The fascinating story of an ancient riddle and what it reveals about the nature of time and spaceThree millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains.
A mathematical guide to understanding why life can seem to be one big coincidence-and why the odds of just about everything are better than we would think
"This book provides an insightful synthesis of the historical and mental revolutions that created humanity's most useful symbols--mathematical expressions."--Stanislas Dehaene, author of "Reading in the Brain" "Mathematical symbols are much more than squiggles on paper--they serve as potent sources of insight into a wonderfully complex language. In this book, Joseph Mazur takes us on a fascinating journey into the origins of these symbols. You cannot ask for a better guide."--Mario Livio, astrophysicist and author of "Brilliant Blunders" "Joseph Mazur teaches us that the history of mathematical notation is the history of human civilization."--Kenneth A. Ribet, University of California, Berkeley "In this thoughtful, entertaining, and carefully researched book, Mazur lays out the development of the mathematical notations and symbols that we take for granted. He offers a fascinating look at the history of the conventions of writing mathematical ideas, and shows how important our choice of conventions has been for the growth of mathematical knowledge."--Emily R. Grosholz, author of "Representation and Productive Ambiguity in Mathematics and the Sciences" "Worldwide, mathematicians speak a common symbolic language. Mazur traces how symbols developed and gradually took hold, uniting arithmetic, algebra, and geometry to give us metaphors as powerful as those of poems. A fascinating history!"--Philip Holmes, coauthor of "Celestial Encounters" "A curiosity cabinet of mathematical gems, curated by Joseph Mazur's cosmopolitan good taste."--Siobhan Roberts, author of "Wind Wizard" ""Enlightening Symbols" explains the origins of symbols used in mathematics. But this fun book is so much more than this. Filled with interesting stories, captivating material, and delightful observations, it offers readers a better understanding of the nature of mathematics and a wonderful overview of mathematical history."--Dominic Klyve, Central Washington University "An enjoyable and informative tour of mathematics history, "Enlightening Symbols" describes how our modern system of notation led to the abstraction we work with today. This is an important and interesting story."--Anna Pierrehumbert, Trinity School
"What is time? This question has fascinated philosophers, mathematicians, and scientists for thousands of years. Why does time seem to speed up with age? What is its connection with memory, anticipation, and sleep cycles? Award-winning author and mathematician Joseph Mazur provides an engaging exploration of how the understanding of time has evolved throughout human history and offers a compelling new vision, submitting that time lives within us. Our cells, he notes, have a temporal awareness, guided by environmental cues in sync with patterns of social interaction. Readers learn that, as a consequence of time's personal nature, a forty-eight-hour journey on the Space Shuttle can feel shorter than a six-hour trip on the Soyuz capsule, that the Amondawa of the Amazon do not have ages, and that time speeds up with fever and slows down when we feel in danger. With a narrative punctuated by personal stories of time's effects on truck drivers, Olympic racers, prisoners, and clockmakers, Mazur's journey is filled with fascinating insights into how our technologies, our bodies, and our attitudes can change our perceptions. Ultimately, time reveals itself as something that rides on the rhythms of our minds. 'The Clock Mirage' presents an innovative perspective that will force us to rethink our relationship with time, and how best to use it"--Jacket
Mathematician Mazur traces the history of gambling from the earliest known archaeological evidence of dice-playing among Neolithic peoples to the first systematic mathematical games of change during the Renaissance, and explains the mathematics behind gambling--including the laws of probability, statistics, and betting against expectations. Photos.
A mathematical guide to understanding why life can seem to be one big
coincidence-and why the odds of just about everything are better than we would
think
