Arikah Map

Complexity

For other uses, see Complexity (disambiguation).

Complexity is the opposite of simplicity.



Contents

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.

The use of the term complex is often confused with the term complicated. To understand the differences, it is best to examine the roots of the two words. “Complicated” uses the Latin ending “plic” that means, “to fold” while “complex” uses the “plex” that means, “to weave.” Thus, a complicated structure is one that is folded with hidden facets and stuffed into a smaller space. On the other hand, a complex structure uses interwoven components that introduce mutual dependencies and produce more than a sum of the parts. 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.

Complex systems

Main article: Complex system

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.

Complex systems tend to be high-dimensional, non-linear and hard to model. In specific circumstances they may exhibit low dimensional behaviour.

Complex mechanisms

Recent developments around artificial life, evolutionary computation and genetic algorithms have led to an increasing emphasis on complexity and complex adaptive 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.

Complex behaviour

The behaviour of a complex system is often said to be due to emergence and self-organization.

Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behaviour.

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.

Complexity in data

In information theory, algorithmic information theory is concerned with the complexity of strings of data.

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.

These algorithmic measures of complexity tend to assign high values to random noise. However, those studying complex systems would not consider randomness as complexity.

Information entropy is also sometimes used in information theory as indicative of complexity.

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 <math>O(n^22^n)</math> (where n is the size of the network to visit).

Even though a problem may be solvable computationally in principle, but 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.

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.

Specific meanings

In several scientific fields, "complexity" has a specific meaning :

Quotes about complexity

See also

References

Categories


Abstraction | Holism | Transdisciplinarity

Find

Find

Find