Matter Imagination And Geometry
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Matter Imagination And Geometry
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Author : Dmitriĭ Vladimirovich Nikulin
language : en
Publisher: Ashgate Publishing
Release Date : 2002
Matter Imagination And Geometry written by Dmitriĭ Vladimirovich Nikulin and has been published by Ashgate Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Philosophy categories.
"This book considers conditions of applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction of mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. The author explores questions in the history of philosophy and science, particularly in late antiquity and early modernity. The focus is on key thinkers Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
Matter Imagination And Geometry
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Author : Dmitri Nikulin
language : en
Publisher:
Release Date : 2017
Matter Imagination And Geometry written by Dmitri Nikulin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Electronic books categories.
"This title was first published in 2002: This text considers the applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction and mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. Exploring questions in the history of philosophy and science of late antiquity and early modernity, the key thinkers of focus are Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--Provided by publisher.
Matter Imagination And Geometry
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Author : Dmitri Nikulin
language : en
Publisher: Routledge
Release Date : 2017-12-15
Matter Imagination And Geometry written by Dmitri Nikulin and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with categories.
This title was first published in 2002: This text considers the applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction and mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. Exploring questions in the history of philosophy and science of late antiquity and early modernity, the key thinkers of focus are Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression.
Geometry And The Imagination
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Author : D. Hilbert
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-03-17
Geometry And The Imagination written by D. Hilbert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Education categories.
This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Space
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Author : Andrew Janiak
language : en
Publisher:
Release Date : 2020
Space written by Andrew Janiak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Philosophy categories.
Recurrent questions about space have dogged philosophers since ancient times. Can an ordinary person draw from his or her perceptions to say what space is? Or is it rather a technical concept that is only within the grasp of experts? Can geometry characterize the world in which we live? What is God's relation to space? In Ancient Greece, Euclid set out to define space by devising a codified set of axioms and associated theorems that were then passed down for centuries, thought by many philosophers to be the only sensible way of trying to fathom space. Centuries later, when Newton transformed the 'natural philosophy' of the seventeenth century into the physics of the eighteenth century, he placed the mathematical analysis of space, time, and motion at the center of his work. When Kant began to explore modern notions of 'idealism' and 'realism, ' space played a central role. But the study of space was transformed forever when, in 1915, Einstein published his general theory of relativity, explaining that the world is not Euclidean after all. This volume chronicles the development of philosophical conceptions of space from early antiquity through the medieval period to the early modern era. The chapters describe the interactions at different moments in history between philosophy and various other disciplines, especially geometry, optics, and natural science more generally. Fascinating central figures from the history of mathematics, science and philosophy are discussed, including Euclid, Plato, Aristotle, Proclus, Ibn al-Haytham, Nicole Oresme, Kepler, Descartes, Newton, Leibniz, Berkeley, and Kant. As with other books in the series, shorter essays, or Reflections, enrich the volume by characterizing perspectives on space found in various disciplines including ecology, mathematics, sculpture, neuroscience, cultural geography, art history, and the history of science.
Philosophy And Geometry
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Author : L. Magnani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Philosophy And Geometry written by L. Magnani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Neoplatonism In Late Antiquity
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Author : Dmitri Nikulin
language : en
Publisher: Oxford University Press
Release Date : 2019-05-14
Neoplatonism In Late Antiquity written by Dmitri Nikulin and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-14 with Philosophy categories.
This book is a philosophical study of two major thinkers who span the period of late antiquity. While Plotinus stands at the beginning of its philosophical tradition, setting the themes for debate and establishing strategies of argument and interpretation, Proclus falls closer to its end, developing a grand synthesis of late ancient thought. The book discusses many central topics of philosophy and science in Plotinus and Proclus, such as the one and the many, number and being, the individuation and constitution of the soul, imagination and cognition, the constitution of number and geometrical objects, indivisibility and continuity, intelligible and bodily matter, and evil. It shows that late ancient philosophy did not simply embrace and borrow from the major philosophical traditions of earlier antiquity--Platonism, Aristotelianism, Stoicism--by providing marginal comments on widely-known philosophical texts. Rather, Neoplatonism offered a set of highly original and innovative insights into the nature of being and thought, which can be distinguished in much subsequent philosophical thought, up until modernity.
Space And Political Universalism In Early Modern Physics And Philosophy
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Author : Pablo Bustinduy
language : en
Publisher: Edinburgh University Press
Release Date : 2024-03-05
Space And Political Universalism In Early Modern Physics And Philosophy written by Pablo Bustinduy and has been published by Edinburgh University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-05 with Business & Economics categories.
How did early modern philosophy of space shape the modern concept of political universalism? In this book, Pablo Bustinduy persuasively argues that political universalism emerged from both the developments of Newtonian science and the formulation of the modern philosophy of the State. In the metaphysics of an open, empty, abstract and absolute space, Bustinduy suggests, the universalist project of modern politics found its logical model and foundation. There, the anxiety of a dislocated world was overcome, and the ontology of modern physics found a specific political expression that, despite being besieged by multiple crises, still animates our political imagination. By offering a political reading of early modern philosophy of space, Space and Political Universalism in Early Modern Physics and Philosophy reveals the connections between the logical development of early modern science, the contemporary elaborations of the philosophy of the State, and the historical articulations of the Westphalian system, early capitalist social formations, and the European colonial project. In doing so, it offers a powerful reflection on how we might detach democracy from the 'perilous metaphysics' of infinite space that has engendered political violence and domination, positing space as an emptiness that prevents the closure of the political itself.
The Aim And Structure Of Physical Theory
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Author : Pierre Maurice Marie Duhem
language : en
Publisher: Princeton University Press
Release Date : 2021-08-10
The Aim And Structure Of Physical Theory written by Pierre Maurice Marie Duhem and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Science categories.
This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics.
Mathematizing Space
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Author : Vincenzo De Risi
language : en
Publisher: Birkhäuser
Release Date : 2015-01-31
Mathematizing Space written by Vincenzo De Risi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Mathematics categories.
This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).