What do you see? Colour it in! In the 1970s, Professor Sir Roger Penrose discovered some amazing tiles. They could fill a vast surface to produce beautiful pentagonal patterns at every scale which never repeated. Altair Design is proud to present the world's first Penrose Tilings colouring book. Choose a design. Relax, and look without staring. Slowly, faces, animals, scenes and patterns will appear. Every aperiodic pattern in this pad perfectly overlays every other! Fire up your creativity and enhance your visual imagination!

Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This second volume of a two-volume series covers applications of the theory as well as experimental verifications. From tools to determine light travel times in curved space-time to laser ranging between earth and moon and between satellites, and impacts on the definition of time scales and clock comparison techniques, a variety of effects is discussed. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: J. Simon, A. Fienga: Victor Brumberg and the French school of analytical celestial mechanics T. Fukushima: Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy P. Teyssandier: New tools for determining the light travel time in static, spherically symmetric spacetimes beyond the order G2 J. Muller, L. Biskupek, F. Hofmann and E. Mai: Lunar laser ranging and relativity N. Wex: Testing relativistic celestial mechanics with radio pulsars I. Ciufolini et al.: Dragging of inertial frames, fundamental physics, and satellite laser ranging G. Petit, P. Wolf, P. Delva: Atomic time, clocks, and clock comparisons in relativistic spacetime: a review

This book centers around a dialogue between Roger Penrose and Emanuele Severino about one of most intriguing topics of our times, the comparison of artificial intelligence and natural intelligence, as well as its extension to the notions of human and machine consciousness. Additional insightful essays by Mauro D'Ariano, Federico Faggin, Ines Testoni, Giuseppe Vitiello and an introduction of Fabio Scardigli complete the book and illuminate different aspects of the debate. Although from completely different points of view, all the authors seem to converge on the idea that it is almost impossible to have real "intelligence" without a form of "consciousness". In fact, consciousness, often conceived as an enigmatic "mirror" of reality (but is it really a mirror?), is a phenomenon under intense investigation by science and technology, particularly in recent decades. Where does this phenomenon originate from (in humans, and perhaps also in animals)? Is it reproducible on some "device"? Do we have a theory of consciousness today? Will we arrive to build thinking or conscious machines, as machine learning, or cognitive computing, seem to promise? These questions and other related issues are discussed in the pages of this work, which provides stimulating reading to both specialists and general readers. The Chapter "Hard Problem and Free Will: An Information-Theoretical Approach" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, "The Road to Reality" carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

Death And Anti-Death, Volume 6: Thirty Years After Kurt Gdel (1906-1978)[Charles Tandy, Ph.D., Editor] [ISBN 978-1-934297-03-2] ------Volume 6, as indicated by the anthology's subtitle, is in honor of Kurt Gdel (1906-1978). The chapters do not necessarily mention him. The chapters (by professional philosophers and other professional scholars) are directed to issues related to death, life extension, and anti-death, broadly construed. Most of the contributions consist of scholarship unique to this volume. As was the case with all previous volumes in the Death And Anti-Death Series By Ria University Press, the anthology includes an Index as well as an Abstracts section that serves as an extended table of contents. (Volume 6 also includes a BRIEF COMMUNICATIONS section.) The ten chapters are entitled as follows: ------> 1. Life And Death Economics: A Dialogue by Giorgio Baruchello and Valerio Lintner (pages 33-52) ------> 2. Charles Hartshorne by Daniel A. Dombrowski (pages 53-78) ------> 3. Choosing Death in Cases of Anorexia Nervosa - Should We Ever Let People Die From Anorexia? PART II by Simona Giordano (pages 79-100) ------> 4. The Ethics Of Enhancement by Bill Grote and William Grey (pages 101-126) ------> 5. Cosmology And Theology by John Leslie (pages 127-156) ------> 6. Positive Logicality: The Development Of Normative Reason by J. R. Lucas (pages 157-222) ------> 7. The Basic Ideas Of Conformal Cyclic Cosmology by Roger Penrose (pages 223-242) ------> 8. Deconstructing Deathism: Personal Immortality As A Desirable Outcome by R. Michael Perry (pages 243-264) ------> 9. What Mary Knows: Actual Mentality, Possible Paradigms, Imperative Tasks by Charles Tandy (pages 265-284) ------> 10. The Future Of Scientific Simulations: From Artificial Life To Artificial Cosmogenesis by Clment Vidal (pages 285-318)

What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas--string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.

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 into a single quantum theory of gravity? Can quantum and cosmos ever be combined? In The Nature of Space and Time, two of the world's most famous physicists--Stephen Hawking (A Brief History of Time) and Roger Penrose (The Road to Reality)--debate these questions. The authors outline how their positions have further diverged 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 further to go in their quest for a quantum theory of gravity.

Nobel laureate Erwin Schroedinger's What is Life? is one of the great science classics of the twentieth century. It was written for the layman, but proved to be one of the spurs to the birth of molecular biology and the subsequent discovery of DNA. What is Life? appears here together with Mind and Matter, his essay investigating a relationship which has eluded and puzzled philosophers since the earliest times. Brought together with these two classics are Schroedinger's autobiographical sketches, which offer a fascinating account of his life as a background to his scientific writings.

For many decades, the proponents of `artificial intelligence' have maintained that computers will soon be able to do everything that a human can do. In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating tour through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine. Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.

Volume 1 introduces and systematically develops the calculus in a first detailed exposition of this technique which provides shortcuts for some very tedious calculations.

The concept of symmetry has widespread manifestations and many diverse applications--from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics--one of the greatest chapters in the intellectual history of humankind.

Since his first appearance over sixty years ago, Mr Tompkins has become known and loved by many thousands of readers as the bank clerk whose fantastic dreams and adventures lead him into a world inside the atom. George Gamow's classic provides a delightful explanation of the central concepts in modern physics, from atomic structure to relativity, and quantum theory to fusion and fission. Roger Penrose's foreword introduces Mr Tompkins to a new generation of readers, and reviews his adventures in light of recent developments in physics.

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

Spinor and Twistor Methods in Space-Time Geometry introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.

Roger Penrose's views on the large-scale physics of the Universe, the small-scale world of quantum physics and the physics of the mind are controversial and widely discussed. This book is a fascinating and accessible summary of Roger Penrose's current thinking on those areas of physics in which he feels there are major unresolved problems. It is also a stimulating introduction to the radically new concepts that he believes will be fruitful in understanding the workings of the brain and the nature of the human mind.

What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas--string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.

This book gets to the heart of science by asking a fundamental question about its essence: what is the true nature of space and time? Both defy modern physics, and scientists find themselves continually searching for answers. This unique volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology, to provide fresh insights into the deep structure of space and time. In an attempt to understand the question, subjects ranging from dark matter to the philosophical and theological implications of spacetime are covered, ensuring that the issue is thoroughly explored. Interesting and thought-provoking answers provide a well-rounded read.

This groundbreaking book presents a new perspective on three of cosmology's essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us?
Penrose shows how the expected fate of our ever-accelerating and expanding universe--heat death or ultimate entropy--can actually be reinterpreted as the conditions that will begin a new "Big Bang." He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, "Cycles of Time" is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.

Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way—as a highbrow comic book!

A New York Times bestseller when it appeared in 1989, Roger Penrose's The Emperor's New Mind was universally hailed as a marvelous survey of modern physics as well as a brilliant reflection on the human mind, offering a new perspective on the scientific landscape and a visionary glimpse of the possible future of science. Now, in Shadows of the Mind, Penrose offers another exhilarating look at modern science as he mounts an even more powerful attack on artificial intelligence. But perhaps more important, in this volume he points the way to a new science, one that may eventually explain the physical basis of the human mind.

Penrose contends that some aspects of the human mind lie beyond computation. This is not a religious argument (that the mind is something other than physical) nor is it based on the brain's vast complexity (the weather is immensely complex, says Penrose, but it is still a computable thing, at least in theory). Instead, he provides powerful arguments to support his conclusion that there is something in the conscious activity of the brain that transcends computation--and will find no explanation in terms of present-day science. To illuminate what he believes this "something" might be, and to suggest where a new physics must proceed so that we may understand it, Penrose cuts a wide swathe through modern science, providing penetrating looks at everything from Turing machines (computers programmed for artificial intelligence) to the implications of Godel's theorem maintaining that conscious thinking must indeed involve ingredients that cannot adequately be simulated by mere computation. Of particular interest is Penrose's extensive examination of quantum mechanics, which introduces some new ideas that differ markedly from those advanced in The Emperor's New Mind, especially concerning the mysterious interface where classical and quantum physics meet. But perhaps the most interesting wrinkle in Shadows of the Mind is Penrose's excursion into microbiology, where he examines cytoskeletons and microtubules, minute substructures lying deep within the brain's neurons. (He argues that microtubules--not neurons--may indeed be the basic units of the brain, which, if nothing else, would dramatically increase the brain's computational power.)

For physics to accommodate something that is as foreign to our current physical picture as the phenomenon of consciousness, we must expect a profound change--one that alters the very underpinnings of our philosophical viewpoint as to the nature of reality. Shadows of the Mind provides an illuminating look at where these changes may take place and what our future understanding of the world may be.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Developing ideas sketched in the first volume, twistor theory is now applied to genuine issues of physics, and there are the beginnings of twistor diagram theory (an analogue of Feynman Diagrams). This collection includes joint papers with Stephen Hawking, and uncovers certain properties of black holes. The idea of cosmic censorship is also first proposed. Along completely different lines, the first methods of aperiodic tiling for the Euclidean plane that come to be known as Penrose tiles are described. This volume also contains Penrose's three prize-winning essays for the Gravity Foundation (two second places with both Ezra Newman and Steven Hawking, and a solo first place for 'The Non-linear graviton').

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Many important realizations concerning twistor theory occurred during the short period of this third volume, providing a new perspective on the way that mathematical features of the complex geometry of twistor theory relate to actual physical fields. Following on from the nonlinear graviton construction, a twistor construction was found for (anti-)self-dual electromagnetism allowing the general (anti-)self-dual Yang-Mills field to be obtained. It became clear that some features of twistor contour integrals could be understood in terms of holomorphic sheaf cohomology. During this period, the Oxford research group founded the informal publication, Twistor Newsletter. This volume also contains the influential Weyl curvature hypothesis and new forms of Penrose tiles.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Among the new developments that occurred during this period was the introduction of a particular notion of 'quasi-local mass-momentum and angular momentum', the topic of Penrose's Royal Society paper. Many encouraging results were initially obtained but, later, difficulties began to emerge and remain today. Also, an extensive paper (with Eastwood and Wells) gives a thorough account of the relation between twistor cohomology and massless fields. This volume witnesses Penrose's increasing conviction that the puzzling issue of quantum measurement could only be resolved by the appropriate unification of quantum mechanics with general relativity, where that union must involve an actual change in the rules of quantum mechanics as well as in space-time structure. Penrose's first incursions into a possible relation between consciousness and quantum state reduction are also covered here.