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.

Presents the author's thesis that consciousness, in its manifestation in the human quality of understanding, is doing something that mere computation cannot; and attempts to understand how such non-computational action might arise within scientifically comprehensive physical laws.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

"Chronological explanation of physics from early history through current studies geared to lay readers with limited mathematical training"--

USA TODAY BESTSELLER A Master Chief story and original full-length novel set in the Halo universe—based on the New York Times bestselling video game series! October 2559. It has been a year since the renegade artificial intelligence Cortana issued a galaxy-wide ultimatum, subjecting many worlds to martial law under the indomitable grip of her Forerunner weapons. Outside her view, the members of Blue Team—John-117, the Master Chief; Fred-104; Kelly-087; and Linda-058—are assigned from the UNSC Infinity to make a covert insertion onto the ravaged planet Reach. Their former home and training ground—and the site of humanity’s most cataclysmic military defeat near the end of the Covenant War—Reach still hides myriad secrets after all these years. Blue Team’s mission is to penetrate the rubble-filled depths of CASTLE Base and recover top-secret assets locked away in Dr. Catherine Halsey’s abandoned laboratory—assets which may prove to be humanity’s last hope against Cortana. But Reach has been invaded by a powerful and ruthless alien faction, who have their own reasons for being there. Establishing themselves as a vicious occupying force on the devastated planet, this enemy will soon transform Blue Team’s simple retrieval operation into a full-blown crisis. And with the fate of the galaxy hanging in the balance, mission failure is not an option…

One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the Fourth Dimension. Includes problems, puzzles, and 200 drawings. "Informative and mind-dazzling." — Martin Gardner.