  Mutual information among three or more dimensions (mu-star = - 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.
