you were a little harum-scarum and inaccurate now and then about the exact order and arrangement of sheets, pages, and paragraphs, et cetera,” I huffed, thoroughly exasperated. “Witness that paragraph which you so carelessly pasted over! I suppose that I must set to work to write something better, if I can, as a substitute. The same precisely I could not recall. I think I should be able in a couple of days to do something. However I should be deucedly inclined to swear at you, I will allow.”
I did not swear at him, though, and he replied with such abashed apologies that I quickly forgave him. It would have been my own undoing not to, for our collaboration was proceeding so well—aside from the aforementioned incidents and a few others involving his careless substitution of a previous version of a table for one that had been properly revised—that I cannot think how I would have fared without him.
The more I worked upon my Notes, the prouder I became. I began to refer to them as my firstborn mathematical child and expressed hopes that other younger siblings might follow it. “I cannot refrain from expressing my amazement at my own child,” I wrote to Mr. Babbage as my revised Notes were going into proofs. “The pithy and vigorous nature of the style seems to me to be most striking; and there is at times a half-satirical and humorous dryness, which would I suspect make me a most formidable reviewer. I am quite thunderstruck at the power of the writing. It is especially unlike a woman’s style surely; but neither can I compare it with any man’s exactly.”
Enchantress of Numbers Page 46