New Foundations For Physical Geometry

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New Foundations for Physical Geometry

Tim Maudlin
New Foundations for Physical Geometry Book PDF

Author : Tim Maudlin
Publisher : OUP Oxford
Page : 376 pages
File Size : 55,8 Mb
Release : 2014-03-06
Category : Philosophy
ISBN : 9780191022692

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New Foundations for Physical Geometry by Tim Maudlin Pdf

Topology is the mathematical study of the most basic geometrical structure of a space. Mathematical physics uses topological spaces as the formal means for describing physical space and time. This book proposes a completely new mathematical structure for describing geometrical notions such as continuity, connectedness, boundaries of sets, and so on, in order to provide a better mathematical tool for understanding space-time. This is the initial volume in a two-volume set, the first of which develops the mathematical structure and the second of which applies it to classical and Relativistic physics. The book begins with a brief historical review of the development of mathematics as it relates to geometry, and an overview of standard topology. The new theory, the Theory of Linear Structures, is presented and compared to standard topology. The Theory of Linear Structures replaces the foundational notion of standard topology, the open set, with the notion of a continuous line. Axioms for the Theory of Linear Structures are laid down, and definitions of other geometrical notions developed in those terms. Various novel geometrical properties, such as a space being intrinsically directed, are defined using these resources. Applications of the theory to discrete spaces (where the standard theory of open sets gets little purchase) are particularly noted. The mathematics is developed up through homotopy theory and compactness, along with ways to represent both affine (straight line) and metrical structure.

New Foundations for Physical Geometry

Tim Maudlin
New Foundations for Physical Geometry Book PDF

Author : Tim Maudlin
Publisher : OUP Oxford
Page : 352 pages
File Size : 48,7 Mb
Release : 2014-03-06
Category : Philosophy
ISBN : 9780191004551

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New Foundations for Physical Geometry by Tim Maudlin Pdf

Topology is the mathematical study of the most basic geometrical structure of a space. Mathematical physics uses topological spaces as the formal means for describing physical space and time. This book proposes a completely new mathematical structure for describing geometrical notions such as continuity, connectedness, boundaries of sets, and so on, in order to provide a better mathematical tool for understanding space-time. This is the initial volume in a two-volume set, the first of which develops the mathematical structure and the second of which applies it to classical and Relativistic physics. The book begins with a brief historical review of the development of mathematics as it relates to geometry, and an overview of standard topology. The new theory, the Theory of Linear Structures, is presented and compared to standard topology. The Theory of Linear Structures replaces the foundational notion of standard topology, the open set, with the notion of a continuous line. Axioms for the Theory of Linear Structures are laid down, and definitions of other geometrical notions developed in those terms. Various novel geometrical properties, such as a space being intrinsically directed, are defined using these resources. Applications of the theory to discrete spaces (where the standard theory of open sets gets little purchase) are particularly noted. The mathematics is developed up through homotopy theory and compactness, along with ways to represent both affine (straight line) and metrical structure.

New Foundations for Classical Mechanics

D. Hestenes
New Foundations for Classical Mechanics Book PDF

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020

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New Foundations for Classical Mechanics by D. Hestenes Pdf

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

New Foundations in Mathematics

Garret Sobczyk
New Foundations in Mathematics Book PDF

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 46,8 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856

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New Foundations in Mathematics by Garret Sobczyk Pdf

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Spacetime

Marcus Kriele
Spacetime Book PDF

Author : Marcus Kriele
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 41,6 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540483540

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Spacetime by Marcus Kriele Pdf

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Topology, Geometry, and Gauge Fields

Gregory Naber
Topology Geometry and Gauge Fields Book PDF

Author : Gregory Naber
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 45,7 Mb
Release : 1997-04-24
Category : Mathematics
ISBN : 0387949461

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Topology, Geometry, and Gauge Fields by Gregory Naber Pdf

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

New Foundations for Classical Mechanics

David Hestenes
New Foundations for Classical Mechanics Book PDF

Author : David Hestenes
Publisher : Springer Science & Business Media
Page : 703 pages
File Size : 45,7 Mb
Release : 1999-09-30
Category : Language Arts & Disciplines
ISBN : 0792353021

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New Foundations for Classical Mechanics by David Hestenes Pdf

This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programs, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors. Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly a hundred pages on relativistic mechanics. The treatment is unique in its exclusive use of geometric algebra and in its detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.

Topology, Geometry, and Gauge Fields

Gregory L. Naber
Topology Geometry and Gauge Fields Book PDF

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 53,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475727425

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Topology, Geometry, and Gauge Fields by Gregory L. Naber Pdf

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Differential Sheaves And Connections: A Natural Approach To Physical Geometry

Mallios Anastasios,Zafiris Elias
Differential Sheaves And Connections A Natural Approach To Physical Geometry Book PDF

Author : Mallios Anastasios,Zafiris Elias
Publisher : World Scientific
Page : 304 pages
File Size : 42,9 Mb
Release : 2015-09-17
Category : Mathematics
ISBN : 9789814719483

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Differential Sheaves And Connections: A Natural Approach To Physical Geometry by Mallios Anastasios,Zafiris Elias Pdf

This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.

New Foundations for Classical Mechanics

David Hestenes
New Foundations for Classical Mechanics Book PDF

Author : David Hestenes
Publisher : Springer Science & Business Media
Page : 716 pages
File Size : 48,6 Mb
Release : 1999-09-30
Category : Science
ISBN : 9780792355144

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New Foundations for Classical Mechanics by David Hestenes Pdf

(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Spooky Action at a Distance

George Musser
Spooky Action at a Distance Book PDF

Author : George Musser
Publisher : Scientific American / Farrar, Straus and Giroux
Page : 304 pages
File Size : 54,8 Mb
Release : 2015-11-03
Category : Science
ISBN : 9780374713553

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Spooky Action at a Distance by George Musser Pdf

Long-listed for the 2016 PEN/E. O. Wilson Literary Science Writing Award “An important book that provides insight into key new developments in our understanding of the nature of space, time and the universe. It will repay careful study.” —John Gribbin, The Wall Street Journal “An endlessly surprising foray into the current mother of physics' many knotty mysteries, the solving of which may unveil the weirdness of quantum particles, black holes, and the essential unity of nature.” —Kirkus Reviews (starred review) What is space? It isn't a question that most of us normally ask. Space is the venue of physics; it's where things exist, where they move and take shape. Yet over the past few decades, physicists have discovered a phenomenon that operates outside the confines of space and time: nonlocality-the ability of two particles to act in harmony no matter how far apart they may be. It appears to be almost magical. Einstein grappled with this oddity and couldn't come to terms with it, describing it as "spooky action at a distance." More recently, the mystery has deepened as other forms of nonlocality have been uncovered. This strange occurrence, which has direct connections to black holes, particle collisions, and even the workings of gravity, holds the potential to undermine our most basic understandings of physical reality. If space isn't what we thought it was, then what is it? In Spooky Action at a Distance, George Musser sets out to answer that question, offering a provocative exploration of nonlocality and a celebration of the scientists who are trying to explain it. Musser guides us on an epic journey into the lives of experimental physicists observing particles acting in tandem, astronomers finding galaxies that look statistically identical, and cosmologists hoping to unravel the paradoxes surrounding the big bang. He traces the often contentious debates over nonlocality through major discoveries and disruptions of the twentieth century and shows how scientists faced with the same undisputed experimental evidence develop wildly different explanations for that evidence. Their conclusions challenge our understanding of not only space and time but also the origins of the universe-and they suggest a new grand unified theory of physics. Delightfully readable, Spooky Action at a Distance is a mind-bending voyage to the frontiers of modern physics that will change the way we think about reality.

Believing in Dawkins

Eric Steinhart
Believing in Dawkins Book PDF

Author : Eric Steinhart
Publisher : Springer Nature
Page : 412 pages
File Size : 47,5 Mb
Release : 2020-09-16
Category : Science
ISBN : 9783030430528

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Believing in Dawkins by Eric Steinhart Pdf

Dawkin's militant atheism is well known; his profound faith less well known In this book, atheist philosopher Eric Steinhart explores the spiritual dimensions of Richard Dawkins’ books, which are shown to encompass: · the meaning and purpose of life · an appreciation of Platonic beauty and truth · a deep belief in the rationality of the universe · an aversion to both scientism and nihilism As an atheist, Dawkins strives to develop a scientific alternative to theism, and while he declares that science is not a religion, he also proclaims it to be a spiritual enterprise. His books are filled with fragmentary sketches of this ‘spiritual atheism’, resembling a great unfinished cathedral. This book systematises and completes Dawkins’ arguments and reveals their deep roots in Stoicism and Platonism. Expanding on Dawkins’ ideas, Steinhart shows how atheists can develop powerful ethical principles, compelling systems of symbols and images, and meaningful personal and social practices. Believing in Dawkins is a rigorous and potent entreaty for the use of science and reason to support spiritually rich and optimistic ways of thinking and living.

Atheistic Platonism

Eric Charles Steinhart
Atheistic Platonism Book PDF

Author : Eric Charles Steinhart
Publisher : Springer Nature
Page : 345 pages
File Size : 43,9 Mb
Release : 2022-11-30
Category : Philosophy
ISBN : 9783031177521

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Atheistic Platonism by Eric Charles Steinhart Pdf

Atheistic Platonism is an alternative to both theism and nihilistic atheism. It shows how any jobs allegedly done by God are better done by impersonal Platonic objects. Without Platonic objects, atheism degenerates into an illogical nihilism. Atheistic Platonism instead provides reality with foundations that are eternal, necessary, rational, beautiful, and utterly mindless. It argues for a plenitude of mathematical objects, and an infinite plurality of possible universes. It provides mindless rational grounds for objective values, and for objective moral laws for the persons who evolve in universes. It defines a meaningful way of life, which facilitates self-improvement. Atheistic Platonists argue for computational theories of life after death. Atheistic Platonism includes a rich system of spiritual symbols. It values transformational practices and ecstatic experiences. Where atheisms based on materialism fail, atheisms based on Platonism succeed.

New Foundations for Applied Electromagnetics: The Spatial Structure of Electromagnetic Fields

Said Mikki,Yahia Antar
New Foundations for Applied Electromagnetics The Spatial Structure of Electromagnetic Fields Book PDF

Author : Said Mikki,Yahia Antar
Publisher : Artech House
Page : 600 pages
File Size : 52,7 Mb
Release : 2016-05-31
Category : Technology & Engineering
ISBN : 9781630813680

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New Foundations for Applied Electromagnetics: The Spatial Structure of Electromagnetic Fields by Said Mikki,Yahia Antar Pdf

This comprehensive new resource focuses on applied electromagnetics and takes readers beyond the conventional theory with the use of contemporary mathematics to improve the practical use of electromagnetics in emerging areas of field communications, wireless power transfer, metamaterials, MIMO and direction-of-arrival systems. The book explores the existing and novel theories and principles of electromagnetics in order to help engineers analyze and design devices for today's applications in wireless power transfers, NFC, and metamaterials. This book is organized into clear and logical sections spanning from fundamental theory, to applications, promoting clear understanding through-out. This resource presents the theory of electromagnetic near fields including chapters on reactive energy, spatial and spectral theory, the scalar antenna, and the morphogenesis of electromagnetic radiation in the near field zone. The Antenna Current Green's Function Formalism is explored with an emphasis on the foundations, the organic interrelationships between the fundamental operational modes of general antenna systems, and the spectral approach to antenna-to-antenna interactions. The book offers perspective on nonlocal metamaterials, including the material response theory, the far-field theory, and the near-field theory.

The Foundations of Geometry

David Hilbert
The Foundations of Geometry Book PDF

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 53,8 Mb
Release : 2014-07-07
Category : Mathematics
ISBN : 9781473395947

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The Foundations of Geometry by David Hilbert Pdf

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.