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

Information capacity of the Hopfield model

The information capacity of general forms of memory is formalized. The number of bits of information that can be stored in the Hopfield model of associative memory is estimated. It is found that the asymptotic information capacity of a Hopfield network of N neurons is of the order N^3b. The number of arbitrary state vectors that can be made stable in a Hopfield network of N neurons is proved to be bounded above by N

Loops and Knots as Topoi of Substance. Spinoza Revisited

The relationship between modern philosophy and physics is discussed. It is shown that the latter develops some need for a modernized metaphysics which shows up as an ultima philosophia of considerable heuristic value, rather than as the prima philosophia in the Aristotelian sense as it had been intended, in the first place. It is shown then, that it is the philosophy of Spinoza in fact, that can still serve as a paradigm for such an approach. In particular, Spinoza's concept of infinite substance is compared with the philosophical implications of the foundational aspects of modern physical theory. Various connotations of sub-stance are discussed within pre-geometric theories, especially with a view to the role of spin networks within quantum gravity. It is found to be useful to intro-duce a separation into physics then, so as to differ between foundational and empirical theories, respectively. This leads to a straightforward connection bet-ween foundational theories and speculative philosophy on the one hand, and between empirical theories and sceptical philosophy on the other. This might help in the end, to clarify some recent problems, such as the absence of time and causality at a fundamental level. It is implied that recent results relating to topos theory might open the way towards eventually deriving logic from physics, and also towards a possible transition from logic to hermeneutic.Comment: 42 page

Software development: A paradigm for the future

A new paradigm for software development that treats software development as an experimental activity is presented. It provides built-in mechanisms for learning how to develop software better and reusing previous experience in the forms of knowledge, processes, and products. It uses models and measures to aid in the tasks of characterization, evaluation and motivation. An organization scheme is proposed for separating the project-specific focus from the organization's learning and reuse focuses of software development. The implications of this approach for corporations, research and education are discussed and some research activities currently underway at the University of Maryland that support this approach are presented

Information and Experience in Metaphor: A Perspective From Computer Analysis

Novel linguistic metaphor can be seen as the assignment of attributes to a topic through a vehicle belonging to another domain. The experience evoked by the vehicle is a significant aspect of the meaning of the metaphor, especially for abstract metaphor, which involves more than mere physical similarity. In this article I indicate, through description of a specific model, some possibilities as well as limitations of computer processing directed toward both informative and experiential/affective aspects of metaphor. A background to the discussion is given by other computational treatments of metaphor analysis, as well as by some questions about metaphor originating in other disciplines. The approach on which the present metaphor analysis model is based is consistent with a theory of language comprehension that includes both the intent of the originator and the effect on the recipient of the metaphor. The model addresses the dual problem of (a) determining potentially salient properties of the vehicle concept, and (b) defining extensible symbolic representations of such properties, including affective and other connotations. The nature of the linguistic analysis underlying the model suggests how metaphoric expression of experiential components in abstract metaphor is dependent on the nominalization of actions and attributes. The inverse process of undoing such nominalizations in computer analysis of metaphor constitutes a translation of a metaphor to a more literal expression within the metaphor-nonmetaphor dichotomy