The Information

by James Gleick

  Miss Stamp desires me to say that at present she is not particularly pleased with me on account of some very foolish conduct yesterday about a simple thing, and which she said was not only foolish but showed a spirit of inattention, and though today she has not had reason to be dissatisfied with me on the whole yet she says that she can not directly efface the recollection of the past.♦

  She was growing up in a well-kept cloister of her mother’s arranging. She had years of sickliness, a severe bout of measles, and episodes of what was called neurasthenia or hysteria. (“When I am weak,” she wrote, “I am always so exceedingly terrified, at nobody knows what, that I can hardly help having an agitated look & manner.”♦) Green drapery enclosed the portrait of her father that hung in one room. In her teens she developed a romantic interest in her tutor, which led to a certain amount of sneaking about the house and gardens and to lovemaking as intimate as possible without, she said, actual “connection.” The tutor was dismissed. Then, in the spring, wearing white satin and tulle, the seventeen-year-old made her ritual debut at court, where she met the king and queen, the most important dukes, and the French diplomat Talleyrand, whom she described as an “old monkey.”♦

  A month later she met Charles Babbage. With her mother, she went to see what Lady Byron called his “thinking machine,” the portion of the Difference Engine in his salon. Babbage saw a sparkling, self-possessed young woman with porcelain features and a notorious name, who managed to reveal that she knew more mathematics than most men graduating from university. She saw an imposing forty-one-year-old, authoritative eyebrows anchoring his strong-boned face, who possessed wit and charm and did not wear these qualities lightly. He seemed a kind of visionary—just what she was seeking. She admired the machine, too. An onlooker reported: “While other visitors gazed at the working of this beautiful instrument with the sort of expression, and I dare say the sort of feeling, that some savages are said to have shown on first seeing a looking-glass or hearing a gun, Miss Byron, young as she was, understood its working, and saw the great beauty of the invention.”♦ Her feeling for the beauty and abstractions of mathematics, fed only in morsels from her succession of tutors, was overflowing. It had no outlet. A woman could not attend university in England, nor join a scientific society (with two exceptions: the botanical and horticultural).

  AUGUSTA ADA BYRON KING, COUNTESS OF LOVELACE, AS PAINTED IN 1836 BY MARGARET CARPENTER. “I CONCLUDE SHE IS BENT ON DISPLAYING THE WHOLE EXPANSE OF MY CAPACIOUS JAW BONE, UPON WHICH I THINK THE WORD MATHEMATICS SHOULD BE WRITTEN.”

  Ada became a tutor for the young daughters of one of her mother’s friends. When writing to them, she signed herself, “your affectionate & untenable Instructress.” On her own she studied Euclid. Forms burgeoned in her mind. “I do not consider that I know a proposition,” she wrote another tutor, “until I can imagine to myself a figure in the air, and go through the construction & demonstration without any book or assistance whatever.”♦ She could not forget Babbage, either, or his “gem of all mechanism.”♦ To another friend she reported her “great anxiety about the machine.” Her gaze turned inward, often. She liked to think about herself thinking.

  Babbage himself had moved far beyond the machine on display in his drawing room; he was planning a new machine, still an engine of computation but transmuted into another species. He called this the Analytical Engine. Motivating him was a quiet awareness of the Difference Engine’s limitations: it could not, merely by adding differences, compute every sort of number or solve any mathematical problem. Inspiring him, as well, was the loom on display in the Strand, invented by Joseph-Marie Jacquard, controlled by instructions encoded and stored as holes punched in cards.

  What caught Babbage’s fancy was not the weaving, but rather the encoding, from one medium to another, of patterns. The patterns would appear in damask, eventually, but first were “sent to a peculiar artist.” This specialist, as he said,

  punches holes in a set of pasteboard cards in such a manner that when those cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.♦

  The notion of abstracting information away from its physical substrate required careful emphasis. Babbage explained, for example, that the weaver might choose different threads and different colors—“but in all these cases the form of the pattern will be precisely the same.” As Babbage conceived his machine now, it raised this very process of abstraction to higher and higher degrees. He meant the cogs and wheels to handle not just numbers but variables standing in for numbers. Variables were to be filled or determined by the outcomes of prior calculations, and, further, the very operations—such as addition or multiplication—were to be changeable, depending on prior outcomes. He imagined these abstract information quantities being stored in cards: variable cards and operation cards. He thought of the machine as embodying laws and of the cards as communicating these laws. Lacking a ready-made vocabulary, he found it awkward to express his fundamental working concepts; for example,

  how the machine could perform the act of judgment sometimes required during an analytical inquiry, when two or more different courses presented themselves, especially as the proper course to be adopted could not be known in many cases until all the previous portion had been gone through.♦

  He made clear, though, that information—representations of number and process—would course through the machinery. It would pass to and from certain special physical locations, which Babbage named a store, for storage, and a mill, for action.

  In all this he had an intellectual companion now in Ada, first his acolyte and then his muse. She married a sensible and promising aristocrat, William King, her senior by a decade and a favorite of her mother. In the space of a few years he was elevated to the peerage as earl of Lovelace—making Ada, therefore, a countess—and, still in her early twenties, she bore three children. She managed their homes, in Surrey and London, practiced the harp for hours daily (“I am at present a condemned slave to my harp, no easy Task master”♦), danced at balls, met the new queen, Victoria, and sat for her portrait, self-consciously (“I conclude [the artist] is bent on displaying the whole expanse of my capacious jaw bone, upon which I think the word Mathematics should be written”). She suffered terrible dark moods and bouts of illness, including cholera. Her interests and behavior still set her apart. One morning she went alone in her carriage, dressed plainly, to see a model of Edward Davy’s “electrical telegraph” at Exeter Hall

  & the only other person was a middle-aged gentleman who chose to behave as if I were the show [she wrote to her mother] which of course I thought was the most impudent and unpardonable.—I am sure he took me for a very young (& I suppose he thought rather handsome) governess.… He stopped as long as I did, & then followed me out.—I took care to look as aristocratic & as like a Countess as possible.… I must try & add a little age to my appearance.… I would go & see something everyday & I am sure London would never be exhausted.♦

  Lady Lovelace adored her husband but reserved much of her mental life for Babbage. She had dreams, waking dreams, of something she could not be and something she could not achieve, except by proxy, through his genius. “I have a peculiar way of learning,” she wrote to him, “& I think it must be a peculiar man to teach me successfully.”♦ Her growing desperation went side by side with a powerful confidence in her untried abilities. “I hope you are bearing me in mind,” she wrote some months later, “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.…”

  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.♦

 
The mathematician and logician Augustus De Morgan, a friend of Babbage and of Lady Byron, became Ada’s teacher by post. He sent her exercises. She sent him questions and musings and doubts (“I could wish I went on quicker”; “I am sorry to say I am sadly obstinate about the Term at which Convergence begins”; “I have enclosed my Demonstration of my view of the case”; “functional Equations are complete Will-o-the-wisps to me”; “However I try to keep my metaphysical head in order”). Despite her naïveté, or because of it, he recognized a “power of thinking … so utterly out of the common way for any beginner, man or woman.” She had rapidly mastered trigonometry and integral and differential calculus, and he told her mother privately that if he had encountered “such power” in a Cambridge student he would have anticipated “an original mathematical investigator, perhaps of first rate eminence.”♦ She was fearless about drilling down to first principles. Where she felt difficulties, real difficulties lay.

  One winter she grew obsessed with a fashionable puzzle known as Solitaire, the Rubik’s Cube of its day. Thirty-two pegs were arranged on a board with thirty-three holes, and the rules were simple: Any peg may jump over another immediately adjacent, and the peg jumped over is removed, until no more jumps are possible. The object is to finish with only one peg remaining. “People may try thousands of times, and not succeed in this,” she wrote Babbage excitedly.

  I have done it by trying & observation & can now do it at any time, but I want to know if the problem admits of being put into a mathematical Formula, & solved in this manner.… There must be a definite principle, a compound I imagine of numerical & geometrical properties, on which the solution depends, & which can be put into symbolic language.♦

  A formal solution to a game—the very idea of such a thing was original. The desire to create a language of symbols, in which the solution could be encoded—this way of thinking was Babbage’s, as she well knew.

  She pondered her growing powers of mind. They were not strictly mathematical, as she saw it. She saw mathematics as merely a part of a greater imaginative world. Mathematical transformations reminded her “of certain sprites & fairies one reads of, who are at one’s elbows in one shape now, & the next minute in a form most dissimilar; and uncommonly deceptive, troublesome & tantalizing are the mathematical sprites & fairies sometimes; like the types I have found for them in the world of Fiction.”♦ Imagination—the cherished quality. She mused on it; it was her heritage from her never-present father.

  We talk much of Imagination. We talk of the Imagination of Poets, the Imagination of Artists &c; I am inclined to think that in general we don’t know very exactly what we are talking about.…

  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 … may then with the fair white wings of Imagination hope to soar further into the unexplored amidst which we live.♦

  She began to believe she had a divine mission to fulfill. She used that word, mission. “I have on my mind most strongly the impression that Heaven has allotted me some peculiar intellectual-moral mission to perform.”♦ She had powers. She confided in her mother:

  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.… The belief has been forced upon me, & most slow have I been to admit it even.

  She listed her qualities:

  Firstly: Owing to some peculiarity in my nervous system, I have perceptions of some things, which no one else has; or at least very few, if any.… Some might say an intuitive perception of hidden things;—that is of things hidden from eyes, ears & the ordinary senses.…

  Secondly;—my immense reasoning faculties;

  Thirdly;… the power not only of throwing my whole energy & existence into whatever I choose, but also bring to bear on any one subject or idea, a vast apparatus from all sorts of apparently irrelevant & extraneous sources. I can throw rays from every quarter of the universe into one vast focus.

  She admitted that this sounded mad but insisted she was being logical and cool. She knew her life’s course now, she told her mother. “What a mountain I have to climb! It is enough to frighten anyone who had not all that most insatiable & restless energy, which from my babyhood has been the plague of your life & my own. However it has found food I believe at last.”♦ She had found it in the Analytical Engine.

  Babbage meanwhile, restless and omnivorous, was diverting his energies to another burgeoning technology, steam’s most powerful expression, the railroad. The newly formed Great Western Railway was laying down track and preparing trial runs of locomotive engines from Bristol to London under the supervision of Isambard Kingdom Brunel, the brilliant engineer, then just twenty-seven years old. Brunel asked Babbage for help, and Babbage decided to begin with an information-gathering program—characteristically ingenious and grandiose. He outfitted an entire railway carriage. On a specially built, independently suspended table, rollers unwound sheets of paper a thousand feet long, while pens drew lines to “express” (as Babbage put it) measurements of the vibrations and forces felt by the carriage in every direction. A chronometer marked the passage of time in half seconds. He covered two miles of paper this way.

  As he traversed the rails, he realized that a peculiar danger of steam locomotion lay in its outracing every previous means of communication. Trains lost track of one another. Until the most regular and disciplined scheduling was imposed, hazard ran with every movement. One Sunday Babbage and Brunel, operating in different engines, barely avoided smashing into each other. Other people, too, worried about this new gap between the speeds of travel and messaging. An important London banker told Babbage he disapproved: “It will enable our clerks to plunder us, and then be off to Liverpool on their way to America at the rate of twenty miles an hour.”♦ Babbage could only express the hope that science might yet find a remedy for the problem it had created. (“Possibly we might send lightning to outstrip the culprit.”)

  As for his own engine—the one that would travel nowhere—he had found a fine new metaphor. It would be, he said, “a locomotive that lays down its own railway.”

  Bitter as he was about England’s waning interest in his visionary plans, Babbage found admirers on the continent, particular in Italy—“the country of Archimedes and Galileo,” as he put it to his new friends. In the summer of 1840 he gathered up his sheaves of drawings and journeyed by way of Paris and Lyon, where he watched the great Jacquard loom at Manufacture d’Étoffes pour Ameublements et Ornements d’Église, to Turin, the capital of Sardinia, for an assembly of mathematicians and engineers. There he made his first (and last) public presentation of the Analytical Engine. “The discovery of the Analytical Engine is so much in advance of my own country, and I fear even of the age,”♦ he said. He met the Sardinian king, Charles Albert, and, more significantly, an ambitious young mathematician named Luigi Menabrea. Later Menabrea was to become a general, a diplomat, and the prime minister of Italy; now he prepared a scientific report, “Notions sur la machine analytique,”♦ to introduce Babbage’s plan to a broader community of European philosophers.

  As soon as this reached Ada Lovelace, she began translating it into English, correcting errors on the basis of her own knowledge. She did that on her own, without telling either Menabrea or Babbage.

  When she finally did show Babbage her draft, in 1843, he responded enthusiastically, urging her to write on her own behalf, and their extraordinary collaboration began in earnest. They sent letters by messenger back and forth across London at a ferocious pace—“My Dear Babbage” and “My Dear Lady Lovelace”—and met whenever they could at her home in St. James’s Square. The pace was almost frantic. Though he was the eminence, fifty-one years old to her twenty-seven, she took charge, mixing stern command with banter. “I want you to answer me the following question by
return of post”; “Be kind enough to write this out properly for me”; “You were a little harum-scarum and inaccurate”; “I wish you were as accurate and as much to be relied on as myself.” She proposed to sign her work with her initials—nothing so forward as her name—not to “proclaim who has written it,” merely to “individualize and identify it with other productions of the said A.A.L.”♦

  Her exposition took the form of notes lettered A through G, extending to nearly three times the length of Menabrea’s essay. They offered a vision of the future more general and more prescient than any expressed by Babbage himself. How general? The engine did not just calculate; it performed operations, she said, defining an operation as “any process which alters the mutual relation of two or more things,” and declaring: “This is the most general definition, and would include all subjects in the universe.”♦ The science of operations, as she conceived it,

  is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.… One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used.