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The second difficulty is that a number of physical theories actually predict the occurrence of clustered variation. These theories are idealizations, but they are reasonable and useful idealizations, that can only be avoided at substantial cost. The best known of these (discussed in [fleck, is the bouncing ball (figure The simplest and most straightforward model of a ball bouncing on the ground is that the ball is a rigid object, and that at each bounce, the ball bounces up with a speed that is a fixed fraction p of the speed with which it hit.4 Since the time between bounces is proportional to the speed leaving the ground, it follows that the time between bounces decreases in a geometric series, and that therefore the ball attains perfect rest in a finite time, having carried out infinitely many bounces. (note that this is different from a standard damped harmonic oscillator, in which the frequency is constant, and the system therefore in principle never reaches a state of absolute rest.) Admittedly, this is an idealization; with an actual ball, beyond a certain point, the system will be dominated by the internal vibrations of the ball, which have a fixed frequency. However, to take this into account would require modelling the ball as an elastic object, which greatly complicates reasoning.
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Infinite Loops in Finite Time Some Observations (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This compelling book investigates the complex interplay between time and space, a subject that fascinated the likes of Zeno, Aristotle, and Einstein. The author, a renowned expert on physical reasoning, contemplates how we might perceive the world differently if time and space were not continuous. The book also examines the philosophical quandaries posed by clustered variation, a phenomenon where there are infinite variations within a finite period. This concept has sparked intense debate among philosophers and physicists, leading to new perspectives on the fundamental nature of reality. The author delves deep into the implications of space and time being finite or infinite, and explores the related paradoxes that have puzzled thinkers for centuries. Along the way, they provide novel insights into the nature of physical reality and its implications for our understanding of the universe. This book brings fresh insights and perspectives to an age-old philosophical conundrum. It is a must-read for anyone interested in the foundations of physics, the nature of time and space, and the limits of human understanding. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332143825_0
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