# A Simple Modularity Measure For Search Spaces Based On Information Theory

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Daniel Polani, Principal Lecturer, Computer Science, University of Hertfordshire, United Kingdom
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In striving to understand of how complex systems can consistently
arise from simpler ones (e.g. evolvability), a number of central
motifs are increasingly coming into focus: the need for a unified
language in which complex phenomena can be described, analysed and
ultimately constructed, and the insight that a systematically
sustained drive for increasing global complexity requires control of
local complexities. For the first, information theory is a natural
candidate, the second emphasizes the importance of modularity in many
complex systems.
We present a measure to quantify modularity in a classical simple, but
instructive search space scenario. For this purpose, the scenario is
translated into the language of information theory. It turns out that,
while successful as universal language for dynamical processes,
information theory requires some unexpectedly subtle treatment in this
static context. Among other, the measure provides a handle for
studying the connection between search space complexity and
evolvability.