Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 7845

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Are Numbers Real?

The Uncanny Relationships Between Maths and the Physical World

Author: Brian Clegg

Publisher: Hachette UK

ISBN: 1472139771

Category: Science

Page: 304

View: 1474

Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.

Mathematics and the physical world

inaugural lecture of the professor of applied mathematics delivered at the College on March 2, 1954

Author: J. G. Oldroyd

Publisher: N.A


Category: Mathematics

Page: 28

View: 5221


Eine kleine Geschichte der Unendlichkeit

Author: Brian Clegg

Publisher: Rowohlt Verlag GmbH

ISBN: 364404371X

Category: Fiction

Page: 352

View: 4460

Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.

Unser mathematisches Universum

Auf der Suche nach dem Wesen der Wirklichkeit

Author: Max Tegmark

Publisher: Ullstein eBooks

ISBN: 3843710783

Category: Mathematics

Page: 520

View: 8903

„Max Tegmark, Prophet der Parallelwelten, flirtet mit der Unendlichkeit.“ ULF VON RAUCHHAUPT, FRANKFURTER ALLGEMEINE SONNTAGSZEITUNG WORUM GEHT ES? Max Tegmark entwickelt eine neue Theorie des Kosmos: Das Universum selbst ist reine Mathematik. In diesem Buch geht es um die physikalische Realität des Kosmos, um den Urknall und die „Zeit davor“ und um die Evolution des Weltalls. Welche Rollen spielen wir dabei – die Wesen, die klug genug sind, das alles verstehen zu wollen? Tegmark findet, dieses Terrain sollte nicht länger den Philosophen überlassen bleiben. Denn die Physiker von heute haben die besseren Antworten auf die ewigen Fragen. WAS IST BESONDERS? „Eine hinreißende Expedition, die jenseits des konventionellen Denkens nach der wahren Bedeutung von Realität sucht.“ BBC „Tegmark behandelt die großen Fragen der Kosmologie und der Teilchenphysik weitaus verständlicher als Stephen Hawking.“ THE TIMES WER LIEST? • Jeder, der das Universum verstehen will • Die Leser von Richard Dawkins und Markus Gabriel

Mathematics and the Divine

A Historical Study

Author: Teun Koetsier,Luc Bergmans

Publisher: Elsevier

ISBN: 9780080457352

Category: Mathematics

Page: 716

View: 3255

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. · Mathematics and man's quest for the Absolute · A selective history highlighting key figures, schools and trains of thought · An international team of historians presenting specific new findings as well as general overviews · Confronting and uniting otherwise compartmentalized information

Mathematics and the Natural Sciences

The Physical Singularity of Life

Author: Francis Bailly,Giuseppe Longo

Publisher: World Scientific

ISBN: 1908977795

Category: Science

Page: 336

View: 8272

This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work. The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations. Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline

A History of the Circle

Mathematical Reasoning and the Physical Universe

Author: Ernest Zebrowski

Publisher: Rutgers University Press

ISBN: 9780813528984

Category: Mathematics

Page: 215

View: 6466

Ranging from ancient times to twentieth-century theories of time and space, looks at how exploring the circle has lead to increased knowledge about the physical universe.

From Paradox to Reality

Our Basic Concepts of the Physical World

Author: Fritz Rohrlich

Publisher: Cambridge University Press

ISBN: 9780521376051

Category: Science

Page: 227

View: 7869

Using a clear, non-technical style, Professor Rohrlich discusses the two major theories of twentieth-century physics: relativity and quantum mechanics. Discussed conceptually and philosophically, rather than using mathematics, the philosophical issues raised show how new discoveries forced physicists to accept often strange and unconventional notions. He aims to remove the mystery and misrepresentation that often surround the ideas of modern physics and to show how modern scientists construct theories, so that the reader can appreciate their successes and failures and understand problems that are as yet unresolved.

The World of Mathematics

Author: James Roy Newman

Publisher: Courier Corporation

ISBN: 9780486411507

Category: Mathematics

Page: 720

View: 4434

Vol. 2 of a monumental 4-volume set covers mathematics and the physical world, mathematics and social science, and the laws of chance, with non-technical essays by eminent mathematicians, economists, scientists, and others.

What if? Was wäre wenn?

Wirklich wissenschaftliche Antworten auf absurde hypothetische Fragen

Author: Randall Munroe

Publisher: Albrecht Knaus Verlag

ISBN: 364114311X

Category: Nature

Page: 368

View: 2776

Endlich erfindet wieder jemand das Pop-Science-Erklärbuch neu! Wenn einen neuen Science Cartoon postet, vibriert das Internet. Sein Blog What if, auf dem der Physiker Randall Munroe jede Woche scheinbar unsinnige Fragen mit exakter Wissenschaft und genialen Strichmännchen beantwortet, ist Kult. Wie lange würde es dauern, bis wir merken würden, dass sich der Erdumfang verändert? Was wäre, wenn der gesamte Niederschlag in einem – quasi omnidirektionalen - Überschall-Regentropfen fiele? Endlich auch als Buch und endlich auf Deutsch!

Die Wirklichkeit, die nicht so ist, ...

Eine Reise in die Welt der Quantengravitation

Author: Carlo Rovelli

Publisher: Rowohlt Verlag GmbH

ISBN: 3644052514

Category: Science

Page: 320

View: 713

Was ist Wirklichkeit? Existieren Raum und Zeit tatsächlich, wenn wir uns anschicken, die elementarsten Grundlagen unserer Existenz zu erforschen? Wie viel davon können wir überhaupt verstehen? Carlo Rovelli beschäftigt sich seit vielen Jahren damit, die Grenzen unseres Verstehens zu erweitern. In diesem Buch nimmt er uns mit auf eine Reise, die von dem Realitätsverständnis der griechischen Klassik bis zur Schleifenquantengravitation führt. Ein großer Physiker unserer Zeit macht sich auf, uns ein neues Welt-Bild zu zeichnen: mit einem physikalischen Universum ohne Zeit, einer Raumzeit, die aus Schleifen und Körnchen besteht und in der Unendlichkeit nicht existiert. Einer Kosmologie, die ohne Urknall und Paralleluniversen auskommt und hier zum ersten Mal von einem ihrer «Erfinder» für ein breites Publikum einfach und ausführlich erklärt wird. Ein Buch über «die großen Herausforderungen der gegenwärtigen Naturwissenschaften, die all unser Wissen über die Natur in Frage stellen» (Rovelli).

Mathematics and the Body

Material Entanglements in the Classroom

Author: Elizabeth de Freitas,Nathalie Sinclair

Publisher: Cambridge University Press

ISBN: 1139952528

Category: Psychology

Page: N.A

View: 3760

This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive materialist' approach to studying mathematics education. This approach offers a fresh perspective on human and nonhuman bodies, challenging current assumptions about the role of the senses, language, and ability in teaching and learning mathematics. Each chapter provides empirical examples from the classroom that demonstrate how inclusive materialism can be applied to a wide range of concerns in the field. The authors analyze recent studies on students' gestures, expressions, and drawings in order to establish a link between mathematical activity and mathematical concepts. Mathematics and the Body expands the landscape of research in mathematics education and will be an essential resource for teachers, students, and researchers alike.


Die Physik der Zeit

Author: Richard A. Muller

Publisher: S. Fischer Verlag

ISBN: 3104038228

Category: Science

Page: 480

View: 5025

Sie lesen jetzt das Wort »jetzt« – und schon ist es vergangen. Das flüchtige Dasein der Gegenwart hat Philosophen und Physiker vor die größten Rätsel gestellt: Was ist die Zeit? Und warum fließt sie? Generationen von Wissenschaftlern haben sich vergeblich um Antworten bemüht, einige haben es aufgegeben. Nicht so Richard A. Muller. Er hat eine Theorie der Zeit aufgestellt, die neu ist und experimentell überprüfbar. Um sie vorzustellen, erklärt er zunächst mit großem Geschick die physikalischen Grundkonzepte wie Relativität, Entropie, Verschränkung, Antimaterie und Urknall. Darauf aufbauend entfaltet er seine provozierend neue Sicht mit all ihren Folgen für die Philosophie oder die Frage nach der Willensfreiheit. Eine kraftvolle und überzeugende Vision für die Lösung des alten Rätsels der Zeit. »Muller hat einen bemerkenswert frischen und aufregenden Ansatz für die Erklärung der Zeit.« Saul Perlmutter, Physik-Nobelpreisträger »Ein provokatives und gut argumentiertes Buch über die Natur der Zeit.« Lee Smolin

Strict Finitism and the Logic of Mathematical Applications

Author: Feng Ye

Publisher: Springer Science & Business Media

ISBN: 9789400713475

Category: Science

Page: 272

View: 1806

This book intends to show that radical naturalism (or physicalism), nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry (sufficient for the applications in classical quantum mechanics and general relativity). The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book.