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How We Know

Fitch-Febvrel Gallery
Érik Desmazières: La Salle des planètes, from his series of illustrations for Jorge Luis Borges’s story ‘The Library of Babel,’ 1997–2001. A new volume of Desmazières’s catalogue raisonné will be published by the Fitch-Febvrel Gallery later this year. Illustration © 2011 Artists Rights Society (ARS), New York/ADAGP, Paris.

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.

Another example illustrating the central dogma is the French optical telegraph. Until the year 1793, the fifth year of the French Revolution, the African drummers were ahead of Europeans in their ability to transmit information rapidly over long distances. In 1793, Claude Chappe, a patriotic citizen of France, wishing to strengthen the defense of the revolutionary government against domestic and foreign enemies, invented a device that he called the telegraph. The telegraph was an optical communication system with stations consisting of large movable pointers mounted on the tops of sixty-foot towers. Each station was manned by an operator who could read a message transmitted by a neighboring station and transmit the same message to the next station in the transmission line.

The distance between neighbors was about seven miles. Along the transmission lines, optical messages in France could travel faster than drum messages in Africa. When Napoleon took charge of the French Republic in 1799, he ordered the completion of the optical telegraph system to link all the major cities of France from Calais and Paris to Toulon and onward to Milan. The telegraph became, as Claude Chappe had intended, an important instrument of national power. Napoleon made sure that it was not available to private users.

Unlike the drum language, which was based on spoken language, the optical telegraph was based on written French. Chappe invented an elaborate coding system to translate written messages into optical signals. Chappe had the opposite problem from the drummers. The drummers had a fast transmission system with ambiguous messages. They needed to slow down the transmission to make the messages unambiguous. Chappe had a painfully slow transmission system with redundant messages. The French language, like most alphabetic languages, is highly redundant, using many more letters than are needed to convey the meaning of a message. Chappe’s coding system allowed messages to be transmitted faster. Many common phrases and proper names were encoded by only two optical symbols, with a substantial gain in speed of transmission. The composer and the reader of the message had code books listing the message codes for eight thousand phrases and names. For Napoleon it was an advantage to have a code that was effectively cryptographic, keeping the content of the messages secret from citizens along the route.

After these two historical examples of rapid communication in Africa and France, the rest of Gleick’s book is about the modern development of information technology. The modern history is dominated by two Americans, Samuel Morse and Claude Shannon. Samuel Morse was the inventor of Morse Code. He was also one of the pioneers who built a telegraph system using electricity conducted through wires instead of optical pointers deployed on towers. Morse launched his electric telegraph in 1838 and perfected the code in 1844. His code used short and long pulses of electric current to represent letters of the alphabet.

Morse was ideologically at the opposite pole from Chappe. He was not interested in secrecy or in creating an instrument of government power. The Morse system was designed to be a profit-making enterprise, fast and cheap and available to everybody. At the beginning the price of a message was a quarter of a cent per letter. The most important users of the system were newspaper correspondents spreading news of local events to readers all over the world. Morse Code was simple enough that anyone could learn it. The system provided no secrecy to the users. If users wanted secrecy, they could invent their own secret codes and encipher their messages themselves. The price of a message in cipher was higher than the price of a message in plain text, because the telegraph operators could transcribe plain text faster. It was much easier to correct errors in plain text than in cipher.

Claude Shannon was the founding father of information theory. For a hundred years after the electric telegraph, other communication systems such as the telephone, radio, and television were invented and developed by engineers without any need for higher mathematics. Then Shannon supplied the theory to understand all of these systems together, defining information as an abstract quantity inherent in a telephone message or a television picture. Shannon brought higher mathematics into the game.

When Shannon was a boy growing up on a farm in Michigan, he built a homemade telegraph system using Morse Code. Messages were transmitted to friends on neighboring farms, using the barbed wire of their fences to conduct electric signals. When World War II began, Shannon became one of the pioneers of scientific cryptography, working on the high-level cryptographic telephone system that allowed Roosevelt and Churchill to talk to each other over a secure channel. Shannon’s friend Alan Turing was also working as a cryptographer at the same time, in the famous British Enigma project that successfully deciphered German military codes. The two pioneers met frequently when Turing visited New York in 1943, but they belonged to separate secret worlds and could not exchange ideas about cryptography.

In 1945 Shannon wrote a paper, “A Mathematical Theory of Cryptography,” which was stamped SECRET and never saw the light of day. He published in 1948 an expurgated version of the 1945 paper with the title “A Mathematical Theory of Communication.” The 1948 version appeared in the Bell System Technical Journal, the house journal of the Bell Telephone Laboratories, and became an instant classic. It is the founding document for the modern science of information. After Shannon, the technology of information raced ahead, with electronic computers, digital cameras, the Internet, and the World Wide Web.

According to Gleick, the impact of information on human affairs came in three installments: first the history, the thousands of years during which people created and exchanged information without the concept of measuring it; second the theory, first formulated by Shannon; third the flood, in which we now live. The flood began quietly. The event that made the flood plainly visible occurred in 1965, when Gordon Moore stated Moore’s Law. Moore was an electrical engineer, founder of the Intel Corporation, a company that manufactured components for computers and other electronic gadgets. His law said that the price of electronic components would decrease and their numbers would increase by a factor of two every eighteen months. This implied that the price would decrease and the numbers would increase by a factor of a hundred every decade. Moore’s prediction of continued growth has turned out to be astonishingly accurate during the forty-five years since he announced it. In these four and a half decades, the price has decreased and the numbers have increased by a factor of a billion, nine powers of ten. Nine powers of ten are enough to turn a trickle into a flood.

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    London: Carey Ringsgate, 1949. 

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