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The Best Writing on Mathematics 2013

by Roger Penrose Mircea Pitici

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more.In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

Ciclos del tiempo

by Roger Penrose

La revolucionaria y exitosa obra de Roger Penrose El camino a la realidad presentaba una guía completa y comprensible de las leyes que rigen el universo desde nuestro conocimiento actual. En Ciclos del tiempo, su libro más ambicioso, Penrose va mucho más allá: desarrolla una visión inédita de la cosmología y propone una respuesta inesperada a la pregunta: ¿Qué pasó antes del Big Bang?Las dos ideas clave que hay detrás de esta nueva visión son un penetrante análisis de la Segunda Ley de la termodinámica (que establece el principio de la entropía) y el estudio de la geometría de cono de luz del espacio-tiempo. Penrose logra combinar estos dos temas para demostrar que el destino último de nuestro universo en expansión y aceleración puede ser visto como el Big Bang de uno nuevo. Por el camino, nos explica muchos otros ingredientes básicos de esta idea y comenta varios modelos cosmológicos, tanto ortodoxos como heterodoxos, así como el papel fundamental y ubicuo de la radiación cósmica de microondas. Otra parte crucial de su exposición es la relativa a los inmensos agujeros negros detectados en los centros de las galaxias, y su eventual desaparición a través del misterioso proceso de evaporación de Hawking. Una obra fundamental para todos los amantes de la ciencia.

Cycles of Time

by Roger Penrose

From the best-selling author of The Emperor's New Mind and The Road to Reality, a groundbreaking book that provides new views on three of cosmology's most profound questions: What, if anything, came before the Big Bang? What is the source of order in our universe? What is its ultimate future?Current understanding of our universe dictates that all matter will eventually thin out to zero density, with huge black holes finally evaporating away into massless energy. Roger Penrose--one of the most innovative mathematicians of our time--turns around this predominant picture of the universe's "heat death," arguing how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the "Big Bang" of a new one.Along the way to this remarkable cosmological picture, Penrose sheds new light on basic principles that underlie the behavior of our universe, describing various standard and nonstandard cosmological models, the fundamental role of the cosmic microwave background, and the key status of black holes. Ideal for both the amateur astronomer and the advanced physicist--with plenty of exciting insights for each--Cycles of Time is certain to provoke and challenge.Intellectually thrilling and accessible, this is another essential guide to the universe from one of our preeminent thinkers.From the Hardcover edition.

The Emperor's New Mind

by Roger Penrose

Winner of the 1990 Science Book Prize arguing AGAINST artificial intelligence, and exploring the mystery of the mind and consciousness, Roger Penrose takes the reader on the most engaging and creative tour of modern physics, cosmology, mathematics and philosophy that has ever been written.

Naturaleza del espacio y del tiempo

by Roger Penrose Stephen Hawking

Einstein afirmaba que lo más incomprensible acerca del Universo es que es comprensible ¿estaba en lo cierto? ¿pueden la teoría cuántica de campos y la teoría de la relatividad general de Einstein, las dos teorías, más precisas y exitosas de toda la física, unirse en una única teoría cuántica de la gravedad? Aunque se ha avanzado mucho en esta búsqueda, Hawking y Penrose insisten en que es necesario llegar mucho más lejos. En La naturaleza del espacio y el tiempo , estos dos gigantes de la física entablan un debate fundamental sobre el origen del universo.Un libro escrito a cuatro manos, con un epílogo actualizado, en el que los autores resumen cómo los recientes acontecimientos han provocado que sus posturas difieran en cuestiones tan importantes como la geometría espacial del universo o la paradoja de la desaparición de información en los agujeros negros.

The Nature of Space and Time

by Roger Penrose Stephen Hawking

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor's New Mind and Shadows of the Mind)--disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.In a new afterword, the authors outline how recent developments have caused their positions to further diverge on a number of key issues, including the spatial geometry of the universe, inflationary versus cyclic theories of the cosmos, and the black-hole information-loss paradox. Though much progress has been made, Hawking and Penrose stress that physicists still have much farther to go in their quest for a quantum theory of gravity.

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