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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.
A detailed description of what the fourth dimension would be like.
Space, Time and Einstein by J. B. KennedyThis book is a threefold invitation to the philosophy of space andtime. It introduces - gently and simply - the new, revolutionary ideasof Einstein. It introduces the concepts and arguments of philosophers,both ancient and modern, which have proved of lasting value. Finally,it introduces the most recent discoveries and the debates raging now,in philosophy and physics, and points out how future developmentsmay unfold.The text does aim to teach one skill. Careful thinking is at the coreof our conception of philosophy. Now that many nations havereorganized themselves as democracies, which depend so much onreasoned debate and persuasion, careful thinking has become afoundation of our social and political lives as well. But clear thinkingis an art: it requires patience, practice and cultivation. This text doesnot teach or use formal logic, but it pays great attention to the careful analysis and interpretation of ideas. It slows down to dissect moment-ous claims and seeks out the hidden assumptions underlying the greatarguments of the past. It aims throughout to show how the analysis ofarguments deepens our appreciation of philosophy, and points theway towards future progress.This is a conservative text in the sense that it covers the standardtopics, outlines mainstream debates and introduces the views of someleading contemporary philosophers. Unusually, from the outset, itemphasizes the controversy between Einstein and Lorentz over theinterpretation of relativity (following essays by J. S. Bell and the moremathematical text by D. Bohm), which is now again a hot topic ofdebate. For accessibility, I have edited the quotations to conform to auniform terminology, ruthlessly preferred concrete over technicalterms (e.g. "rulers and clocks" rather than "reference frames") andpostponed all spacetime diagrams to an appendix. In general, I havefavoured bold, plausible claims and used the guide for further readingin Appendix E to point toward more advanced and nuanced litera-ture. This approach has worked well in courses I have taught atStanford University and the University of Notre Dame in the US andthe University of Manchester in the UK. There was no room forchapters on debates over space and time in the feminist philosophy ofscience and in art history, but some reference.
The Internal Temporal Element of the Nervous System, Considered as an Evaluating Factor in Man's Active Behavior in Health or Mental Diseases.
Flatland, a place of two dimensions peopled by a hierarchy of geometrical forms, is the home of narrator A. Square, who takes a tour of his bizarre homeland. This tour provides a hilarious satire on Victorian society with questions about the nature of the universe.
The Einstein's Theory of Relativity has compelled the revision of the time concept as used in classical physics. One result of this has been to introduce the notion of curved time.These two ideas, of curved time and higher space, by their very nature are bound to profoundly modify human thought. They loosen the bonds within which advancing knowledge has increasingly labored, they lighten the dark abysses of consciousness, they reconcile the discoveries of Western workers with the inspirations of Eastern dreamers; but best of all, they open vistas, they offer "glimpses that may make us less forlorn."
Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
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.