The Information

by James Gleick

  It may sound ridiculous to say that Bell and his successors were the fathers of modern commercial architecture—of the skyscraper. But wait a minute. Take the Singer Building, the Flatiron Building, the Broad Exchange, the Trinity, or any of the giant office buildings. How many messages do you suppose go in and out of those buildings every day? Suppose there was no telephone and every message had to be carried by a personal messenger? How much room do you think the necessary elevators would leave for offices? Such structures would be an economic impossibility.♦

  To enable the fast expansion of this extraordinary network, the telephone demanded new technologies and new science. They were broadly of two kinds. One had to do with electricity itself: measuring electrical quantities; controlling the electromagnetic wave, as it was now understood—its modulation in amplitude and in frequency. Maxwell had established in the 1860s that electrical pulses and magnetism and light itself were all manifestations of a single force: “affectations of the same substance,” light being one more case of “an electromagnetic disturbance propagated through the field according to electromagnetic laws.”♦ These were the laws that electrical engineers now had to apply, unifying telephone and radio among other technologies. Even the telegraph employed a simple kind of amplitude modulation, in which only two values mattered, a maximum for “on” and a minimum for “off.” To convey sound required far stronger current, far more delicately controlled. The engineers had to understand feedback: a coupling of the output of a power amplifier, such as a telephone mouthpiece, with its input. They had to design vacuum-tube repeaters to carry the electric current over long distance, making possible the first transcontinental line in 1914, between New York and San Francisco, 3,400 miles of wire suspended from 130,000 poles. The engineers also discovered how to modulate individual currents so as to combine them in a single channel—multiplexing—without losing their identity. By 1918 they could get four conversations into a single pair of wires. But it was not currents that preserved identity. Before the engineers quite realized it, they were thinking in terms of the transmission of a signal, an abstract entity, quite distinct from the electrical waves in which it was embodied.

  A second, less well defined sort of science concerned the organizing of connections—switching, numbering, and logic. This branch descended from Bell’s original realization, dating from 1877, that telephones need not be sold in pairs; that each individual telephone could be connected to many other telephones, not by direct wires but through a central “exchange.” George W. Coy, a telegraph man in New Haven, Connecticut, built the first “switch-board” there, complete with “switch-pins” and “switch-plugs” made from carriage bolts and wire from discarded bustles. He patented it and served as the world’s first telephone “operator.” With all the making and breaking of connections, switch-pins wore out quickly. An early improvement was a hinged two-inch plate resembling a jackknife: the “jack-knife switch,” or as it was soon called, the “jack.” In January 1878, Coy’s switchboard could manage two simultaneous conversations between any of the exchange’s twenty-one customers. In February, Coy published a list of subscribers: himself and some friends; several physicians and dentists; the post office, police station, and mercantile club; and some meat and fish markets. This has been called the world’s first telephone directory, but it was hardly that: one page, not alphabetized, and no numbers associated with the names. The telephone number had yet to be invented.

  That innovation came the next year in Lowell, Massachusetts, where by the end of 1879 four operators managed the connections among two hundred subscribers by shouting to one another across the switchboard room. An epidemic of measles broke out, and Dr. Moses Greeley Parker worried that if the operators succumbed, they would be hard to replace. He suggested identifying each telephone by number. He also suggested listing the numbers in an alphabetical directory of subscribers. These ideas could not be patented and arose again in telephone exchanges across the country, where the burgeoning networks were creating clusters of data in need of organization. Telephone books soon represented the most comprehensive listings of, and directories to, human populations ever attempted. (They became the thickest and densest of the world’s books—four volumes for London; a 2,600-page tome for Chicago—and seemed a permanent, indispensable part of the world’s information ecology until, suddenly, they were not. They went obsolete, effectively, at the turn of the twenty-first century. American telephone companies were officially phasing them out by 2010; in New York, the end of automatic delivery of telephone directories was estimated to save 5,000 tons of paper.)

  At first, customers resented the impersonality of telephone numbers, and engineers doubted whether people could remember a number of more than four or five digits. The Bell Company finally had to insist. The first telephone operators were teenage boys, cheaply hired from the ranks of telegraph messengers, but exchanges everywhere discovered that boys were wild, given to clowning and practical jokes, and more likely to be found wrestling on the floor than sitting on stools to perform the exacting, repetitive work of a switchboard operator.♦ A new source of cheap labor was available, and by 1881 virtually every telephone operator was a woman. In Cincinnati, for example, W. H. Eckert reported hiring sixty-six “young ladies” who were “very much superior” to boys: “They are steadier, do not drink beer, and are always on hand.”♦ He hardly needed to add that the company could pay a woman as little as or less than a teenage boy. It was challenging work that soon required training. Operators had to be quick in distinguishing many different voices and accents, had to maintain a polite equilibrium in the face of impatience and rudeness, as they engaged in long hours of athletic upper-body exercise, wearing headsets like harnesses. Some men thought this was good for them. “The action of stretching her arms up above her head, and to the right and left of her, develops her chest and arms,” said Every Woman’s Encyclopedia, “and turns thin and weedy girls into strong ones. There are no anaemic, unhealthy looking girls in the operating rooms.”♦ Along with another new technology, the typewriter, the telephone switchboard catalyzed the introduction of women into the white-collar workforce, but battalions of human operators could not sustain a network on the scale now arising. Switching would have to be performed automatically.

  This meant a mechanical linkage to take from callers not just the sound of their voice but also a number—identifying a person, or at least another telephone. The challenge of converting a number into electrical form still required ingenuity: first push buttons were tried, then an awkward-seeming rotary dial, with ten finger positions for the decimal digits, sending pulses down the line. Then the coded pulses served as an agent of control at the central exchange, where another mechanism selected from an array of circuits and set up a connection. Altogether this made for an unprecedented degree of complexity in the translations between human and machine, number and circuitry. The point was not lost on the company, which liked to promote its automatic switches as “electrical brains.” Having borrowed from telegraphy the electromechanical relay—using one circuit to control another—the telephone companies had reduced it in size and weight to less than four ounces and now manufactured several million each year.

  “The telephone remains the acme of electrical marvels,” wrote a historian in 1910—a historian of the telephone, already. “No other thing does so much with so little energy. No other thing is more enswathed in the unknown.”♦ New York City had several hundred thousand listed telephone customers, and Scribner’s Magazine highlighted this astounding fact: “Any two of that large number can, in five seconds, be placed in communication with each other, so well has engineering science kept pace with public needs.”♦ To make the connections, the switchboard had grown to a monster of 2 million soldered parts, 4,000 miles of wire, and 15,000 signal lamps.♦ By 1925, when an assortment of telephone research groups were formally organized into the Bell Telephone Laboratories, a mechanical “line finder” with a capacity of 400 lines was replacing 22-point electrom
echanical rotary switches. The American Telephone & Telegraph Company was consolidating its monopoly. Engineers struggled to minimize the hunt time. At first, long-distance calling required reaching a second, “toll” operator and waiting for a call back; soon the interconnection of local exchanges would have to allow for automatic dialing. The complexities multiplied. Bell Labs needed mathematicians.

  What began as the Mathematics Consulting Department grew into a center of practical mathematics like none other. It was not like the prestigious citadels, Harvard and Princeton. To the academic world it was barely visible. Its first director, Thornton C. Fry, enjoyed the tension between theory and practice—the clashing cultures. “For the mathematician, an argument is either perfect in every detail or else it is wrong,” he wrote in 1941. “He calls this ‘rigorous thinking.’ The typical engineer calls it ‘hair-splitting.’ ”♦

  The mathematician also tends to idealize any situation with which he is confronted. His gases are “ideal,” his conductors “perfect,” his surfaces “smooth.” He calls this “getting down to essentials.” The engineer is likely to dub it “ignoring the facts.”

  In other words, the mathematicians and engineers could not do without each other. Every electrical engineer could now handle the basic analysis of waves treated as sinusoidal signals. But new difficulties arose in understanding the action of networks; network theorems were devised to handle these mathematically. Mathematicians applied queuing theory to usage conflicts; developed graphs and trees to manage issues of intercity trunks and lines; and used combinatorial analysis to break down telephone probability problems.

  Then there was noise. This did not at first (to Alexander Graham Bell, for example) seem like a problem for theorists. It was just there, always crowding the line—pops, hisses, crackles interfering with, or degrading, the voice that had entered the mouthpiece. It plagued radio, too. At best it stayed in the background and people hardly noticed; at worst the weedy profusion spurred the customers’ imaginations:

  There was sputtering and bubbling, jerking and rasping, whistling and screaming. There was the rustling of leaves, the croaking of frogs, the hissing of steam, and the flapping of birds’ wings. There were clicks from telegraph wires, scraps of talk from other telephones, curious little squeals that were unlike any known sound.… The night was noisier than the day, and at the ghostly hour of midnight, for what strange reasons no one knows, the babel was at its height.♦

  But engineers could now see the noise on their oscilloscopes, interfering with and degrading their clean waveforms, and naturally they wanted to measure it, even if there was something quixotic about measuring a nuisance so random and ghostly. There was a way, in fact, and Albert Einstein had shown what it was.

  In 1905, his finest year, Einstein published a paper on Brownian motion, the random, jittery motion of tiny particles suspended in a fluid. Antony van Leeuwenhoek had discovered it with his early microscope, and the phenomenon was named after Robert Brown, the Scottish botanist who studied it carefully in 1827: first pollen in water, then soot and powdered rock. Brown convinced himself that these particles were not alive—they were not animalcules—yet they would not sit still. In a mathematical tour de force, Einstein explained this as a consequence of the heat energy of molecules, whose existence he thereby proved. Microscopically visible particles, like pollen, are bombarded by molecular collisions and are light enough to be jolted randomly this way and that. The fluctuations of the particles, individually unpredictable, collectively express the laws of statistical mechanics. Although the fluid may be at rest and the system in thermodynamic equilibrium, the irregular motion perseveres, as long as the temperature is above absolute zero. By the same token, he showed that random thermal agitation would also affect free electrons in any electrical conductor—making noise.

  Physicists paid little attention to the electrical aspects of Einstein’s work, and it was not until 1927 that thermal noise in circuits was put on a rigorous mathematical footing, by two Swedes working at Bell Labs. John B. Johnson was the first to measure what he realized was noise intrinsic to the circuit, as opposed to evidence of flawed design. Then Harry Nyquist explained it, deriving formulas for the fluctuations in current and in voltage in an idealized network. Nyquist was the son of a farmer and shoemaker who was originally called Lars Jonsson but had to find a new name because his mail was getting mixed up with another Lars Jonsson’s. The Nyquists immigrated to the United States when Harry was a teenager; he made his way from North Dakota to Bell Labs by way of Yale, where he got a doctorate in physics. He always seemed to have his eye on the big picture—which did not mean telephony per se. As early as 1918, he began working on a method for transmitting pictures by wire: “telephotography.” His idea was to mount a photograph on a spinning drum, scan it, and generate currents proportional to the lightness or darkness of the image. By 1924 the company had a working prototype that could send a five-by-seven-inch picture in seven minutes. But Nyquist meanwhile was looking backward, too, and that same year, at an electrical engineers’ convention in Philadelphia, gave a talk with the modest title “Certain Factors Affecting Telegraph Speed.”

  It had been known since the dawn of telegraphy that the fundamental units of messaging were discrete: dots and dashes. It became equally obvious in the telephone era that, on the contrary, useful information was continuous: sounds and colors, shading into one another, blending seamlessly along a spectrum of frequencies. So which was it? Physicists like Nyquist were dealing with electric currents as waveforms, even when they were conveying discrete telegraph signals. Nowadays most of the current in a telegraph line was being wasted. In Nyquist’s way of thinking, if those continuous signals could represent anything as complex as voices, then the simple stuff of telegraphy was just a special case. Specifically, it was a special case of amplitude modulation, in which the only interesting amplitudes were on and off. By treating the telegraph signals as pulses in the shape of waveforms, engineers could speed their transmission and could combine them in a single circuit—could combine them, too, with voice channels. Nyquist wanted to know how much—how much telegraph data, how fast. To answer that question he found an ingenious approach to converting continuous waves into data that was discrete, or “digital.” Nyquist’s method was to sample the waves at intervals, in effect converting them into countable pieces.

  A circuit carried waves of many different frequencies: a “band” of waves, engineers would say. The range of frequencies—the width of that band, or “band width”—served as a measure of the capacity of the circuit. A telephone line could handle frequencies from about 400 to 3,400 hertz, or waves per second, for a bandwidth of 3,000 hertz. (That would cover most of the sound from an orchestra, but the high notes of the piccolo would be cut off.) Nyquist wanted to put this as generally as he could. He calculated a formula for the “speed of transmission of intelligence.”♦ To transmit intelligence at a certain speed, he showed, a channel needs a certain, measurable bandwidth. If the bandwidth was too small, it would be necessary to slow down the transmission. (But with time and ingenuity, it was realized later, even complex messages could be sent across a channel of very small bandwidth: a drum, for example, beaten by hand, sounding notes of only two pitches.)

  Nyquist’s colleague Ralph Hartley, who had begun his career as an expert on radio receivers, extended these results in a presentation in the summer of 1927, at an international congress on the shore of Lake Como, Italy. Hartley used a different word, “information.” It was a good occasion for grand ideas. Scientists had gathered from around the world for the centennial of Alessandro Volta’s death. Niels Bohr spoke on the new quantum theory and introduced for the first time his concept of complementarity. Hartley offered his listeners both a fundamental theorem and a new set of definitions.

  The theorem was an extension of Nyquist’s formula, and it could be expressed in words: the most information that can be transmitted in any given time is proportional to the available frequency range (he d
id not yet use the term bandwidth). Hartley was bringing into the open a set of ideas and assumptions that were becoming part of the unconscious culture of electrical engineering, and the culture of Bell Labs especially. First was the idea of information itself. He needed to pin a butterfly to the board. “As commonly used,” he said, “information is a very elastic term.”♦ It is the stuff of communication—which, in turn, can be direct speech, writing, or anything else. Communication takes place by means of symbols—Hartley cited for example “words” and “dots and dashes.” The symbols, by common agreement, convey “meaning.” So far, this was one slippery concept after another. If the goal was to “eliminate the psychological factors involved” and to establish a measure “in terms of purely physical quantities,” Hartley needed something definite and countable. He began by counting symbols—never mind what they meant. Any transmission contained a countable number of symbols. Each symbol represented a choice; each was selected from a certain set of possible symbols—an alphabet, for example—and the number of possibilities, too, was countable. The number of possible words is not so easy to count, but even in ordinary language, each word represents a selection from a set of possibilities:

  For example, in the sentence, “Apples are red,” the first word eliminated other kinds of fruit and all other objects in general. The second directs attention to some property or condition of apples, and the third eliminates other possible colors.…

  The number of symbols available at any one selection obviously varies widely with the type of symbols used, with the particular communicators and with the degree of previous understanding existing between them.♦

  Hartley had to admit that some symbols might convey more information, as the word was commonly understood, than others. “For example, the single word ‘yes’ or ‘no,’ when coming at the end of a protracted discussion, may have an extraordinarily great significance.” His listeners could think of their own examples. But the point was to subtract human knowledge from the equation. Telegraphs and telephones are, after all, stupid.