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Redundancy in Systems which Entertain a Model of Themselves: Interaction
Information and the Self-organization of Anticipation, 

Entropy 12(1) (2010) 63-79 <> 

Mutual information among three or more dimensions (* = -Q) has been
considered as interaction information. However, Krippendorff (2009a, 2009b)
has shown that this measure cannot be interpreted as a unique property of
the interactions and has proposed an alternative measure of interaction
information based on iterative approximation of maximum entropies. Q can
then be considered as a measure of the difference between interaction
information and redundancy generated in a model entertained by an observer.
I argue that this provides us with a measure of the imprint of a
second-order observing system-a model entertained by the system itself-on
the underlying information processing. The second-order system communicates
meaning hyper-incursively; an observation instantiates this
meaning-processing within the information processing. The net results may
add to or reduce the prevailing uncertainty. The model is tested empirically
for the case where textual organization can be expected to contain
intellectual organization in terms of distributions of title words, author
names, and cited references.
Loet Leydesdorff 
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam.
Tel. +31-20-525 6598; fax: +31-842239111
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