Aha! Gotcha: Paradoxes to Puzzle and Delight
(Here the book is paired with “Aha! Insight” which I haven’t read yet. My copy just has “Aha! Gotcha”)
I imagine there are a lot of adults like myself out there who were lucky enough to stumble across Martin Gardner’s
great work when they were teenagers. (My own Gardner experience came from a Piers Anthony footnote, I think, and led to me digging through many, many old Scientific Americans to read Gardner’s Mathematical Games column.)
Presumably some of those teens grew up to be math folks. Not me. In fact I was not a good math student. But I LOVED reading Gardner and recently got the bug again after picking up a copy of this book.
This is a great book, but I’m not exactly sure what age group it’s meant for. It’s related to some Aha! filmstrips that were made for schools, but some of the material is deeper than what an average math student could handle. (Or at least deeper than what this average math student can handle.)
But that’s okay, because the whole point of the book is to melt your brain anyway. So any clever high schooler and some middle schoolers should get a big kick out of this book. And every adult should give it a try.
Cartoons illustrate some of the paradoxes and you can follow a cartoon, right? Maybe sometimes the explanation gets a little heady, but it’s all making you smarter.
The simplest of the paradoxes are things like:
This Sentence is False
The more complicated stuff includes time-travel, cycloid curves, mirrors, confused store clerks, infinities of different sizes and all that sort of thing.
One of the great things about this book is that it is NOT a quiz book. I hate those stupid books that are set up with answers in the back. You have to flip to the back, try to read one answer while not reading the others and the whole thing makes you feel stupid because you can’t get any right. The authors of these books, meanwhile, give the impression that the came out of the womb with all the right answers.
Anyway, Gardner just wants to explain it all and elucidate and make you think, without turning it into a contest. It creates a different relationship between author and reader. Really!
There’s also an interesting thing about two semi-kid-lit authors: Lewis Carroll and Edgar Allen Poe.
While Carroll gets credit for all kinds of deep thoughts and clever tricks, Poe shows up for including a logic blunder in one of his books.
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