A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the authors' approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach.Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.This expanded edition stresses and illustrates computer algorithms with many new worked-out examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations.

Timekeeping is an essential activity in the modern world and we take it for granted that our lives our shaped by the hours of the day. Yet what seems so ordinary today is actually the extraordinary outcome of centuries of technical innovation and circulation of ideas about time.
Shaping the Day is a pathbreaking study of the practice of timekeeping in England and Wales between 1300 and 1800. Drawing on many unique historical sources, ranging from personal diaries to housekeeping manuals, Paul Glennie and Nigel Thrift illustrate how a particular kind of common sense about time came into being, and how it developed during this period.
Many remarkable figures make their appearance, ranging from the well-known, such as Edmund Halley, Samuel Pepys, and John Harrison, who solved the problem of longitude, to less familiar characters, including sailors, gamblers, and burglars.
Overturning many common perceptions of the past-for example, that clock time and the industrial revolution were intimately related-this unique historical study engages all readers interested in how 'telling the time' has come to dominate our way of life.

Responding to the upsurge in interest in "the Maya prophecies," Prof. Mark Van Stone has spent the last several years researching What the Ancient Maya Actually Said about 2012. The result is a full-color, 170-page book, *2012 - Science and Prophecy of the Ancient Maya*, based entirely on science, archaeology and Precolumbian art. Starting as a physicist, working in the University of New Hampshire's Space Science Center, Van Stone pursued a career in art, and eventually earned his Ph.D. in Maya Hieroglyphs under the legendary Linda Schele and David Stuart. Dr. Van Stone is also co-author, with Michael Coe, of *Reading the Maya Glyphs* (2001), the leading book on deciphering Maya inscriptions.

Clock synchronisation is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronisation needed over satellite-to-ground and satellite-to-satellite distances requires the use of general relativistic concepts. The role of geometrical optics and antenna phase centre approximations are discussed in high accuracy work. The clock synchronisation problem is explored from a general relativistic point of view, with emphasis on the local measurement process and the use of the tetrad formalism as the correct model of relativistic measurements. The treatment makes use of J. L. Synge's world function of space-time as a basic co-ordinate independent geometric concept. A metric is used for space-time in the vicinity of the Earth, where co-ordinate time is proper time on the geoid. The problem of satellite clock syntonisation is analysed by numerically integrating the geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit (GEO), and highly elliptical orbit (HEO) satellites. Proper time minus co-ordinate time is computed for satellites in these orbital regimes. The frequency shift as a function of time is computed for a signal observed on the Earth's geoid from a LEO, GEO, and HEO satellite. Finally, the problem of geolocation in curved space-time is briefly explored using the world function formalism.

The system of numbering the years A.D. (Anni Domini, Years of the Lord) originated with Dionysius Exiguus. Dionysius drafted a 95-year table of dates for Easter beginning with the year 532 A.D. Why Dionysius chose the year that he did to number as '1' has been a source of controversy and speculation for almost 1500 years. According to the Gospel of Luke (3.1; 3.23), Jesus was baptized in the 15th year of the emperor Tiberius and was about 30 years old at the time. The 15th year of Tiberius was A.D. 29. If Jesus was 30 years old in A.D. 29, then he was born in the year that we call 2 B.C. Most ancient authorities dated the Nativity accordingly.
Alden Mosshammer provides the first comprehensive study of early Christian methods for calculating the date of Easter to have appeared in English in more than one hundred years. He offers an entirely new history of those methods, both Latin and Greek, from the earliest such calculations in the late second century until the emergence of the Byzantine era in the seventh century. From this history, Mosshammer draws the fresh hypothesis that Dionysius did not calculate or otherwise invent a new date for the birth of Jesus, instead adopting a date that was already well established in the Greek church. Mosshammer offers compelling new conclusions on the origins of the Christian era, drawing upon evidence found in the fragments of Julius Africanus, of Panodorus of Alexandria, and in the traditions of the Armenian church.

This fascinating work begins with a scientific appraisal of time and its relationship with 3D space. It explains in clear, understandable language, the complex theories of such famous men as Newton, Einstein, and Stephen Hawking. Is time infinite, or does it have a beginning and an end? Do Black Holes and White Vortices distort time, or penetrate it? The authors also analyse and evaluate puzzling, well documented reports of time travel and reincarnation, and strange cases of deja vu. Can time travel account for such anachronistic discoveries as a 20th century sparkplug found encased among fossils half a million years old? Finally, the authors bring all the unsolved time-related mysteries together in a unified field theory that suggests an awesome answer to the mysteries of time-travel and reincarnation.

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments (which support a more 'constructive' approach to relativistic effects in Einstein's terminology), after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity. Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics.

The smooth functioning of an ordered society depends on the possession of a means of regularising its activities over time. That means is a calendar, and its regularity is a function of how well it models the more or less regular movements of the celestial bodies - of the moon, the sun or the stars. Greek and Roman Calendars examines the ancient calendar as just such a time-piece, whose elements are readily described in astronomical and mathematical terms. The story of these calendars is one of a continuous struggle to maintain a correspondence with the regularity of the seasons and the sun, despite the fact that the calendars were usually based on the irregular moon. But on another, more human level, Greek and Roman Calendars steps beyond the merely mathematical and studies the calendar as a social instrument, which people used to organise their activities. It sets the calendars of the Greeks and Romans on a stage occupied by real people, who developed and lived with these time-pieces for a variety of purposes - agricultural, religious, political and economic. This is also a story of intersecting cultures, of Greeks with Greeks, of Greeks with Persians and Egyptians, and of Greeks with Romans, in which various calendaric traditions clashed or compromised.

This volume provides a balanced set of reviews which introduce the central topics in the philosophy of time. This is the first introductory anthology on the subject to appear for many years; the contributors are distinguished, and two of the essays are specially written for this collection. In their introduction, the editors summarise the background to the debate, and show the relevance of issues in the philosophy of time for other branches of philosophy and for science.

Why should there be anything at all? Why, in particular, should a material world exist? Bede Rundle advances clear, non-technical answers to these perplexing questions. If, as the theist maintains, God is a being who cannot but exist, his existence explains why there is something rather than nothing. However, this can also be explained on the basis of a weaker claim. Not that there is some particular being that has to be, but simply that there has to be something or other. Rundle proffers arguments for thinking that that is indeed how the question is to be put to rest. Traditionally, the existence of the physical universe is held to depend on God, but the theist faces a major difficulty in making clear how a being outside space and time, as God is customarily conceived to be, could stand in an intelligible relation to the world, whether as its creator or as the author of events within it. Rundle argues that a creator of physical reality is not required, since there is no alternative to its existence. There has to be something, and a physical universe is the only real possibility. He supports this claim by eliminating rival contenders; he dismisses the supernatural, and argues that, while other forms of being, notably the abstract and the mental, are not reducible to the physical, they presuppose its existence. The question whether ultimate explanations can ever be given is forever in the background, and the book concludes with an investigation of this issue and of the possibility that the universe could have existed for an infinite time. Other topics discussed include causality, space, verifiability, essence, existence, necessity, spirit, fine tuning, and laws of Nature. Why There Is Something Rather Than Nothing offers an explanation of fundamental facts of existence in purely philosophical terms, without appeal either to theology or cosmology. It will provoke and intrigue anyone who wonders about these questions.

The subject of 'time' is currently experiencing a revival in the most diverse areas of academic discourse. Contemporary time theory attempts to relate theoretical time concepts both to one another and to everyday experience of time. This book deals with the philosopher Martin Heidegger and the chemo-physicist Iyla Prigogine (Nobel Prize for Chemistry 1977), two prominent advocates of pioneering time concepts in the 20th century. The author not only provides a transdisciplinary introduction to modern debate on the problem of time, but suggests how the basic tendencies in this debate might be pragmatically interlinked with each other.

Questions of Time and Tense brings together new essays on a major focus of debate in contemporary metaphysics: does time really pass, or is our ordinary experience of time as consisting of past, present, and future an illusion? The international line-up of contributors broaden this debate by demonstrating the importance of questions about the nature of time for philosophical issues in ethics, aesthetics, psychology, science, religion, and language.

God and Time is a collection of previously unpublished essays written by leading philosophers about God's relation to time. The essays have been selected to represent current debates written between those who believe God to be atemporal and those who do not. The essays highlight issues such as how the nature of time is relevant to whether God is temporal and how God's other attributes are compatible with his mode of temporal being. By focusing on the metaphysical aspects of time and temporal existence, God and Time will make a unique contribution to the current resurgence of interest in philosophical theology within the analytic tradition.

In this text, science writer Barry Parker takes on one of the most fascinating and fantastical aspects of modern quantum theory - time travel. From the stuff of fiction to Einstein's theory of relativity and Hawking's view of the universe, time travel has captured modern man's excitement and been as much talked about as space travel.

This book traces the development of the Jewish calendar from its origin until it reached, in the tenth century CE, its present form. Drawing on a wide range of sources - literary, documentary and epigraphic; Jewish, Graeco-Roman and Christian - this is the first comprehensive book to have been written on this subject. The unification of the calendar is seen as an element in the unification of Jewish identity.

This book studies the transition from local to national timekeeping, a process that led to Standard Time--the world-wide system of timekeeping by which we all live. Prior to the railroads' adoption of Standard Railway Time in 1883, timekeeping was entirely a local matter, and America lacked any uniform system to coordinate times and public activities. For example, in the middle of the nineteenth century, Boston had three authoritative times, which differed by seconds and minutes.
The story begins in the 1830s with the building of the first railroads. Since railway safety depended upon maintaining the temporal separation of trains through precise timing, railroads were the first to establish time standards to govern their operations. The railroads' switch to five time standards indexed to the Greenwich meridian inaugurated the modern era of public timekeeping and led directly to cities adopting Greenwich-indexed civil time zones.
Central to the story are those college and university astronomers who, starting in the 1850s, sold time signals to nearby cities and railroads. From the start, they competed with other entrepreneurs trying to make money by selling time. Decades of negotiations, government lobbying, and battles over customers followed, all in the name of "public service." Improvements by a host of clockmakers, civil and electrical engineers, telegraph and railway technicians, and instrument makers finally changed the market for accurate time. Public timekeeping became the realm of business investors.
Despite the efforts of astronomers and various of their Congressional supporters, who argued for the necessity of a national system of time authorized by the federal government, the railroads' success with their own system blocked legislation for a national system of time until the First World War. By then, a single source for correct time dominated the public's timekeeping: the U.S. Naval Observatory's noon signal.
In this first comprehensive, scholarly history of timekeeping in America, the author has drawn upon a rich, untapped archival record, municipal and legislative documents, newspapers, and science and engineering journals to challenge several myths that have grown up around the subject.

Chronology is the factual basis for contextualising archaeology. This collection of papers aims to integrate local chronogical schemes with more comprehensive and general "master" chronologies. The studies focus on Germanic or Germanised populations during and after the Roman Empire's fall in the West: the rich Germanic archaeological sites provide a yardstick for other areas. The authors also play close attention to terminology with definitions of major periods, sub-periods and artefact-types and to the relationship between typology and computerised quantitive and statistical techniques. The papers, all in English, cover North-West Europe, Denmark and Britain.

With the advent of the new millennium, the notion of the future, and of time in general, has taken on greater significance in postmodern thought. Although the equally pervasive and abstract concept of space has generated a vast body of disciplines, time, and the related idea of "becoming" (transforming, mutating, and metamorphosing) have until now received little theoretical attention. This volume explores the ontological, epistemic, and political implications of rethinking time as a dynamic and irreversible force. Drawing on ideas from the natural sciences, as well as from literature, philosophy, politics, and cultural analyses, its authors seek to stimulate further research in both the sciences and the humanities which highlights the temporal foundations of matter and culture.The first section of the volume, "The Becoming of the World," provides a broad introduction to the concepts of time. The second section, "Knowing and Doing Otherwise," addresses the forces within cultural and intellectual practices which produce various becomings and new futures. It also analyzes how alternative models of subjectivity and corporeality may be generated through different conceptions of time. "Global Futures," the third section, considers the possibilities for the social, political, and cultural transformation of individuals and nations.

IN Time:A Traveller's Guide. CLifford A. Pickover takes readers to the forefront of science as he illuminates the most mysterious phenomenon in the universe - time itself. Is time travel possible? Is time real? Does it flow in one direction only? Does it have a beginning or an end? What is eternity? These are questions that Pickover tackles in this stimulating blend of Chopin, philosophy, Einstein and modern physics, spiced with diverting side-trips to such topics as the history of clocks, the nature of free will and the reason that gold glitters. By the time we finish this book, we understand such seemingly arcane concepts as space time diagrams, light cones, cosmic moment lines, transcendent infinite speeds, Lorentz transformations, superluminal and ultra-luminal motions, closed timelike curves, and Tipler cylinders. And most important, we will understand that time travel need not be confined to myth, science fiction, Hollywood fantasies, or scientific speculation. Time travel, we will realise, is possible.