Real-World Probability Books: Miscellaneous

Langville, Amy and Meyer, Carl. Who's #1?: The Science of Rating and Ranking. Princeton University Press, 2012.

This isn't about probability, but is a potential source of projects for my course. I can't improve on this review.

Skiena, Steven and Ward, Charles B. Who's Bigger?: Where Historical Figures Really Rank. Cambridge University Press, 2014.

Stupid but fun, and a potential source of projects for my course. See my comments here. Also, it isn't about probability

Puskar, Jason. Accident Society: Fiction, Collectivity, and the Production of Chance. Stanford University Press, 2012.

The author's thesis is that, over a period 1880 - 1940, the public perception of chance was in part shaped, not merely reflected, by literature. The book is structured around analyses of chance in the following handful of books.

William Dean Howells' accident-driven novels, exemplified by A Hazard of New Fortunes, and Stephen Crane's chance-driven novels exemplified by the Civil War novel The Red Badge of Courage.
Anna Katherine Greens' detective novels (the solutions depending more on chance than deduction) exemplified by The Woman in the Alcove, juxtaposed with the philosophy of Charles Peirce.
The industrial sociology of Crystal Eastman's study Work Accidents and the Law, juxtaposed with Edith Wharton's novels such as The Fruit of the Tree (centered on a work accident).
Theodore Dreiser's novel An American Tragedy and James Cain's novel Double Indemnity, based on "criminally falsified accidents"

As a mathematician I am of course completely unqualified to review such a work. The descriptions of general content and of specific "points to note" in those books are informative and often quite fascinating. Though these specifics are embedded into the kind of broader socio-political prose style ("the feminization of chance"; "the rationale behind chance collectivity thus configures chance itself as a dangerous and alien other that has infiltrated every aspect of daily life") that makes scientists look askance at the humanities.

A central argument of the book is that the growth of life insurance in the second half of the 19th century, and the emergence of basic worker safety and workers' compensation schemes in the early 20th century, were major factors in creating the modern perception of "accident" as a matter of chance, rather than as the effect of a specific cause with responsibility traceable back to some individual. This perception has various consequences. One is the "moral hazard" that no-one has motivation to prevent accidents if an insurance company will recompense. Another is that life insurance advertising (very prominent in that era) naturally emphasized risks and created exaggerated perceptions of abounding dangers (as does the media today, for equally natural reasons). This line of argument is quite plausible, though assessing the relative contribution of literature is surely impossible.

To me, there is one way in which the author's discussion is misplaced. The metaphor of "chance" as akin to the roll of a die is misleading. In everyday life, chance refers to unpredictability -- we don't buy life insurance because we think the possibility of dying each day is like the possible outcomes of the throw of a die, we buy it because we know the future is unpredictable and we want to mitigate the financial consequences of our possible death to our family. Every accident has a proximate cause, but the possibility of an accident tomorrow has a "chance" because we cannot in practice trace back the chain of causality to today -- in other words because it is unpredictable. So the modern perception of "accident", which the author seems to view as some undesirable consequence of modernity, is perfectly correct, once we replace some metaphysical notion of "chance" by "unpredictability".

Bruce, Colin. Conned Again, Watson. Perseus, Cambridge MA, 2002.

See my review.

Rosenhouse, Jason. The Monty Hall Problem. Oxford University Press, 2009.

Not to my own taste -- apart from the actual TV game version it is all hypothetical rather than real-world -- but worth noting for the mathematical enthusiast. Here is a precis of the Math Reviews review.
....... a superb source of variants of the problem, paying careful attention to the hidden assumptions behind the problems, written in a witty accessible style. The reader will find discussions of many variants -- progressive versions, Bayesian treatments of the problems, computer simulations, quantum versions, information-theoretic representations, common cognitive fallacies associated with the problem, and much more. This is a model of how to accessibly introduce mathematical material at an elementary level that is not a mere popularization of the material. Although not suited, nor designed, to teach elementary probability theory, it could usefully serve as a supplementary text for the stronger students in such a course, especially in conveying the ideas of replacing an appeal to intuitions by an explicit mathematical treatment and the care needed in setting up under-specified problems for a rigorous mathematical analysis.

Stewart, Ian. Letters to a Young Mathematician. Perseus, 2006.

The declared goal is "to give an inside view of the mathematical enterprise, and explain what it is really like to be a mathematician". Half the book is popular mathematics, and the other half is remarks on "being a mathematician". The book is well written, easy and fun to read, sensible throughout, and prospective mathematicians could only benefit from reading it. But I was disappointed (as a professional mathematician) to find few particularly new or individualistic insights in either half. The popular mathematics half relies on well-worn topics like "Platonism versus realism" and "can't computers solve everything?". And only the following three thoughts on being a mathematician struck me as particularly insightful.

(i) [as conclusion of "what is mathematics/mathematicians?" discussion] A mathematician is someone who sees opportunities for doing mathematics.

(ii) Being a research mathematician is akin to being a writer or an artist; any glamour that's apparent to outsiders fades quickly in the face of [the reality]. Your satisfaction must come from the high you get when you suddenly, for the first time, understand the problem you're working on .....

(iii) As your career develops, the worldwide mathematical community will be increasingly important to you. You will become part of it, and then you will have a home in every city on Earth.

A nice introductory chapter extols the breadth of uses of mathematics, and could be used by Math Dept web sites to recruit majors. There is also a well-balanced "pure or applied" chapter. But the rest of the book identifies "mathematics" as "theorem-proof mathematics", as illustrated by quotes such as

(i) There has been a spate of popular math books in recent years ...... there are even books on the applications of mathematics.

(ii) The true mathematician is not satisfied until the statement is proved.

This attitude is irritating to those of us who regard this identification as akin to identifying "visual art" with oil painting. What matters isn't the tools, it's how competently and creatively you use them.

A final irreverent thought: instead of A Mathematician's Apology, wouldn't The Screwtape Letters have made a more intriguing model?

Schoenberg, Frederic Paik. Introduction to Probability with Texas Hold'em Examples. Chapman and Hall, 2011.

A concise (140 pages) version of a first undergraduate course in mathematical probability -- a selection of key points found in typical, much longer, textbooks. The distinctive feature is an additional 20 pages of detailed study of some aspects of poker: "structured hand analysis; pot odds; luck and skill [in poker]". There is also an 8-page chapter on computer simulation and approximation.

Eckhardt, William. Paradoxes in Probability Theory. Springer, 2012.

See my review.

Simon, Marc T. Your Intuition is Wrong! Dorrance, 1996.

Unpretentious slim volume of 29 multiple choice questions with little stories, both standard (birthday, matching, runs) and less standard (ballot theorem, arc sine law) intended to test the reader's intuition. Gives solutions without detailed calculations. Fun, but I doubt anyone has good enough intuition to guess answers without knowing beforehand or doing mental calculations.

Back to complete book list.