The History Of Continua

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press, USA. This book was released on 2021 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press. This book was released on 2020-12-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.

Download or read book A Luta Continua written by Lizette Rabe and published by African Sun Media. This book was released on 2020-10-16 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: What has media freedom entailed over the couple of centuries and successive governments of the geopolitical region that became South Africa since it was colonised by Westerners? And why can media freedom be described as both pillar and cornerstone of a democracy? It’s simple, as in the words of Nelson Mandela, first state president of a democratic South Africa: Press freedom is the “lifeblood of democracy”. This book tells the tale of the various states of press freedom, or unfreedom, from colonial times to today – from a British governor called a dictator and a despot, through apartheid’s “pigmentocracy”, or “sjambokracy”, where the rule of law “has been replaced by the rule of the whip”, up to the dawn of liberation, with media freedom entrenched in Article 16 of South Africa’s Bill of Rights. And why should all of this concern you? Because media freedom is not about the freedom of the media. It is about your freedom. As was formulated by an editor under apartheid: “If we don’t have a public sympathetic to a free press, not only will we not have a free press, we won’t have a democracy either.” Or, in the words of former Sowetan editor and SANEF chair, Mpumelelo Mhkabela: “Media freedom has nothing to do with the media, but with the freedom of citizens.” And that is why you should know that a free media is the only guarantee for your freedom. As we have seen, both under apartheid and also under a democratic dispensation, it is a matter of a luta continua. The struggle continues. But you, the public, are the guardian of those that guard democracy. Help ensure the rights of a free media, and thereby your democratic rights and a democratic South Africa.

Download or read book The Mechanics and Thermodynamics of Continua written by Morton E. Gurtin and published by Cambridge University Press. This book was released on 2010-04-19 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Download or read book Mechanics of Generalized Continua written by Gérard A. Maugin and published by Springer Science & Business Media. This book was released on 2010-03-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Download or read book Continua written by Howard Cook and published by CRC Press. This book was released on 2020-12-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio. It also features the Houston Problem Book which includes a recently updated set of 200 problems accumulated over several years at the University of Houston.;These proceedings and problems are aimed at pure and applied mathematicians, topologists, geometers, physicists and graduate-level students in these disciplines.