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as played on the piano by Glenn Gould. More generally, perhaps the meaning is “There is intelligent life here.” Besides the Bach prelude, the record includes music samples from several different cultures and a selection of earthly sounds: wind, surf, and thunder; spoken greetings in fifty-five languages; the voices of crickets, frogs, and whales; a ship’s horn, the clatter of a horse-drawn cart, and a tapping in Morse code. Along with the phonograph record are a cartridge and needle and a brief pictographic instruction manual. The committee did not bother with a phonograph player or a source of electrical power. Maybe the aliens will find a way to convert those analog metallic grooves into waves in whatever fluid serves as their atmosphere—or into some other suitable input for their alien senses.

THE “GOLDEN RECORD” STOWED ABOARD THE VOYAGER SPACECRAFT (Illustration credit 12.1)

Would they recognize the intricate patterned structure of the Bach prelude (say), as distinct from the less interesting, more random chatter of crickets? Would the sheet music convey a clearer message—the written notes containing, after all, the essence of Bach’s creation? And, more generally, what kind of knowledge would be needed at the far end of the line—what kind of code book—to decipher the message? An appreciation of counterpoint and voice leading? A sense of the tonal context and performance practices of the European Baroque? The sounds—the notes—come in groups; they form shapes, called melodies; they obey the rules of an implicit grammar. Does the music carry its own logic with it, independent of geography and history? On earth, meanwhile, within a few years, even before the Voyagers had sailed past the solar system’s edge, music was seldom recorded in analog form anymore. Better to store the sounds of the Well-Tempered Clavier as bits: the waveforms discretized without loss as per the Shannon sampling theorem, and the information preserved in dozens of plausible media.

In terms of bits, a Bach prelude might not seem to have much information at all. As penned by Bach on two manuscript pages, this one amounts to six hundred notes, characters in a small alphabet. As Glenn Gould played it on a piano in 1964—adding the performer’s layers of nuance and variation to the bare instructions—it lasts a minute and thirty-six seconds. The sound of that performance, recorded onto a CD, microscopic pits burned by a laser onto a slim disc of polycarbonate plastic, comprises 135 million bits. But this bitstream can be compressed considerably with no loss of information. Alternatively, the prelude fits on a small player-piano roll (descendant of Jacquard’s loom, predecessor of punched-card computing); encoded electronically with the MIDI protocol, it uses a few thousands bits. Even the basic six-hundred-character message has tremendous redundancy: unvarying tempo, uniform timbre, just a brief melodic pattern, a word, repeated over and over with slight variations till the final bars. It is famously, deceptively simple. The very repetition creates expectations and breaks them. Hardly anything happens, and everything is a surprise. “Immortal broken chords of radiantly white harmonies,” said Wanda Landowska. It is simple the way a Rembrandt drawing is simple. It does a lot with a little. Is it then rich in information? Certain music could be considered information poor. At one extreme John Cage’s composition titled 4′33″ contains no “notes” at all: just four minutes and thirty-three seconds of near silence, as the piece absorbs the ambient sounds around the still pianist—the listeners’ shifting in their seats, rustling clothes, breathing, sighing.

How much information in the Bach C-major Prelude? As a set of patterns, in time and frequency, it can be analyzed, traced, and understood, but only up to a point. In music, as in poetry, as in any art, perfect understanding is meant to remain elusive. If one could find the bottom it would be a bore.

In a way, then, the use of minimal program size to define complexity seems perfect—a fitting apogee for