Companions of the Prophet Arabic Sahaba or Ashab Follow¬ ers of Muhammad who had personal contact with him, including any Mus¬ lim contemporary who saw him. As eyewitnesses, they are the most important sources of Hadith. Sunnite Muslims regard the first four caliphs (among the 10 Companions to whom Muhammad promised paradise) as the most important. ShCite Muslims disregard the Companions, whom they consider responsible for the loss of the caliphate by the family of 'All
comparative advantage Economic theory first advanced by Rob¬ ert Torrens and David Ricardo that analyzes international trade in terms of differences in relative opportunity costs. The theory suggests that coun¬ tries should specialize in the goods they can produce most efficiently rather than trying for self-sufficiency and argues strongly in favour of free international trade.
comparative psychology Study of similarities and differences in behavioral organization among living beings. The discipline pays particu¬ lar attention to the psychological nature of humans in comparison with other animals. It began to emerge in the late 19th century and grew rap¬ idly in the 20th century, involving experimental studies on human and animal brain function, learning, and motivation. Well-known studies have included those of Ivan Pavlov on conditioning in laboratory dogs, those of Harry Harlow (1905-81) on the effects of social deprivation in monkeys, and those of various researchers on language abilities in apes.
comparator Vkom-'par-o-torV Instrument for comparing something with a similar thing or with a standard measure, in particular to measure small displacements in mechanical devices. In astronomy, the blink com¬ parator is used to examine photographic plates for signs of moving bod¬ ies. Machinists use comparators or visual gauges to centre or align work in MACHINE TOOLS.
compass In navigation or surveying, the chief device for direction find¬ ing on the Earth’s surface. Compasses may operate on magnetic or gyro¬ scopic (see gyroscope) principles or by determining the direction of the Sun or a star. The oldest and most familiar type is the magnetic compass, used in different forms in aircraft, ships, and land vehicles and by sur¬ veyors. Magnetic compasses work as they do because the Earth itself is a magnet with a north-south field (see geomagnetic field) that causes freely moving magnets to align themselves with the field.
compatibilism Thesis that free will, in the sense required for moral responsibility, is consistent with universal causal determinism. It is impor¬ tant to distinguish the question of the logical consistency of belief in uni¬ versal causal determinism with belief in free will from the question whether the thesis of free will (or that of causal determinism) is true. Compatibilists need not assert (though many have) the reality both of free will and of causal determinism. Among incompatibilists, some maintain the existence of free will and accordingly deny universal causal deter¬ minism, while others uphold universal causal determinism and deny the existence of free will. See also free will problem.
compiler Computer software that translates (compiles) source code written in a high-level language (e.g., C++) into a set of machine-language
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442 I complement ► Compromise of 1867
instructions that can be understood by a digital computer’s CPU. Compil¬ ers are very large programs, with error-checking and other abilities. Some compilers translate high-level language into an intermediate assembly lan¬ guage, which is then translated (assembled) into machine code by an assembly program or assembler. Other compilers generate machine lan¬ guage directly.
complement In physiology, a complex system of at least 20 proteins (complement components) in normal blood serum. The binding of one component to an antigen-antibody complex begins a chemical chain reac¬ tion important in many immunological processes, including breakdown of foreign and infected cells, ingestion of foreign particles and cell debris, and inflammation of surrounding tissue. Complement components and antibodies are the substances in human serum responsible for killing bac¬ teria.
complementary medicine See alternative medicine
completeness Concept of the adequacy of a formal system that is employed both in proof theory and in model theory (see logic). In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in the system is such that either it or its negation is provable in the system. In model theory, a formal system is said to be semantically complete if and only if every theorem of the system is prov¬ able in the system.
complex number Any number consisting of both real numbers and imaginary numbers. It has the form a + bi, where a and b are real numbers and i = V—T; a is called the real part and bi the imaginary part. Because a or b can equal 0, any real or imaginary number is also a complex num¬ ber. Invented as an extension of the real numbers so that certain algebraic equations such as x 2 + 1 = 0 would have solutions, the complex numbers form an algebraic field, meaning that they obey the commutative law and the associative law (with respect to addition and multiplication), as well as certain other rules in much the same way real numbers do (see field theory).
complex variable In mathematics, a variable that can take on the value of a complex number. In basic algebra, the variables x and y generally stand for values of real numbers. The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + bi. The modulus of z is its absolute value. A complex variable may be graphed as a vector from the origin to the point (a,b) in a rectangular coordinate system, its modulus corresponding to the vector’s length. Called an Argand diagram, this representation establishes a connection between complex analysis and vector analysis. See also Euler's formula.
composite family Family Compositae, one of the largest plant fami¬ lies (also known as Asteraceae, daisy family, and aster family), which con¬ tains more than 1,100 genera and almost 20,000 species of herbaceous plants, shrubs, and trees, found throughout the world. Though diverse in habit and habitat, composites tend to grow in sunlit places in temperate and subtropical regions. The family includes many garden ornamentals, including ageratums, asters, chrysanthemums, cosmos, dahlias, marigolds, and zinnias. Some genera include weeds such as dandelion, ragweed, and thistle. Artemisia, artichoke, endive, safflower, salsify, lettuce, and sunflower are important for the products derived from their flowers, seeds, leaves, roots, or tubers. Flower heads in this family are composed of many small flowers (florets) surrounded by bracts. Bell-shaped disk florets form the centre of each head; strap-shaped ray florets extend out like petals from the centre and are sometimes reflexed (bent back). Some species have flowers with only disk or only ray florets.
composite material Solid material that results when two or more substances are combined (physically, not chemically) to create a new material whose properties are superior in a specific application to those of the original substances. The term specifically refers to a structural matrix (such as plastic) within which a fibrous material (such as silicon carbide) is embedded. Fibreglass-reinforced plastic is the best-known composite. Because of their stiffness, lightness, and heat resistance, com¬ posites are the materials of choice in numerous structural, reinforcing, and high-performance applications.