A Cook Book of Paradoxes

A review of “Sleight of Mind” by Matt Cook (due out in late March):

Paradoxes, I think, say a lot about the workings of the human mind and human logic… they’ve always fascinated me, and they come in a myriad of forms.

Oddly, author Matt Cook is listed as an economist and a magician… I say oddly only because most books on paradoxes that I’m familiar with are written by either mathematicians or philosophers. Yet Matt has put together one of the overall best and broadest compendiums I’ve seen of wonderful paradoxes (divided into 13 categories), ranging across mathematics/probability, philosophy, and logic, before ending with 3 chapters on physics-related paradoxes (by contributing authors) that aren’t usually included in such math-related compendiums. And then to conclude, Matt recruits Grant Sanderson (of 3blue1brown YouTube fame) to add a final essay on whether mathematics is invented or discovered. I didn’t honestly feel this essay (on a well-worn issue) fit that well in the overall volume, but still always interesting to hear Sanderson’s take on any topic.

The volume covers (according to its own promotion) 75+ paradoxes, including most all the best-known and studied ones that a reader would expect, but also with some that most readers may find new to them. I did manage to think of a couple that I’ve covered here on the blog previously which I didn't find in the book, but which I think would make fine additions (the second below is a probability paradox, and the first is what Cook would perhaps classify as an “operations” paradox):

https://math-frolic.blogspot.com/2015/07/gladly-paying-110-for-dollar-bill.html

https://math-frolic.blogspot.com/2013/01/the-shooting-room-doozy.html

The format throughout Cook's book is to state/describe the paradox, and then give two (or more) possible ways of, or approaches to, explaining it, followed by a discussion of why one explanation is true and the other(s) is/are not. Some of these discussions I think are a bit too short, not quite always convincing (needing a bit more fleshing out), but in most cases the discussion seems about right: not too brief, but not too deep into the weeds either. Cook’s writing is sometimes rather pedantic, and occasionally there is some serious math involved, so even though the paradoxes are usually inherently interesting, the volume is more appropriate to a college level student than a lower level (though, again, the majority of the paradoxes could be understood by young students -- and I've long been a believer that paradoxes offer a great example for young people of the imprecision/uncertainty of human logic and analytical thinking; in short, it would be fun and instructive to share many parts of the volume with primary/secondary students).

I am particularly interested in “self-reference,” and appropriately (to me) by far the longest chapter in Cook’s book is on self-reference paradoxes. Other favorite topics for this reader are supertasks, probability, induction, and geometry, but your own personal preferences will guide which of the 14 chapters you find most interesting.

There are by now several good compendiums and discussions of paradoxes available; the scope and readability of this volume makes it a great addition to the subject-area. I recommend it. …and, that sentence is not false.

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==> will just note that I'm reviewing a review copy of the volume that was sent to me back in January December and am assuming there will be no major revisions in the final March-released edition.