• Mathematics

Mind and Nature

Selected Writings on Philosophy, Mathematics, and Physics
Author: Hermann Weyl
Publisher: Princeton University Press
ISBN: 9781400833320
Category: Mathematics
Page: 272
View: 7142
Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

    • Philosophy

Mathematics and Its Applications

A Transcendental-Idealist Perspective
Author: Jairo José da Silva
Publisher: Springer
ISBN: 3319630733
Category: Philosophy
Page: 276
View: 8929
This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies.

    • Philosophy

Einstein, Tagore and the Nature of Reality


Author: Partha Ghose
Publisher: Routledge
ISBN: 1134859341
Category: Philosophy
Page: 238
View: 2665
The nature of reality has been a long-debated issue among scientists and philosophers. In 1930, Rabindranath Tagore and Albert Einstein had a long conversation on the nature of reality. This conversation has been widely quoted and discussed by scientists, philosophers and scholars from the literary world. The important question that Tagore and Einstein discussed was whether the world is a unity dependent on humanity, or the world is a reality independent on the human factor. Einstein took the stand adopted by Western philosophers and mathematicians, namely that reality is something independent of the mind and the human factor. Tagore, on the other hand, adopted the opposite view. Nevertheless, both Einstein and Tagore claimed to be realists despite the fundamental differences between their conceptions of reality. Where does the difference lie? Can it be harmonized at some deeper level? Can Wittgenstein, for example, be a bridge between the two views? This collection of essays explores these two fundamentally different conceptions of the nature of reality from the perspectives of theories of space-time, quantum theory, general philosophy of science, cognitive science and mathematics.

    • Philosophy

Quantum Physics Meets the Philosophy of Mind

New Essays on the Mind-Body Relation in Quantum-Theoretical Perspective
Author: Antonella Corradini,Uwe Meixner
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110351064
Category: Philosophy
Page: 218
View: 3927
Quantum physics, unlike classical physics, suggests a non-physicalistic metaphysics. Whereas physicalism implies a reductive position in the philosophy of mind, quantum physics is compatible with non-reductionism, and actually seems to support it. The essays in this book explore, from various points of view, the possibilities of basing a non-reductive philosophy of mind on quantum physics.

    • Philosophy

The Quest for Reality: Bohr and Wittgenstein - Two Complementary Views


Author: Stig Stenholm
Publisher: Oxford University Press
ISBN: 0199603588
Category: Philosophy
Page: 222
View: 5239
In both science and philosophy, the twentieth century saw a radical breakdown of certainty in the human worldview. Quantum theorist Stig Stenholm presents Bohr and Wittgenstein as central figures undertaking the necessary replacement of apparent order and certainty with an understanding based on limited concepts in constant flux.

    • Literary Collections

The Best Writing on Mathematics 2010


Author: Mircea Pitici
Publisher: Princeton University Press
ISBN: 9780691148410
Category: Literary Collections
Page: 407
View: 5271
This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it's headed.

    • Science

Beyond Measure

Modern Physics, Philosophy, and the Meaning of Quantum Theory
Author: J. E. Baggott
Publisher: Oxford University Press on Demand
ISBN: 9780198525363
Category: Science
Page: 379
View: 4476
Quantum theory is one of the most important and successful theories of modern physical science. A fact all the more remarkable because quatum theory is a theory that few understand. Most academic textbooks on the subject are written for specialists, filled with complex jargon and dense mathematics. In contrast there are many popular presentations of the inherent 'weirdness' of the quantum world that are light on jargon and contain no mathematics.Together these presentations serve tocreate the impression that there are two theories - the 'serious, one and the 'wierd' one. Baggott successfully bridges the gulf between these presentations by grounding the discussion of the theory's profound problems directly in its mathematical formalism in a way that under-graduate students and interested individuals can follow.

    • Mathematics

Infinity and the Mind

The Science and Philosophy of the Infinite
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 1400849047
Category: Mathematics
Page: 368
View: 5452
In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Quantum Mind

The Edge Between Physics and Psychology
Author: Arnold Mindell, PH.D.
Publisher: Deep Democracy Exchange
ISBN: 1619710145
Category:
Page: N.A
View: 8630
Quantum Mind. The Edge Between Physics and Psychology This is the second edition with new preface from the author. In a single volume, Arnold Mindell brings together psychology, physics, math, myth, and shamanism – not only mapping the way for next-generation science but also applying this wisdom to personal growth, group dynamics, social and political processes, and environmental issues. Beginning with a discussion of cultural impacts on mathematics, he presents esoteric but plausible interpretations of imaginary numbers and the quantum wavefunction. In this context he discusses dreams, psychology, illness, shape-shifting (moving among realities), and the self-reflecting Universe – bringing in not only shamanism but also the Aboriginal, Greek, and Hindu myths and even sacred geometry from the Masonic orders and the Native Americans. The book is enriched by several psychological exercises that enable the reader to subjectively experience mathematics (counting, discounting, squaring, complex conjugating), physics (parallel worlds, time travel), and shamanism (shape-shifting).

    • Philosophy

Philosophy in an Age of Science

Physics, Mathematics, and Skepticism
Author: Hilary Putnam,Mario De Caro,David Macarthur
Publisher: N.A
ISBN: 9780674050136
Category: Philosophy
Page: 659
View: 7520
Hilary Putnam has at last paused from philosophizing to collect his papers for publication—his first volume in almost two decades. Contributing to a broad range of philosophical inquiry, Putnam has been said to represent a “history of recent philosophy in outline.” In this volume he suggests philosophy's possible future, as well.

    • Science

Seeing Double

Shared Identities in Physics, Philosophy, and Literature
Author: Peter Pesic
Publisher: MIT Press
ISBN: 026233898X
Category: Science
Page: 192
View: 5004
The separateness and connection of individuals is perhaps the central question of human life: What, exactly, is my individuality? To what degree is it unique? To what degree can it be shared, and how? To the many philosophical and literary speculations about these topics over time, modern science has added the curious twist of quantum theory, which requires that the elementary particles of which everything consists have no individuality at all. All aspects of chemistry depend on this lack of individuality, as do many branches of physics. From where, then, does our individuality come?In Seeing Double, Peter Pesic invites readers to explore this intriguing set of questions. He draws on literary and historical examples that open the mind (from Homer to Martin Guerre to Kafka), philosophical analyses that have helped to make our thinking and speech more precise, and scientific work that has enabled us to characterize the phenomena of nature. Though he does not try to be all-inclusive, Pesic presents a broad range of ideas, building toward a specific point of view: that the crux of modern quantum theory is its clash with our ordinary concept of individuality. This represents a departure from the usual understanding of quantum theory. Pesic argues that what is bizarre about quantum theory becomes more intelligible as we reconsider what we mean by individuality and identity in ordinary experience. In turn, quantum identity opens a new perspective on us.

    • Science

Lost in Math

How Beauty Leads Physics Astray
Author: Sabine Hossenfelder
Publisher: Basic Books
ISBN: 0465094260
Category: Science
Page: 304
View: 9715
A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    • Science

The Singular Universe and the Reality of Time


Author: Roberto Mangabeira Unger,Lee Smolin
Publisher: Cambridge University Press
ISBN: 1107074061
Category: Science
Page: 566
View: 8732
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.

    • Computers

The Large, the Small and the Human Mind


Author: Roger Penrose,Abner Shimony,Malcolm Longair,Nancy Cartwright,Stephen Hawking
Publisher: Cambridge University Press
ISBN: 9780521785723
Category: Computers
Page: 201
View: 2477
Accessible and stimulating introduction to Roger Penrose's vision of theoretical physics for the twenty-first century.

    • Science

Atomic Physics and Human Knowledge


Author: Niels Bohr
Publisher: Pickle Partners Publishing
ISBN: 1787208931
Category: Science
Page: 97
View: 4291
This collection of articles, which were first published in 1958 and written on various occasions between 1932 and 1957, forms a sequel to Danish physician Niels Bohr’s earlier essays in Atomic Theory and the Description of Nature (1934). “The theme of the papers is the epistemological lesson which the modern development of atomic physics has given us and its relevance for analysis and synthesis in many fields of human knowledge. “The articles in the previous edition were written at a time when the establishment of the mathematical methods of quantum mechanics had created a firm foundation for the consistent treatment of atomic phenomena, and the conditions for an unambiguous account of experience within this framework were characterized by the notion of complementarity. In the papers collected here, this approach is further developed in logical formulation and given broader application.”

    • Science

Mathematics: A Concise History and Philosophy


Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 1461208750
Category: Science
Page: 265
View: 5116
This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.

    • Philosophy

Conjectures and Refutations

The Growth of Scientific Knowledge
Author: Karl Popper
Publisher: Routledge
ISBN: 1135971374
Category: Philosophy
Page: 608
View: 7966
Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

    • Science

Information and the Nature of Reality

From Physics to Metaphysics
Author: Paul Davies,Niels Henrik Gregersen
Publisher: Cambridge University Press
ISBN: 1107684536
Category: Science
Page: 506
View: 4226
From quantum to biological and digital, here eminent scientists, philosophers and theologians chart various aspects of information.

    • Philosophy

Philosophy of Mathematics

Selected Writings
Author: Charles S. Peirce
Publisher: Indiana University Press
ISBN: 0253004691
Category: Philosophy
Page: 336
View: 8064
The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.