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Paradoxes in Mathematics

Stanley J. Farlow
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Glenn Becker
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A more descriptive title for this book would have been Farlow’s Miscellany. The author admits up front that he includes the widest possible variety of things that could answer to the description “paradox”, but even with that disclaimer in pocket he goes pretty far afield.

The best example of this is what Farlow calls “The China Paradox,” where it is revealed that children (in the US, anyway) who dig deep enough holes don’t, in fact, run the risk of popping out in China, but will instead surface — more or less — in the middle of the Indian Ocean. So “paradox,” here, winds up being scarcely more paradoxical than “a diverting fact.”

Farlow tries for an informal “hey — isn’t that cool?” approach, which is often charming but sometimes goes a little astray. This is especially true when the topic at hand is an old chestnut. For example, I’d be disinclined to title a chapter “The Birthday Paradox: You’re NOT Going to Believe This” when the paradox is one that most people have very probably heard and come to terms with.

That said, there are many enjoyable chapters where reasonably sophisticated mathematics is introduced in a gentle and engaging manner. “Through Cantor’s Looking Glass” is one of the better basic introductions to transfinite cardinals I’ve read. Teachers might find it very useful. Other chapters cover concepts in probability, physics, fractals and more.

This short book of short chapters seems to have been something of a labor of love, and will provide some good clean fun for younger readers who are looking for reasons to like mathematics. They’ll also enjoy puzzling out the Greek ciphers at the ends of the chapters. If you are reading this, however — unless you grew up on a desert island with no books — you’ve probably seen most of what’s in this book before.

Glenn Becker is a staff member at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA, where he toils in the data archive of the Chandra X-Ray telescope. He is a “reborn astronomy and mathematics fellow traveler” who spent far too many years getting advanced degrees in theater, only to ultimately abandon the entire discipline. 

The table of contents is not available.