4 Measure of Ideas, Rule of Language: Mathematics and Language in the 18th Century

### Mechanical Communication

In the final decade of the 18th century, French revolutionary expansionism lent special urgency to the problem of long-distance communication.[31] The logistic necessity of swift and sure communi-

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cation with allied military units on distant fronts called for a language simple enough to be transmitted over many miles. Here was an obvious and practical instance of the importance, as proclaimed by philosophers, for a simple, clear, expressive, unequivocal language. In most of the late 18th-century proposals for an optical or military telegraph, the preferred means of transmission were mechanical; the elements of the message were geometrical or numerical.

The first telegraph to attract international attention was the invention of Claude Chappe. Chappe began by exploring the possibility of electrical telegraphy.[32] In 1790 he abandoned the electrical for the mechanical as a means of transmitting language and built a prototype optical telegraph. By 1791 he had extended its range to 15 kilometers. Revolutionary crowds, however, feared telegraphy as a royalist instrument and tore down Chappe's Parisian stations.[33]

The apparatus consisted of a 1-foot pole atop a tower or tall building, a 14-foot crossbar pivoting at the center, a 6-foot arm at each end of the crossbar, control wires by which an operator could manipulate the arms, and lanterns on the arms for nighttime operation. The crossbar could be positioned either horizontally or vertically; the arms then pivoted around the ends of the crossbar. Each arm could assume seven different positions with respect to the crossbar. Each possible position was assigned a number.

With the help of a friend familiar with diplomatic codes, Chappe formulated a manual of nearly 10,000 words. As in the numerical dictionaries,[34] each word corresponded to a number. The positions of

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the arms signaled first the page number and then the numbered word on that page. Eventually Chappe added two more code books—one containing phrases and another containing place names. Operators would then transmit sets of three signals: the first indicated which code book to use; the second, the page number; and the third, the number of the word on the page. The scheme thus resembled Hourwitz's numerical dictionary and de Maimieux's matrix of knowledge. As a reviewer commented, Chappe had coupled his mechanical apparatus with an analysis of language: "The table of characters . . . is a tachygraphic method. . . fruit of [Chappe's] long and laborious meditations."[35] In the interest of enhancing its tachygraphic possibilities, a member of the Chappe organization later suggested the use of two-person teams, one to dictate in a sort of numerical shorthand what he saw on the distant tower, the other to record the information.

Through the good offices of his brother, a deputy in the Legislative Assembly, Chappe's system came to the attention of the Assembly's committee on public instruction. After the demise of the Assembly, its successor, the National Convention, was persuaded in April 1793 to order a test "in order to determine the utility of the telegraph" and to consider the use in war of such a "rapid messenger of thought." The commissaires appointed by the Convention—Lakanal, Arbogast, and Daunou—were joined by "several celebrated savants and artists" on the day of the test.[36] They were apparently impressed: Lakanal's official report on the merit of Chappe's telegraph envisioned its "great utility . . . especially in wars on land and at sea, where prompt communication and rapid awareness of maneuvers can have a great influence on success."[37] The positive report led to Chappe's appointment as official ingénieur-télégraphe and, more telling, a high-priority claim on scarce supplies with which to construct a full-scale telegraph system. In September 1794 public enthusiasm was

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buoyed (and suspicions about Chappe's loyalties presumably quelled) when the newly constructed telegraph line carried to the capital news of the capture of Condé. A year later the Directory authorized continued support of Chappe's venture, and in 1798 a second line (connecting Paris and Strasbourg) was completed. Eventually the system consisted of eight principal lines and covered some 3,000 miles.[38]

News of the successful deployment of Chappe's system spread quickly. The first printed version of the "alphabet Chappe" appeared anonymously in Leipzig in 1794; periodicals carried accounts of the bullétin télégraphique reporting the capture of Condé a second edition of Chappe's Beschreibung und Abbildung des Telegraphen appeared in 1795. The need for an optical telegraph was widely felt. From 1794, for example, committees of the Patriotic Society of Hamburg had discussed the development of a telegraph system to replace the cumbersome apparatus of messenger boats, observers, and towers used to regulate shipping traffic between Hamburg and Cuxhaven. The Society's secretary, Friedrich Johann Lorenz Meyer, also noted the military potential of a telegraph system. On a visit to Paris in 1796, Meyer witnessed a demonstration of Chappe's optical telegraph, and carried the news of its success back to Hamburg, where a select committee was convened to study its merits. Their cost-benefit analysis argued against establishing a Chappe-style system in Hamburg, on grounds both of cost (estimated at 20,000 marks) and of poor visibility in the northern German climate.[39]

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The issue of the optical telegraph also engaged the attention of savants and royalty elsewhere in the German states. In Berlin, the academician and chemist Franz Karl Achard demonstrated his version of the telegraph to Friedrich Wilhelm II in 1795, successfully sending such meaningful messages as "The King is loved by his subjects just as much as he is feared by his enemies." As reward for his efforts, Achard received a substantial bonus of 500 Reichstaler, equal to one-third of his annual salary at the Berlin Academy.[40]

Another savant inspired to imitate or improve upon Chappe's invention was the Swedish academician and natural philosopher Abraham Niklas Edelcrantz. He seized on its military possibilities: "In case of war," a telegraph would afford the possibility of "quick communication for discussion between several armies or divisions of the same army."[41] Edelcrantz began his investigations in September 1794 with variants on Chappe's design of crossbars and pivoting arms. He then switched to a lattice of ten "holes" or windows with shades visible in daylight and lanterns behind them at night. This arrangement permitted 1,024 different signals. The first trials of the Swedish telegraph took place between Stockholm and Drotningholm on 30 October and 1 November 1794. Demonstrations of the system the following year were conducted in "the presence of the king, the regent, and the whole royal court."[42]

Like Chappe, Edelcrantz compiled a codebook, which he called a telegraphische Chiffren-Tabelle . It contained short words, syllables, and a few phrases, each corresponding to a three-digit number.[43] Each

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number designated one of the 1024 signals possible with the ten-window lattice. Edelcrantz saw his codebook as the basis for a universal language: "A cipher-table or dictionary explaining signs for all languages should be made to go along with this language-instrument, which can be completely portable."[44]

Thomas Northmore, inspired by what he knew of Polybius' telegraph, also linked his proposal for a Nocturnal or Diurnal Telegraph (which used reflecting lamps moved by a winch) with an account of his new universal character. He proclaimed the "ground-work of the whole super-structure" to be "that if the same numerical figure be made to represent the same word in all languages, an universal medium is immediately obtained." "Diversity of idioms" would prove no obstacle in Northmore's simplified language, which required as a "constant companion" only a "small pocket numerical dictionary," containing some 5,000 to 6,000 "select words."[45]

One of de Maimieux's royalist disciples likewise saw the connection between universal language and telegraphy. The comte de Firmas-Périès, who served in the army of the prince de Condé, recognized the versatility of de Maimieux's pasigraphy and reformulated it for use in telegraphy. Firmas-Périès' mechanical semaphore system, which he labeled "pasitelegraphy," converted de Maimieux's latitude and longitude indicators to arrangements of wooden "hands" on a large clock face operated by chains and pulleys à la Vaucanson.[46] To decipher the message, the operator turned to de Maimieux's tables of words (and knowledge).

Reports concerning the French telegraph, including one retrieved from the pocket of a French prisoner in 1794, also inspired English inventors, including John Gamble, chaplain of the staff of H.R.H.

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Frederick, Duke of York and Albany. As would Edelcrantz, Gamble analyzed "the different modes which have been, or may be adopted for the purpose of distant communication"—this at the request of the Duke.[47] Gamble recognized the need for a "figurative language" adequate for communication and capable of quick transmission, and settled on a portable apparatus of five shutters ("lever boards"), which in various combinations denoted the letters of the alphabet. The use of lamps behind the shutters looked promising for nighttime transmissions.[48] The Admiralty implemented Gamble's suggestion on a series of "telegraph hills" between London and Deal as early as 1796 and found that a short message could be relayed in a minute's time. Like the other systems of the late 18th century, the Admiralty telegraph was quick (though labor-intensive) and promptly proved its value for the transmission of military intelligence.[49]

The efficiency of mechanical-optical telegraph systems itself came under scrutiny in Edelcrantz' study. He treated the visibility of signals at a distance like a problem in exact experimental physics, and assessed the accuracy of contemporary telescopes, threshold values for the angular diameter of an object visible at a given distance, and differential effects of color and humidity on visibility. The analysis was informed by Edelcrantz' familiarity with contemporary work on experimental optics, meteorology, and other branches of 18th-century physics. Indeed, Edelcrantz saw the possibility that a network of telegraph operators and stations, suitably equipped with an array of scientific instruments, might also advance the cause of science: "Every telegraph is a real Observatory, which can become an

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astronomical one, with the appropriate instruments and the understanding of the director, and science would be enriched with new discoveries."[50]

4 Measure of Ideas, Rule of Language: Mathematics and Language in the 18th Century