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Natures Mirror of Symmetry

Natures Mirror of Symmetry
Author: Cheryl Caine
Publisher: Xlibris Us
Total Pages: 162
Release: 2019-09-19
Genre:
ISBN: 9781796039061

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This is a picture of myself along the Columbia River placed in symmetry. It shows the yielding receptive power of the yin aspect of the I-Ching which is the trigram number two "The Receptive". In the center of this picture is a golden chalice. The top of the chalice looks like a blue butterfly. This is the transforming womb of Mother Wisdom, and her face is in the center of it. On each side, the fallopian tubes reach out towards my head, where the dancers are dancing life into being. The charioteer is poised above like "the creative heaven", which is the first trigram of the I-Ching representing the yang aspect. He waits for the right time to move forward and as he sits in his chariot, he too meditates on the Holy Grail in front of him. In the hidden third he can bring it into motion through spirit in matter. For many decades my prayer has been for the renewing of my mind. This picture tells me that my prayer is in line with the process. I pray this for everyone. May we find our holy grail, land live our destiny.


Natures Mirror of Symmetry

Natures Mirror of Symmetry
Author: Cheryl Caine
Publisher: Xlibris Corporation
Total Pages: 317
Release:
Genre: Body, Mind & Spirit
ISBN: 1796039047

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This is a picture of myself along the Columbia River placed in symmetry. It shows the yielding receptive power of the yin aspect of the I-Ching which is the trigram number two “The Receptive”. In the center of this picture is a golden chalice. The top of the chalice looks like a blue butterfly. This is the transforming womb of Mother Wisdom, and her face is in the center of it. On each side, the fallopian tubes reach out towards my head, where the dancers are dancing life into being. The charioteer is poised above like “the creative heaven”, which is the first trigram of the I-Ching representing the yang aspect. He waits for the right time to move forward and as he sits in his chariot, he too meditates on the Holy Grail in front of him. In the hidden third he can bring it into motion through spirit in matter. For many decades my prayer has been for the renewing of my mind. This picture tells me that my prayer is in line with the process. I pray this for everyone. May we find our holy grail, land live our destiny.


Natures Mirror Of Symmetry

Natures Mirror Of Symmetry
Author: Cheryl Caine
Publisher:
Total Pages: 176
Release: 2021-01-22
Genre: Education
ISBN: 9781953397621

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Natures Mirror of Symmetry takes us beyond our normal 3D way of seeing and shows us a whole new dimension that few see. This dimension gives us a glimpse of the divine in everything including ourselves.We enter what I call the "hidden third", which is in the center of what is being mirrored through symmetry. There are archetypal images in this center that reappear over and over again that I talk about them and how they affect us


Mirror Symmetry

Mirror Symmetry
Author: Kentaro Hori
Publisher: American Mathematical Soc.
Total Pages: 954
Release: 2003
Genre: Mathematics
ISBN: 0821829556

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This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.


Classical Mirror Symmetry

Classical Mirror Symmetry
Author: Masao Jinzenji
Publisher: Springer
Total Pages: 140
Release: 2018-04-18
Genre: Science
ISBN: 9811300569

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This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.On the B-model side, the process of construction of a pair of mirror Calabi–Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard–Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.


Homological Mirror Symmetry

Homological Mirror Symmetry
Author: Anton Kapustin
Publisher: Springer Science & Business Media
Total Pages: 281
Release: 2009
Genre: Mathematics
ISBN: 3540680292

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An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.


Shadowlands

Shadowlands
Author: Robert Foot
Publisher: Universal-Publishers
Total Pages: 256
Release: 2002
Genre: Science
ISBN: 9781581126457

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In a revolutionary new theory, Dr. Robert Foot of the University of Melbourne argues that meteorites composed of mirror matter could impact with the Earth without leaving any ordinary fragments. Indeed, the theory seems to provide a simple explanation for the puzzling Tunguska event--the blast which destroyed a huge area of Siberian forest in 1908. While scientists have attributed this explosion to an ordinary meteorite, no traces of such an object have ever been found. Moreover, there are frequent smaller such events, occurring on a yearly basis, which are even more puzzling. Foot's new book lays clear the scientific case for mirror matter. It describes the fascinating evidence for its existence including, astronomical observations suggesting that most of our galaxy is made from a new form of matter--dark matter. It explains puzzling Jupiter sized planets only a few million miles from their host star, and the mysterious slowing down of spacecraft in our solar system. Remarkably, it is also possible that Pluto might even be a mirror world, which would explain various anomalous features of its orbit. Perhaps the most important consequence of all this--if true--is the possibility of actually extracting the mirror matter from the Tunguska impact site and other such sites on earth. Invisible asteroids and other cosmic bodies made of a new form of matter may pose a threat to Earth, agrees a noted Australian physicist. But the mirror matter idea has not attracted a huge following among physicists. In a recent UPI article, Howard Georgi of Harvard University says, "Foot's ideas have not attracted a huge following in the community that cares about these things, perhaps because the problems they solve, while interesting, are not the most critical puzzles that we are wrestling with." Nevertheless, mirror matter, if it exists, would be a completely new type of material with a potentially huge commercial value. Its scientific value would be of no less importance. FROM THE BACK COVER Nearly 50 years ago it was discovered that the fundamental particles, such as the electron and proton, have `left-handed' interactions; they do not respect mirror symmetry. This experimental fact motivates the idea that a set of `mirror particles' exist. The left-handedness of the ordinary particles can then be balanced by the right-handedness of the mirror particles. In this way mirror reflection symmetry can exist but requires something profoundly new. It requires the existence of a completely new form of matter called `mirror matter'. Remarkably the mirror matter theory is capable of simply explaining a large number of contemporary puzzles in astrophysics and particle physics. The evidence ranges from observations suggesting that most of the matter in the Universe is invisible, to unexpected properties of ghostly particles called `neutrinos'. This book explains this fascinating theory and its evidence at a level accessible to the non-specialist.


Nature's Numbers

Nature's Numbers
Author: Ian Stewart
Publisher: Basic Books
Total Pages: 179
Release: 2008-08-04
Genre: Science
ISBN: 0786723920

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"It appears to us that the universe is structured in a deeply mathematical way. Falling bodies fall with predictable accelerations. Eclipses can be accurately forecast centuries in advance. Nuclear power plants generate electricity according to well-known formulas. But those examples are the tip of the iceberg. In Nature's Numbers, Ian Stewart presents many more, each charming in its own way.. Stewart admirably captures compelling and accessible mathematical ideas along with the pleasure of thinking of them. He writes with clarity and precision. Those who enjoy this sort of thing will love this book."—Los Angeles Times


Symmetry as a Developmental Principle in Nature and Art

Symmetry as a Developmental Principle in Nature and Art
Author: Werner Hahn
Publisher: World Scientific
Total Pages: 533
Release: 1998
Genre: Mathematics
ISBN: 9810223633

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Looking beyond the boundaries of various disciplines, the author demonstrates that symmetry is a fascinating phenomenon which provides endless stimulation and challenges. He explains that it is possible to readapt art to the sciences, and vice versa, by means of an evolutionary concept of symmetry. Many pictorial examples are included to enable the reader to fully understand the issues discussed. Based on the artistic evidence that the author has collected, he proposes that the new ars evolutoria can function as an example for the sciences.The book is divided into three distinct parts, each one focusing on a special issue. In Part I, the phenomenon of symmetry, including its discovery and meaning is reviewed. The author looks closely at how Vitruvius, Polyclitus, Democritus, Plato, Aristotle, Plotinus, Augustine, Alberti, Leonardo da Vinci and Durer viewed symmetry. This is followed by an explanation on how the concept of symmetry developed. The author further discusses symmetry as it appears in art and science, as well as in the modern age. Later, he expounds the view of symmetry as an evolutionary concept which can lead to a new unity of science. In Part II, he covers the points of contact between the form-developing process in nature and art. He deals with biological questions, in particular evolution.The collection of new and precise data on perception and knowledge with regard to the postulated reality of symmetry leads to further development of the evolutionary theory of symmetry in Part III. The author traces the enormous treasure of observations made in nature and culture back to a few underlying structural principles. He demonstrates symmetry as a far-reaching, leading, structuring, causal element of evolution, as the idea lying behind nature and culture. Numerous controllable reproducible double-mirror experiments on a new stereoscopic vision verify a symmetrization theory of perception.


Hidden Unity in Nature's Laws

Hidden Unity in Nature's Laws
Author: John C. Taylor
Publisher: Cambridge University Press
Total Pages: 506
Release: 2001-04-09
Genre: Mathematics
ISBN: 9780521659383

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A wide-ranging and illuminating account of how our understanding of the world has developed by uncovering 'hidden unities' in nature.