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Descartes' Dream: The World According to Mathematics

Philip J. Davis and Reuben Hersh
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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Like many Dover editions, this is a reprint. It is a chance to enjoy a book that was maybe missed the first time around. The original appeared in 1987.

The pieces collected in this book encourage thought. The first thought I took from this book was, “is there anyone else that uses this verb ‘mathematize’?” Well, just as surely as Robert Anton Wilson (R.I.P.) said that by synchronicity merely thinking about quarters will make them appear to me on the ground, I now see the verb is here in the article “Galileo’s Construction of Idealized Fall in the Void” in number xliii of History of Science (2005).

This is appropriate enough, since many of the articles contained in Descartes’ Dream strike us now as historical. This is because the “mathematization” explored in this book tends more toward computerization than toward Descartes. The breathless pace of change since this work’s inception has left it considering the implications of COBOL but unable to foresee the impact of the Internet.  Nevertheless, there is as value here as in other ostensibly dated works on applied computer science, such as Programming Pearls (Jon Bentley) or The Cuckoo’s Egg (Clifford Stoll).

Following on the heels of their success with The Mathematical Experience , the authors compiled another book on mathematics (as opposed to a mathematics book). Specific to applied mathematics, this volume focuses a lot on the application of computer technology, applied statistics and the like. The articles are grouped in such categories as “Cognitions and Computation” and “Mathematics and Ethics”. The pieces take a very high, even philosophical, view.

Many of the pieces are much too short and superficial to make much headway in their weighty topics they examine, but some among the longer ones succeed particularly well. Among the strongest offerings is “The Stochastized World: A Matter of Style?” Despite the inclusion of another apparent neologism, this article is an interesting look at the basic applications of probability and enlightens through a simple example where the outcome of a basic coin toss can be modeled probabilistically in contradictory ways that are each are sound in isolation. It all depends on what premises are allowed.

“Feedback and Control: The Equilibrium Machine” is a blueprint for the workshop hobbyist to exhibit Torricelli’s Law and model other fluid dynamics principles. Comedic relief occurs during the lively “Social Tyranny in Numbers” article, particularly the section “Mathematics and Rhetoric”. If you want to sound profound in ridiculing a pompous lecture or devalue the label “refereed”, you will find ample ammunition here.

File this between Clifford Pickover and Douglas R. Hofstadter, but it gets there topically, not by quality or by being memorable. Still, reading this text, which can be started anywhere, will inspire conversations among the mathematically inclined. In that, perhaps, the authors have achieved their goal. This is a book that still stirs thought two decades after its birth.

Tom Schulte ( “mathematizes” in the Industrial Applied Mathematics graduate program at Oakland University ( and enjoys Jules Verne and David Bowie.

The table of contents is not available.