Author: Ernst Mach
Publisher: Courier Corporation
ISBN: 0486439097
Category : Science
Languages : en
Pages : 162
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Book Description
These three essays by an eminent scientist explore the nature, origin, and development of our concepts of space from the points of view of the senses, history, and physics. They examine the subject from every direction, in a manner suitable for both undergraduates and other readers. 25 figures.1906 edition.
Author: Ulf Leonhardt
Publisher: Courier Corporation
ISBN: 0486134903
Category : Science
Languages : en
Pages : 290
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Book Description
Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
Author: Thomas C. Vinci
Publisher:
ISBN: 019938116X
Category : Philosophy
Languages : en
Pages : 265
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Book Description
Thomas C. Vinci aims to reveal and assess the structure of Kant's argument in the Critique of Pure Reason called the "Transcendental Deduction of the Categories." At the end of the first part of the Deduction in the B-edition Kant states that his purpose is achieved: to show that all intuitions in general are subject to the categories. On the standard reading, this means that all of our mental representations, including those originating in sense-experience, are structured by conceptualization. But this reading encounters an exegetical problem: Kant states in the second part of the Deduction that a major part of what remains to be shown is that empirical intuitions are subject to the categories. How can this be if it has already been shown that intuitions in general are subject to the categories? Vinci calls this the Triviality Problem, and he argues that solving it requires denying the standard reading. In its place he proposes that intuitions in general and empirical intuitions constitute disjoint classes and that, while all intuitions for Kant are unified, there are two kinds of unification: logical unification vs. aesthetic unification. Only the former is due to the categories. A second major theme of the book is that Kant's Idealism comes in two versions-for laws of nature and for objects of empirical intuition-and that demonstrating these versions is the ultimate goal of the Deduction of the Categories and the similarly structured Deduction of the Concepts of Space, respectively. Vinci shows that the Deductions have the argument structure of an inference to the best explanation for correlated domains of explananda, each arrived at by independent applications of Kantian epistemic and geometrical methods.
Author: James J. Callahan
Publisher: Springer Science & Business Media
ISBN: 1475767366
Category : Science
Languages : en
Pages : 474
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Book Description
Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Author: Peter Gardenfors
Publisher: MIT Press
ISBN: 9780262572194
Category : Psychology
Languages : en
Pages : 324
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Book Description
Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.
Author: Olive Whicher
Publisher: Rudolf Steiner Press
ISBN: 185584379X
Category : Mathematics
Languages : en
Pages : 294
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Book Description
Whicher explores the concepts of polarity and movement in modern projective geometry as a discipline of thought that transcends the limited and rigid space and forms of Euclid, and the corresponding material forces conceived in classical mechanics. Rudolf Steiner underlined the importance of projective geometry as, "a method of training the imaginative faculties of thinking, so that they become an instrument of cognition no less conscious and exact than mathematical reasoning." This seminal approach allows for precise scientific understanding of the concept of creative fields of formative (etheric) forces at work in nature--in plants, animals and in the human being. Olive Whicher's groundbreaking book presents an accessible--non-mathematician's--approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will be of interest to anyone wishing to cultivate the power of inner visualization in a realm of structural beauty.
Author: Sean M. Carroll
Publisher: Cambridge University Press
ISBN: 1108488390
Category : Science
Languages : en
Pages : 529
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Book Description
An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author: Shing-Tung Yau
Publisher: Il Saggiatore
ISBN: 0465020232
Category : Mathematics
Languages : en
Pages : 398
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Book Description
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Author: Arkan Zeytinoglu
Publisher: Springer
ISBN: 9783709105382
Category : Architecture
Languages : en
Pages : 0
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Book Description
Arkan Zeytinoglu calls his projects "built theory." Since many years, he has dealt with "the geometry of light", which describes best his special approach to architecture. But as an architect, Zeytinoglu, who studied at University of Technology TU Graz under Günther Domenig and later on at Cooper Union in New York, devotes himself mainly to building activities. Since his office’s foundation in 1995, realizations have included works in the field of hotels and resorts, gastronomy, and luxury residences. In May 2010, the internationally much-noticed Austrian pavilion at Expo 2010 Shanghai (ARGE SPAN & Zeytinoglu) was inaugurated. The book contains all essential realizations as well as a work list and an outlook at the buildings to be completed soon.
Author: Michael Frame
Publisher: University of Chicago Press
ISBN: 022680092X
Category : Biography & Autobiography
Languages : en
Pages : 175
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Book Description
Geometry -- Grief -- Beauty -- Story -- Fractal -- Beyond -- Appendix: More Math.
