complexity


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complexity,

in science, field of study devoted to the process of self-organization. The basic concept of complexity is that all things tend to organize themselves into patterns, e.g., ant colonies, immune systems, and human cultures; further, they go through cycles of growth, mass extinction, regeneration, and evolution. Complexity looks for the mathematical equations that describe the middle ground between equilibrium (see staticsstatics,
branch of mechanics concerned with the maintenance of equilibrium in bodies by the interaction of forces upon them (see force). It incorporates the study of the center of gravity (see center of mass) and the moment of inertia.
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) and chaos (see chaos theorychaos theory,
in mathematics, physics, and other fields, a set of ideas that attempts to reveal structure in aperiodic, unpredictable dynamic systems such as cloud formation or the fluctuation of biological populations.
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), such as the interplay between supply and demand in an economy or the relationship among living organisms in an ecosystem.

Complexity theory had its beginnings with American mathematician Norbert Wiener'sWiener, Norbert,
1894–1964, American mathematician, educator, and founder of the field of cybernetics, b. Columbia, Mo., grad. Tufts College, 1909, Ph.D. Harvard, 1913.
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 development of cyberneticscybernetics
[Gr.,=steersman], term coined by American mathematician Norbert Wiener to refer to the general analysis of control systems and communication systems in living organisms and machines.
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, Canadian biologist Ludwig von Bertalanffy's development of general system theory, and American mathematician John H. Holland's development of a computerized artificial life simulation. More recent efforts are centered at the Santa Fe Institute in New Mexico, which was established in 1984, and are found in the work of multidisciplinary researchers such as American economist Kenneth ArrowArrow, Kenneth Joseph,
1921–, American economist, b. New York City, grad. City College of New York (B.S. 1940), Columbia (M.A. 1941, Ph.D. 1951). He taught economics at the Univ. of Chicago (1947–49) and Stanford Univ.
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 and American physicist Murray Gell-Mann. Because complex systems typically cross the boundaries of traditional disciplines, the study of complexity is an interdisciplinary science. Much of the progress in the field can be attributed to advances in nonlinear dynamicsnonlinear dynamics,
study of systems governed by equations in which a small change in one variable can induce a large systematic change; the discipline is more popularly known as chaos (see chaos theory).
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, in the power of computerscomputer,
device capable of performing a series of arithmetic or logical operations. A computer is distinguished from a calculating machine, such as an electronic calculator, by being able to store a computer program (so that it can repeat its operations and make logical
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 and in computer graphicscomputer graphics,
the transfer of pictorial data into and out of a computer. Using analog-to-digital conversion techniques, a variety of devices—such as curve tracers, digitizers, and light pens—connected to graphic computer terminals, computer-aided design
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, and in adaptive programs and fuzzy logicfuzzy logic,
a multivalued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 or 1, black or white, yes or no; in terms of Boolean algebra, everything is in one set or another but
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.

Bibliography

See M. M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (1992); R. Lewin, Complexity: Life at the Edge of Chaos (1993); J. H. Holland, Hidden Order (1995).

Complexity

Consisting of various parts united or connected together, formed by a combination of different elements; intricate, interconnecting parts that are not easily disentangled.

complexity

[kəm′plek·səd·ē]
(computer science)
The number of elementary operations used by a program or algorithm to accomplish a given task.

complexity

(algorithm)
The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively).

The interesting aspect is usually how complexity scales with the size of the input (the "scalability"), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N).

See also NP-complete.
References in classic literature ?
Alfred Ainger has done such good service, the great and peculiar change which was begun at the end of the last century, and dominates our own; that sudden increase of the width, the depth, the complexity of intellectual interest, which has many times torn and distorted literary style, even with those best able to comprehend its laws.
intestinal pang of strange complexity and raises the song.
It absorbs something of his intelligence and purpose--more of them in proportion to the complexity of the resulting machine and that of its work.
Hence, if certain insectivorous birds (whose numbers are probably regulated by hawks or beasts of prey) were to increase in Paraguay, the flies would decrease--then cattle and horses would become feral, and this would certainly greatly alter (as indeed I have observed in parts of South America) the vegetation: this again would largely affect the insects; and this, as we just have seen in Staffordshire, the insectivorous birds, and so onwards in ever-increasing circles of complexity.
Phrases are often repeated in the ballads, just as in the talk of the common man, for the sake of emphasis, but there is neither complexity of plot or characterization nor attempt at decorative literary adornment--the story and the emotion which it calls forth are all in all.
And the punishment of it is an invasion of complexity, a tormenting, forcibly tortuous involution of feelings, the deepest form of suffering from which indeed something significant may come at last, which may be criminal or heroic, may be madness or wisdom--or even a straight if despairing decision.
There complexity engendered license, and here disease; whereas simplicity in music was the parent of temperance in the soul; and simplicity in gymnastic of health in the body.
for the light was of many colours and some complexity, broken up by many mirrors and dancing on many gilt and gaily-coloured cakes and sweetmeats.
This complexity of causes in psychology might be connected with Bergson's arguments against repetition in the mental world.
But later too, and the next day and the third day, she still found no words in which she could express the complexity of her feelings; indeed, she could not even find thoughts in which she could clearly think out all that was in her soul.
Nor could I consider the magnitude and complexity of my plan as any argument of its impracticability.
To beautify it is to take away its character of complexity - it is to destroy it.