Zipf's law and L. Levin's probability distributions

Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation. In this paper I suggest that at least in certain situations, Zipf's law can be explained as a special case of the a priori distribution introduced and studied by L. Levin. The Zipf ranking corresponding to diminishing probability appears then as the ordering determined by the growing Kolmogorov complexity. One argument justifying this assertion is the appeal to a recent interpretation by Yu. Manin and M. Marcolli of asymptotic bounds for error--correcting codes in terms of phase transition. In the respective partition function, Kolmogorov complexity of a code plays the role of its energy. This version contains minor corrections and additions.Comment: 19 page

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Lost Voices and Singing Texts: Reconstructing the Cultural Past of Ioannina During the First Half of the 1870s

Conducting fieldwork in the ethnomusicological past, among other things may consist of coping with a wide variety of textual records, such as newspapers, magazines, public or private archives and so on. Especially, as far as newspapers and magazines of any kind are concerned, historical awareness is of great importance, for instance when the understanding of the relevant political and cultural mentalité of the writers, is a critical determinant of one’s ability to fully comprehend and make use of the possible findings, or -sometimes- even the lack of them. Quite often, the hardest part is when trying to “decrypt”, analyze and reconstruct the narration of a person whose Self emerges only through his corresponding writings. This is the case with Jonah (aka Konstantínos Aravantinós), writer of the satirical calendar of Ioannina, Karavida, during 1873-1874. Following the above paradigm, it is evident that a historical ethnomusicological research of this kind has to deal with a two-fold methodological challenge: thoroughly creating a virtual historical space in which specially customized text analysis skills can provide the ability to reach out closer to voices and sounds of the past. The latter, is a problematic leading to research theories and methodologies offered by relevant scientific fields

Complexity vs Energy: Theory of Computation and Theoretical Physics

This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested recently, in which mathematics related to (un)computability is inspired by and to a degree reproduces formalisms of statistical physics and quantum field theory.Comment: 23 pages. Talk at the satellite conference to ECM 2012, "QQQ Algebra, Geometry, Information", Tallinn, July 9-12, 201

Life and Space Dimensionality: A Brief Review of Old and New Entangled Arguments

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed

A Pluridisciplinary Treatise of the Fractal Complexity in John Mukum Mbaku’s Corruption in Africa: Causes, Consequences and Cleanups

While my extensive search yielded about 20,500 mentions, seven scholarly citations, and three scholarly book reviews of John Mukum Mbaku’s Corruption in Africa: Causes, Consequences and Cleanups (2007), no systematic analysis has been done on the text, even though such potential exists. This is a serious gap in the literature on Africa’s international affairs and development studies because the book is one of the major works, if not the most comprehensive work, on a topic that has significant implications for the continent’s international relations and development. This paper is an attempt to fill this gap. Specifically, I employ the mathematical concept of Fractal Dimension and Complexity Theory to explore the idea of the spectrum progressing from more orderly to less orderly or to pure disorder which reflect the major postulates on corruption in Africa. This called for the utilization of the Pluridisciplinary approach that helped me to mix linguistics and mathematical approaches—more precisely, Linguistic Presupposition and Fractal Methodology. The results generated after the MATLAB computer runs suggest that the combination of negative and positive feedback loops, which form the basis of several African knowledge systems, also form a key mechanism of general self-organizing systems in Corruption in Africa: Causes, Consequences and Cleanups

Protention and retention in biological systems

This paper proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called "extended present" as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of "biological inertia".Comment: This paper was made possible only as part of an extended collaboration with Francis Bailly (see references), a dear friend and "ma\^itre \'a penser", who contributed to the key ideas. Francis passed away in february 2008: we continue here our inspiring discussions and joint wor

Reconceptualizing College Impact Studies Through a Fractal Assemblage Theory

College impact studies have formed the common sense of understanding institutional relationships to student growth and change for decades. In this time, they have become entangled with the production of the neoliberal university. This paper1 presents an alternative theorization of student change on campus, a fractal assemblage theory. Assemblage theory is discussed through a single common language of major assemblage theory concepts across four authors. After exploring these concepts in depth, this paper returns to the stakes of assemblage theory: higher education research not to channel student to predetermined outcomes, but to create student futures in excess of our imaginations