irrational number Among the real numbers, any of those that cannot be represented as quotients of integers. In decimal form, irrational num¬ bers are represented by nonterminating, nonrepeating decimals. Examples include square roots of prime numbers and such transcendental numbers as k and e.
Irrawaddy \,ir-a-'wa-de\ River River, Myanmar (Burma). It flows 1,350 mi (2,170 km) across the centre of the country and empties into the Bay of Bengal. The country’s most important commercial waterway, it is formed by the confluence of the Nmai and the Mali rivers; in the central dry zone it is joined by its major tributary, the Chindwin River. Chief ports are Mandalay, Chauk, Prome (Pye), and Henzada.
irrigation Artificial supply of water to land, to maintain or increase yields of food crops, a critical element of modern agriculture. Irrigation can compensate for the naturally variable rate and volume of rain. Water is pumped from natural ponds, lakes, streams, and wells; basin systems and dams hold back larger streams and annual floods. Below the dam, gates to concrete-lined canals are opened, conveying the water over the land through gravity flow. More elaborate, expensive canals flow from huge constructed reservoirs, which hold a year-round water supply. Today portable irrigation systems of lightweight aluminum pipe are in wide use. Drip irrigation, a newer method, uses narrow tubing to supply water directly to the base of each plant. Agricultural irrigation, water towers, and machines invented to lift and distribute water are ancient innovations. Early Egyptians were irrigating with Nile River water by 5000 bc, and
of perennial plants constituting the
Western ironweed (Vernonia fascicu- lata )
DAN MORRILL
© 2006 Encyclopaedia Britannica, Inc.
irritable bowel syndrome ► Isabella II I 961
such other ancient civilizations as Babylon and China seem to have devel¬ oped largely as a result of irrigation-based agriculture.
irritable bowel syndrome or IBS Chronic disorder characterized by abdominal pain, intestinal gas, and diarrhea, constipation, or both. Other symptoms may include abdominal pain that is relieved after def¬ ecation or a sensation of incomplete rectal evacuation. IBS is caused by a motility disturbance of the intestines that may result from increased intestinal sensitivity to distension. Stress or the consumption of fatty foods, milk products, certain fruits or vegetables (e.g., broccoli and cab¬ bage), alcohol, or caffeine may cause similar symptoms. Treatment includes relaxation, exercise, and avoidance of aggravating foods. Antid- iarrheal medications or fibre supplements may help lessen symptoms. Although IBS may cause discomfort and emotional distress, the disorder does not result in any permanent intestinal damage.
Irtysh \ir-'tosh\ River Kazakh Ertis \er-'tis\ River rising in the Altai Mountains in Xinjiang autonomous region, China. It flows west across the Chinese border and then northwest through Kazakhstan into Russian Sibe¬ ria, where it becomes the largest tributary of the Ob River. It is 2,640 mi (4,248 km) long and is navigable for most of its course. Its main ports include Tobolsk, Tara, Omsk, Pavlodar, Semey, and Oskemen.
Iruna See Pamplona
Irvine Royal burgh and seaport (pop., 1991: 32,988), North Ayrshire council area, on the Atlantic coast of Scotland. The last of Scotland’s five new towns, it was designated in 1967 to house overflow population from Glasgow and provide a focus for the economic and industrial rehabilita¬ tion of the area. It had declined in the 18th and 19th centuries because of competition from other towns and the silting of the harbour. It became an industrial centre that produces chemicals, engineering, electrical goods, and clothing.
Irving City (pop., 2000: 191,615), northeastern Texas, U.S. Established in 1903 and incorporated in 1914, the city developed into an industrial hub during the 1950s. A suburb of Dallas, it is the site of the University of Dallas and DeVry University as well as of Texas Stadium, home of the Dallas Cowboys professional gridiron football team.
Irving, Sir Henry orig. John Henry Brodribb (b. Feb. 6, 1838, Keinton Mandeville, Somerset, Eng.—d. Oct. 13, 1905, Bradford, York¬ shire) British actor. He toured for 10 years with a stock company before making his London debut in 1866. With his success in The Bells (1871), he became a leading actor in H.L. Bateman’s company (1871-77). As actor- manager of the Lyceum Theatre (from 1878), he made it London’s most successful theatre. He formed a celebrated acting partnership with Ellen Terry that lasted until the company dissolved in 1902. They were noted for their Shakespearean roles, and their theatrical qualities complemented each other: he the brooding introvert, she the spontaneous charmer.
Irving, John (Winslow) (b. March 2, 1942, Exeter, N.H., U.S.) U.S. novelist. He taught at several universities before beginning to write full¬ time in the late 1970s. His best-selling The World According to Garp (1978; film, 1982) is notable, like his other works, for its engaging story line, colourful characterizations, macabre humour, and examination of contemporary issues. Later novels include The Hotel New Hampshire (1981; film, 1984), The Cider House Rules (1985; film, 1999), and A Prayer for Owen Meany (1989).
Irving, Washington (b. April 3,
1783, New York, N.Y., U.S.—d.
Nov. 28, 1859, Tarrytown, N.Y.)
U.S. author, called the “first Ameri¬ can man of letters.” He began his career as a lawyer but soon became a leader of the group that published Salmagundi (1807-08), a periodical containing whimsical essays and poems. After his comic A History of New York...by Diedrich Knicker¬ bocker (1809), he wrote little until his very successful The Sketch Book (1819-20), containing his best- known stories, “The Legend of Sleepy Hollow” and “Rip Van
Winkle.” It was followed by a sequel, Bracebridge Hall (1822). He held diplomatic positions in Madrid, Spain, and writings such as The Alham¬ bra (1832) reflect his interest in Spain’s past.
Isaac \e-'zak\, Heinrich (b. c. 1450, Brabant—d. 1517, Florence) Flem¬ ish composer. He spent much of his career in Italy, especially Florence, but was known as a leading representative of the Netherlandish style. As court composer to Emperor Maximilian I (from 1497), he was allowed to travel. He had many students, including Ludwig Senfl, and his historical importance in Germany is as the main disseminator of the progressive Northern style there. The beauty and quality of his works, which include over 100 masses, dozens of motets, and secular songs, have led some to regard him as second only to Josquin des Prez among his contemporaries.
Isaac II Angelus (b. c. 1135—d. February 1204) Byzantine emperor (1185-95). Proclaimed emperor by the Constantinople mob that murdered his cousin, Andronicus I Comnenus, he drove the Normans out of Greece (1185) but failed to regain Cyprus from rebels. He was forced to help Frederick I Barbarossa in the Third Crusade. He defeated the Serbians (1190), but before he could carry out a planned expedition against the Bulgarians, he was overthrown by his brother, who imprisoned and blinded him (1195). His son Alexius diverted the Fourth Crusade to restore him to power (1203), and father and son briefly ruled as co-emperors before being dethroned and killed in a revolution.
Isaac of Stella (b. c. 1100, England—d. c. 1169, Etoile, near Poitiers, Aquitaine) Monk, philosopher, and theologian. Isaac joined the Cistercians during the reforms carried out by St. Bernard de Clairvaux. His scholarly works make use of logical argumentation and are influenced by the Neo¬ platonism of St. Augustine. His principal work, Letter to Alcher on the Soul (1162), integrates Aristotelian and Neoplatonic psychological theories with Christian mysticism. A leader of humanism in his day, he suggests that the intellect enables humans to grasp eternal ideas in time and that intelligence allows humans to intuit the reality of God.