Cauchy \ko-'she\, Augustin-Louis, Baron (b. Aug. 21, 1789, Paris, France—d. May 23, 1857, Sceaux) French mathematician, pioneer of analysis and group theory. After a career as a military engineer in Napo¬ leon’s navy, he wrote a treatise in 1813 that became the basis of the theory of complex variables. He also clarified the theory of calculus by develop¬ ing the concepts of limits and continuity, laid the foundations for the math¬ ematical theory of elasticity, and made important contributions to number theory. He is considered one of the greatest mathematicians of the mod¬ ern era.
Cauchy-Schwarz \'shworts\ inequality Any of several related inequalities developed by Augustin-Louis Cauchy and, later, Herman Schwarz (1843-1921). The inequalities arise from assigning a real num¬ ber measurement, or norm, to the functions, vectors, or integrals within a particular space in order to analyze their relationship. For functions/and g, whose squares are integrable and thus usable as a norm, (.Ifgf ^ df)(lg 2 )- For vectors a = (a u a 2 , a 3 ,..., a„) and b = (b 3 , b 2 , b 3 ,..., b n ), together with the inner product (see inner product space) for a norm, (Z(aj, bf) 2 < Z(fl f ) 2 Z(ft f ) 2 . In addition to functional analysis, these inequali¬ ties have important applications in statistics and probability theory.
caudillo \kau-'de-y6\ Latin American military dictator. In the wake of the Latin American independence movement in the early 19th century.
Carrie Chapman Catt.
COURTESY OF THE LEAGUE OF WOMEN VOTERS OF ILLINOIS
© 2006 Encyclopaedia Britannica, Inc.
Caulaincourt ► Cavallini I 355
politically unstable conditions and the long experience of armed conflict led to the emergence in many of the new countries of strongmen who were often charismatic and whose hold on power depended on control over armed followers, patronage, and vigilance. Because their power was based on violence and personal relations, the legitimacy of the caudillos’ rule was always in doubt, and few could withstand the challenges of new leaders who emerged among their own followers and wealthy patrons. See also machismo; personalismo.
Caulaincourt \,ko-,la n - , kur\ / Armand (-Augustin-Louis), mar¬ quis de (b. Dec. 9, 1773, Caulaincourt, France—d. Feb. 19, 1827, Paris) French general and diplomat. He became aide-de-camp to Napoleon (1802) and was the emperor’s loyal master of horse from 1804. He later served as ambassador to Russia (1807-11) and foreign minister (1813— 14, 1815). Created duke de Vicence (1808), he was at Napoleon’s side in his great battles. His Memoires provide an important source for the period 1812 to 1814.
cauliflower Form of cabbage ( Brassica oleracea, Botrytis group) in the mustard family, consisting of a com¬ pact terminal mass of greatly thick¬ ened, modified, and partially developed flower structures, together with their embracing fleshy stalks.
This terminal cluster forms a firm, white, succulent “curd” that is served as a cooked vegetable and is highly nutritious. The separated flower structures are also eaten raw.
Caulkins, Tracy (b. Jan. 11,1963,
Winona, Minn., U.S.) U.S. swimmer.
In 1978 she became (at age 15) the first woman to swim the 200-yd medley in under two minutes. By 1982 she had surpassed Johnny Weissmuller’s record of 36 U.S. national titles and had won more titles than any other U.S. amateur ath¬ lete. After the 1984 Olympics, where she won three gold medals, she retired having won 48 national titles and having set 66 world or U.S. records. Caulkins is the only swimmer to set U.S. records in every stroke.
causation Relation that holds between two temporally simultaneous or successive events when the first event (the cause) brings about the other (the effect). According to David Hume, when we say of two types of object or event that “X causes Y” (e.g., fire causes smoke), we mean that (i) Xs are “constantly conjoined” with Ys, (ii) Ys follow Xs and not vice versa, and (iii) there is a “necessary connection” between Xs and Ys such that whenever an X occurs, a Y must follow. Unlike the ideas of contiguity and succession, however, the idea of necessary connection is subjective, in the sense that it derives from the act of contemplating objects or events that we have experienced as being constantly conjoined and succeeding one another in a certain order, rather than from any observable properties in the objects or events themselves. This idea is the basis of the classic problem of induction, which Hume formulated. Hume’s definition of cau¬ sation is an example of a “regularity” analysis. Other types of analysis include counterfactual analysis, manipulation analysis, and probabilistic analysis.
caustic soda Sodium hydroxide (NaOH), an inorganic compound. The alkalies called caustic soda and caustic potash (potassium hydroxide) are very important industrial chemicals, with uses in the manufacture of soaps, glass, and numerous other products. They have been easily extracted since ancient times by soaking wood ashes in water (see lye). Industrial methods of caustic-soda production developed in the 18th cen¬ tury (the Leblanc process) and 19th century (the Solvay, or ammonia-soda, process) have been largely displaced by electrolysis.
Cauvery River See Kaveri River
Cavafy \k9-'vaf-e\, Constantine orig. Konstantinos Petrou K a vans (b. April 17, 1863, Alexandria—d. April 29, 1933, Alexandria) Poet of Turkish-Greek ancestry. Born to Greek parents, Cavafy worked as an obscure civil servant in Alexandria his entire adult life. His small body of work, some 200 poems in an intimate, realistic, lyrical style, is written in a strange combination of classically based and modern Greek. Many deal with history, principally the Hellenistic era; many others reflect
Cavafy’s homosexual life. His poems became popular and influen¬ tial after his death, and he is now widely regarded as one of the great¬ est of modern Greek poets.
Cavaignac \ka-ven-'yak\/ Louis- Eugene (b. Oct. 15, 1802, Paris,
France—d. Oct. 28, 1857, Sarthe)
French general. He served with dis¬ tinction in the French conquest of Algeria in the 1840s. In the Revolu¬ tions of 1848 he was appointed min¬ ister of war. In June he suppressed a workers’ revolt, becoming known as “the butcher of June” (see June Days). That month he was named chief executive of France. In Decem¬ ber he lost the presidential election to Louis-Napoleon Bonaparte (later Napoleon III) but remained a leader of the opposition.
Cavaille-Coll \k3-vI-ya-'kol\, Aristide (b. Feb. 4, 1811, Montpellier, France—d. Oct. 13, 1899, Paris) French organ builder. He settled in Paris in 1833 at Gioacchino Rossini’s suggestion and with his brother and father built almost 500 organs in France, Belgium, The Netherlands, and else¬ where, including those in the Paris churches of Notre-Dame, La Madeleine, Ste. Clotilde, and La Trinite. With the goal of achieving an orchestral richness and variety of timbre, he introduced countless inno¬ vations; he is regarded as the creator of the French Romantic organ (which had great influence elsewhere as well), and composers such as Cesar Franck, Camille Saint-Saens, and Olivier Messiaen wrote particularly with the Cavaille-Coll sound in mind.
Cavalcanti X.ka-val-'kan-teV Guido (b. c. 1255, Florence—d. Aug. 27/28, 1300, Florence) Italian poet. Born into an influential Florentine family, he studied with the philosopher and scholar Brunetto Latini, who had earlier taught Dante, Cavalcanti’s close friend. After Dante, he is con¬ sidered the greatest Italian poet and personality in 13th-century Italian lit¬ erature. He left about 50 poems, many addressed to two women and on the theme of love. His language demonstrates the grace and directness of the dolce stil nuovo (“sweet new style”). Dante Gabriel Rossetti and Ezra Pound translated his poems.