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The first study of its kind, The Impact of Idealism assesses the impact of classical German philosophy on science, religion and culture. This volume explores German Idealism's impact on philosophy and scientific thought. Fourteen essays, by leading authorities in their respective fields, each focus on the legacy of a particular idea that emerged around 1800, when the underlying concepts of modern philosophy were being formed, challenged and criticised, leaving a legacy that extends to all physical areas and all topics in the philosophical world. From British Idealism to phenomenology, existentialism, pragmatism and French postmodernism, the story of German Idealism's impact on philosophy is here interwoven with man's scientific journey of self-discovery in the nineteenth and early twentieth centuries – from Darwin to Nietzsche to Freud and beyond. Spanning the analytical and Continental divide, this first volume examines Idealism's impact on contemporary philosophical discussions.
Abstract. In an effort to aid communication among different fields and perhaps facilitate progress on problems common to all of them, this article discusses hidden Markov processes from several viewpoints, especially that of symbolic dynamics, where they are known as sofic measures or continuous shift-commuting images of Markov measures. It provides background, describes known tools and methods, surveys some of the literature, and proposes several open problems.
Symbolic dynamics is the study of shift (and other) transformations on spaces of infinite sequences or arrays of symbols and maps between such systems. A symbolic dynamical system, with a shift-invariant measure, corresponds to a stationary stochastic process. In the setting of information theory, such a system amounts to a collection of messages. Markov measures and hidden Markov measures, also called sofic measures, on symbolic dynamical systems have the desirable property of being determined by a finite set of data. But not all of their properties, for example the entropy, can be determined by finite algorithms. This article surveys some of the known and unknown properties of hidden Markov measures that are of special interest from the viewpoint of symbolic dynamics. To keep the article self contained, necessary background and related concepts are reviewed briefly. More can be found in [47, 56, 55, 71].
We discuss methods and tools that have been useful in the study of symbolic systems, measures supported on them, and maps between them.
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