What Is Random?: Chance and Order in Mathematics and Life

This is an excellent study of what randomness means, particularly in Beltrami's treatment of averages.

This is a wonderful book both for the science and mathematics laymen and also for those scientists whose experience with random phenomena may be limited to a particular application area. Professor Beltrami, with great erudition, wit and literacy, leads us on a fascinating journey through current mathematical thought on "What is Random". Using examples from diverse fields, such as Statistics, Engineering , Anthropology (evolution), Linguistics, Psychology, Computer Science etc., he demonstrates how critical a role randomness plays in current scientific thought, and we see over and over again. clearly, how much of our "organization" hovers between order and disorder. We learn that the difference between a Shakespeare sonnet and the random output of a Monkey pecking at typewriter can be expressed in terms of its algorithmic complexity and that often, the difference between beauty and boring is often a mixture of just the right amount of randomness and redundancy. And also, for the non neophyte, Professor Beltrami offers a uniform vision of randomness connecting its many diverse faces. The mathematics throughout is the minimum required to remain rigorous and will not be daunting to the non-mathematical reader. Appendices with more mathematical details are available for those who wish to probe a little deeper. Accessible, readable and in many ways charming, I wholeheartedly recommend this book as an all around good read.

This is one of the best popularizations of mathematics that I have ever read. It narrates technically and philosophically deep concepts in an engaging non-technical way. Must-read to non-experts and experts alike!