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37
Science of Chaos or Chaos in Science?
, 1996
"... I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, ..."
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I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, are criticized.
Hilbert’s twentyfourth problem
 American Mathematical Monthly
, 2001
"... 1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Cong ..."
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Cited by 9 (4 self)
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1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of
Effective field theories, reductionism and scientific explanation
 Studies in the History and Philosophy of Modern Physics
"... Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective sho ..."
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Cited by 6 (0 self)
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Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and
Modeling And Control Of DiscreteEvent Systems With Hierarchical Abstraction
, 2000
"... Control theory traditionally has been focused on analysis and control of continuous systems with numerical characteristics. In the past decade, however, there has been a growing concern with the symbolic aspect of systems owing to the advances in computer engineering. As a result the discipline of D ..."
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Cited by 4 (0 self)
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Control theory traditionally has been focused on analysis and control of continuous systems with numerical characteristics. In the past decade, however, there has been a growing concern with the symbolic aspect of systems owing to the advances in computer engineering. As a result the discipline of DiscreteEvent Systems (DES) is emerging from the system control community. In the framework of Ramadge and Wonham (RW), signals of interest no longer assume the form of continuously valued functions of numbers, but instead are discrete strings of symbols. The system is controlled by disablements of controllable events. In practice, RW control theory is found to be effective for systems of small size, but in the case of large systems, the computational complexity may become intractable. This thesis proposes a generalization of the RW framework. Systems are modeled as multilevel hierarchies in which highlevel dynamics are obtained via abstraction of the lowlevel models, and this vertical mod...
Models as a tool for theory construction: Some strategies of preliminary physics
 In
, 1995
"... Theoretical models are an important tool for many aspects of scientific activity. They are used, i.a., to structure data, to apply theories or even to construct new theories. But what exactly is a model? It turns out that there is no proper definition of the term “model ” that covers all these aspec ..."
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Cited by 4 (1 self)
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Theoretical models are an important tool for many aspects of scientific activity. They are used, i.a., to structure data, to apply theories or even to construct new theories. But what exactly is a model? It turns out that there is no proper definition of the term “model ” that covers all these aspects. Thus, I restrict myself here to evaluate the function of models in the research process while using “model ” in the loose way physicists do. To this end, I distinguish four kinds of models. These are (1) models as special theories, (2) models as a substitute for a theory, (3) toy models and (4) developmental models. I argue that models of the types (3) and (4) are considerably useful in the process of theory construction. This will be demonstrated in an extended casestudy from HighEnergy Physics. ∗ I wish to thank M. Stöckler (Bremen) for many illuminating discussions and R. Müller and M. Schön (both Konstanz) for reading the manuscript. A slightly revised version of
Kranitotis G V, A possible explanation of Galactic Velocity Rotation Curves in terms of a Cosmological Constant preprint astroph/9911485
"... This paper describes how the nongravitational contribution to galactic velo city rotation curves can be explained in terms of a Cosmological Constant (Λ). The velocity rotation curve for the nearby galaxy M33 will be analysed in detail while several other galaxies will be superficially studied. It ..."
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This paper describes how the nongravitational contribution to galactic velo city rotation curves can be explained in terms of a Cosmological Constant (Λ). The velocity rotation curve for the nearby galaxy M33 will be analysed in detail while several other galaxies will be superficially studied. It will be shown that the Cosmological Constant leads to a contribution to the acceleration proportional to the radii, at large radii, and depending on the mass of the galaxy. It was found to dominate at approximately 13Kpc for M33. The Cosmological Constant experimentally derived from the M33 data was found to be: ΛExp = 1.33 × 10 −52 cm −2, which compares favourably with the theoretical value of ΛTheory = 0.91 ×10 −54 cm −2. The experimental and theoretical results presented in this paper support recent evidence suggesting that the Universe is accelerating. It will be shown that the Cosmological Constant, in the Weak Field Approximation, leads to a correction term for the Newtonian potential and the corresponding acceleration [ of a test particle. The modified Newtonian equation is given by: Fm1 = m1 −Gm0 r2 + GΛr]. Here the force experienced by a mass m1 is given by the sum of the gravitational fields produced by m0 and Λ. An equivalent expression for the Cosmological Constant will be derived from the Extended Large Number Hypothesis, which predicts a positive nonzero Cosmological Constant. The extended LNH will then be used to define other cosmological parameters: gravitational constant, energy density, the Cosmological Constant and Hubble ’s Constant in terms of a fundamental length. A speculative theory for the evolution of the Universe is outlined, where, building on the work of Eddington, Dirac, Zel’dovich, Sakharov and Matthews, it is shown how the Universe can be defined, in any particular era, by two parameters: the fundamental length and the energy density of the vacuum for that epoch (GUT, electroweak, Quark Hadron Confinement). The theory is
Useful fiction or miracle maker: The competing epistemological foundations of rational choice theory
 American Political Science Review
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Quantum Formalism with StateCollapse and Superluminal Communication, to appear
 in Foundations of Physics
, 1998
"... Given the collapse hypothesis (CH) of quantum measurement, EPRtype correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses impl ..."
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Given the collapse hypothesis (CH) of quantum measurement, EPRtype correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that lorentz covariance along with the second law of thermodynamics imply a nonentropic version of ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the hilbertspace model of quantum mechanics have their origin in spacetime structure. 1