How We Know

James Gleick’s first chapter has the title “Drums That Talk.” It explains the concept of information by looking at a simple example. The example is a drum language used in a part of the Democratic Republic of Congo where the human language is Kele. European explorers had been aware for a long time that the irregular rhythms of African drums were carrying mysterious messages through the jungle. Explorers would arrive at villages where no European had been before and find that the village elders were already prepared to meet them.

Sadly, the drum language was only understood and recorded by a single European before it started to disappear. The European was John Carrington, an English missionary who spent his life in Africa and became fluent in both Kele and drum language. He arrived in Africa in 1938 and published his findings in 1949 in a book, The Talking Drums of Africa.

¹ Before the arrival of the Europeans with their roads and radios, the Kele-speaking Africans had used the drum language for rapid communication from village to village in the rain forest. Every village had an expert drummer and every villager could understand what the drums were saying. By the time Carrington wrote his book, the use of drum language was already fading and schoolchildren were no longer learning it. In the sixty years since then, telephones made drum language obsolete and completed the process of extinction.

Carrington understood how the structure of the Kele language made drum language possible. Kele is a tonal language with two sharply distinct tones. Each syllable is either low or high. The drum language is spoken by a pair of drums with the same two tones. Each Kele word is spoken by the drums as a sequence of low and high beats. In passing from human Kele to drum language, all the information contained in vowels and consonants is lost. In a European language, the consonants and vowels contain all the information, and if this information were dropped there would be nothing left. But in a tonal language like Kele, some information is carried in the tones and survives the transition from human speaker to drums. The fraction of information that survives in a drum word is small, and the words spoken by the drums are correspondingly ambiguous. A single sequence of tones may have hundreds of meanings depending on the missing vowels and consonants. The drum language must resolve the ambiguity of the individual words by adding more words. When enough redundant words are added, the meaning of the message becomes unique.

In 1954 a visitor from the United States came to Carrington’s mission school. Carrington was taking a walk in the forest and his wife wished to call him home for lunch. She sent him a message in drum language and explained it to the visitor. To be intelligible to Carrington, the message needed to be expressed with redundant and repeated phrases: “White man spirit in forest come come to house of shingles high up above of white man spirit in forest. Woman with yam awaits. Come come.” Carrington heard the message and came home. On the average, about eight words of drum language were needed to transmit one word of human language unambiguously. Western mathematicians would say that about one eighth of the information in the human Kele language belongs to the tones that are transmitted by the drum language. The redundancy of the drum language phrases compensates for the loss of the information in vowels and consonants. The African drummers knew nothing of Western mathematics, but they found the right level of redundancy for their drum language by trial and error. Carrington’s wife had learned the language from the drummers and knew how to use it.

The story of the drum language illustrates the central dogma of information theory. The central dogma says, “Meaning is irrelevant.” Information is independent of the meaning that it expresses, and of the language used to express it. Information is an abstract concept, which can be embodied equally well in human speech or in writing or in drumbeats. All that is needed to transfer information from one language to another is a coding system. A coding system may be simple or complicated. If the code is simple, as it is for the drum language with its two tones, a given amount of information requires a longer message. If the code is complicated, as it is for spoken language, the same amount of information can be conveyed in a shorter message.