The Difference Engine
Two Theories, One TrainImagine that on a train crossing England in the mid 1800s, Charles Babbage watched a common house fly travel into the future. Bumbling from the rear of the carriage to the front, the fly stopped atop a lady’s floral hat and regurgitated. It’s what flies do when they aren’t flying. At that instant, as the creature ceased moving forward, Babbage thought that the time the fly had flown through—moments arrayed behind it like consecutive bread slices—was catching up with the fly now that it had stopped moving forward. Times already experienced were slamming into the fly again as it idled, as the train gained on London. “Wonderful,” Babbage thought, even if his theory wasn’t entirely correct.
Louis Pasteur, another passenger on this mythic train, twisted his paper into a sword and swatted at the fly. The behatted woman screamed as Pasteur hit his mark. “Madame,” he begged, “forgive me,” and began to explain how house flies’ secret regurgitations are repositories for germs. The woman quickly changed seats thinking she’d encountered a madman. As Pasteur was on his way to share his theory with the Royal Society, his confidence was shaken. He had been considering how best to phrase it: “The reason that so many people are dying is because the air and water are filled with tiny, lethal beings that we cannot see.” Pasteur’s heart sank. It did sound crazy, despite being entirely correct. He did not need to travel into Babbage’s future to know how his ideas would be received in Town.
Imaginary NumbersCharles Babbage (1791–1871)—whose full title is ESQ., M.A., F.R.S., F.R.S.E., F.R.A.S., F. STAT. S., HON. M.R.I.A., M.C.P.S., COMMANDER OF THE ITALIAN ORDER OF ST. MAURICE AND ST. LAZARUS, INST. IMP. (ACAD. MORAL.) PARIS CORR., ACAD. AMER. ART. ET SC. BOSTON, REG. OECON. BORUSS., PHYS. HIST. NAT. GENEV., ACAD. REG. MONAC., HAFN., MASSIL., ET DIVION., SOCIUS. ACAD. IMP. ET REG. PETROP., NEAP., BRUX., PATAV., GEORG. FLOREN., LYNCEI. ROM., MUT., PHILOMATH. PARIS, SOC. CORR., ETC.—was an expert lock-picker, inventor of the heliograph, the cowcatcher, the first speedometer, occulting lights for lighthouses, standard railway gauges, standard screw threads, and a device for walking on water that almost worked. He was also the father of the modern computer, working at a time when the Romantics’ Nature twisted a vine around the Victorians’ wrought-iron Science and Computation, encouraging fertile, if erroneous, experiments that often disregarded the boundaries between the physical and metaphysical. These bold, if mistaken, Frankensteins blossomed into half-bred philosophies such as floral numbers, loose morality, Mesmerism, the musical calculus of the nervous system, independent female intellectuals, algebraic fairies, and robotic life, at a time when poetry drenched scientific thought.
In 1833, Babbage, 42, met Ada Byron, 17, daughter of Annabella Milbanke and everyone’s favorite depraved bard, Lord Byron. Soon after Ada’s birth, following Byron’s alleged affair with his sister, Annabella had taken her five-month-old daughter from her father and begun a lifelong project of rooting out the Byronic, not only from Ada but from all British society. Ada was fed on Reason, strict morality, and math, resulting in an appropriate response: she conducted her scandalous first love affair at age thirteeen, with her math tutor. When she met Babbage, he was intensely interested in both stomach pumps and the railway, as they could reverse natural processes; i.e. digestion could now move from both mouth to stomach and stomach to mouth, while locomotion could move from London to Manchester and Manchester to London. These about-faces contained the kernel of Babbage’s favorite theory, one he perhaps explained to Ada this way: “I believe that if you know a number of facts about an object, you should be able, via computation, to travel these conditions forward and thus to know how the object will exist in time to come.” He imagined riding a train into the by-and-by and returning later that night with a forecast.
“You mean,” Ada might have said, “through math you can predict the future?”
“Not predict. Know.”
“Anything that can be translated into numbers.” And Babbage had yet to meet an object, he thought, that could not be rendered numerically.
“For example,” Ada perhaps proposed, “which horse will place first in Saturday’s race?”
Charles needed money badly. For years he had been developing a machine called the Difference Engine, never wholly constructed in his lifetime, but which even in skeleton form could tabulate terrifically. More important, even, than tabulation, Charles saw a way in which the apparatus could store what it had learned and act on it again. The Difference Engine and a second version, the Analytical Engine, became, by the 1850s, proto-computers—or they would have been, had Charles had the money to complete construction. The Difference Engine could think for itself. By using a method of finite differences, the engine was able to compute a programmed formula on an infinite string of integers without human prompting—a wonder to a budding Victorian, for whom automation still existed almost exclusively in dreams.
The Difference Engine was terrifically bulky and ornate. Nearly as large as a wardrobe, it was made up of two thousand shiny brass and steel parts, some of which were etched with tiny numbers where results could be read. Babbage initially tried to pitch the Difference Engine as a mechanism for tabulating exact logarithms and nautical chart numbers that would aid in latitude and longitude navigation—a sensible use, but one that employed only a fraction of the engine’s powers. One theory says that Ada saw a different application for the Difference Engine: gambling on horses.
To these mathematicians, a horse was the number of teeth in its mouth, the length of its mane, the variety of its dapples, how fast it could run, even the sum total of putrefaction that its carcass would produce once the maggots were sold for medicinal purposes. Babbage wrote:...MUCH MORE
Small pieces of horse flesh are piled up. In a few days the putrid flesh is converted into a living mass of maggots. These are sold by measure: One horse yields maggots which sell for 1s. 5d. The rats which frequent the fresh carcass of a horse are innumerable. 16,000 rats were killed in one room in four weeks, without any perceptible diminution of their number. The furriers purchase the rat skins at about 3s the hundred.
Ada was mesmerized. Not with love, but by a view of the world that allowed for both the mechanical morality of Annabella and Byron’s wild curves. She, too, needed money. So it was an easy next step to take, applying the years of math tutoring to her newest gaming interest.
To proceed with the computational adventure and place bets in public, booking agents required Ada to secure a letter of permission from her husband, William Lovelace, that would permit her to gamble. As a woman, without her husband’s allowance, Ada was worth nothing, and so could not be responsible for any debt she incurred. Though the fortune they lived on was hers, women were not legally entitled to own things—a restriction that easily explains her monstrously “unfeminine” attraction to wagering in the first place. Permission granted, Ada began to act as bookie for a syndicate of acquaintances. Simultaneously, she set to work publishing articles on the wonders of the Difference Engine, drafting programs for the machine to run on and scheming over ways that the Analytical Engine could marry music to numbers. Though much of the written evidence for Ada’s “gaming fever” was ultimately veiled or destroyed by Annabella, one irresistible theory is that, drawing upon her earlier experience writing a Difference Engine program to tabulate Bernoulli numbers (the sums of powers of consecutive integers; extremely important to number theory), she developed a formula to render racehorses as numerics: weight, speed in past races, places won, jockey’s height, horse’s leg length, horse’s age, etc. These values could be plugged into the Difference Engine to produce what would today be called odds....