Chaos Theology: A New Creation Theology and Its Applications

The problems inherent in creatio ex nihilo have led the author to the development of a new creation theology: chaos theology. Its main points are creation from an unexplained initial chaos, a remaining chaos element that is the source of physical and moral evil, and continuing creation toward fulfilment on the Last Day. Chaos theology can be reconciled with the scientific account of cosmic and biological evolution. Combining chaos theology with the physical theory of chaos helps in the understanding of God\'s action in the world. Jesus Christ is shown to be the cosmic Christ, who reconciles the entire cosmos, not only humanity. The problem of evil is readily solved in chaos theology as the effect of the remaining chaos element. From chaos theology and scientific insight in cancer, a theology of illness can be derived

Different Facets of Chaos in Quantum Mechanics

Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of dynamical chaos and the time scales associated with chaos suppression in quantum mechanics. Summary: 1. Introduction 2. Quantum Chaology and Spectral Statistics 3. From Poisson to GOE Transition: Comparison with Experimental Data 3.1 Atomic Nuclei 3.2 The Hydrogen Atom in the Strong Magnetic Field 4. Quantum Chaos and Field Theory 5. Alternative Approaches to Quantum Chaos 6. Dynamical Quantum Chaos and Time Scales 6.1 Mean-Field Approximation and Dynamical Chaos 7. ConclusionsComment: RevTex, 25 pages, 7 postscript figures, to be published in Int. J. Mod. Phys.

Evolution of Philosophical Strategies for Interacting with Chaos

After the discoveries of such scholars as J. H. Poincaré, E. N. Lorenz, I. Prigogine, etc. the term ‘chaos’ is used actively by representatives of various scientific fields; however, one important aspect remains uninvestigated: which attitude one should have toward chaotic phenomena. This is a philosophical question and my dissertation aims to find the answer in the history of philosophy, where chaos theme has had its investigators from ancient philosophy to the philosophical theories of the 21st century. My dissertation is based on the idea that sciences and philosophy can achieve significant success in exploring chaos theme when their efforts are combined. This dissertation research is designed to help in the planning of conscious, rational actions towards chaotic phenomena, since it is aimed at exploration and systematic presentation, as well as comprehension of possible systems of such actions – philosophical strategies for interacting with chaos. Results of the dissertation are the following. I reveal, reconstruct, and explain the content of six possible strategies for interacting with chaos that were worked out in history of philosophical thought: ordering, avoiding, transfiguring, preventing, controlling, and integrating. I argue that the first philosophical strategies for interacting with chaos were worked out in the 19th century by German philosophers K. W. F. Schlegel and F. W. Nietzsche on the basis of their rethinking the ideas which were expressed by different thinkers during classical antiquity, the Middle Ages, and the modern period. I show that ideas of strategic views towards chaos were also elaborated by such 20th-century thinkers as H. Rickert, N. Berdyaev, I. Prigogine, H. Haken, G. Deleuze, Q. Meillassoux, and others. I outline the main stages of the evolution of philosophical strategies for interacting with chaos as well as its regularities. The dissertation shows perspectives of further development of each one of the six strategies for interacting with chaos. In contemporary scientific and philosophical research on chaos, my exploration contributes to the new approach to improving the understanding of aims of acts towards chaotic phenomena. I think that knowing a range of different strategic views of chaos help researchers of chaotic phenomena to choose the most appropriate and rational reactions. In the area of history of philosophy, my research contributes detailed data about development and conceptual transformations of the notion of ‘chaos’ through all periods of Western philosophy. The dissertation consists of five chapters: 1) Literature Review, Methodology and Key Research Terms, 2) Ancient and Medieval Philosophical Ideas about Chaos, 3) Genesis of the First Strategies for Interacting with Chaos, 4) Strategies for Interacting with Chaos in the 20th and 21st Centuries, 5) Regularities and Prospects of the Development of Philosophical Strategies for Interacting with Chaos. In the first chapter I analyze more than five hundred books, articles, and other philosophical and scientific sources in which the chaos theme is raised. I also argue the necessity of applying methods such as analysis, the structural method, the hermeneutic method of interpretation, and the comparative method in my dissertation research. Moreover, in this chapter, I define key terms for my dissertation – ‘chaos’ and ‘philosophical strategies for interacting with chaos.’ Then, in the next chapter, I analyze the appearance and development of Ancient and Medieval philosophical ideas about chaotic phenomena and order. Particularly, I explore thoughts of philosophers such as Anaxagoras, Anaximander, Heraclitus, Empedocles, Plato, Aristotle, Augustine of Hippo, Bernard Silvestris, Ramon Llull, etc. In this chapter I also compare the first Western ideas about chaos with similar thoughts from Eastern philosophy, analyzing Indian and Chinese philosophical ideas about disorder. In the third chapter I explore transformations in understanding the meaning of the term ‘chaos’ in philosophy from the 15th to the end of the 19th century. I analyze ideas about chaos and order from thinkers such as M. Ficino, Paracelsus, F. Bacon, P. Bayle, Voltaire, J. G. Herder, I. Kant, F. W. J. Schelling and other philosophers from the Renaissance, the Age of Enlightenment, and the German idealist period, showing that these thinkers’ new approaches to interpreting the notion of ‘chaos’ were the background for K. W. F. Schlegel’s and F. W. Nietzsche’s creations of the first strategies for interacting with chaos in the 19th century. I finish the chapter with detailed analysis of K. W. F. Schlegel’s strategy for transfiguring chaos and F. W. Nietzsche’s strategy for ordering chaos. The development of philosophical strategies for interacting with chaos in the 20th and the beginning of the 21st century is the topic of the fourth chapter. I research new ideas about ordering chaos (H. Rickert) and transfiguring chaos (N. Berdyaev). Also, I reveal thoughts about avoiding chaos (A. Camus), preventing chaos (J. Ortega y Gasset), integrating chaos (G. Deleuze, Q. Meillassoux). Moreover, I analyze a philosophical component of the strategy for chaos control (I. Prigogine, H. Haken). In the final fifth chapter of the dissertation I trace the major features of philosophical strategies for interacting with chaos and find out the main conditions and periods of their development. Then I outline the prospects for the development of the philosophical strategies for interacting with chaos and show the most productive ways of their progress

On Kac's Chaos And Related Problems

This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac in his study of mean-field limit for systems of $N$ undistinguishable particles. First, we quantitatively liken three usual measures of Kac's chaos, some involving the all $N$ variables, other involving a finite fixed number of variables. Next, we define the notion of entropy chaos and Fisher information chaos in a similar way as defined by Carlen et al (KRM 2010). We show that Fisher information chaos is stronger than entropy chaos, which in turn is stronger than Kac's chaos. More importantly, with the help of the HWI inequality of Otto-Villani, we establish a quantitative estimate between these quantities, which in particular asserts that Kac's chaos plus Fisher information bound implies entropy chaos. We then extend the above quantitative and qualitative results about chaos in the framework of probability measures with support on the Kac's spheres. Additionally to the above mentioned tool, we use and prove an optimal rate local CLT in $L^\infty$ norm for distributions with finite 6-th moment and finite $L^p$ norm, for some $p>1$. Last, we investigate how our techniques can be used without assuming chaos, in the context of probability measures mixtures introduced by De Finetti, Hewitt and Savage. In particular, we define the (level 3) Fisher information for mixtures and prove that it is l.s.c. and affine, as that was done previously for the level 3 Boltzmann's entropy.Comment: 80 pages. Last version before publicatio

DxHash: A Scalable Consistent Hash Based on the Pseudo-Random Sequence

Consistent hasing has played a fundamental role as a data router and a load balancer in various fields, such as distributed database, cloud infrastructure, and peer-to-peer network. However, the existing consistent hashing schemes can't meet the requirements simultaneously, including full consistency, scalability, small memory footprint, low update time and low query complexity. Thus, We propose DxHash, a scalable consistent hashing algorithm based on the pseudo-random sequence. For the scenario of distributed storage, there are two optimizations based on DXHash are proposed. First, the Weighted DxHash can adjust the workloads on arbitrary nodes. Second, the Asymmetric Replica Strategy (ARS) is combining the replica strategy in distributed storage with the scaleup process to improve the availability of the system and reduce the remapping rate. The evaluation indicates that compared with the state-of-art works, DxHash achieves significant improvements on the 5 requirements. Even with 50% failure ratio, DxHash still can complete 16.5 million queries per second. What's more, the two optimizations both achieve their own results