# What Is Random?

###### Edward Beltrami
Publisher:
Springer
Publication Date:
2020
Number of Pages:
212
Format:
Paperback
Edition:
2nd
Series:
Copernicus
Price:
24.99
ISBN:
978-1-0716-0798-5
Category:
General
[Reviewed by
David Aldous
, on
05/23/2021
]
This short book fits the popular science genre, containing minimal mathematics.  It touches upon some of the usual topics in popular expositions of Probability (some history, the Normal and Poisson distributions, coincidences, the Monte Hall problem etc.) but the central content is four chapters on the following specific topics.

• Shannon entropy within information and data compression;
• algorithmic randomness, complexity and undecidability;
• self-organized complexity and power laws;
• and what the author calls "Janus-faced randomness", illustrated by the stationary process $x \to 2x \mod 1$ which is deterministic forwards but random backwards.

The writing is clear, so as a first non-technical "easy reading" look at these topics it is useful.  However,  I suspect there is neither enough mathematics to satisfy readers interested in mathematics nor enough critical discussion of the real-world scope of these topics to satisfy readers interested in applications.  Though there are useful suggestions for further reading.

These four topics are very specialized and relate to perhaps only 2 out of 100 contexts where chance arises in Life, the Universe and Everything.  Much broader and more representative accounts of chance and randomness in the real world can be found elsewhere, for instance in Nate Silver's The Signal and the Noise.

David Aldous (www.stat.berkeley.edu/~aldous) is retired from U.C. Berkeley after 39 years but retains interests in theoretical and applied probability and in the popular exposition of probability in the real world.