* * *
William King was socially prominent, financially secure, quietly intelligent, and as taciturn as Ada was excitable. Like her, he was a student of science, but his focus was more practical and less poetic: his primary interests were crop rotation theories and advances in livestock breeding techniques. He proposed marriage within a few weeks of meeting Ada, and she accepted. Her mother, with motives that only a psychiatrist could fathom, decided it was imperative to tell William about Ada’s attempted elopement with her tutor. Despite this news, William was willing to proceed with the wedding, which was held in July 1835. “Gracious God, who has so mercifully given you an opportunity of turning aside from the dangerous paths, has given you a friend and guardian,” Lady Byron wrote her daughter, adding that she should use this opportunity to “bid adieu” to all of her “peculiarities, caprices, and self-seeking.”19
The marriage was a match made in rational calculus. For Ada, it offered the chance to adopt a more steady and grounded life. More important, it allowed her to escape dependence on her domineering mother. For William, it meant having a fascinating, eccentric wife from a wealthy and famous family.
Lady Byron’s first cousin Viscount Melbourne (who had the misfortune of having been married to Lady Caroline Lamb, by then deceased) was the prime minister, and he arranged that, in Queen Victoria’s coronation list of honors, William would become the Earl of Lovelace. His wife thus became Ada, Countess of Lovelace. She is therefore properly referred to as Ada or Lady Lovelace, though she is now commonly known as Ada Lovelace.
That Christmas of 1835, Ada received from her mother the family’s life-size portrait of her father. Painted by Thomas Phillips, it showed Lord Byron in romantic profile, gazing at the horizon, dressed in traditional Albanian costume featuring a red velvet jacket, ceremonial sword, and headdress. For years it had hung over Ada’s grandparents’ mantelpiece, but it had been veiled by a green cloth from the day her parents had separated. Now she was trusted not only to see it but to possess it, along with his inkstand and pen.
Her mother did something even more surprising when the Lovelaces’ first child, a son, was born a few months later. Despite her disdain for her late husband’s memory, she agreed that Ada should name the boy Byron, which she did. The following year Ada had a daughter, whom she dutifully named Annabella, after her mother. Ada then came down with yet another mysterious malady, which kept her bedridden for months. She recovered well enough to have a third child, a son named Ralph, but her health remained fragile. She had digestive and respiratory problems that were compounded by being treated with laudanum, morphine, and other forms of opium, which led to mood swings and occasional delusions.
Ada was further unsettled by the eruption of a personal drama that was bizarre even by the standards of the Byron family. It involved Medora Leigh, the daughter of Byron’s half sister and occasional lover. According to widely accepted rumors, Medora was Byron’s daughter. She seemed determined to show that darkness ran in the family. She had an affair with a sister’s husband, then ran off with him to France and had two illegitimate children. In a fit of self-righteousness, Lady Byron went to France to rescue Medora, then revealed to Ada the story of her father’s incest.
This “most strange and dreadful history” did not seem to surprise Ada. “I am not in the least astonished,” she wrote her mother. “You merely confirm what I have for years and years felt scarcely a doubt about.”20 Rather than being outraged, she seemed oddly energized by the news. She declared that she could relate to her father’s defiance of authority. Referring to his “misused genius,” she wrote to her mother, “If he has transmitted to me any portion of that genius, I would use it to bring out great truths and principles. I think he has bequeathed this task to me. I have this feeling strongly, and there is a pleasure attending it.”21
Once again Ada took up the study of math in order to settle herself, and she tried to convince Babbage to become her tutor. “I have a peculiar way of learning, and I think it must be a peculiar man to teach me successfully,” she wrote him. Whether due to her opiates or her breeding or both, she developed a somewhat outsize opinion of her own talents and began to describe herself as a genius. In her letter to Babbage, she wrote, “Do not reckon me conceited, . . . but I believe I have the power of going just as far as I like in such pursuits, and where there is so decided a taste, I should almost say a passion, as I have for them, I question if there is not always some portion of natural genius even.”22
Babbage deflected Ada’s request, which was probably wise. It preserved their friendship for an even more important collaboration, and she was able to secure a first-rate math tutor instead: Augustus De Morgan, a patient gentleman who was a pioneer in the field of symbolic logic. He had propounded a concept that Ada would one day employ with great significance, which was that an algebraic equation could apply to things other than numbers. The relations among symbols (for example, that a + b = b + a) could be part of a logic that applied to things that were not numerical.
Ada was never the great mathematician that her canonizers claim, but she was an eager pupil, able to grasp most of the basic concepts of calculus, and with her artistic sensibility she liked to visualize the changing curves and trajectories that the equations were describing. De Morgan encouraged her to focus on the rules for working through equations, but she was more eager to discuss the underlying concepts. Likewise with geometry, she often asked for visual ways to picture problems, such as how the intersections of circles in a sphere divide it into various shapes.
Ada’s ability to appreciate the beauty of mathematics is a gift that eludes many people, including some who think of themselves as intellectual. She realized that math was a lovely language, one that describes the harmonies of the universe and can be poetic at times. Despite her mother’s efforts, she remained her father’s daughter, with a poetic sensibility that allowed her to view an equation as a brushstroke that painted an aspect of nature’s physical splendor, just as she could visualize the “wine-dark sea” or a woman who “walks in beauty, like the night.” But math’s appeal went even deeper; it was spiritual. Math “constitutes the language through which alone we can adequately express the great facts of the natural world,” she said, and it allows us to portray the “changes of mutual relationship” that unfold in creation. It is “the instrument through which the weak mind of man can most effectually read his Creator’s works.”
This ability to apply imagination to science characterized the Industrial Revolution as well as the computer revolution, for which Ada was to become a patron saint. She was able, as she told Babbage, to understand the connection between poetry and analysis in ways that transcended her father’s talents. “I do not believe that my father was (or ever could have been) such a Poet as I shall be an Analyst; for with me the two go together indissolubly,” she wrote.23
Her reengagement with math, she told her mother, spurred her creativity and led to an “immense development of imagination, so much so that I feel no doubt if I continue my studies I shall in due time be a Poet.”24 The whole concept of imagination, especially as it was applied to technology, intrigued her. “What is imagination?” she asked in an 1841 essay. “It is the Combining faculty. It brings together things, facts, ideas, conceptions in new, original, endless, ever-varying combinations. . . . It is that which penetrates into the unseen worlds around us, the worlds of Science.”25
By then Ada believed she possessed special, even supernatural abilities, what she called “an intuitive perception of hidden things.” Her exalted view of her talents led her to pursue aspirations that were unusual for an aristocratic woman and mother in the early Victorian age. “I believe myself to possess a most singular combination of qualities exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature,” she explained in a letter to her mother in 1841. “I can throw rays from every quarter of the universe into one vast focus.”26
It was while in this frame of mind that she de
cided to engage again with Charles Babbage, whose salons she had first attended eight years earlier.
CHARLES BABBAGE AND HIS ENGINES
From an early age, Charles Babbage had been interested in machines that could perform human tasks. When he was a child, his mother took him to many of the exhibition halls and museums of wonder that were springing up in London in the early 1800s. At one in Hanover Square, a proprietor aptly named Merlin invited him up to the attic workshop where there was a variety of mechanical dolls, known as “automata.” One was a silver female dancer, about a foot tall, whose arms moved with grace and who held in her hand a bird that could wag its tail, flap its wings, and open its beak. The Silver Lady’s ability to display feelings and personality captured the boy’s fancy. “Her eyes were full of imagination,” he recalled. Years later he discovered the Silver Lady at a bankruptcy auction and bought it. It served as an amusement at his evening salons where he celebrated the wonders of technology.
At Cambridge Babbage became friends with a group, including John Herschel and George Peacock, who were disappointed by the way math was taught there. They formed a club, called the Analytical Society, which campaigned to get the university to abandon the calculus notation devised by its alumnus Newton, which relied on dots, and replace it with the one devised by Leibniz, which used dx and dy to represent infinitesimal increments and was thus known as “d” notation. Babbage titled their manifesto “The Principles of pure D-ism in opposition to the Dot-age of the University.”27 He was prickly, but he had a good sense of humor.
One day Babbage was in the Analytical Society’s room working on a table of logarithms that was littered with discrepancies. Herschel asked him what he was thinking. “I wish to God these calculations had been executed by steam,” Babbage answered. To this idea of a mechanical method for tabulating logarithms Herschel replied, “It is quite possible.”28 In 1821 Babbage turned his attention to building such a machine.
Over the years, many had fiddled with making calculating contraptions. In the 1640s, Blaise Pascal, the French mathematician and philosopher, created a mechanical calculator to reduce the drudgery of his father’s work as a tax supervisor. It had spoked metal wheels with the digits 0 through 9 on their circumference. To add or subtract numbers, the operator used a stylus to dial a number, as if using a rotary phone, then dialed in the next number; an armature carried or borrowed a 1 when necessary. It became the first calculator to be patented and sold commercially.
Thirty years later, Gottfried Leibniz, the German mathematician and philosopher, tried to improve upon Pascal’s contraption with a “stepped reckoner” that had the capacity to multiply and divide. It had a hand-cranked cylinder with a set of teeth that meshed with counting wheels. But Leibniz ran into a problem that would be a recurring theme of the digital age. Unlike Pascal, an adroit engineer who could combine scientific theories with mechanical genius, Leibniz had little engineering skill and did not surround himself with those who did. So, like many great theorists who lacked practical collaborators, he was unable to produce reliably working versions of his device. Nevertheless, his core concept, known as the Leibniz wheel, would influence calculator design through the time of Babbage.
* * *
Babbage knew of the devices of Pascal and Leibniz, but he was trying to do something more complex. He wanted to construct a mechanical method for tabulating logarithms, sines, cosines, and tangents.II To do so, he adapted an idea that the French mathematician Gaspard de Prony came up with in the 1790s. In order to create logarithm and trigonometry tables, de Prony broke down the operations into very simple steps that involved only addition and subtraction. Then he provided easy instructions so that scores of human laborers, who knew little math, could perform these simple tasks and pass along their answers to the next set of laborers. In other words, he created an assembly line, the great industrial-age innovation that was memorably analyzed by Adam Smith in his description of the division of labor in a pin-making factory. After a trip to Paris in which he heard of de Prony’s method, Babbage wrote, “I conceived all of a sudden the idea of applying the same method to the immense work with which I had been burdened, and to manufacture logarithms as one manufactures pins.”29
Even complex mathematical tasks, Babbage realized, could be broken into steps that came down to calculating “finite differences” through simple adding and subtracting. For example, in order to make a table of squares—12, 22, 32, 42, and so on—you could list the initial numbers in such a sequence: 1, 4, 9, 16. . . . This would be column A. Beside it, in column B, you could figure out the differences between each of these numbers, in this case 3, 5, 7, 9. . . . Column C would list the difference between each of column B’s numbers, which is 2, 2, 2, 2. . . . Once the process was thus simplified, it could be reversed and the tasks parceled out to untutored laborers. One would be in charge of adding 2 to the last number in column B, and then would hand that result to another person, who would add that result to the last number in column A, thus generating the next number in the sequence of squares.
Replica of the Difference Engine.
Replica of the Analytical Engine.
The Jacquard loom.
Silk portrait of Joseph-Marie Jacquard (1752–1834) woven by a Jacquard loom.
Babbage devised a way to mechanize this process, and he named it the Difference Engine. It could tabulate any polynomial function and provide a digital method for approximating the solution to differential equations.
How did it work? The Difference Engine used vertical shafts with disks that could be turned to any numeral. These were attached to cogs that could be cranked in order to add that numeral to (or subtract it from) a disk on an adjacent shaft. The contraption could even “store” the interim results on another shaft. The main complexity was how to “carry” or “borrow” when necessary, as we do with pencils when we calculate 36 + 19 or 42 − 17. Drawing on Pascal’s devices, Babbage came up with a few ingenious contrivances that allowed the cogs and shafts to handle the calculation.
The machine was, in concept, a true marvel. Babbage even figured out a way to get it to create a table of prime numbers up to 10 million. The British government was impressed, at least initially. In 1823 it gave him seed money of £1,700 and would eventually sink more than £17,000, twice the cost of a warship, into the device during the decade Babbage spent trying to build it. But the project ran into two problems. First, Babbage and his hired engineer did not quite have the skills to get the device working. Second, he began dreaming up something better.
* * *
Babbage’s new idea, which he conceived in 1834, was a general-purpose computer that could carry out a variety of different operations based on programming instructions given to it. It could perform one task, then be made to switch and perform another. It could even tell itself to switch tasks—or alter its “pattern of action,” as Babbage explained—based on its own interim calculations. Babbage named this proposed machine the Analytical Engine. He was one hundred years ahead of his time.
The Analytical Engine was the product of what Ada Lovelace, in her essay on imagination, had called “the Combining Faculty.” Babbage had combined innovations that had cropped up in other fields, a trick of many great inventors. He had originally used a metal drum that was studded with spikes to control how the shafts would turn. But then he studied, as Ada had, the automated loom invented in 1801 by a Frenchman named Joseph-Marie Jacquard, which transformed the silk-weaving industry. Looms create a pattern by using hooks to lift selected warp threads, and then a rod pushes a woof thread underneath. Jacquard invented a method of using cards with holes punched in them to control this process. The holes determined which hooks and rods would be activated for each pass of the weave, thus automating the creation of intricate patterns. Each time the shuttle was thrown to create a new pass of the thread, a new punch card would come into play.
On June 30, 1836, Babbage made an entry into what he called his “Scribbling Books” that would represent a mile
stone in the prehistory of computers: “Suggested Jacquard’s loom as a substitute for the drums.”30 Using punch cards rather than steel drums meant that an unlimited number of instructions could be input. In addition, the sequence of tasks could be modified, thus making it easier to devise a general-purpose machine that was versatile and reprogrammable.
Babbage bought a portrait of Jacquard and began to display it at his salons. It showed the inventor sitting in an armchair, a loom in the background, holding a pair of calipers over rectangular punch cards. Babbage amused his guests by asking them to guess what it was. Most thought it a superb engraving. He would then reveal that it was actually a finely woven silk tapestry, with twenty-four thousand rows of threads, each controlled by a different punch card. When Prince Albert, the husband of Queen Victoria, came to one of Babbage’s salons, he asked Babbage why he found the tapestry so interesting. Babbage replied, “It will greatly assist in explaining the nature of my calculating machine, the Analytical Engine.”31
Few people, however, saw the beauty of Babbage’s proposed new machine, and the British government had no inclination to fund it. Try as he might, Babbage could generate little notice in either the popular press or scientific journals.
But he did find one believer. Ada Lovelace fully appreciated the concept of a general-purpose machine. More important, she envisioned an attribute that might make it truly amazing: it could potentially process not only numbers but any symbolic notations, including musical and artistic ones. She saw the poetry in such an idea, and she set out to encourage others to see it as well.