Complex Systems Society

Complexity for dummies

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Complex system: a system with many parts in intricate arrangement. Complex systems tend to be high-dimensional, non-linear and hard to model.

There are many different meanings of complexity

Computational complexity theory - the amounts of resources required for the execution of algorithms.

Algorithmic information theory - the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string.

Information processing - complexity is a measure of the total number of properties transmitted by an object and detected by an observer.

Physical systems - complexity is a measure of the probability of the state vector of the system.

Mathematics - Krohn-Rhodes complexity studies finite semigroups and automata.

Software engineering - programming complexity is a measure of the interactions of the various elements of the software.

Intelligent design theory - complexity refers to the number of bits needed to achieve “something”.

And many concepts and theories, too

Complex adaptive system - a system where number of parts (and types of parts) in the system and the number of relations between the parts is non-trivial; the system has memory or includes feedback; the system can adapt itself according to its history or feedback; the relations between the system and its environment are non-trivial or non-linear; the system can be influenced by, or can adapt itself to, its environment; and the system is highly sensitive to initial conditions.

Chaos theory - the behavior 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.

Social complexity - 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.

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