

Preprint 53/2011
A Geometric Approach to Complexity
Nihat Ay, Eckehard Olbrich, Nils Bertschinger, and Jürgen Jost
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Submission date: 24. Aug. 2011
Pages: 22
published in: Chaos, 21 (2011) 3, art-no. 037103
DOI number (of the published article): 10.1063/1.3638446
Bibtex
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Abstract:
We develop a geometric approach to complexity based on the principle that complexity
requires interactions at different scales of description. Complex systems are more than the sum
of their parts of any size, and not just more than the sum of their elements. Using information
geometry, we therefore analyze the decomposition of a system in terms of an interaction hierarchy.
In mathematical terms, we present a theory of complexity measures for finite random fields using
the geometric framework of hierarchies of exponential families. Within our framework, previously
proposed complexity measures find their natural place and gain a new interpretation.