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Complexity




Complexity is the opposite of Simplicity .

Complexity in systems or behaviour is often described as what is "on the Edge Of Chaos " - between order and Randomness .


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 purely Random - is worthy of interest.

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 in order to study complexity in itself, whether it appears in Anthill s, Human Brain s, or Stock Market s.


Complex systems

See Also: Complex system



Systems Theory has long been concerned with the study of Complex System s (In recent times, complexity theory and '''complex systems''' have also been used as names of the field). These System s can be Biological , Economic , Technological , etc.

Complex systems tend to be high- Dimension al and Non-linear , but may exhibit low dimensional behaviour.


Complex mechanisms


Recent development around Artificial Life , Evolutionary Computation and Genetic Algorithm s have led to an increasing emphasis on complexity and Complex Adaptive Systems .


Complex simulations


In .


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.

It should be noted that 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 O(n^22^n) (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


  • "The complexity of a Document is proportional to the number of fingers that you need to read it." DeMarco's Law is a paraphrase from Tom DeMarco . For example, 'The complexity of a Computer Program is proportional to the number of fingers you need to read it.'

  • "The essence of tyranny is the denial of complexity" Jacob Burkhardt , Swiss historian.

  • "Some days I will say yes, and then odd days it seems things say yes to me. And stranger still, there are those times when I become a yes." (And they are moments of the Calm) -Kevin Hart, quoted by Mark Taylor in 'The Moment of Complexity'



SEE ALSO



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.



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