What Is Random?
Chance and Order in Mathematics and Life
(Sprache: Englisch)
This book is intended to provoke, entertain, and inform by challenging the reader's ideas about randomness, providing first one and then another interpretation of what this elusive concept means. As the book progresses, the author teases out the various...
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Klappentext zu „What Is Random? “
This book is intended to provoke, entertain, and inform by challenging the reader's ideas about randomness, providing first one and then another interpretation of what this elusive concept means. As the book progresses, the author teases out the various threads and shows how mathematics, communication engineering, computer science, philosophy, physics, and psychology all contribute to the discourse by illuminating different facets of the same idea.The material in this book should be readily accessible to anyone with experience in undergraduate mathematics, no calculus needed. Three appendices provide some of the background information regarding binary representations and logarithms that are needed. Although an effort is made to justify most statements of a mathematical nature, a few are presented without corroboration, since they entail close-knit arguments that would detract from the main ideas. Readers can safely bypass the details without any loss, andin any case, the fine points are available in the technical notes assembled at the end.
Inhaltsverzeichnis zu „What Is Random? “
[1] The Taming of Chance.- From Unpredictable to Lawful.- Probability.- Order in the Large.- The Normal Law.- Is It Random?.- More About the Law of Large Numbers.- Where We Stand Now.- [2] Uncertainty and Information.- Messages and Information.- Entropy.- Messages, Codes, and Entropy.- Approximate Entropy.- Again, Is It Random?.- The Perception of Randomness.- [3] Janus-Faced Randomness.- Is Determinism an Illusion?.- Generating Randomness.- Janus and the Demons.- [4] Algorithms, Information, and Chance.- Algorithmic Randomness.- Algorithmic Complexity and Undecidability.- Algorithmic Probability.- [5] The Edge of Randomness.- Between Order and Disorder.- Self-Similarity and Complexity.- What Good is Randomness?.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithims.- References.
Autoren-Porträt von Edward Beltrami
Order is an illusion, the quantum theorists tell us; at bottom the world is ruled by quantum indeterminacy. Yet randomness is also an illusion: the appearance of randomness is only a sign of ignorance, of our inability to detect the pattern. Does randomness really exist? In this wonderfully thought-provoking little book, mathematician Ed Beltrami shows how order and randomness are really two sides of the same mysterious coin.
Bibliographische Angaben
- Autor: Edward Beltrami
- 2012, Softcover reprint of the original 1st ed. 1999, XX, 201 Seiten, Masse: 12,7 x 20,3 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1461271568
- ISBN-13: 9781461271567
Sprache:
Englisch
Pressezitat
From the reviews: THE AMERICAN STATISTICIAN
"In summary, I think that many readers with a strong interest in mathematics, statistics, physics, or other areas of science will find this book interesting and challenging. I strongly recommend it 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."
MATHEMATICAL REVIEWS
"The book is nicely written and should entertain many readers..."
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