The Information (13 page)

This comes as quite an unexpected consequence of the invention of computing machinery. At first, that had seemed to be about numbers.

Light almost solar has been extracted from the refuse of fish; fire has been sifted by the lamp of Davy; and machinery has been taught arithmetic instead of poetry.

—Charles Babbage (1832)
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NO ONE DOUBTED THAT
Charles Babbage was brilliant. Nor did anyone quite understand the nature of his genius, which remained out of focus for a long time. What did he hope to achieve? For that matter, what, exactly, was his vocation? On his death in London in 1871 the
Times
obituarist declared him “one of the most active and original of original thinkers”
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but seemed to feel he was best known for his long, cranky crusade against street musicians and organ-grinders. He might not have minded. He was multifarious and took pride in it. “He showed great desire to inquire into the causes of things that astonish childish minds,”
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said an American eulogist. “He eviscerated toys to ascertain their manner of working.” Babbage did not quite belong in his time, which called itself the Steam Age or the Machine Age. He did revel in the uses of steam and machinery and considered himself a thoroughly modern man, but he also pursued an assortment of hobbies and obsessions—cipher cracking, lock picking, lighthouses, tree rings, the post—whose logic became clearer a century later. Examining the economics of the mail, he pursued a
counterintuitive insight, that the significant cost comes not from the physical transport of paper packets but from their “verification”—the calculation of distances and the collection of correct fees—and thus he invented the modern idea of standardized postal rates. He loved boating, by which he meant not “the manual labor of rowing but the more intellectual art of sailing.”
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He was a train buff. He devised a railroad recording device that used inking pens to trace curves on sheets of paper a thousand feet long: a combination seismograph and speedometer, inscribing the history of a train’s velocity and all the bumps and shakes along the way.

As a young man, stopping at an inn in the north of England, he was amused to hear that his fellow travelers had been debating his trade:

He might have been described as a professional mathematician, yet here he was touring the country’s workshops and manufactories, trying to discover the state of the art in machine tools. He noted, “Those who enjoy leisure can scarcely find a more interesting and instructive pursuit than the examination of the workshops of their own country, which contain within them a rich mine of knowledge, too generally neglected by the wealthier classes.”
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He himself neglected no vein of knowledge. He did become expert on the manufacture of Nottingham lace; also the use of gunpowder in quarrying limestone; precision glass cutting with diamonds; and all known uses of machinery to produce power, save time,
and communicate signals. He analyzed hydraulic presses, air pumps, gas meters, and screw cutters. By the end of his tour he knew as much as anyone in England about the making of pins. His knowledge was practical and methodical. He estimated that a pound of pins required the work of ten men and women for at least seven and a half hours, drawing wire, straightening wire, pointing the wire, twisting and cutting heads from the spiral coils, tinning or whitening, and finally papering. He computed the cost of each phase in millionths of a penny.
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And he noted that this process, when finally perfected, had reached its last days: an American had invented an automatic machine to accomplish the same task, faster.

Babbage invented his own machine, a great, gleaming engine of brass and pewter, comprising thousands of cranks and rotors, cogs and gearwheels, all tooled with the utmost precision. He spent his long life improving it, first in one and then in another incarnation, but all, mainly, in his mind. It never came to fruition anywhere else. It thus occupies an extreme and peculiar place in the annals of invention: a failure, and also one of humanity’s grandest intellectual achievements. It failed on a colossal scale, as a scientific-industrial project “at the expense of the nation, to be held as national property,”
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financed by the Treasury for almost twenty years, beginning in 1823 with a Parliamentary appropriation of £1,500 and ending in 1842, when the prime minister shut it down. Later, Babbage’s engine was forgotten. It vanished from the lineage of invention. Later still, however, it was rediscovered, and it became influential in retrospect, to shine as a beacon from the past.

Like the looms, forges, naileries, and glassworks he studied in his travels across northern England, Babbage’s machine was designed to manufacture vast quantities of a certain commodity. The commodity was numbers. The engine opened a channel from the corporeal world of matter to a world of pure abstraction. The engine consumed no raw materials—input and output being weightless—but needed a considerable force to turn the gears. All that wheel-work would fill a room and weigh several tons. Producing numbers, as Babbage conceived it,
required a degree of mechanical complexity at the very limit of available technology. Pins were easy, compared with numbers.

It was not natural to think of numbers as a manufactured commodity. They existed in the mind, or in ideal abstraction, in their perfect infinitude. No machine could add to the world’s supply. The numbers produced by Babbage’s engine were meant to be those with significance: numbers with a meaning. For example, 2.096910013 has a meaning, as the logarithm of 125. (Whether
every
number has a meaning would be a conundrum for the next century.) The meaning of a number could be expressed as a relationship to other numbers, or as the answer to a certain question of arithmetic. Babbage himself did not speak in terms of meaning; he tried to explain his engine pragmatically, in terms of putting numbers into the machine and seeing other numbers come out, or, a bit more fancifully, in terms of posing questions to the machine and expecting an answer. Either way, he had trouble getting the point across. He grumbled:

Anyway, the machine was not meant to be a sort of oracle, to be consulted by individuals who would travel from far and wide for mathematical answers. The engine’s chief mission was to print out numbers en masse. For portability, the facts of arithmetic could be expressed in tables and bound in books.

To Babbage the world seemed made of such facts. They were the “constants of Nature and Art.” He collected them everywhere. He compiled a Table of Constants of the Class Mammalia: wherever he went he timed the breaths and heartbeats of pigs and cows.
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He invented a statistical methodology with tables of life expectancy for the somewhat
shady business of life insurance. He drew up a table of the weight in Troy grains per square yard of various fabrics: cambric, calico, nankeen, muslins, silk gauze, and “caterpillar veils.” Another table revealed the relative frequencies of all the double-letter combinations in English, French, Italian, German, and Latin. He researched, computed, and published a Table of the Relative Frequency of the Causes of Breaking of Plate Glass Windows, distinguishing 464 different causes, no less than fourteen of which involved “drunken men, women, or boys.” But the tables closest to his heart were the purest: tables of numbers and only numbers, marching neatly across and down the pages in stately rows and columns, patterns for abstract appreciation.

A book of numbers: amid all the species of information technology, how peculiar and powerful an object this is. “Lo! the raptured arithmetician!”
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wrote Élie de Joncourt in 1762. “Easily satisfied, he asks no Brussels lace, nor a coach and six.” Joncourt’s own contribution was a small quarto volume registering the first 19,999 triangular numbers. It was a treasure box of exactitude, perfection, and close reckoning. These numbers were so simple, just the sums of the first
n
whole numbers: 1, 3 (1+2), 6 (1+2+3), 10 (1+2+3+4), 15, 21, 28, and so on. They had interested number theorists since Pythagoras. They offered little in the way of utility, but Joncourt rhapsodized about his pleasure in compiling them and Babbage quoted him with heartfelt sympathy: “Numbers have many charms, unseen by vulgar eyes, and only discovered to the unwearied and respectful sons of Art. Sweet joy may arise from such contemplations.”

Tables of numbers had been part of the book business even before the beginning of the print era. Working in Baghdad in the ninth century, Abu Abdullah Mohammad Ibn Musa al-Khwarizmi, whose name survives in the word
algorithm
, devised tables of trigonometric functions that spread west across Europe and east to China, made by hand and copied by hand, for hundreds of years. Printing brought number tables into their own: they
were a natural first application for the mass production of data in the raw. For people in need of arithmetic, multiplication tables covered more and more territory: 10 × 1,000, then 10 × 10,000, and later as far as 1,000 × 1,000. There were tables of squares and cubes, roots and reciprocals. An early form of table was the ephemeris or almanac, listing positions of the sun, moon, and planets for sky-gazers. Tradespeople found uses for number books. In 1582 Simon Stevin produced
Tafelen van Interest
, a compendium of interest tables for bankers and moneylenders. He promoted the new decimal arithmetic “to astrologers, land-measurers, measurers of tapestry and wine casks and stereometricians, in general, mint masters and merchants all.”
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He might have added sailors. When Christopher Columbus set off for the Indies, he carried as an aid to navigation a book of tables by Regiomontanus printed in Nuremberg two decades after the invention of moveable type in Europe.

Joncourt’s book of triangular numbers was purer than any of these—which is also to say useless. Any arbitrary triangular number can be found (or made) by an algorithm: multiply
n
by
n
+ 1 and divide by 2. So Joncourt’s whole compendium, as a bundle of information to be stored and transmitted, collapses in a puff to a one-line formula. The formula contains all the information. With it, anyone capable of simple multiplication (not many were) could generate any triangular number on demand. Joncourt knew this. Still he and his publisher, M. Husson, at the Hague, found it worthwhile to set the tables in metal type, three pairs of columns to a page, each pair listing thirty natural numbers alongside their corresponding triangular numbers, from 1(1) to 19,999(199,990,000), every numeral chosen individually by the compositor from his cases of metal type and lined up in a galley frame and wedged into an iron chase to be placed upon the press.

Why? Besides the obsession and the ebullience, the creators of number tables had a sense of their economic worth. Consciously or not, they reckoned the price of these special data by weighing the difficulty of computing them versus looking them up in a book. Precomputation
plus data storage plus data transmission usually came out cheaper than ad hoc computation. “Computers” and “calculators” existed: they were people with special skills, and all in all, computing was costly.

Beginning in 1767, England’s Board of Longitude ordered published a yearly
Nautical Almanac
, with position tables for the sun, moon, stars, planets, and moons of Jupiter. Over the next half century a network of computers did the work—thirty-four men and one woman, Mary Edwards of Ludlow, Shropshire, all working from their homes.
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Their painstaking labor paid £70 a year. Computing was a cottage industry. Some mathematical sense was required but no particular genius; rules were laid out in steps for each type of calculation. In any case the computers, being human, made errors, so the same work was often farmed out twice for the sake of redundancy. (Unfortunately, being human, computers were sometimes caught saving themselves labor by copying from one other.) To manage the information flow the project employed a Comparer of the Ephemeris and Corrector of the Proofs. Communication between the computers and comparer went by post, men on foot or on horseback, a few days per message.

A seventeenth-century invention had catalyzed the whole enterprise. This invention was itself a species of number, given the name
logarithm
. It was number as tool. Henry Briggs explained: