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Author: Dmitriĭ Vladimirovich Nikulin
Publisher: Ashgate Publishing
ISBN:
Category : Philosophy
Languages : en
Pages : 328
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Book Description
"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
Author: Dmitriĭ Vladimirovich Nikulin
Publisher: Ashgate Publishing
ISBN:
Category : Philosophy
Languages : en
Pages : 328
Get Book Here
Book Description
"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
Author: D. Hilbert
Publisher: American Mathematical Soc.
ISBN: 1470463024
Category : Education
Languages : en
Pages : 369
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Book Description
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.
Author: Matthew Handelman
Publisher: Fordham Univ Press
ISBN: 0823283852
Category : Philosophy
Languages : en
Pages : 287
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Book Description
This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.
Author: Dmitri Nikulin
Publisher:
ISBN: 9781315192406
Category : Electronic books
Languages : en
Pages :
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Book Description
"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.
Author: Dmitri Nikulin
Publisher: Routledge
ISBN: 9781138724549
Category :
Languages : en
Pages :
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Book Description
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.
Author: Kurt Smith
Publisher: OUP Oxford
ISBN: 0191576913
Category : Philosophy
Languages : en
Pages : 310
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Book Description
Why is there a material world? Why is it fundamentally mathematical? Matter Matters explores a seventeenth-century answer to these questions as it emerged from the works of Descartes and Leibniz. The 'mathematization' of the physics is shown to have been conceptually underwritten by two methods of philosophizing, namely, analysis and synthesis. The connection between these things--mathematics, matter, and the methods of analysis and synthesis--has thus far gone unexplored by scholars. The book is in four Parts: Part I works out the context in which the theory of modern matter arose. Part II develops the method of analysis, showing how it aligns with Descartes's famous doctrine of clear and distinct ideas. Part III develops the method of synthesis, focusing primarily on Leibniz, showing how it establishes the very conditions necessary and sufficient for mathematics. Analysis and synthesis turn out to establish isomorphic conceptual systems, which turn out to be isomorphic to what mathematicians today call a group. The group concept expresses the conditions underwriting all of mathematics. Part IV examines several relatively new interpretations of Descartes--the realist and idealist readings--which appear to be at odds with one another. The examination shows the sense in which these readings are actually compatible, and together reveal a richer picture of Descartes's position on the reality of matter. Ultimately, Matter Matters establishes the claim that mathematics is intelligible if, and only if, matter exists.
Author: Dmitri Nikulin
Publisher: Oxford University Press
ISBN: 0190662379
Category : Philosophy
Languages : en
Pages : 297
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Book Description
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.
Author: Andrew Janiak
Publisher: Oxford University Press
ISBN: 0199914117
Category : Philosophy
Languages : en
Pages : 369
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Book Description
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.
Author: Edward Kasner
Publisher: Courier Corporation
ISBN: 0486320278
Category : Mathematics
Languages : en
Pages : 402
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Book Description
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Author: Marc Frantz
Publisher: Princeton University Press
ISBN: 140083905X
Category : Mathematics
Languages : en
Pages : 259
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Book Description
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)
