Dec. 22, 1883, Paris, France—d.
Nov. 8, 1965, New York, N.Y., U.S.)
French-born U.S. composer. Forbid¬ den to study music by his father, he secretly continued his studies and entered the Schola Cantorum with the help of his cousin, the pianist Alfred Cortot (1877-1962). He soon moved to Berlin, where he met Fer¬ ruccio Busoni and Richard Strauss, musicians in tune with his forward¬
looking ideas. His Bourgogne (1907) caused a scandal because of its dis¬ sonance. His budding conducting career was interrupted by World War I, and he moved to the U.S. In 1921 he cofounded the International Com¬ posers Guild. His output was small, but every piece became a classic, including Ojfrandes, Ameriques (both 1921), Hyperprism, Octandre (both 1923), Arcana (1927), and Ionisation (1931), works remarkable for the way they used instruments, especially percussion, to create blocks of sound. After the early 1950s, when he finally gained access to the elec¬ tronic sound equipment he desired, he concentrated on electronic music.
Vargas Vvar-gos\, Getulio (Dorneles) (b. April 19,1883, Sao Borja, Braz.—d. Aug. 24, 1954, Rio de Janeiro) President of Brazil (1930-45, 1951-54). He was elected governor of Rio Grande do Sul in 1928 and ran unsuccessfully for president in 1930, but later that year he overthrew the government to become head of state. In 1937 he abolished the constitu¬ tional government and set up the totalitarian New State, under which the previously autonomous states became dependent on central authority. He enacted labour reforms and social-security laws, introduced extensive educational reforms, enfranchised women, and granted the secret ballot. Deposed by a coup in 1945, he was elected president again in 1951; restrained by a congress and public opinion, he was unable to hold sup¬ port and, faced with forced retirement, took his own life.
Vargas Llosa \'bar-gas-'yo-sa\, (Jorge) Mario (Pedro) (b. March 28, 1936, Arequipa, Peru) Peruvian writer. Vargas Llosa worked as a jour¬ nalist and broadcaster before publishing The Time of the Hero (1963), his widely acclaimed first novel. It describes adolescents striving for survival in the hostile environment of a military school, the corruption of which reflects the larger malaise afflicting Peru. His commitment to social change is evident in his early novels, essays, and plays. He turned increas¬ ingly conservative, especially in the face of the Maoist Shining Path insur¬ gency, and in 1990 he ran for president of Peru. His best-known works include The Green House (1965), Aunt Julia and the Scriptwriter (1977), and The War of the End of the World (1981), an account of a 19th-century Brazilian religious movement. In 1994 he won the Cervantes Prize (a prestigious literary award given for Spanish-language literature).
variable In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length). Variables should be distinguished from coefficients, fixed values that multiply powers of variables in poly¬ nomials and algebraic equations. In the quadratic equation ax 2 + bx + c = 0, x is the variable, and a, b, and c are coefficients whose values must be specified to solve the equation. In translating word problems into alge¬ braic equations, quantities to be determined can be represented by vari¬ ables.
variable, complex See complex variable variable, random See random variable
variable star Star whose observed brightness varies noticeably in intensity. Pulsating variables expand and contract in cycles, pulsating rhythmically in brightness and size. Explosive variables include novas and supernovas, which brighten rapidly due to sudden outbursts of radi¬ ant energy; the increased brightness lasts a short time, followed by rela¬ tively slow dimming. Eclipsing variable stars are variable only because light from one star is blocked by another in Earth’s direction. Hundreds of thousands of variable stars are known. See also binary star; Cepheid vari¬ able; flare star; pulsar; T Tauri star.
variation In biology, any difference between cells, individual organ¬ isms, or groups of organisms within a species caused either by genetic differences (variation in genotype) or by the effect of environmental fac¬ tors on the expression of genetic potentials (variation in phenotype). Varia¬ tion may be shown in physical appearance, metabolism, fertility, mode of reproduction, behaviour, learning and mental ability, and other obvious or measurable characters. Genotypic variations are caused by differences in number or structure of chromosomes or by differences in the genes carried by the chromosomes. Eye colour, body form, and disease resistance are genotypic variations. Phenotypic variations may result from factors such as climate, food supply, and actions of other organisms. Phenotypic varia¬ tions also include stages in an organism’s life cycle and seasonal varia¬ tions in an individual. Because they do not involve hereditary alteration and in general are not transmitted to future generations, phenotypic varia¬ tions are not important in evolution. See also polymorphism.
Edgard Varese.
THE BETTMANN ARCHIVE
© 2006 Encyclopaedia Britannica, Inc.
1988 I variation ► Vasari
variation In music, basic technique consisting of changing the music melodically, harmonically, or contrapuntally. The simplest variation type is the variation set, in which two or more sections are based on the same musical material, which is treated with different variational techniques in each section. The practice, originally involving use of a repeated bass line (basso ostinato, or ground bass), began in early 16th-century dance music in Italy and Spain. Ground-bass forms include the chaconne and passa- caglia, both of which usually employ a brief bass line repeated many times. In the 17th century, organ and harpsichord variations became a standard form in Germany. Keyboard variations in the 19th century often employed popular tunes or opera melodies; variation form was also com¬ monly used in symphonies, quartets, and sonatas. It declined in impor¬ tance after the classical era but has never ceased to be employed by composers. The music of certain non-Western cultures also uses varia¬ tional techniques. The art music of southern India is built on the concept of a string of pieces, each a variation on a given “theme.” A somewhat different concept of multilevel variation is found in the gamelan (orches¬ tra) music of Indonesia. The variations are not consecutive but are simul¬ taneous, a technique called heterophony.
varicella See chicken pox
varicose Vvar-o-.kosV vein or varix Twisted vein distended with blood. Varix also covers arteries and lymphatic vessels (see lymphatic sys¬ tem). Varicose veins occur mostly in the legs, when malfunctioning valves let blood pool in veins near the skin. Causes include hereditary valve and vein wall weakness and internal or external pressure on veins. Varices are common in pregnancy, suggesting that hormone abnormalities play a role. Symptoms include a heavy feeling, with leg cramps and swelling after standing a long time. Complications include skin ulcers and thrombosis. Treatment involves strong support hose, injection therapy, or surgery. Varices in the esophagus, which often occur in liver disease, can ulcerate and bleed. See also hemorrhoid.
variety theatre See music hall and variety theatre variola See smallpox
Varmus, Harold (Elliot) (b. Dec. 18, 1939, Oceanside, N.Y., U.S.) U.S. virologist. He joined the faculty of UC-San Francisco in 1970. With J. Michael Bishop, he discovered that, under certain circumstances, normal genes in healthy body cells can cause cancer. These oncogenes ordinarily control cell division and growth, but viruses or carcinogens can activate them. Their research superseded a theory that cancer is caused by viral genes, distinct from a cell’s normal genetic material, that lie dormant until activated by carcinogens. For their work, the two shared a 1989 Nobel Prize. Varmus later served as director of the National Institutes of Health (1993-99) and became president of Memorial Sloan-Kettering Cancer Center.