Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page

Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed \emph{coding theorem method} the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal format, R package at http://cran.r-project.org/web/packages/acss/index.htm

Is there a physically universal cellular automaton or Hamiltonian?

It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we introduce a different notion of universality: a CA is called physically universal if every transformation on any finite region can be (approximately) implemented by the autonomous time evolution of the system after the complement of the region has been initialized in an appropriate way. We pose the question of whether physically universal CAs exist. Such CAs would provide a model of the world where the boundary between a physical system and its controller can be consistently shifted, in analogy to the Heisenberg cut for the quantum measurement problem. We propose to study the thermodynamic cost of computation and control within such a model because implementing a cyclic process on a microsystem may require a non-cyclic process for its controller, whereas implementing a cyclic process on system and controller may require the implementation of a non-cyclic process on a "meta"-controller, and so on. Physically universal CAs avoid this infinite hierarchy of controllers and the cost of implementing cycles on a subsystem can be described by mixing properties of the CA dynamics. We define a physical prior on the CA configurations by applying the dynamics to an initial state where half of the CA is in the maximum entropy state and half of it is in the all-zero state (thus reflecting the fact that life requires non-equilibrium states like the boundary between a hold and a cold reservoir). As opposed to Solomonoff's prior, our prior does not only account for the Kolmogorov complexity but also for the cost of isolating the system during the state preparation if the preparation process is not robust.Comment: 27 pages, 1 figur

Towards a quantum evolutionary scheme: violating Bell's inequalities in language

We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space. We argue that the presence of quantum structures in language and the earlier detected quantum structures in conceptual change make the neo-Darwinian evolutionary scheme strictly too limited for Evolutionary Epistemology. We sketch how we believe that evolution in a more general way should be implemented in epistemology and conceptual change, but also in biology, and how this view would lead to another relation between both biology and epistemology.Comment: 20 pages, no figures, this version of the paper is equal to the foregoing. The paper has meanwhile been published in another book series than the one tentatively mentioned in the comments given with the foregoing versio

The Influence of Successful Completion of a Spanish Course on Middle School Students’ Reading Comprehension

This quantitative, causal-comparative study investigated the effect of foreign language education on reading comprehension by students’ biological sex. The theoretical framework for this study is Piaget and Barlett’s Schema Theory. Participants in this study consisted of middle school students within a PK-8 school. A convenience sample of 200 students was selected, 100 males and 100 females. All students were given a pretest and posttest using the Scholastic Reading Inventory (SRI). Independent variables consisted of enrollment in a Spanish course and biological sex while the dependent variable was reading comprehension skills as determined by assessment results on the SRI. An analysis of covariance, ANCOVA, was used in analyzing the data collected in this study. When controlling for pretest scores, there was a significant difference in Lexile scores of students who took a Spanish course and those who did not, a significant difference in the Lexile scores of female students who took Spanish and those who did not, and a significant difference in the Lexile scores of male students who took Spanish and those who did not. However, there was not a significant difference in the Lexile scores based on biological sex of students taking Spanish after controlling for the pretest Lexile scores. For future studies, the following are recommended: using data from schools in different settings, such as in an urban environment, analyzing data from students of different grade levels, such as elementary or high school students, analyzing data from students who completed a foreign language course other than Spanish, and comparing results from students who completed different foreign language courses