Randomnicity, Rules and Randomness in the Realm of the Infinite

This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature -- this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in.

Reading the book is like visiting a museum, and as the reader goes successively through the chapters he (or she) encounters beautiful ideas and interesting comments. Although the book is not a book on the history of mathematics, it contains interesting historical facts. --Zentralblatt MATH

I recommend reading it to those who want a quick introduction to ideas about randomness and those whose exposure to these ideas has been piecemeal, as mine was. The book may spark the imaginations of readers and advance our science through innovative application of the concepts. Someone might just find life-changing inspiration. --Vadose Zone Journal

As a contribution to popular science this book is welcome. Tsonis explains randomness as it enters into mathematics, science and everyday life. --Mathematical Reviews