Enchantress of Numbers

by Jennifer Chiaverini

  It was all I could do to restrain myself from skipping with glee. Mr. Babbage had already decided there would be another visit.

  “I do have another lady I would like you both to meet,” he said, his smile turning mischievous. “You’ve come just in time. I was just about to show her off.”

  Mystified, my mother and I exchanged a look—my mother raised her eyebrows; I shrugged—and we followed Mr. Babbage into an adjacent drawing room, where already at least three dozen other guests had gathered. I recognized a few of them from Lord and Lady Copley’s party, and still others from the Court Ball, including Arthur Wellesley, first Duke of Wellington, former prime minister and great military hero who had defeated Napoléon at Waterloo. When Mr. Babbage entered, conversations trailed off and everyone turned to face him, expectant and curious. When the people shifted, I glimpsed a gleam of silver behind them, and I realized they had gathered around an object standing upon a table in the center of the room.

  “Come closer, everyone,” Mr. Babbage beckoned as he headed toward the table where the mysterious object was displayed. His guests parted for him, but I was obliged to wend my way through the crowd to a better vantage point, quickly, so that I did not miss a moment of whatever exhibition was about to begin.

  What I saw made me gasp in wonder: an exquisite silver automaton, a perfectly and delicately fashioned female figure about a foot tall, every feature rendered in astonishingly lifelike detail. Clad in the pink-and-green Chinese crêpe costume of a ballerina, she was posed in a graceful arabesque, and upon her right forefinger perched a tiny silver bird.

  A hush fell over the room as Mr. Babbage pressed the dancer’s back, activating a mechanism concealed by her costume. With scarcely a sound, she gracefully glided forward, raised her hand, and tilted her head as if to observe the tiny bird on her finger as it flapped its tail, spread its wings, and opened its beak. The bird held still once more, the dancer pirouetted and glided back to her starting position, and after a moment, the mechanical dance began anew.

  A murmur rose, and a smattering of applause broke out. Enchanted, I gazed at the graceful silver figure as it smoothly danced forward and back, compelled by some sort of clockwork mechanism concealed within the slender silver form. “How marvelous,” I breathed, drawing closer, longing to trace the lines of the dancer’s face with my fingertip. Even her eyes seemed alive, full of mischief and imagination. “Did you create her, Mr. Babbage?”

  “I did not design her, but I did assemble her,” Mr. Babbage clarified, addressing his reply to the room. “I first observed my Silver Lady as a boy, when my mother took me to visit Merlin’s Mechanical Museum in Hanover Square.” A few chuckles of recognition and remembrance went up from the older members of his audience, but I had never heard of it. “Clockworks and automata fascinated me, as did nearly anything mechanical, and as I gaped at the musical clocks, and the steel tarantula that crawled out of its box and scurried about, and the umbrellas that opened and closed without the touch of a human hand, Mr. John Joseph Merlin himself took note of my precocious understanding of mechanics. He invited me to tour his attic workshop, where he was constructing newer, more extraordinary mechanized wonders.” He gazed at the dancer with fond admiration. “This lovely creature was among them.”

  “She is rather scantily clad,” said one gray-haired lady, raising a lorgnette to her eyes and studying the Silver Lady reprovingly. “She is in need of a petticoat.”

  “My dear Lady Morgan, I am very much indebted to you for your helpful suggestion,” said Mr. Babbage, so dryly that I suspected he had already dismissed it. “As I was saying, Mr. Merlin had many astonishing works in progress in his workshop, but many of them were yet incomplete when he died thirty years ago. His museum closed in 1803, and his collection, including the contents of his workshop, was acquired by Mr. Thomas Weeks, a jeweler, who opened his own mechanical museum on Tichborne Street in Haymarket. Perhaps some of you remember it.”

  I glimpsed a few nods here and there, but I did not offer one, nor did my mother, who had joined me in the innermost circle around the Silver Lady. She frowned slightly to rebuke me for darting off, but I kept my gaze fixed on the dancer and pretended not to notice.

  “It was a rather impressive museum, one of the better of its kind, with a main gallery more than one hundred feet long, lined with blue satin.” For a moment, Mr. Babbage’s eyes took on a faraway look. “But as we all know, fashions change. The mania for intricate automata faded, and eventually, Weeks’s Mechanical Museum closed too. His collection went up for auction—”

  “And you were first in line to purchase the lot?” a man interrupted, to the amusement of the other ladies and gentlemen.

  Mr. Babbage shook his head, smiling, and waited for the laughter to fade. “Not the entire collection, certainly not. Only this exquisite creature, which I discovered in pieces in an attic, utterly and disgracefully neglected. For a bid of twenty-three pounds, I acquired the dancer and a box of her spare parts, which I brought home, carefully restored, and meticulously assembled into the Silver Lady you see before you.”

  “Money well spent,” remarked another gentleman.

  “You have certainly been a skilled and faithful Pygmalion to your lovely Galatea, Mr. Babbage,” said a lady.

  He gave her a little bow. “Thank you, Lady Bennett.” He pressed the dancer’s back a second time, and she halted, frozen in a graceful arabesque once more. “Now, my friends, if you would follow me into the next room, I shall show you an even more astonishing mechanical marvel.”

  My pulse quickened as Mr. Babbage opened a different door than the one we had entered through, and I joined the throng filing into the adjacent chamber. I was at the trailing end, and I paused just inside the doorway to allow the crowd to disperse throughout the room, the better to take in the miraculous invention from a distance before drawing closer to inspect the details.

  And there it was—Mr. Babbage’s Difference Engine. Like the Silver Lady, the model stood upon a table in the center of the room, an intriguing apparatus of gleaming brass and steel about the size of a steamer trunk placed on one end. Sturdy brass columns supported two heavy brass plates between which were an assemblage of interlocking gears and levers, as well as many wheels with numerals engraved upon their edges, horizontally aligned and arranged in vertical columns along axes. A crank handle was fastened to the top of the machine, the handle facing downward. There was neither ornamentation nor embellishment, and whereas a watchmaker usually concealed the workings of his timepieces behind a decorative clockface, the functioning mechanisms of Mr. Babbage’s demonstration model were visible to the observer from every angle.

  “Your Grace, ladies, and gentlemen,” Mr. Babbage intoned from the top of the room, “you are about to behold a calculating machine like none ever created before, or even dreamed of. At one-seventh the finished size, I give to you . . . the demonstration model of the Difference Engine.”

  His audience applauded, myself perhaps loudest of all, and our eyes followed the inventor as he strode toward the large central table supporting the machine. He circled it once, inspecting it thoroughly, and then, tucking one hand behind his back and grasping his lapel with the other, he said, “Earlier today, I set up the Difference Engine to execute a simple mathematical operation, the increase of a number in increments of two. We will begin at zero.” He smiled. “We are all so familiar with this particular calculation that each of us will know immediately if an error occurs.”

  A few chuckles went up from the crowd, and I observed many nods and murmurs of anticipation too.

  Mr. Babbage placed his hand on the crank at the top of his machine. “And now, my friends, you’re going to witness something truly extraordinary.”

  I felt a thrill of excitement, even as my mother gave a skeptical sniff. Mr. Babbage cranked the handle vigorously, and with a whir of cogs and wheels, the entire array was set in motion. He stepped back, his gaze
fixed on the engine, and even as he did the figure wheels began displaying the anticipated sequence, 0, 2, 4, 6, 8, 10 . . . and on and on.

  It was most impressive in its accuracy and regularity, but after a time I sensed the people around me losing interest in its perfection. Just as I, too, was beginning to wonder if Mr. Babbage intended to show us anything else, he suddenly gave the handle another vigorous crank. Suddenly, without any intervention on his part, the number displayed leapt ahead a few dozen to 121, which became 123, then 125, 127, and on and on in the sequence he had originally promised.

  There were a few gasps and murmurs of surprise. “How did it do that?” I asked, incredulous. “How did you make it change to a new value out of sequence and then continue on as before?” Machines simply did not behave that way. They were never so . . . erratic. Not like people.

  “Something must have gone wrong,” a gentleman declared, gesturing imperiously at the machine. “A fly, or perhaps a large spider, got caught in a cogwheel and threw it off kilter.”

  “I assure you, my good fellow, nothing has gone wrong.” With a touch upon a lever or two, Mr. Babbage stopped the whirring and spinning of the engine. “We shall try again, and prove it. This time you may give me the values.” He turned to his right, and his gaze alighted upon the Duke of Wellington. “Unless the honor should go to His Grace the duke?”

  “By all means, His Grace should decide,” said the other gentleman diffidently.

  The duke thought for a moment and said, “Let us make the interval of increase be five, and let the value leap ahead fifteen when it reaches thirty.”

  “Very good, sir.” Mr. Babbage nodded approvingly and commenced working behind the machine. I heard the faint click of levers, and I quickly made my way around the edge of the table so that I could better observe what he was doing, but the calculation was apparently so easily arranged that he was almost finished by the time I drew close enough to see. I did glimpse something that had been hidden from my view before: several pieces of sheet music apparently left upon the table and forgotten.

  “Remember His Grace’s formula,” Mr. Babbage instructed us, and again he turned the crank, releasing it with a flourish. I quickly returned to the front so I could see the display wheels—and there the sequence was, exactly as it should have been: 0, 5, 10, 15, 20, 25, 30, 45, 50, and onward.

  An exclamation of surprise rose from the onlookers, and this time the applause was not merely polite. But Mr. Babbage was not finished. Adjusting the levers, he had his Difference Engine raise numbers to their second and third powers, quickly and perfectly every time. Next, he extracted the roots of a quadratic equation, and although we did not have sufficient time for him to show us, he declared his machine was capable of a great many other astonishing mathematical feats, including the generation of a table of all the prime numbers between zero and ten million.

  “This machine is sublime,” I heard my mother say in an undertone, and I tore my eyes away from the machine to stare at her, astounded. I could not believe that she had been converted from a skeptic to a believer in the space of a quarter hour.

  “Pray, Mr. Babbage,” ventured a lady, “if you put wrong figures into the machine, will the right answers still come out?”

  To me the answer was so obvious that I could not believe anyone would ask the question, but Mr. Babbage smiled affably and said, “No, my dear lady. The Difference Engine is not capable of guessing what I intended. It knows only what I instruct it to do.”

  “Your machine is most impressive, Mr. Babbage,” said the Duke of Wellington, nodding thoughtfully. “Aside from not reading our thoughts, which I’m rather glad is beyond its abilities, is there nothing mathematical your Difference Engine cannot do?”

  “Nothing,” Mr. Babbage replied firmly, but then his gaze fell upon the sheet music lying on the table. Snatching up the pages, he quipped, “It can do everything except compose country-dances.”

  A ripple of laughter went up from the room, but my own amusement dimmed when I realized that my mother had not joined in.

  “I can see how your Difference Engine would be very useful to a general conducting a military campaign,” the duke said, “with so many numbers and factors to consider.”

  “Indeed, but I think its greatest benefits will be seen in commerce and industry.” Mr. Babbage paused significantly before adding, “However, we will not fully realize the extent of its capabilities and the vast reach of its benefits until the full-scale Difference Engine is constructed.”

  He regarded the Duke of Wellington with eager anticipation, but if he had expected a grand pronouncement, he was disappointed, for the duke merely nodded, thanked him for the demonstration, and departed the room accompanied by a few companions. This signaled to the rest of us that the exhibition was over, and while some guests lingered to admire the Difference Engine, still more returned to the drawing room to admire the Silver Lady again, and almost everyone else followed the duke’s example and rejoined the rest of the party.

  I was among those who remained with the Difference Engine, my heart pounding with excitement as I circled the table, admiring the beautiful instrument from all sides. It was ingeniously crafted, not as enchanting to the general observer as the Silver Lady, perhaps, but more complex and impressive. A closer look revealed to me that the numbers were arranged on consecutive carriages comprised of toothed wheels, each of which was marked on the edge with ten digits. When in the course of performing addition a wheel passed from nine to zero, the projecting tooth moved a lever to activate values in other places—tens, hundreds, thousands, and on.

  How enraptured I was as I beheld the Difference Engine in all its mechanical wonder! Tears sprang to my eyes as if I gazed upon Michelangelo’s David—for to me, it was no less a profoundly magnificent work of art.

  “I confess I have but faint glimpses of the principles by which it works,” my mother said in an undertone when I passed her a second time. I almost laughed, certain that she was joking, for she had studied Euclid in the original Greek when she was quite young, and her understanding of various intellectual concepts had always surpassed mine, except for subjects that she deliberately avoided due to profound lack of interest, such as Flyology and animals. It was disconcerting to think that I might grasp the intricacies of Mr. Babbage’s invention better than my mother.

  Yet the Difference Engine was as mechanical as it was mathematical, and unlike myself, my mother had not spent a good amount of her childhood dismantling clocks and windup toys to see how they worked. That surely explained how something that was obvious to me mystified her—although why I was so anxious to prove my mother’s intellectual superiority, I could not say.

  Mr. Babbage approached us then. “Lady Byron, your reputation as a lady of singular understanding precedes you,” he said. “I’m very curious to know what you think of my engine.”

  Her expression was serene as she studied it critically. “I believe your thinking machine has utterly captivated my daughter’s imagination.”

  That last word always carried a note of warning whenever my mother spoke it, but Mr. Babbage would not know that. “It isn’t a thinking machine, Mama. It cannot think,” I said in a rush.

  “It has captivated Miss Byron, you say,” Mr. Babbage mused, regarding my mother appraisingly. “What about you?”

  “I marvel at it,” she admitted. “To think that your apparatus could carry out these finite differences swiftly and with unvaried perfection indefinitely, to make more calculations than the world has known of days and nights—I find myself astonished and humbled.”

  “Thank you, Lady Byron.”

  “There is a sublimity in what you have shown us, perhaps unwittingly, of the ultimate results of intellectual power.” She regarded him frankly. “One question remains.”

  “Only one?” Too late, I pressed my lips together. I truly did not mean to be impertinent.

  My mo
ther gave me a slight frown. “One for now.” Turning back to Mr. Babbage, she said, “Your demonstration of the Difference Engine was well done, despite the occasional touch of a showman’s hyperbole.” Mr. Babbage seemed to strangle back a laugh, but my mother ignored it. “Why did you have to diminish the good impression you had made with that reference to country-dances—and in the presence of the Duke of Wellington, of all people?”

  “Ah. You think I blundered.” He shook his head. “My good lady, don’t assume for a moment that the sheet music had been left on the table by accident. I need the Duke of Wellington. I need him to be impressed by my engine, and I need him to remember how he felt upon seeing it work its marvelous calculations, and not to allow those impressions to be buried beneath the flood of other concerns that I’ve no doubt inundates him every day.” He threw me a comically helpless look, and I nodded encouragement. “The duke frequently attends balls, and country-dances are in fashion. I hoped my little jest would linger in his memory so that every time he encounters a country-dance, whether as dancer or observer, he shall be reminded of my Difference Engine.”

  “You desire his patronage?”

  “Miss Byron, if I am ever to complete the full-scale Difference Engine, I fear that I desperately need his patronage.” Suddenly he smiled, and his serious mood seemed to lift as his genial gaze took in each of his listeners in turn. “I believe that there is no aspect of our lives which cannot be improved by the uplifting benefits of technology. The challenge is to convince the gentlemen who control the national purse to give me enough funding to prove it.”

  His remark evoked somber nods and sympathetic smiles from the others, which made me suspect that a tale of financial woes and torturous politics had inspired it. Before I could inquire, Mr. Babbage gestured to the door and urged us all to rejoin the other guests before they polished off all the delicious food and drink he had prepared for us.

  My mother took my arm, as if she sensed my mind working frantically on a scheme to remain behind to study the marvelous machine in solitude. Reluctantly, I followed Mr. Babbage from the room along with everyone else, but I gave the Difference Engine one last, long, yearning glance over my shoulder before our host closed the door behind us.