Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hiddenwithin one of the classic works of modern literature.Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G�del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, informationtheory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literallyunimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books.Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but alsoexposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.

    The Great Ideas of Classical Physics 2. Describing MotionA Break from Aristotle 3. Describing Ever More Complex Motion 4. Astronomy as a Bridge to Modern Physics 5. Isaac NewtonThe Dawn of Classical Physics 6. Newton QuantifiedForce and Acceleration 7. Newton and the Connections to Astronomy 8. Universal Gravitation 9. Newton's Third Law 10. Conservation of Momentum 11. Beyond NewtonWork and Energy 12. Power and the Newtonian Synthesis 13. Further DevelopmentsStatic Electricity 14. Electricity, Magnetism, and Force Fields 15. Electrical Currents and Voltage 16. The Origin of Electric and Magnetic Fields 17. Unification IMaxwell's Equations 18. Unification IIElectromagnetism and Light 19. Vibrations and Waves 20. Sound Waves and Light Waves 21. The Atomic Hypothesis 22. Energy in SystemsHeat and Thermodynamics 23. Heat and the Second Law of Thermodynamics 24. The Grand Picture of Classical Physics

    Gigabytes, exabytes (that’s one quintillion bytes) of data are sitting on servers across the world. So how can we start to access this explosion of information, this “big data,” and what can it tell us?   Erez Aiden and Jean-Baptiste Michel are two young scientists at Harvard who started to ask those questions. They teamed up with Google to create the Ngram Viewer, a Web-based tool that can chart words throughout the massive Google Books archive, sifting through billions of words to find fascinating cultural trends. On the day that the Ngram Viewer debuted in 2010, more than one million queries were run through it.   On the front lines of Big Data, Aiden and Michel realized that this big dataset—the Google Books archive that contains remarkable information on the human experience—had huge implications for looking at our shared human history. The tool they developed to delve into the data has enabled researchers to track how our language has evolved over time, how art has been censored, how fame can grow and fade, how nations trend toward war. How we remember and how we forget. And ultimately, how Big Data is changing the game for the sciences, humanities, politics, business, and our culture.

    It emphasizes forms suitable for students and researchers whose interest lies in solving equations rather than in general theory. Solutions to odd-numbered problems appear at the end. 1957 edition.

    Half a century later, only robots have been to the Red Planet and our astronauts rarely venture beyond Earth orbit.Now Mars is back With everyone from Elon Musk to Ridley Scott and Donald Trump talking about it, interplanetary exploration is back on the agenda and Mars is once again the prime destination for future human expansion and colonisation. In Destination Mars, astrophysicist and science writer Andrew May traces the history of our fascination with the Red Planet and explores the science upon which a crewed mission would be based, from assembling a spacecraft in Earth orbit to surviving solar storms. With expert insight, he analyses the new space race and assesses what the future holds for human life on Mars.

    

    Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.

    The "Theory of Everything" that appears to be emerging includes everything but us: the feelings, meanings, consciousness, and purposes that make us (and many of our animal cousins) what we are. These most immediate and incontrovertible phenomena are left unexplained by the natural sciences because they lack the physical properties—such as mass, momentum, charge, and location—that are assumed to be necessary for something to have physical consequences in the world. This is an unacceptable omission. We need a "theory of everything" that does not leave it absurd that we exist.Incomplete Nature begins by accepting what other theories try to deny: that, although mental contents do indeed lack these material-energetic properties, they are still entirely products of physical processes and have an unprecedented kind of causal power that is unlike anything that physics and chemistry alone have so far explained. Paradoxically, it is the intrinsic incompleteness of these semiotic and teleological phenomena that is the source of their unique form of physical influence in the world. Incomplete Nature meticulously traces the emergence of this special causal capacity from simple thermodynamics to self-organizing dynamics to living and mental dynamics, and it demonstrates how specific absences (or constraints) play the critical causal role in the organization of physical processes that generate these properties.The book's radically challenging conclusion is that we are made of these specific absenses—such stuff as dreams are made on—and that what is not immediately present can be as physically potent as that which is. It offers a figure/background shift that shows how even meanings and values can be understood as legitimate components of the physical world.

    Theory and practice in the design of data graphics, 250 illustrations of the best (and a few of the worst) statistical graphics, with detailed analysis of how to display data for precise, effective, quick analysis. Design of the high-resolution displays, small multiples. Editing and improving graphics. The data-ink ratio. Time-series, relational graphics, data maps, multivariate designs. Detection of graphical deception: design variation vs. data variation. Sources of deception. Aesthetics and data graphical displays. This is the second edition of The Visual Display of Quantitative Information. Recently published, this new edition provides excellent color reproductions of the many graphics of William Playfair, adds color to other images, and includes all the changes and corrections accumulated during 17 printings of the first edition.

    In this richly illustrated book, accessible examples are used to show how information theory can be understood in terms of everyday games like '20 Questions', and the simple MatLab programs provided give hands-on experience of information theory in action. Written in a tutorial style, with a comprehensive glossary, this text represents an ideal primer for novices who wish to become familiar with the basic principles of information theory.Download chapter 1 from http://jim-stone.staff.shef.ac.uk/Boo...

    Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text.Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.

    

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