Details

What Is Random?


What Is Random?

Chance and Order in Mathematics and Life
2nd ed. 2020

von: Edward Beltrami

26,74 €

Verlag: Copernicus
Format: PDF
Veröffentl.: 30.07.2020
ISBN/EAN: 9781071607992
Sprache: englisch

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Beschreibungen

In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.
(Not for distribution) We all know what randomness is. We sometimes choose between options "at random", and if we toss a coin we know it will land heads or tails at random. But are events like these truly random? Randomness turns out to be one of those concepts, like "solid matter" in physics, that works just fine on an everyday level but mysteriously disappears once we move in to examine its fine structure. In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive--they may be truly random, but Godel's undecidability theorem informs us that we'll never know. Their apparent randomness may be only a shortcoming of our minds. Mathematicians have even discovered a string of numbers that appears random--but when you reverse the string, it's completely deterministic! People familiar with quantum indeterminacy tell us that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Then which is real? Perhaps order and randomness, like waves and particles, are only two sides of the same coin.
The Taming of Chance.- Uncertainty and Information.- Janus-Faced Randomness.- Algorithms, Information, and Chance.- The Edge of Randomness.- Fooled by Chance.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithms.
<p><b>Edward Beltrami</b> is Professor Emeritus in the Department of Applied Mathematics at Stony Brook University in Long Island, New York. His research interests include probability theory, mathematical biology, mathematical modelling, and many more. He is the author of several books on the applications of mathematics.<br> <br> Beltrami lives with his wife and several cats in suburban Long Island. He enjoys cooking, listening to music, and being a part-time wine critic.</p>
<p>We all know what randomness is. Or do we? Randomness turns out to be one of those concepts that works just fine on an everyday level, but becomes muddled upon close inspection. People familiar with quantum indeterminacy tell us that order is an illusion and that the world is fundamentally random. Yet these same people also say that randomness is an illusion: The appearance of randomness is only a sign of our ignorance and inability to detect the pattern.</p>By applying mathematical thinking, mathematician Edward Beltrami removes much of the vagueness that encumbers the concept of randomness. You will discover how to quantify what would otherwise remain elusive. As the book progresses, you will see how mathematics provides a framework for unifying how chance is interpreted across diverse disciplines.<br><p></p><p>This book will provoke, entertain, and inform by challenging your ideas about randomness, providing different interpretations of what this concept means, and showing how order and randomness are really two sides of the same mysterious coin. This second edition brings the question of randomness into the twenty-first century, adding compelling new topics such as quantum uncertainty, cognitive illusions caused by chance,&nbsp;Poisson processes, and Bayesian probability.</p><p><b>On the first edition:</b><br></p><p><i>I strongly recommend&nbsp;</i>[What is Random?]<i>&nbsp;to all who are interested in science and would like to see how the ideas of both theoretical mathematics and statistics have been observed and used in real life throughout history.<b>&nbsp;</b></i><b>The American Statistician</b></p>
<p>Uses approachable mathematical ideas to explore what exactly makes something random</p>

<p>Communicates the concept of chance in an accessible manner that encompasses a range of disciplines<br></p>

<p>Includes in the second edition new coverage of quantum uncertainty and cognitive illusions, alongside expanded technical notes<br></p><br>

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