Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    When famed archaeologist Arthur Evans unearthed the ruins of a sophisticated Bronze Age civilization that flowered on Crete 1,000 years before Greece's Classical Age, he discovered a cache of ancient tablets, Europe's earliest written records. For half a century, the meaning of the inscriptions, and even the language in which they were written, would remain a mystery. Award-winning New York Times journalist Margalit Fox's riveting real-life intellectual detective story travels from the Bronze Age Aegean--the era of Odysseus, Agamemnon, and Helen--to the turn of the 20th century and the work of charismatic English archeologist Arthur Evans, to the colorful personal stories of the decipherers. These include Michael Ventris, the brilliant amateur who deciphered the script but met with a sudden, mysterious death that may have been a direct consequence of the decipherment; and Alice Kober, the unsung heroine of the story whose painstaking work allowed Ventris to crack the code.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Through most of its long history, Greece was poor. But in the classical era, Greece was densely populated and highly urbanized. Many surprisingly healthy Greeks lived in remarkably big houses and worked for high wages at specialized occupations. Middle-class spending drove sustained economic growth. Classical wealth produced a stunning cultural efflorescence lasting hundreds of years.Why did Greece reach such heights in the classical period--and why only then? And how, after "the Greek miracle" had endured for centuries, did the Macedonians defeat the Greeks, seemingly bringing an end to their glory? Drawing on a massive body of newly available data and employing novel approaches to evidence, Josiah Ober offers a major new history of classical Greece and an unprecedented account of its rise and fall.Ober argues that Greece's rise was no miracle but rather the result of political breakthroughs and economic development. The extraordinary emergence of citizen-centered city-states transformed Greece into a society that defeated the mighty Persian Empire. Yet Philip and Alexander of Macedon were able to beat the Greeks in the Battle of Chaeronea in 338 BCE, a victory enabled by the Macedonians' appropriation of Greek innovations. After Alexander's death, battle-hardened warlords fought ruthlessly over the remnants of his empire. But Greek cities remained populous and wealthy, their economy and culture surviving to be passed on to the Romans--and to us.A compelling narrative filled with uncanny modern parallels, this is a book for anyone interested in how great civilizations are born and die.This book is based on evidence available on a new interactive website. To learn more, please visit http://polis.stanford.edu/

    (The also-rans that year included Tom Wolfe, Verlyn Klinkenborg, and Oliver Sacks.) Hayes's work in this genre has also appeared in such anthologies as The Best American Magazine Writing, The Best American Science and Nature Writing, and The Norton Reader. Here he offers us a selection of his most memorable and accessible pieces--including "Clock of Ages"--embellishing them with an overall, scene-setting preface, reconfigured illustrations, and a refreshingly self-critical "Afterthoughts" section appended to each essay.

    In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    

    120-190 CE), the satirist from Samosata on the Euphrates, started as an apprentice sculptor, turned to rhetoric and visited Italy and Gaul as a successful travelling lecturer, before settling in Athens and developing his original brand of satire. Late in life he fell on hard times and accepted an official post in Egypt.Although notable for the Attic purity and elegance of his Greek and his literary versatility, Lucian is chiefly famed for the lively, cynical wit of the humorous dialogues in which he satirises human folly, superstition and hypocrisy. His aim was to amuse rather than to instruct. Among his best works are "A True Story" (the tallest of tall stories about a voyage to the moon), "Dialogues of the Gods" (a 'reductio ad absurdum' of traditional mythology), "Dialogues of the Dead" (on the vanity of human wishes), "Philosophies for Sale" (great philosophers of the past are auctioned off as slaves), "The Fisherman" (the degeneracy of modern philosophers), "The Carousal" or "Symposium" (philosophers misbehave at a party), "Timon" (the problems of being rich), "Twice Accused" (Lucian's defence of his literary career) and (if by Lucian) "The Ass" (the amusing adventures of a man who is turned into an ass).The Loeb Classical Library edition of Lucian is in eight volumes.

    We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

    The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.About the Author:Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.

    Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    Taken in by a goatherd and a shepherd respectively, and raised near the town of Mytilene, they grow to maturity unaware of one another's existence - until the mischievous god of love, Eros, creates in them a sudden overpowering desire for one another. A masterpiece among early Greek romances, attracting both high praise and moral disapproval, this work has proved an enduringly fertile source of inspiration for musicians, writers and artists from Henry Fielding to Jean-Baptiste-Camille Corot and Maurice Ravel. Longus transforms familiar themes from the romance genre - including pirates, dreams, and the supernatural - into a virtuoso love story that is rich in insight, humorous and ironical in its treatment of human sexual experience.

    How To is a guide to the third kind of approach. It's full of highly impractical advice for everything from landing a plane to digging a hole.Bestselling author and cartoonist Randall Munroe explains how to predict the weather by analyzing the pixels of your Facebook photos. He teaches you how to tell if you're a baby boomer or a 90's kid by measuring the radioactivity of your teeth. He offers tips for taking a selfie with a telescope, crossing a river by boiling it, and powering your house by destroying the fabric of space-time. And if you want to get rid of the book once you're done with it, he walks you through your options for proper disposal, including dissolving it in the ocean, converting it to a vapor, using tectonic plates to subduct it into the Earth's mantle, or launching it into the Sun.By exploring the most complicated ways to do simple tasks, Munroe doesn't just make things difficult for himself and his readers. As he did so brilliantly in What If?, Munroe invites us to explore the most absurd reaches of the possible. Full of clever infographics and amusing illustrations, How To is a delightfully mind-bending way to better understand the science and technology underlying the things we do every day.