nancy. The social acceptability of abortion as a means of population con¬ trol has varied from time to time and place to place throughout history. It was apparently a common method of family limitation in the Greco- Roman world, but Christian theologians early and vehemently condemned it. It became widely accepted in Europe in the Middle Ages. Severe crimi¬ nal sanctions to deter abortion became common in the 19th century, but in the 20th century those sanctions were gradually modified in many countries. In the U.S. the 1973 Roe v. Wade decision had the effect of legalizing abortion during the first three months of pregnancy; states were able to implement restrictions on access to abortion after the first trimes¬ ter, though within constraints set by the courts. Since that decision, there has been a fierce debate between supporters and opponents of a liberal¬ ized abortion policy.
Abraham (fl. early 2nd millennium bc) First of the Hebrew patriarchs, revered by Judaism, Christianity, and Islam. Genesis tells how Abraham, at 75, left Ur with his barren wife, Sarai (later Sarah), and others to found a new nation in Canaan. There God made a covenant with him, prom¬ ising that his descendants would inherit the land and become a great nation. Abraham fathered Ishmael by Sarah’s maidservant Hagar; Sarah herself bore Isaac, who inherited the covenant. Abraham’s faith was tested when God ordered him to sacrifice Isaac; he was prepared to obey but God relented. In Judaism he is a model of virtue, in Christianity he is the father of all believers, and in Islam he is an ancestor of Muhammad and a model (in Sufism) of generosity.
Abraham, Karl (b. May 3, 1877, Bremen, Ger.—d. Dec. 25, 1925, Berlin) German psychoanalyst. He helped establish the first branch of the International Psychoanalytic Institute in 1910 and pioneered the psycho¬ analytic treatment of manic-depressive psychosis (bipolar disorder). He suggested that the sexual drive develops in six stages and that if devel¬ opment is arrested at any of the earlier stages, mental disorders will likely result from fixation at that level. His most important work was A Short Study of the Development of the Libido (1924).
Abraham, Plains of Plateau located west of the old walled city of Quebec, Canada. On Sept. 13, 1759, it was the scene of the decisive battle of the French and Indian War, in which the British under James Wolfe defeated the French under the marquis de Montcalm. U.S. forces held the plateau (1775-76) in their siege of Quebec during the American Revolu¬ tion. It is now a park within Quebec city limits.
abrasion platform See wave-cut platform
abrasives Sharp, hard materials used to wear away the surface of softer, less resistant materials. Abrasives are indispensable to the manufacture of the highly precise components and ultrasmooth surfaces required in the manufacture of automobiles, airplanes and space vehicles, mechanical and electrical appliances, and machine tools. Abrasives may be natural (e.g., diamond, corundum, emery) or synthetic (e.g., silicon carbide or Carborun¬ dum, synthetic diamond, alumina—a synthetic form of corundum). They range from the relatively soft particles used in household cleansers and jeweler’s polish to diamonds.
Abruzzo \a-'briit-so\ or Abruzzi \a-'brut-se\ Region (pop., 2004 est.: 1 ,285,896), central Italy. Its capital is L'Aquila. Most of the region is moun¬ tainous or hilly, traversed by the Apennines. The ancient Italic tribes of the region long resisted conquest by the Romans. The Normans established themselves in the 12th century, and the region later sided with the Hohen- staufens against the papacy. As Abruzzi e Molise, the area became part of the Kingdom of Italy in 1860-61; in 1965 it was divided into the separate regions of Abruzzo and Mouse. The economy is primarily agricultural.
Absalom (fl. c. 1020 bc, Palestine) In ancient Israel, the third and most beloved son of David. His story is told in 2 Samuel 13-19. An attractive but lawless man, he killed his half brother Amnon as revenge for the lat¬ ter’s rape of Tamar, Absalom’s sister, and was banished from the king¬ dom for a time. He later raised a rebellion against his father, capturing Jerusalem but meeting defeat in the forest of Ephraim, where he was killed by his cousin Joab, who found him caught by the hair in an oak tree. Despite Absalom’s treachery, David greatly lamented his son’s death.
Absaroka \ab-'sar-3-k9\ Range Range of the Rocky Mountains in the U.S. It extends from southern Montana into northwestern Wyoming, crossing portions of Gallatin, Shoshone, and Custer national forests, as well as the northeastern portion of Yellowstone National Park. The range is about 175 mi (280 km) long; its highest point is Franks Peak, at 13,140 ft (4,005 m).
© 2006 Encyclopaedia Britannica, Inc.
abscess ► Abu Muslim I 7
abscess \'ab-,ses\ Localized collection of pus in a cavity in the deeper layers of the skin or within the body, formed from tissues broken down by white blood cells (leukocytes) in response to inflammation caused by bacteria. A wall develops, separating the thick yellowish pus from the extracellular fluid of nearby healthy tissues. Rupture of the abscess allows the pus to escape and relieves swelling and pain. Treatment consists of cutting into the wall to drain the pus and giving antibiotics. If infective contents enter the bloodstream, they may be carried to remote tissues, seeding new abscesses.
absentee ownership Ownership of land by those who do not live on it but who enjoy income from it. Criticized for centuries as an eco¬ nomic injustice, absentee ownership was a feature of pre-Revolutionary France and English rule of Ireland. Ending the practice continues to be a goal of LAND reform programs in many developing countries.
absolute value Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnega¬ tive. If a real number a is positive or zero, its absolute value is itself; if a is negative, its absolute value is -a. A complex number z is typically represented by an ordered pair {a, b ) in the complex plane. Thus, the absolute value (or modulus) of z is defined as the real number v< 2 2 + b 2 , which corresponds to z’ s distance from the origin of the complex plane. Vectors, like arrows, have both magnitude and direction, and their alge¬ braic representation follows from placing their “tail” at the origin of a multidimensional space and extracting the corresponding coordinates, or components, of their “point.” The absolute value (magnitude) of a vector is then given by the square root of the sum of the squares of its compo¬ nents. For example, a three-dimensional vector v, given by (a , b, c), has absolute value Va 2 + b 2 + c 2 . Absolute value is symbolized by vertical bars, as in \x\, \z\, or |v|, and obeys certain fundamental properties, such as \a ■ b\ = \a\ • \b\ and \a + b\ < \a\ + \b.
absolute zero Temperature at which a thermodynamic system (see thermodynamics) has the lowest energy, 0 kelvin (K). It corresponds to -459.67°F (-273.15°C) and is the lowest possible temperature theoreti¬ cally achievable by a system. A gas at constant pressure contracts as the temperature is decreased. A perfect gas would reach zero volume at abso¬ lute zero. However, a real gas condenses to a liquid or a solid at a tem¬ perature higher than absolute zero. At absolute zero, the system’s molecular energy is minimal and none is available for transfer to other systems. The Kelvin temperature scale has absolute zero as its zero point, and its fundamental unit is the kelvin.