Between Order and Chaos: The Quest for Meaningful Information

Abstract

The notion of meaningful information seems to be associated with the sweet spot between order and chaos. This form of meaningfulness of information, which is primarily what science is interested in, is not captured by both Shannon information and Kolmogorov complexity. In this paper I develop a theoretical framework that can be seen as a first approximation to a study of meaningful information. In this context I introduce the notion of facticity of a data set. I discuss the relation between thermodynamics and algorithmic complexity theory in the context of this problem. I prove that, under adequate measurement conditions, the free energy of a system in the world is associated with the randomness deficiency of a data set with observations about this system. These insights suggest an explanation of the efficiency of human intelligence in terms of helpful distributions. Finally I give a critical discussion of Schmidhuber's views specifically his notion of low complexity art, I defend the view that artists optimize facticity instead.

Value of digital information networks: a holonic framework

“…Shannon defined information as a reduction of uncertainty [149]. Adriaans addresses the idea of meaningful information [4]. Buckland defined information-as-thing, information-asknowledge and information-as-process [26].…”

A Critical Analysis of Floridi’s Theory of Semantic Information

“…Since Kolmogorov complexity is non-computable we have to rely on approximations to apply this theory in practical situations, but work of Cilibrasi and Vitányi (2006;Vitányi et al 2008) and Adriaans (2009) has shown that using industrial data compression programs is a viable option for a rich class of problems. The mutual information between two objects for instance can be approximated with industrial compression algorithms using the so-called normalized compression distance (NCD): NCD x; y ð Þ ¼ C xy ð Þ À min CðxÞ; CðyÞ ð Þ max CðxÞ; CðyÞ ð Þ Here C(xy) indicates the complexity of the concatenation of x and y.…”

“…It is quite surprising that this notion of facticity that is closely related to Sartre's notion of the absurd, and is supposed to belong to the more obscure phenomena in Heidegger's philosophy, emerges in the context of a philosophy of information (Heidegger 1977;Gadamer 1975). It is possible to develop a theory of informational esthetics (Adriaans 2009) on the basis of this formal notion of facticity (with the central insight that good artists optimize facticity).…”

“…Conditional probabilities can perfectly be used to analyze the validity of definitions for instance: if P(John is a bachelor | John is an unmarried male) = P(John is an unmarried male | John is a bachelor) =1 this indicates that the messages 'John is a bachelor' and 'John is an unmarried male' in the context of this specific set of messages not only carry the same amount of information, but have the same meaning. Thus a formal treatment of semantic information in the context of classical information theory seems possible (Adriaans 2009). …”

“…Indeed, we consider Kolmogorov complexity to be more fundamental than Shannon entropy. It is the ultimate data compression and leads to a logically consistent procedure for inference" (Cover and Thomas 2006) The relation between Free energy and randomness deficiency has been investigated in Adriaans (2009).…”