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Shadows of Reality~tqw~ darksiderg

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Shadows of Reality
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General Information
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Type.................: Ebook
Part Size............: 1,876,115 bytes




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Posted by............: ~tqw~

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Release Notes
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In this insightful book, which is a revisionist math history as well as a
revisionist art history, Tony Robbin, well known for his innovative computer
visualizations of hyperspace, investigates different models of the fourth
dimension and how these are applied in art and physics. Robbin explores the
distinction between the slicing, or Flatland, model and the projection, or
shadow, model. He compares the history of these two models and their uses and
misuses in popular discussions. Robbin breaks new ground with his original
argument that Picasso used the projection model to invent cubism, and that
Minkowski had four-dimensional projective geometry in mind when he structured
special relativity. The discussion is brought to the present with an exposition
of the projection model in the most creative ideas about space in contemporary
mathematics such as twisters, quasicrystals, and quantum topology. Robbin
clarifies these esoteric concepts with understandable drawings and diagrams.
Robbin proposes that the powerful role of projective geometry in the development
of current mathematical ideas has been long overlooked and that our attachment
to the slicing model is essentially a conceptual block that hinders progress in
understanding contemporary models of spacetime. He offers a fascinating review
of how projective ideas are the source of some of today’s most exciting
developments in art, math, physics, and computer visualization.

Table of Contents

Ch. 1 The origins of four-dimensional geometry 3
Ch. 2 Fantasies of four-dimensional space 19
Ch. 3 The fourth dimension in painting 28
Ch. 4 The truth 41
Ch. 5 A very short course in projective geometry 53
Ch. 6 Patterns, crystals, and projections 61
Ch. 7 Twistors and projections 72
Ch. 8 Entanglement, quantum geometry, and projective reality 83
Ch. 9 Category theory, higher-dimensional algebra, and the dimension ladder 93
Ch. 10 The computer revolution in four-dimensional geometry 105
Ch. 11 Conclusion : art, math, and technical drawing 114

Product Details

* ISBN: 0300110391
* ISBN-13: 9780300110395
* Format: Hardcover, 137pp
* Publisher: Yale University Press
* Pub. Date: March 2006

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