Summary Of Joseph Mazur S The Motion Paradox

Please note: This is a companion version & not the original book. Sample Book Insights: #1 Zeno’s paradoxes are a series of arguments that contradict common sense and have been misunderstood for more than two and a half millennia. They raise a fundamental question about the universe: Are time and space continuous like an unbroken line, or do they come in discrete units, like a string of beads. #2 Zeno’s paradoxes were absurd, and many thought so. They were considered embarrassments to mathematicians’ investigations of infinity and the continuum, and the Greeks abandoned such investigations. #3 The paradox of the dichotomy is a demonstration that our understanding of motion is intricately tangled between the discrete and continuous impressions of time and space. We measure time as a duration and think of motion as continuous. #4 Zeno of Elea, a philosopher who came to Athens from Croton in southern Italy, was reading from his famous book on philosophy. He argued that if a thing can be divided, its divided parts can also be divided and such divisions can continue indefinitely. From this, he concluded that change is not possible.

Traces the epic history of Greek philosopher Zeno's yet-unsolved paradox of motion, citing the contributions of top minds to the scientific community's understanding of the elusive basic structure of time and space.

The fascinating story of an ancient riddle and what it reveals about the nature of time and space Three 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.

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.

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

This book is unique in its utilization of the natural sciences to explain and illustrate key concepts of communist philosophy. In its recapitulation of the spirit of Engels’s unfinished manuscript, The Dialectics of Nature, it relies on the physical sciences developed since Engels’s time to reaffirm the validity of materialist dialectics, a point which is more easily made in the context of natural phenomena than it is in social phenomena. The basic philosophical tenets underlying Communist ideology are all supported by the natural sciences. The book is situated within the Marxist-Leninist-Maoist tradition. Its overarching theme is the need to reclaim our most fundamental weapon of that tradition—it’s methodology or philosophy—which has been vitiated or even scrapped by well-intentioned revolutionaries throughout the 20th century. In particular, some of Mao’s philosophical formulations are found to be erroneous and in opposition to his practice. With the rapidly accelerating deterioration of the global capitalist order in progress since 2007, the urgency of this reclamation cannot be over-emphasized.