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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.
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.
A detailed description of what the fourth dimension would be like.
Einstein shocked the world by revealing that time can be different for different observers. This book offers a possible explanation of why it is so. It offers a never-attempted-before approach to understand the secret of time. As we all know, there is an intimate relationship between time and age of objects. But what is this relationship? The author dives deep into the possible relationships between time and age of objects- animate or inanimate- and, in turn, emerges with a novel concept of time- time is a measurement of age. The book proposes that time is acquired by age, not required for it; and thus, time is an acquired property of objects. The author also proposes that just as length, width and height are the measurements of physical extensions of objects (their three spatial dimensions) and not any independent entities; time too, being the measurement of their age, is not independent of objects. In this sense, time seems to be the fourth dimension of objects instead of space. The book attempts to justify its hypothesis by testing its compatibility with Theory of Relativity. Also discussed is the meaning of the so called passage of time and the arrow of time on the basis of the model of time proposed here. The meaning of the much debated concept of time-travel is thoroughly discussed here and it is proposed that this concept, in the sense that we usually take, is a myth. Even if you can manage to reach your future by overcoming all technological limitations (as we all know, theory of relativity allows it), all your friends will be there with you, witnessing the same future. The only difference will be- your clocks will not agree with those of your friends.
A book that combines science fiction, satire of Victorian society and politics, proving to be a great literary allegory. The illustrated world is populated by Squares, Triangles, Circles and Lines living in a two-dimensional universe, all strictly divided by class and gender. The narrator is precisely one of them, a Square. He will guide readers into his world by explaining the brilliant implications of two-dimensional life. Later, however, he will tell of his discovery of other, more geometrically complex universes such as the three-dimensional one, represented by his encounter with a Sphere. Thus begins a true journey of knowledge, which will lead him to that which can hardly be conceived by the mind. A unique book that has become a cult object by the scientific community and beyond.
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.
From the infinity of space to the eternity of time to the possibility of the afterlife, both science and religion have attempted to answer a number of existential quandaries about our place in the universe. Yet these perplexing puzzles cannot be solved by anything provided in our limited three dimensional perspective. This provocative book by atomic physicist Dr. Nasr Saad proposes that a fourth dimension of existence can provide the perspective and comprehension necessary to arrive at logical answers to the unanswered questions of our existence. The Fourth Dimension of Existence draws on Saad's unique education. He is schooled in both philosophy and theology alongside his rigorous training in atomic physics. “I was sure that rational answers could only come from a perfect synthesis of the methodologies of the three major disciplines of the human mind: science, philosophy, and religion,” says Saad. “Most of the times they are in open conflict with one another in their findings and their conclusions; however, this situation should not be the norm all the time; these disciplines are the product of the human reason and the human reason is one.” Saad feels that a thorough fusion of the methodologies of science, philosophy, and religion could yield logical answers to the questions humans have been asking themselves since the dawn of human consciousness. The author admits that the fourth dimension has a robust history of representation in science fiction. He mentions flatland and hyperspace among other fictional fourth dimensions to illustrate the rich and imaginative preoccupations of the human mind. He even explains the curved space-time fourth dimension that haunts the minds of “science fiction mathematicians.” The fourth dimension that preoccupies the author is not the fantastical sci-fi scenario of the popular imagination. Rather, it is an existential dimension that would provide us with the necessary distance to understand our own world and its heretofore unsolvable mysteries. He feels the search for such a dimension is not a pipe dream but can be carried out and executed by rational means. At the same time, we need to realize the fourth dimension would exist on principles completely unrelated to our own three-dimensional world. “It will provide a scientific explanation for the strong link that should exist between matter and spirit and between this life and our existence,” says Saad. “It will make us realize in a logical and powerful way how and why our life is short but our existence is not.” Despite these intriguing scenarios, Saad feels there remains a fourth existential dimension that can bring a rational explanation to all our perplexing questions. His book is a guide to this possible reality and the various ways it could be ascertained.
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.