**Complexity** in general usage is the opposite of simplicity. **Complexity** in specific usage is the opposite of independence, while complication is the opposite of simplicity. Simplicity is the property, condition, or quality of being simple or un-combined. ...
## Study of complexity
Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. Indeed, some would say that only what is somehow complex – what displays variation without being random – is worthy of interest. Part of a scientific laboratory at the University of Cologne. ...
The word random is used to express lack of order, purpose, cause, or predictability in non-scientific parlance. ...
The use of the term complex is often confused with the term complicated. In today’s systems, this is the difference between a myriad of connecting “stovepipes” and effective “integrated” solutions. (Lissack and Roos, 2000) This means that complex is the opposite of independent, while complicated is the opposite of simple. While this has led some fields to come up with specific definitions of complexity, there is a more recent movement to regroup observations from different fields to study complexity in itself, whether it appears in anthills, human brains, or stock markets. Interdisciplinarity is a type of academic collaboration in which specialists drawn from two or more academic disciplines work together in pursuit of common goals. ...
Categories: Stub | Myrmecology ...
A sketch of the human brain by artist Priyan Weerappuli, imposed upon the profile of Michelangelos David. ...
A stock market is a market for the trading of company stock, and derivatives of same; both of these are securities listed on a stock exchange as well as those only traded privately. ...
### Complex systems -
Systems theory has long been concerned with the study of complex systems (In recent times, **complexity theory** and **complex systems** have also been used as names of the field). These systems can be biological, economic, technological, etc. Recently, complexity is a natural domain of interest of the real world socio-cognitive systems and emerging systemics research. There are many definitions of complexity, therefore many natural, artificial and abstract objects or networks can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. ...
Systems theory is a transdisciplinary/multiperspectual scientific domain that seeks to derive and formulate those principles that are isomorphic to all fields of scientific inquiry. ...
There are many definitions of complexity, therefore many natural, artificial and abstract objects or networks can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. ...
System (from Latin systÄ“ma, in turn from Greek systÄ“ma) is a set of entities, real or abstract, comprising a whole where each component interacts with or is related to at least one other component and they all serve a common objective. ...
This article or section does not cite any references or sources. ...
Economics (deriving from the Greek words Î¿Î¯ÎºÏ‰ [okos], house, and Î½ÎÎ¼Ï‰ [nemo], rules hence household management) is the social science that studies the allocation of scarce resources to satisfy unlimited wants. ...
By the mid 20th century humans had achieved a mastery of technology sufficient to leave the surface of the Earth for the first time and explore space. ...
Systems theory or general systems theory or systemics is an interdisciplinary field which studies systems as a whole. ...
Complex systems tend to be high-dimensional, non-linear and hard to model. In specific circumstances they may exhibit low dimensional behaviour. 2-dimensional renderings (ie. ...
Non-linearity is a slight distortion of a single frequency into multiple frequencies within the human or mammalian auditory system. ...
#### Complex mechanisms Recent developments around artificial life, evolutionary computation and genetic algorithms have led to an increasing emphasis on complexity and complex adaptive systems. Artificial Life, (commonly Alife or alife) is a field of study and art form that examines systems related to life, its processes and its evolution through simulations using computer models, robotics, and biochemistry [1] (called soft, hard, and wet approaches respectively[2]). Artificial life complements traditional Biology by trying to...
In computer science evolutionary computation is a subfield of artificial intelligence (more particularly computational intelligence) involving combinatorial optimization problems. ...
A genetic algorithm (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. ...
Complex adaptive systems, are a special case of complex systems. ...
#### Complex simulations In social science, the study on the emergence of macro-properties from the micro-properties, also known as macro-micro view in sociology. The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e.: computational sociology. The social sciences are groups of academic disciplines that study the human aspects of the world. ...
This article or section does not adequately cite its references or sources. ...
Social complexity is the approach to social phenomena that tries to analyze a social system as a complex system. ...
A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ...
Computational sociology is a recently developed branch of sociology that uses computation to analyze social phenomena. ...
#### Complex behaviour The behaviour of a complex system is often said to be due to emergence and self-organization. A termite cathedral mound produced by a termite colony: a classic example of emergence in nature. ...
Self-organization refers to a process in which the internal organization of a system, normally an open system, increases automatically without being guided or managed by an outside source. ...
Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behaviour. A plot of the Lorenz attractor for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). ...
One of the main claims in Stephen Wolfram's book *A New Kind of Science* is that such behaviour can be generated by simple systems, such as the rule 110 cellular automaton. Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ...
A New Kind of Science is a controversial book by Stephen Wolfram, published in 2002. ...
// The rule 110 cellular automaton is a one-dimensional two-state cellular automaton with the following rule table: Rule 110, like the Game of Life, exhibits what Stephen Wolfram calls Class 4 behavior, which is neither completely random nor completely repetitive. ...
### Complexity in data In information theory, algorithmic information theory is concerned with the complexity of strings of data. A bundle of optical fiber. ...
In computer science, algorithmic information theory is a field of study which attempts to define the complexity (aka descriptive complexity, Kolmogorov complexity, Kolmogorov-Chaitin complexity, or algorithmic entropy) of a string as the length of the shortest binary program which outputs that string. ...
In computer programming and some branches of mathematics, strings are sequences of various simple objects. ...
Complex strings are harder to compress. While intuition tells us that this may depend on the codec used to compress a string (a codec could be theoretically created in any arbitrary language, including one in which the very small command "X" could cause the computer to output a very complicated string like '18995316'"), any two Turing-complete languages can be implemented in each other, meaning that the length of two encodings in different languages will vary by at most the length of the "translation" language - which will end up being negligible for sufficiently large data strings. A codec is a device or program capable of performing encoding and decoding on a digital data stream or signal. ...
In computability theory, an abstract machine or programming language is called Turing complete, Turing equivalent, or (computationally) universal if it has a computational power equivalent to a universal Turing machine (a simplified model of a programmable computer). ...
These algorithmic measures of complexity tend to assign high values to random noise. However, those studying complex systems would not consider randomness as complexity. In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector. ...
The word random is used to express lack of order, purpose, cause, or predictability in non-scientific parlance. ...
Information entropy is also sometimes used in information theory as indicative of complexity. Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ...
### Complexity of problems Computational complexity theory is the study of the complexity of problems - that is, the difficulty of solving them. Problems can be classified by complexity class according to the time it takes for an algorithm to solve them as function of the problem size. For example, the travelling salesman problem can be solved in time *O*(*n*^{2}2^{n}) (where *n* is the size of the network to visit). As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ...
Problem solving forms part of thinking. ...
In computational complexity theory, a complexity class is a set of problems of related complexity. ...
In the fields of algorithm analysis and computational complexity theory, the running time or space requirements of an algorithm are expressed as a function of the problem size. ...
If a salesman starts at point A, and if the distances between any two points is known, what is the shortest round-trip the salesman can make which will visit all points once and return to point A? The travelling salesman problem[1] [2](TSP) is a problem in discrete...
Even though a problem may be computationally solvable in principle, in actual practice it may not be that simple. These problems might require large amounts of time or an inordinate amount of space. Computational complexity may be approached from many different aspects. Computational complexity can be investigated on the basis of time, memory or other resources used to solve the problem. Time and space are two of the most important and popular considerations when problems of complexity are analyzed. Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...
Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...
There exist a certain class of problems that although they are solvable in principle they require so much time or space that it is not practical to attempt to solve them. These problems are called Intractable. Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...
## Specific meanings In several scientific fields, "complexity" has a specific meaning : - In computational complexity theory, the
**time complexity** of a problem is the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm. This allows to classify problems by complexity class (such as P, NP ... ) such analysis also exists for space, that is, the memory used by the algorithm. - In algorithmic information theory, the
**Kolmogorov complexity** (also called **descriptive complexity** or **algorithmic entropy**) of a string is the length of the shortest binary program which outputs that string. - In information processing, complexity is a measure of the total number of properties transmitted by an object and detected by an observer. Such a collection of properties is often referred to as a state.
- In physical systems, complexity is a measure of the probability of the state vector of the system. This is often confused with entropy, but is a distinct Mathematical analysis of the probability of the state of the system, where two distinct states are never conflated and considered equal as in statistical mechanics.
- In mathematics, Krohn-Rhodes complexity is an important topic in the study of finite semigroups and automata.
- In the sense of how complicated a problem is from the perspective of the person trying to solve it, limits of complexity are measured using a term from cognitive psychology, namely the hrair limit.
- Specified complexity is a term used in intelligent design theory, first coined by William Dembski.
- Irreducible complexity is a term used in arguments against the generally accepted theory of biological evolution, being a concept popularized by the biochemist Michael Behe.
- Unruly complexity denotes situations that do not have clearly defined boundaries, coherent internal dynamics, or simply mediated relations with their external context, as coined by Peter Taylor.
As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ...
In the fields of algorithm analysis and computational complexity theory, the running time or space requirements of an algorithm are expressed as a function of the problem size. ...
In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a defined end-state. ...
In computational complexity theory, a complexity class is a set of problems of related complexity. ...
In computational complexity theory, P is the complexity class containing decision problems which can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. ...
In computational complexity theory, NP (Non-deterministic Polynomial time) is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine. ...
This article or section does not adequately cite its references or sources. ...
In computer science, algorithmic information theory is a field of study which attempts to define the complexity (aka descriptive complexity, Kolmogorov complexity, Kolmogorov-Chaitin complexity, or algorithmic entropy) of a string as the length of the shortest binary program which outputs that string. ...
In computer programming and some branches of mathematics, strings are sequences of various simple objects. ...
A computer program is a collection of instructions that describe a task, or set of tasks, to be carried out by a computer. ...
In general, information processing is the changing (processing) of information in any manner detectable by an observer. ...
Property designates those things that are commonly recognized as being the possessions of a person or group. ...
Observation is an activity of a sapient or sentient living being (e. ...
In information processing, a state is the complete set of properties (for example, its energy level, etc. ...
A physical system is a system that is comprised of matter and energy. ...
Probability is the chance that something is likely to happen or be the case. ...
System (from Latin systÄ“ma, in turn from Greek systÄ“ma) is a set of entities, real or abstract, comprising a whole where each component interacts with or is related to at least one other component and they all serve a common objective. ...
Look up entropy, entropy in Wiktionary, the free dictionary. ...
Analysis is the branch of mathematics most explicitly concerned with the notion of a limit, either the limit of a sequence or the limit of a function. ...
Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...
Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
Krohn-Rhodes theory is an approach to the study of finite semigroups and automata, which seeks to decompose them in terms of finite aperiodic semigroups and finite groups. ...
In mathematics, a semigroup is an algebraic structure consisting of a set S closed under an associative binary operation. ...
In theoretical computer science, automata theory is the study of abstract machines and problems they are able to solve. ...
Cognitive Psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. ...
The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information is a 1956 paper by the cognitive psychologist George A. Miller. ...
Specified complexity is a concept developed by intelligent design proponent William Dembski. ...
For other uses, see Intelligent design (disambiguation). ...
William Dembski Dr William Albert Bill Dembski (born July 18, 1960) is an American mathematician, philosopher and theologian known for advocating the controversial idea of intelligent design. ...
Irreducible complexity (IC) is the argument that certain biological systems are too complex to have evolved from simpler, or less complete predecessors, and are at the same time too complex to have arisen naturally through chance mutations. ...
Michael Behe Michael J. Behe (born January 18, 1952) is an American biochemist and intelligent design advocate. ...
## See also A plot of the Lorenz attractor for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). ...
Complexity theory can refer to more than one thing: Computational complexity theory: a field in theoretical computer science and mathematics dealing with the resources required during computation to solve a given problem Systems theory (or systemics or general systems theory): an interdisciplinary field including engineering, biology and philosophy that incorporates...
// The Command and Control Research Program (CCRP) within the Office of the Assistant Secretary of Defense (NII) focuses upon (1) improving both the state of the art and the state of the practice of command and control (C2) and (2) enhancing DoDs understanding of the national security implications of...
Interconnectedness is one of many concepts gaining popularity as part of the terminology of a worldview which sees a oneness in all things. ...
This is a list of important publications in computer science, organized by field. ...
William of Ockham Occams razor (also spelled Ockhams razor) is a principle attributed to the 14th-century English logician and Franciscan friar William of Ockham. ...
The complexity of most computer programs and programming languages is one of the unsolved problems in software engineering. ...
Holism in science, or Holistic science, is an approach to research that emphasizes the study of complex systems. ...
In combinatorial game theory, game complexity is a measure of the complexity of a game. ...
## References - Roger Lewin.
*Complexity: Life at the Edge of Chaos*. Macmillan, 1992. - M. Mitchell Waldrop,
*Complexity: The Emerging Science at the Edge of Order and Chaos.* Simon and Schuster, 1992. - R. V. Solé and B. C. Goodwin,
*Signs of Life: How Complexity Pervades Biology*, Basic Books, 2001. - Micahel R. Lissack and Johan Roos.
*The Next Common Sense, The e-Manager’s Guide to Mastering Complexity.* Nicholas Brealey Publishing. - Complexity Theory and Network Centric Warfare by James Moffat (CCRP, 2003)
- Complexity, Networking, and Effects Based Approaches to Operations by Edward Smith (CCRP, 2006)
- Complexity, Global Politics, and National Security by Alberts and Czerwinski (CCRP, 1997)
- Coping with the Bounds by Czerwinski (CCRP, 1998)
## External links |