Enchantress of Numbers

by Jennifer Chiaverini

  While our mothers were off pursuing good health and vitality, I passed the time with Lady Gosford’s daughters, Annabella, who had been named after my mother, and Olivia. They were five and four years older than I, respectively, but I was enough like my mother that I took the lead. They were amiable and bright girls, but rather indolent, so when they spoke admiringly of my love of learning, I offered to tutor them in mathematics. I hoped that at least one of them would be inspired to take up mathematics as I had done. Annabella seemed to be the most likely candidate; Olivia preferred music, but that did not lower her in my esteem, because I loved music too.

  I quite enjoyed teaching, and my friends were avid to learn, so when my mother decided it was time to resume our tour, we agreed to continue our lessons through the post.

  I was quite surprised when my mother announced that our next destination was Doncaster, so that I could see the races. Just as she had sent me to see my first opera so that I could make an informed judgment, she wanted me to observe the famous racecourse “on principle,” as she put it. “I abhor gambling,” she said, “and I am indifferent to horses as long as they pull my carriage well, but want you to see for yourself how shamefully people disport themselves there. If I forbade you to go to the races, you would only become more curious and seek them out somehow. When you see them for what they are, they shall no longer tantalize you.”

  They never had tantalized me until my mother described them in such enticing terms, but I adored horses and my curiosity was piqued, so I was willing to defer our return to London a little while longer. Doncaster proved to be quite unlike anyplace I had visited before. The crowds were drunken and riotous, and my ears fairly burned from the shouted curses I overheard when a sure bet faded in the home stretch, but I found it new and exciting, and I was not at all repulsed. The horses were beautiful, magnificent, and I never tired of watching them run, and when a gentleman seated near us won fifty pounds, in my excitement I was tempted to ask my mother if I might place a bet. Fortunately I thought better of it, and I pretended to be shocked and dismayed by the boisterous antics of the gamblers, but I knew my mother’s plan to make me dislike the races had failed utterly.

  From Doncaster we returned to Fordhook, and over the last five miles I mentally composed a letter to Mr. Babbage, asking if I might call on him as soon as I could travel to London, for my tour of the industrial Midlands had inspired me with an idea for an adaptation to his Difference Engine.

  At last we reached home, for I had come to think of Fordhook as home. I intended to get started on my letter right away, but my mother insisted that I unpack before I did anything else, and then I wanted to see Puff and check on my horses. By the time I returned indoors, my mother had sorted the post that had arrived in our absence, and there was a letter for me.

  27 September 1834

  Royal Hospital Chelsea

  My Dear Miss Byron,

  With a sorrowful heart, I write to inform you of a tragedy that has struck our good friend Mr. Babbage. Yesterday afternoon, his daughter, Georgiana, passed away after a sudden illness. There are no words for this, the worst heartbreak a parent can suffer, and I know he will rely upon the consolation of friends to endure it.

  I regret that this letter will reach you just when you will have arrived home after a long journey. Please accept my apologies for diminishing the happiness of your homecoming, and extend my apologies to your most excellent mother as well.

  I remain, as always, your friend,

  Mary Somerville

  Chapter Eighteen

  With My Knowledge Grew the Thirst of Knowledge

  October 1834–January 1835

  Miss Georgiana Babbage was only seventeen when she perished, as shy as her father was confident, fair-haired, blue-eyed, sweet, and smiling. Although we were close in age, I did not know her well. She did not live with Mr. Babbage but with her paternal grandmother and two younger brothers on Devonshire Street, a ten-minute walk away, and since she was not yet out in Society she had only rarely attended her father’s soirées. Still, I had always liked her, and I had hoped that we would become very good friends in time. Too late I wished that I had befriended her when I had had the chance rather than taking for granted that we had years and years ahead of us. But overwhelming every other feeling was sorrow for Mr. Babbage, and a deep, helpless regret that I could do nothing to ease his suffering.

  My mother and I had received the news of Georgiana’s death too late to attend the funeral, but as soon as my mother could make arrangements, we traveled to London to pay our respects to her family.

  The Dorset Street house, the setting for so many merry gatherings, was shrouded in the colors of mourning—black crepe on the front door and over the mirrors and above his daughter’s portrait in the sitting room. Mr. Babbage’s mother greeted us when we arrived, served us tea, and accepted our condolences with a heavy heart. She told us that she and Mr. Babbage’s three sons—all the children that were left to him of the eight his wife had borne—were staying with him at present, but Herschel, the eldest, would likely return to his engineering apprenticeship soon, and she expected to take the two younger boys back home with her when she departed.

  “We’ll stay as long as he needs us, of course,” she said, but she abruptly broke off when Mr. Babbage appeared in the doorway.

  He was dressed in a black suit and armband, and when he greeted us his manners were as gracious as ever, but his eyes were red and his face was haggard and drawn, and his expression betrayed an unsettling air of bewilderment. He thanked us gruffly when we offered our condolences, but otherwise he diverted our few attempts to reminisce about Georgiana. We spoke instead of Mrs. Somerville’s book, which I had read twice since Mr. Murray had presented me with a copy in March and my mother had finished while we were in Buxton. A trace of his familiar animation returned while the subject was science, but not even that could distract him from his sorrow for long. On the way over, my mother and I had agreed that we should take care not to exhaust him, but just as I was beginning to worry that we were approaching that moment, my mother gave me a subtle signal that we should depart.

  Mr. Babbage led us to the door, and just before we left, he said, “I’ve decided not to hold my regular weekly soirées for the time being.”

  “Of course, Mr. Babbage,” said my mother, surprised. “I assumed you would not.”

  “But I would like you to call again soon,” he quickly added, his gaze flicking from my mother to me. “I had some thoughts about the Difference Engine that I’d like to share with you, Miss Byron.”

  “I’ve had some as well,” I told him. “Our industrial tours were most illuminating. I’ll return whenever you’re ready to receive me.”

  “Let it be soon,” he said hoarsely. “Work is the only remedy for grief—work, toil, and time. I must think of something else or I’ll—” His voice broke off and he shook his head, and I saw to my dismay that his eyes were shining with tears. “Call on me soon. We have much to discuss and even more to do.”

  I bowed assent, and as my mother and I departed, my heart ached to think that we were leaving him alone with his pain. If he believed that work would distract him from his grief, I was determined to provide it.

  I would have returned the next day if my mother had permitted, but my mother said that would be disrespectful and inconsiderate, and she insisted that I wait a week. When she finally decided I might go, she was feeling indisposed and could not accompany me, but since his mother would be present, she agreed that I might go alone.

  Mrs. Babbage remained with us long enough to serve tea and to ask after my mother’s health, but she soon excused herself and left us alone to discuss the Difference Engine. “I have decided, in honor of my beloved daughter, to devote myself to solving a difficult problem with the machine,” Mr. Babbage told me, his gaze piercing and determined. “The arduous effort it requires shall occupy my thoughts and exhaust me enoug
h that I shall be able to sleep at night. My inevitable success—for I shall not rest until I solve this problem—will be a fitting tribute to my Georgiana, who loyally believed me capable of anything.”

  I felt a pang of worry. “Are you not sleeping, Mr. Babbage?”

  “Not well,” he said curtly, dismissing that concern as unworthy of further discussion. “The problem I speak of resides not in the engine, but in the formulae. For certain calculations, the results become increasingly inaccurate as the creation of the table progresses, because some values have to be rounded off.”

  “Not just some numbers, but many,” I said, nodding. “Every repeating decimal, in fact.”

  “Precisely. Certain numbers consist of an infinite number of decimals—one divided by three, for example—but it is impossible to create an engine with an infinite number of cogwheels.” He leaned forward, impassioned. “What I must do is to find a way—some new device or adaptation—that would eliminate this persistent, compounding reduction in accuracy. I think—that is, I believe very strongly—that such a machine would also then be capable of far more than creating mathematical tables.”

  “It’s an intriguing concept,” I said, my excitement rising. “Perhaps I have an idea that may help you find that solution.”

  Eagerly I told him about the Jacquard loom—the speed, accuracy, and complexity of its production and the punch cards that controlled it. Mr. Babbage listened intently, nodding, and when I finished he told me that he had seen a Jacquard loom at work many years before but had not considered that its system of imparting instructions could be applied to a calculating machine. “I sense that it could work,” he said, “but how to adapt it to the mechanisms of the Difference Engine, I cannot quite envision. But it could be possible.”

  “I’m relieved that you think so,” I confessed. “I was afraid that I had overlooked some obvious fatal flaw that would oblige you to dismiss the idea out of hand.”

  “I would never dismiss any of your ideas out of hand,” he protested. “On the contrary, Miss Byron, I marvel at your insight. Not one in a hundred thousand people would observe a loom at work and consider how its mechanism might improve a calculating engine. I’m quite astounded by the powers of your imagination.”

  “Thank you, Mr. Babbage,” I said, warming to the praise. How unfamiliar and new was the inflection Mr. Babbage gave to that word, “imagination,” which had always conveyed so much apprehension and warning when my mother spoke it. How unexpected and strange and somehow reassuring it was to hear imagination valued as much as intellect.

  We chatted more about the Difference Engine, examining from one perspective and then another the problem of repeating decimals and compounding errors. I mused aloud that I could better understand the workings of the engine if I had illustrated plates or plans to study on my own, and he promised to have copies of both sent to me at Fordhook. In the meantime, he let me borrow several papers about steam engines he thought might interest me, and when I promised to return them as soon as I copied them over, he said, “Take all the time you require. I trust you implicitly, and I know my papers will be as safe in your care as they would be on my own bookshelves.”

  Mr. Babbage’s praise lingered in my thoughts for several days afterward, and I found it very curious how much I cherished it. This was not a man who would stifle anyone’s intellectual or imaginative pursuits, I realized, not even a woman’s. He would celebrate her genius and encourage it to thrive.

  One evening, as my mother helped me dress for a ball, I could not help reflecting upon what was meant to be the primary purpose for me to attend—to attract the interest of an eligible gentleman. My thoughts turned to my recent conversation with Mr. Babbage, and I mused aloud that he possessed many of the qualities I thought I would be wise to look for in a husband.

  “Oh, Ada, no,” my mother said, appalled. “You cannot think of marrying Mr. Babbage.”

  “I didn’t say I wanted to marry him, only someone like him.” But my instinctive, defensive reply jolted me with the realization that, unbeknownst even to myself, I had considered it.

  “He is almost forty-four,” my mother protested. “More than twice your age.”

  “Why should that matter? Girls my age marry older widowers all the time.”

  “Ada,” she said firmly, taking me by the shoulders and fixing me with a steady look, “has Mr. Babbage spoken to you of marriage? Do you have an understanding with him?”

  “Of course not,” I replied, indignant. I had no right to take offense; I had made a secret engagement once before, and for all she knew, I might again. “We’re friends, that’s all—but I meant what I said, before you misinterpreted my innocent admiration. Mr. Babbage has many admirable qualities that I would like my future husband to have also. Courtesy, for one. Kindness. Intellectual curiosity. A passion for mathematics and science. The sincere belief in women’s capabilities and genius. That’s all that I meant.”

  “Ada,” my mother said again, but her tone was softer. “I agree that Mr. Babbage has many virtues. However, I am very glad that he has not proposed to you, for you would have to refuse him.”

  “Why? Because of the difference in our ages?”

  “You must marry someone of our own class,” she said, bewildered, because of course I ought to know this already. “Wealth is not enough. Your husband must be an aristocrat, ideally with a title more than a century old. These things matter. They always have and they always will.” She released my shoulders and studied me as if she suspected I might be a changeling, and her real daughter, the dutiful, pious, serene child she should have been dressing for the ball that evening, was languishing in the land of fairy. “You’re very lucky you’re still regarded as eligible to marry at all. If certain stories from the past were to emerge—”

  I felt a jolt of fear. “I’m not the same person I was last year. I’ve worked very hard to redeem myself in your eyes, and I wish you would believe me that I’ve changed, changed utterly.”

  The appraising look she gave me said more clearly than words that she could never be certain. She would worry that I might yet fall into irredeemable ruin until the day I was safely wed.

  How grateful I was for friends and mentors who knew nothing of the scandal in my past, who never looked at me with apprehension, as if I were a wild beast that had not yet figured out that the lock on its cage was broken. I could not bear to disappoint them, especially Mr. Babbage and Mrs. Somerville, who respected my genius, held high expectations for me, and seemed to genuinely like me. Thus when Mrs. Somerville expressed misgivings that I was ignoring the requisite feminine accomplishments in favor of Euclid, I offered to sew her a new cap as soon as I finished the bonnet I was making for myself. And when Mr. Babbage, as promised, sent the illustrated plates and several pages of notes about the Difference Engine, not only did I write to thank him profusely before I allowed myself the pleasure of studying the pages, but I also wrote to Mrs. Somerville and asked her to thank him on my behalf the next time she saw him, in case my letter was delayed.

  As the autumn days grew colder, I rode every day, savoring the brisk air, the brilliant colors of the foliage overhead, and the sweet melancholy of a once bright season fading into winter. Each afternoon I practiced my music, not only voice and guitar but also the harp, which especially captivated my interest in those days. I spent hours examining Mr. Babbage’s illustrations and notes, and I studied mathematics with increasing delight, making swift progress thanks to Mrs. Somerville’s gentle guidance, although Dr. King was still officially my tutor.

  In mid-November, Mr. Babbage invited my mother and me to attend a small gathering at his home, the first he had hosted since his daughter’s death. It would not be one of his famous soirées, he hastened to explain, even though it would take place on a Saturday, but something rather smaller and quieter. My mother had a prior commitment regarding her Ealing Grove school and could not attend, but she app
roved of my intellectual circle of friends, and since Mrs. Somerville would also be present, she agreed that I could attend if one of the Furies accompanied me. Of the three, only Miss Montgomery reluctantly admitted that she was free that evening, and since the alternative was to stay home, I resigned myself to her company.

  Fortunately, soon after our arrival, Miss Montgomery struck up a lively conversation with Mrs. Babbage and quite forgot about me, so I was able to slip away and find Mr. Babbage, who had gathered with Mrs. Somerville, Mr. Dickens, Mr. Lyell, and a few others in the library. What a fascinating circle of friends I had acquired, I marveled, reflecting upon my lonely childhood, when my few playmates had been judiciously selected by my mother and had rarely been in my company. I could not help wondering, wistfully, how much happier I would have been if I had met them long ago.

  My friends were discussing politics, not science or mathematics, but a frisson of tension in the air told me that the conversation could become quite animated, so I greeted everyone pleasantly, found myself a chair next to Mr. Dickens, quietly congratulated him for several excellent sketches and essays he had recently published, and settled in to watch the show.

  Mr. Babbage could not keep to his chair, but bounded out of it and paced back and forth, agitated. “These rumors are diabolically confounding,” he said, glowering. “I just want to know if he’s in or out, and if he’s out, who’s going in?”

  “Are we talking about sport?” I asked innocently.