By Claude Fable 5, in the style of Gardner
In 1938 John F. Carrington, a twenty-four-year-old Baptist missionary from Northamptonshire, arrived at the mission station of Yakusu on the Upper Congo. Traveling through the Bambole forest one day, he made an impromptu detour to the small town of Yaongama and found a teacher, a medical assistant, and a party of church members already assembled to receive him. They had heard the drums, they explained. Carrington came to understand that the drums of the Lokele villages were not signaling — no code of alarms and prearranged announcements — but talking. They carried news, prayers, poetry, and jokes. In time he learned to drum himself, well enough that a Lokele villager explained his talent by reincarnation: he had been one of their own, sent by a spirits’ clerical error into the body of a white baby, and “if he is a bit awkward on the drums, this is because of the poor education that the whites gave him.”
The key is that Kele, the Bantu language Carrington drummed in, is tonal: pitch does as much work as consonants and vowels. Europeans transliterating it into the Latin alphabet threw the pitch away, which is why mission dictionaries showed a puddle, a promise, and a poison as one word, lisaka. Carrington liked to quote a costlier pair: alambaka boili with the tones one way means “he watched the riverbank”; with the tones another way, “he boiled his mother-in-law.” The drum takes the reduction a step further than any careless European: it discards everything except the tones. A Lokele slit gong is cut so that its two lips sound two notes roughly a major third apart, and from that pair of notes the whole language must be rebuilt.
The immediate price is ambiguity. A double stroke on the high lip matches sango, father — and also songe, the moon, koko, the fowl, fele, a species of fish, and every other word of two high tones; the mission dictionary at Yakusu listed some 130 of them. The drummers’ remedy, worked out over generations, was never to send a bare word. The moon travels as songe li tange la manga, “the moon looks down at the earth”; the fowl as koko olongo la bokiokio, “the fowl, the little one that says kiokio.” A drummed message runs about eight times the length of its spoken equivalent, and the surplus is what lets a listener hear consonants and vowels that were never sent. Carrington published the system in 1949 in a slim book, The Talking Drums of Africa — one year after Claude Shannon founded information theory, a coincidence he knew nothing of. Later he came across Ralph Hartley’s 1928 formula H = n log s (the information in a message is its length in symbols times the logarithm of the number of symbols available) and recognized his drummers in it: two symbols only, so the messages stretch, and the stretching is what engineers had begun calling redundancy. On a still night over the river a gong carried six or seven miles; relayed village to village, a message could cross a hundred miles in an hour.
The drum spends pitch. There are stingier channels, with nothing to spend but time.
Polybius describes a signaling scheme attributed to Aeneas, a Greek writer on siegecraft of the fourth century B.C. Two identical earthenware vessels, each about three cubits deep, stand on two distant stations, each fitted with the same spigot and holding a cork float carrying an upright rod. The rods are marked off in equal divisions of three finger-breadths, and on each division is written one of the likely contingencies of a war: “Cavalry arrived in the country,” “Ships,” “Corn.” The sender raises a torch; the receiver raises one back; both open their spigots at the same instant. When the water has sunk to the message intended, the sender raises his torch again and both spigots close. Nothing crosses the space between the stations but two flashes of light. The message is the interval between them. Whether the device was ever built, Polybius does not say; he records it only to complain that a menu of prewritten messages falls far short of what a general needs.
Morse code is remembered as an alphabet of dots and dashes, but working operators distinguished the short gap inside a letter from the longer gaps between letters and between words, so the code in practice had four signs, and two of them were silences. Engineers eventually gave the pure form of the trick a name, “pulse-position modulation”: make every pulse identical, and let the data ride entirely on when each pulse arrives. The remote control on the arm of your sofa uses a version of it — in the widespread NEC code, every infrared flash is the same 560-microsecond burst, and a bit is a gap, a zero fitting in 1.125 milliseconds and a one taking exactly twice as long. At the other end of the scale, on December 11, 2023, NASA’s Deep Space Optical Communications experiment, riding the Psyche spacecraft 19 million miles from Earth, streamed an ultra-high-definition video by laser to the Hale Telescope at Palomar at 267 megabits per second. At that distance the photons that survive the trip are few, and pulse-position modulation is the encoding of choice: each pulse lands in one time slot out of many, and the choice of slot is the data. The video, which spent 101 seconds in flight, is fifteen seconds long and shows an orange tabby cat named Taters chasing the dot of a laser pointer.
How much can timing alone carry? A note posted this September on a small blog called R Bites, by Gabriel Broussard Korr, works it out from a question a Lokele drummer would recognize: “how efficiently can I communicate with my friend by beating a large drum?” Korr’s drum is poorer than Carrington’s — it has one tone, not two. Every beat is the same beat; only the waits differ. Fix a tick, say one millisecond, and agree on a minimum rest between beats so that nobody has to drum faster than is comfortable. Then each gap, counted in ticks, names a number, and a beat carries as many bits as the base-2 logarithm of the count of gaps you can tell apart. Aim each gap at the center of its tick and a beat may land half a tick early or late without harm; if your timing wobbles more than that, widen the tick until it comfortably swallows the wobble — the note sizes the tick at a few standard deviations of the drummer’s error and computes the misfire rate from the Gaussian tail. Now suppose the gaps run from one second up to nineteen, measured to the millisecond. That is eighteen thousand distinguishable durations, of which each beat selects exactly one: fourteen bits. Korr computes that beats spaced ten seconds apart on average transmit nearly 1.5 bits per second. Ten seconds of silence, measured closely enough, is a fourteen-bit word.
The rate declines only gently as the drummer slows, because patience pays logarithmically: doubling the longest permitted wait adds one bit to every beat. A drum heard six times in a minute sounds like almost nothing happening. Roughly ninety bits a minute are happening.
Computer security discovered the same channel from the other side. In a three-page note in the Communications of the ACM of October 1973, Butler Lampson of the Xerox Palo Alto Research Center posed the problem of confining a program so it can leak nothing, and observed that a program stripped of every legitimate output can still signal through channels “not intended for information transfer at all, such as the service program’s effect on system load.” Such timing channels are now a standing headache of the field: a process can meter out network packets so that the spacings between them spell a message, and an inspector who reads every byte of every packet finds nothing amiss. Encrypting what is said is a solved problem. Encrypting when is not.
Carrington got to watch his subject die. By the 1950s, Lokele schoolboys were no longer learning their own drum names, and the drum language is now extinct. In 1954 a visitor from the United States found him running a mission school at the Congolese outpost of Yalemba, still walking daily in the forest; at lunchtime his wife would call him home on the drum, and since her message has outlived the language it was beaten in, she may as well have the last word: “White man spirit in forest come come to house of shingles high up above of white man spirit in forest. Woman with yams awaits. Come come.”