There’s no getting around it: Risk and Meaning is an odd book. This is clear from the moment you pick it up, as the book is the size of a typical book, but it is bound “sideways”, with the spine on the short edge of the rectangle. (Moreover, despite the fact that it is published by Springer-Verlag, the spine is bright red rather than their trademark yellow, but I suppose only a mathematician would find that part odd.) The cover shows part of a watercolor depicting Samson getting revenge on the temple of Gaza — not a typical image for a book that is ostensibly about probability.
But the oddness of this book does not stop at the cover — the chapters of the book include titles such as “Cicero and Divination”, “Democracy by Chance”, “The Third Dimension of Risk”, “From Fortuitism to Animism”, and “The Legitimacy of Science and Love.” The book is filled with illustrations, ranging from architectural drawings to pictures of classical sculptures to photographs of nature, and many of these illustrations overlap with the text. Flipping through the book, one notices many changes in the color of paper, the size of the text, and the fonts used. Oh, and significant chunks of the text are dedicated to excerpts from other writings, including writers such as Euler, Thomas Kuhn, Cournot, Noam Chomsky, Milan Kundera, and Claude Levi-Strauss. Basically, this feels far more like an art book than a math book in its layout and design — it even has one of those built-in cloth bookmarks attached to the spine.
But enough about the physical book — what is it about? According to the introduction (which Bouleau and his translators Dene Oglesby and Martin Crossley call an “Entrance”), “the guiding thread of this book is the confrontation between the presence of meaning and the possibility of chance, our ultimate goal being to shed light on our tendency to adhere to scientific representations.” Which is to say that the book is an exploration of the concepts of chance and risk from a variety of perspectives, including the philosophical, the artistic, the economic, and yes the mathematical. Bouleau dedicates a full chapter to “Mathematical Probabilities”, in which he discusses at length the different points of view about the nature of probability theory. Although in the end he concludes that “I do not believe that there is any real dispute between the supporters of the objective theory and those of the subjective theory except in academic encyclopedias and theses on the history of probability.” Other chapters are dedicated to discussions of pattern and structure that will resonate with mathematicians who believe that those concepts are at the heart of our studies much more than equations and numbers.
Several chapters of Bouleau’s book deal with the nature of scientific inquiry and the extent to which science is just “guessing” the future with varying levels of certainty. As he writes, “Science may not proceed by guesswork, but it is certainly capable of predicting facts not yet observed.” He refers to the chemist Berthelot’s claim that “the world cannot be guessed” as “one of the greatest idiocies ever written”, giving the existence of the planet Neptune, the existence of positrons, and the statement of Fermat’s Last Theorem as examples of things that were “guessed” long before they were known to be true. He also writes at length on an analogy between scientific inquiry and falling in love, both of which often begin with a chance discovery and grow into something much deeper.
It would be easy to interpret what I have written thus far as meaning that I did not like the book, but that would not be entirely accurate. Risk and Meaning is a quirky book, both in its topic and its physical layout and the writing style that the author adopts, but it is certainly not a bad book — I found parts of it to be annoying, but I also had trouble putting it down. My guess is that the quirkiness will turn many readers off, and that might be for the best, as this is not a book for everyone who reads MAA Reviews. It is certainly not a mathematics book, but it is a book that is mathematics-adjacent, and I think that anyone who is able to get past (or even relish) some of the quirkiness in the book will certainly find themselves with plenty to think about. And I’m not sure what more one could ask for in a book.
Darren Glass is an Associate Professor of Mathematics at Gettysburg College. He worked really hard to not just have his review simply say “Take a risk with this book.” He can be reached at firstname.lastname@example.org.
Entrance: Interpretation and Paradigms.- I. Cicero and Divination.- II. Cournot’s "Philosophic Probabilities".- III. Mathematical Probabilities.- IV. Democracy by Chance.- V. Gestalt, Structure, Pattern.- VI. The Third Dimension of Risk.- VII. ''Modern" Architecture.- VIII. The Ideal City.- IX. Daring the Abstract in Art.- X. Saussure or the Dread of Mathematical Probabilities.- XI. Jacques Monod’s Roulette.- XII. From Fortuitism to Animism.- XIII. The Slip as Fortuity and Meaning.- XIV. Guessing Astronomy.- XV. The Legitimacy of Science and Love.- Hints and Index.