Edward Beltrami

What Is Random? (eBook, PDF)

Chance and Order in Mathematics and Life

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer New York
• Seitenzahl: 201
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461214724
• Artikelnr.: 44178492

Autorenporträt

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.

Inhaltsangabe

[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.

Rezensionen

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..."