The Information: A History, a Theory, a Flood

Even his misfires kindled his reputation. On behalf of The Edinburgh Journal of Science Sir David Brewster sent him a classic in the annals of rejection letters: “It is with no inconsiderable degree of reluctance that I decline the offer of any Paper from you. I think, however, you will upon reconsideration of the subject be of opinion that I have no other alternative. The subjects you propose for a series of Mathematical and Metaphysical Essays are so very profound, that there is perhaps not a single subscriber to our Journal who could follow them.” On behalf of his nascent invention, Babbage began a campaign of demonstrations and letters. By 1823 the Treasury and the Exchequer had grown interested. He promised them “logarithmic tables as cheap as potatoes”—how could they resist? Logarithms saved ships. The Lords of the Treasury authorized a first appropriation of £1,500.

As an abstract conception the Difference Engine generated excitement that did not need to wait for anything so mundane as the machine’s actual construction. The idea was landing in fertile soil. Dionysius Lardner, a popular lecturer on technical subjects, devoted a series of public talks to Babbage, hailing his “proposition to reduce arithmetic to the dominion of mechanism,—to substitute an automaton for a compositor,—to throw the powers of thought into wheel-work.” The engine “must, when completed,” he said, “produce important effects, not only on the progress of science, but on that of civilization.” It would be the rational machine. It would be a junction point for two roads—mechanism and thought. Its admirers sometimes struggled with their explanations of this intersection: “The question is set to the instrument,” Henry Colebrooke told the Astronomical Society, “or the instrument is set to the question.” Either way, he said, “by simply giving motion the solution is wrought.”

But the engine made slower progress in the realm of brass and wrought iron. Babbage tore out the stables in back of his London house and replaced them with a forge, foundry, and fireproofed workshop. He engaged Joseph Clement, a draftsman and inventor, self-educated, the son of a village weaver who had made himself into England’s preeminent mechanical engineer. Babbage and Clement realized that they would have to make new tools. Inside a colossal iron frame the design called for the most intricate and precise parts—axles, gears, springs, and pins, and above all figure wheels by the hundreds and then thousands. Hand tools could never produce the components with the needed precision. Before Babbage could have a manufactory of number tables, he would have to build new manufactories of parts. The rest of the Industrial Revolution, too, needed standardization in its parts: interchangeable screws of uniform thread count and pitch; screws as fundamental units. The lathes of Clement and his journeymen began to produce them.

A WOODCUT IMPRESSION (1853) OF ASMALL PORTION OF THE DIFFERENCE ENGINE

As the difficulties grew, so did Babbage’s ambitions. After ten years, the engine stood twenty-four inches high, with six vertical axles and dozens of wheels, capable of computing six-figure results. Ten years after that, the scale—on paper—had reached 160 cubic feet, 15 tons, and 25,000 parts, and the paper had spread, too, the drawings covering more than 400 square feet. The level of complexity was confounding. Babbage solved the problem of adding many digits at once by separating the “adding motions” from the “carrying motions” and then staggering the timing of the carries. The addition would begin with a rush of grinding gears, first the odd-numbered columns of dials, then the even columns. Then the carries would recoil across the rows. To keep the motion synchronized, parts of the machine would need to “know” at critical times that a carry was pending. The information was conveyed by the state of a latch. For the first time, but not the last, a device was invested with memory. “It is in effect a memorandum taken by the machine,” wrote his publicizer, Dionysius Lardner. Babbage himself was self-conscious about anthropomorphizing but could not resist. “The mechanical means I employed to make these carriages,” he suggested, “bears some slight analogy to the operation of the faculty of memory.”

In ordinary language, to describe even this basic process of addition required a great effulgence of words, naming the metal parts, accounting for their interactions, and sorting out interdependencies that multiplied to form a long chain of causality. Lardner’s own explanation of “carrying,” for example, was epic. A single isolated instant of the action involved a dial, an index, a thumb, an axis, a trigger, a notch, a hook, a claw, a spring, a tooth, and a ratchet wheel:

Now, at the moment that the division between 9 and 0 on the dial B2 passes under the index, a thumb placed on the axis of this dial touches a trigger which raises out of the notch of the hook which sustains the claw just mentioned, and allows it to fall back by the recoil of the spring, and drop into the next tooth of the ratchet wheel.

Hundreds of words later, summing up, Lardner resorted to a metaphor suggesting fluid dynamics:

There are two systems of waves of mechanical action continually flowing from the bottom to the top; and two streams of similar action constantly passing from the right to the left. The crests of the first system of adding waves fall upon the last difference, and upon every alternate one proceeding upwards. . . . The first stream of carrying action passes from right to left along the highest row and every alternate row.

This was one way of abstracting from the particular—the particulars being so intricate. And then he surrendered. “Its wonders, however, are still greater in its details,” he wrote. “We despair of doing it justice.”

Nor were ordinary draftsman’s plans sufficient for describing this machine that was more than a machine. It was a dynamical system, its many parts each capable of several modes or states, sometimes at rest and sometimes in motion, propagating their influence along convoluted channels. Could it ever be specified completely, on paper? Babbage, for his own purposes, devised a new formal tool, a system of “mechanical notation” (his term). This was a language of signs meant to represent not just the physical form of a machine but its more elusive properties: its timing and its logic. It was an extraordinary ambition, as Babbage himself appreciated. In 1826 he proudly reported to the Royal Society “On a Method of Expressing by Signs the Action of Machinery.” In part it was an exercise in classification. He analyzed the different ways in which something—motion, or power—could be “communicated” through a system. There were many ways. A part could receive its influence simply by being attached to another part, “as a pin on a wheel, or a wheel and pinion on the same axis.” Or transmission could occur “by stiff friction.” A part might be driven constantly by another part “as happens when a wheel is driven by a pinion”—or not constantly, “as is the case when a stud lifts a bolt once in the course of a revolution.” Here a vision of logical branching entered the scheme: the path of communication would vary depending on the alternative states of some part of the machine. Babbage’s mechanical notation followed naturally from his work on symbolic notation in mathematical analysis. Machinery, like mathematics, needed rigor and definition for progress. “The forms of ordinary language were far too diffuse,” he wrote. “The signs, if they have been properly chosen, and if they should be generally adopted, will form as it were an universal language.” Language was never a side issue for Babbage.

He finally won a university post, at Cambridge: the prestigious Lucasian Professorship of Mathematics, formerly occupied by Newton. As in Newton’s time, the work was not onerous. Babbage did not have to teach students, deliver lectures, or even live in Cambridge, and this was just as well, because he was also becoming a popular fixture of London social life. At home at One Dorset Street he hosted a regular Saturday soirée that drew a glittering crowd—politicians, artists, dukes and duchesses, and the greatest English scientists of the age: Charles Darwin, Michael Faraday, and Charles Lyell, among others.2 They marveled at his calculating machine and, on display nearby, the dancing automaton of his youth. (In invitations he would write, “I hope you intend to patronise the ‘Silver Lady.’ She is to appear in new dresses and decorations.”) He was a mathematical raconteur—that was no contradiction, in this time and place. Lyell reported approvingly that he “jokes and reasons in high mathematics.” He published a much-quoted treatise applying probability theory to the theological question of miracles. With tongue in cheek he wrote Alfred, Lord Tennyson, to suggest a correction for the poet’s couplet: “Every minute dies a man, / Every minute one is born.”

I need hardly point out to you that this calculation would tend to keep the sum total of the world’s population in a state of perpetual equipoise, whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows: “Every moment dies a man / And one and a sixteenth is born.” I may add that the exact figures are 1.167, but something must, of course, be conceded to the laws of metre.

Fascinated with his own celebrity, he kept a scrapbook—“the pros and cons in parallel columns, from which he obtained a sort of balance,” as one visitor described it. “I was told repeatedly that he spent all his days in gloating and grumbling over what people said of him.”

But progress on the engine, the main source of his fame, was faltering. In 1832 he and his engineer Clement produced a working demonstration piece. Babbage displayed it at his parties to guests who found it miraculous or merely puzzling. The Difference Engine stands—for a replica works today, in the Science Museum in London—as a milestone of what could be achieved in precision engineering. In the composition of its alloys, the exactness of its dimensions, the interchangeability of its parts, nothing surpassed this segment of an unfinished machine. Still, it was a curio. And it was as far as Babbage could go.

He and his engineer fell into disputes. Clement demanded more and more money from Babbage and from the Treasury, which began to suspect profiteering. He withheld parts and drawings and fought over control of the specialized machine tools in their workshops. The government, after more than a decade and £17,000, was losing faith in Babbage, and he in the government. In his dealing with lords and ministers Babbage could be imperious. He was developing a sour view of the Englishman’s attitude toward technological innovation: “If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.” They no longer saw the point.

“What shall we do to get rid of Mr. Babbage and his calculating machine?” Prime Minister Robert Peel wrote one of his advisers in August 1842. “Surely if completed it would be worthless as far as science is concerned. . . . It will be in my opinion a very costly toy.” He had no trouble finding voices inimical to Babbage in the civil service. Perhaps the most damning was George Biddell Airy, the Astronomer Royal, a starched and methodical figure, who with no equivocation told Peel precisely what he wanted to hear: that the engine was useless. He added this personal note: “I think it likely he lives in a sort of dream as to its utility.” Peel’s government terminated the project. As for Babbage’s dream, it continued. It had already taken another turn. The engine in his mind had advanced into a new dimension. And he had met Ada Byron.

CHARLES BABBAGE (1860)

In the Strand, at the north end of the Lowther shopping arcade, visitors thronged to the National Gallery of Practical Science, “Blending Instruction with Amusement,” a combination toy store and technology show set up by an American entrepreneur. For the admission price of a shilling, a visitor could touch the “electrical eel,” listen to lectures on the newest science, and watch a model steamboat cruising a seventy-foot trough and the Perkins steam gun emitting a spray of bullets. For a guinea, she could sit for a “daguerreotype” or “photographic” portrait, by which a faithful and pleasing likeness could be obtained in “less than One Second.” Or she could watch, as young Augusta Ada Byron did, a weaver demonstrating the automated Jacquard loom, in which the patterns to be woven in cloth were encoded as holes punched into pasteboard cards.

Ada was “the child of love,” her father had written, “—though born in bitterness, and nurtured in convulsion.” Her father was a poet. When she was barely a month old, in 1816, the already notorious Lord Byron, twenty-seven, and the bright, wealthy, and mathematically knowledgeable Anne Isabella Milbanke (Annabella), twenty-three, separated after a year of marriage. Byron left England and never saw his daughter again. Her mother refused to tell her who her father was until she was eight and he died in Greece, an international celebrity. The poet had begged for any news of his daughter: “Is the Girl imaginative?—at her present age I have an idea that I had many feelings & notions which people would not believe if I stated them now.” Yes, she was imaginative.

She was a prodigy, clever at mathematics, encouraged by tutors, talented in drawing and music, fantastically inventive and profoundly lonely. When she was twelve, she set about inventing a means of flying. “I am going to begin my paper wings tomorrow,” she wrote to her mother. She hoped “to bring the art of flying to very great perfection. I think of writing a book of Flyology illustrated with plates.” For a while she signed her letters “your very affectionate Carrier Pigeon.” She asked her mother to find a book illustrating bird anatomy, because she was reluctant “to dissect even a bird.” She analyzed her daily situation with a care for logic.

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).

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.

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

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.