Information2014, 5(2), 219-254; doi:10.3390/info5020219 - published online 10 April 2014 Show/Hide Abstract
Abstract: This review examines some particular, but important and basic aspects of information: Information is related to questions and should provide at least partial answers. Information comes in pieces, and it should be possible to aggregate these pieces. Finally, it should be possible to extract that part of a piece of information which relates to a given question. Modeling these concepts leads to an algebraic theory of information. This theory centers around two different but closely related types of information algebras, each containing operations for aggregation or combination of information and for extracting information relevant to a given question. Generic constructions of instances of such algebras are presented. In particular, the close connection of information algebras to logic and domain theory will be exhibited.
Information2014, 5(2), 209-218; doi:10.3390/info5020209 - published online 4 April 2014 Show/Hide Abstract
Abstract: Wheeler’s observer-participancy and the related it from bit credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck’s dessins d’enfants to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.
Information2014, 5(1), 190-208; doi:10.3390/info5010190 - published online 7 March 2014 Show/Hide Abstract
Abstract: Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent knowledge about. This paper develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time). By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical action principles). From this perspective, traditional quantum states would represent incomplete information about possible spacetime histories, conditional on the future measurement geometry. Without dynamical laws imposing additional restrictions, those histories can have a classical probability distribution, where exactly one history can be said to represent an underlying reality.
Information2014, 5(1), 172-189; doi:10.3390/info5010172 - published online 27 February 2014 Show/Hide Abstract
Abstract: The symbol grounding problem is the problem of specifying a semantics for the representations employed by a physical symbol system in a way that is neither circular nor regressive. The quantum system identification problem is the problem of relating observational outcomes to specific collections of physical degrees of freedom, i.e., to specific Hilbert spaces. It is shown that with reasonable physical assumptions these problems are equivalent. As the quantum system identification problem is demonstrably unsolvable by finite means, the symbol grounding problem is similarly unsolvable.
Information2014, 5(1), 134-170; doi:10.3390/info5010134 - published online 20 February 2014 Show/Hide Abstract
Abstract: This article is an attempt to capture, in a reasonable space, some of the major developments and currents of thought in information theory and the relations between them. I have particularly tried to include changes in the views of key authors in the field. The domains addressed range from mathematical-categorial, philosophical and computational approaches to systems, causal-compositional, biological and religious approaches and messaging theory. I have related key concepts in each domain to my non-standard extension of logic to real processes that I call Logic in Reality (LIR). The result is not another attempt at a General Theory of Information such as that of Burgin, or a Unified Theory of Information like that of Hofkirchner. It is not a compendium of papers presented at a conference, more or less unified around a particular theme. It is rather a highly personal, limited synthesis which nonetheless may facilitate comparison of insights, including contradictory ones, from different lines of inquiry. As such, it may be an example of the concept proposed by Marijuan, still little developed, of the recombination of knowledge. Like the best of the work to which it refers, the finality of this synthesis is the possible contribution that an improved understanding of the nature and dynamics of information may make to the ethical development of the information society.