Klaus Jaffe

Measuring complexity in multidimensional systems with high degrees of freedom and a variety of types of information, remains an important challenge. Complexity of a system is related to the number and variety of components, the number and type of interactions among them, the degree of redundancy, and the degrees of freedom of the system. Examples show that different disciplines of science converge in complexity measures for low and high dimensional problems. For low dimensional systems, such as coded strings of symbols (text, computer code, DNA, RNA, proteins, music), Shannon’s Information Entropy (expected amount of information in an event drawn from a given distribution) and Kolmogorov‘s Algorithmic Complexity (the length of the shortest algorithm that produces the object as output), are used for quantitative measurements of complexity. For systems with more dimensions (ecosystems, brains, social groupings), network science provides better tools for that purpose. For complex highly multidimensional systems, none of the former methods are useful. Useful Information Φ, as proposed by Infodynamics, can be related to complexity. It can be quantified by measuring the thermodynamic Free Energy F and/or useful Work it produces. Complexity measured as Total Information I, can then be defined as the information of the system, that includes Φ, useless information or Noise N, and Redundant Information R. Measuring one or more of these variables allows quantifying and classifying complexity.

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