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Quantum Field Mechanics: ComplexDynamical Completion of Fundamental
 Physics and Its Experimental Implications”, arXiv:physics/0401164. See also arXiv:physics/0410269, arXiv:quantph/0012069, arXiv:quantph/9902015
"... This report provides a brief review of a recently developed new framework for the fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary particles, their inherent properties, quantum and relativist ..."
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This report provides a brief review of a recently developed new framework for the fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary particles, their inherent properties, quantum and relativistic behaviour, interactions and their results. The essential progress with respect to the conventional theory is attained due to the unreduced, nonperturbative analysis of arbitrary interaction process revealing the qualitatively new phenomenon of dynamic multivaluedness of interaction results and their dynamically entangled internal structure, which gives rise to the universally defined dynamic complexity and is absent in the conventional, always perturbative and dynamically singlevalued models corresponding to the zero value of unreduced complexity (including the substitutes used for “complexity”, “chaoticity”, “selforganisation”, etc.). It is shown how the observed world structure, starting from elementary particles and their interactions, dynamically emerges from the unreduced interaction between two initially homogeneous, physically real protofields. In that way one avoids arbitrary imposition of abstract entities and improvable postulates or “principles”, let alone “mysteries”, of the conventional theory, which now obtain their unified, consistent and realistic explanation in terms of the unreduced dynamic complexity. We complete the theoretical description of the fundamental world structure emergence and properties by an outline of the ensuing experimental implications of the quantum field mechanics and the resulting causally substantiated change of the basic research strategy.
What is good mathematics
, 2007
"... Abstract. Some personal thoughts and opinions on what “good quality mathematics” is, and whether one should try to define this term rigorously. As a case study, the story of Szemerédi’s theorem is presented. 1. The many aspects of mathematical quality We all agree that mathematicians should strive t ..."
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Abstract. Some personal thoughts and opinions on what “good quality mathematics” is, and whether one should try to define this term rigorously. As a case study, the story of Szemerédi’s theorem is presented. 1. The many aspects of mathematical quality We all agree that mathematicians should strive to produce good mathematics. But how does one define “good mathematics”, and should one even dare to try at all? Let us first consider the former question. Almost immediately one realises that there are many different types of mathematics which could be designated “good”. For instance, “good mathematics ” could refer (in no particular order) to (i) Good mathematical problemsolving (e.g. a major breakthrough on an important mathematical problem); (ii) Good mathematical technique (e.g. a masterful use of existing methods, or the development of new tools); (iii) Good mathematical theory (e.g. a conceptual framework or choice of notation which systematically unifies and generalises an existing body of results);
Language Games: A Foundation for Semantics and Ontology
 In Game Theory and Linguistic Meaning, edited by AhtiVeikko Pietarinen, Elsevier, 2007
"... The issues raised by Wittgenstein’s language games are fundamental to any theory of semantics, formal or informal. Montague’s view of natural language as a version of formal logic is at best an approximation to a single language game or a family of closely related games. But it is not unusual for a ..."
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The issues raised by Wittgenstein’s language games are fundamental to any theory of semantics, formal or informal. Montague’s view of natural language as a version of formal logic is at best an approximation to a single language game or a family of closely related games. But it is not unusual for a short phrase or sentence to introduce, comment on, or combine aspects of multiple language games. The option of dynamically switching from one game to another enables natural languages to adapt to any possible subject from any perspective for any humanly conceivable purpose. But the option of staying within one precisely defined game enables natural languages to attain the kind of precision that is achieved in a mathematical formalism. To support the flexibility of natural languages and the precision of formal languages within a common framework, this article drops the assumption of a fixed logic. Instead, it proposes a dynamic framework of logics and ontologies that can accommodate the shifting points of view and methods of argumentation and negotiation that are common during discourse. Such a system is necessary to characterize the openended variety of language use in different applications at different stages of life — everything from an infant learning a first language to the most sophisticated adult language in science and engineering.
The Last Scientific Revolution
"... Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is proposed as a unified solution. 1. The End of Lie, or What&apos ..."
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Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is proposed as a unified solution. 1. The End of Lie, or What's Wrong With Science Whereas today's spectacular technologic progress seems to strongly confirm the utility of underlying scientific activities, the modern state of fundamental science itself shows catastrophically accumulating degradation signs, including both knowledge content and organisation/practice [152]. That striking contradiction implies that we are close to a deeply rooted change in the whole system of human knowledge directly involving its fundamental nature and application quality rather than only superficial, practically based influences of empirical technology, social tendencies, etc. Science problems, in their modern form, have started appearing in the 20 th century, together with accelerated science development itself [5358], but their current culmination and now already longlasting, welldefined crisis clearly designate the advent of the biggest ever scientific revolution involving not only serious changes in special knowledge content but also its qualitatively new character, meaning and
Quantum Field Mechanics: ComplexDynamical Completion of Fundamental Physics and Its Experimental Implications
, 2006
"... This report provides a brief review of recently developed extended framework ..."
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This report provides a brief review of recently developed extended framework
A Mathematical Mystery Tour: Discovering the Truth and Beauty of the Cosmos
"... Debate about whether mathematics is invented or discovered has endured, emerging unresolved from every development in mathematics, philosophy, and science. Although most practicing mathematicians find this controversy irrelevant to their work—a preoccupation of philosophers who worry about distincti ..."
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Debate about whether mathematics is invented or discovered has endured, emerging unresolved from every development in mathematics, philosophy, and science. Although most practicing mathematicians find this controversy irrelevant to their work—a preoccupation of philosophers who worry about distinctions without a difference—many of the world’s greatest mathematicians have joined the fray. Yet despite remarkable agreement on questions of mathematical truth, on this one topic that probes the very nature of their discipline, mathematicians seem unable to agree. The witnesses for mathematics as an invention or creation of the human mind include Augustus de Morgan (“The moving power of mathematical invention is not reasoning but imagination”), Janos Bolyai (“Out of nothing I have created a strange new universe”), David Hilbert (“Nothing will drive us out of the paradise that Cantor has created”), Albert Einstein (“The series of integers is obviously an invention of the human mind, a selfcreated tool which simplifies the ordering of certain sensory experiences”), and George Pólya (“If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing,
Conceptions of the Continuum
"... Abstract: A number of conceptions of the continuum are examined from the perspective of conceptual structuralism, a view of the nature of mathematics according to which mathematics emerges from humanly constructed, intersubjectively established, basic structural conceptions. This puts into question ..."
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Abstract: A number of conceptions of the continuum are examined from the perspective of conceptual structuralism, a view of the nature of mathematics according to which mathematics emerges from humanly constructed, intersubjectively established, basic structural conceptions. This puts into question the idea from current set theory that the continuum is somehow a uniquely determined concept. Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions. 1. What is the continuum? On the face of it, there are several distinct forms of the continuum as a mathematical concept: in geometry, as a straight line, in analysis as the real number system (characterized in one of several ways), and in set theory as the power set of the natural numbers and, alternatively, as the set of all infinite sequences of zeros and ones. Since it is common to refer to the continuum, in what sense are these all instances of the same concept? When one speaks of the continuum in current settheoretical
REFLECTIONS AND PROSPECTIVES
"... Abstract. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. 1. ..."
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Abstract. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. 1.