The Information - James Gleick [95]
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.