Aha! Gotcha: Paradoxes to Puzzle & Delight

by Martin Gardner, Brenn Lea Pearson (Designed by)

A pocket book of riddles, full of fun and illustrations

Genres: Mathematics, Puzzles, Science, Nonfiction, Logic, Philosophy, Games

164 pages, Paperback

First published January 1, 1975

About the author

Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature (especially the writings of Lewis Carroll), philosophy, scientific skepticism, and religion. He wrote the Mathematical Games column in Scientific American from 1956 to 1981, and published over 70 books.

Reviews

[Maricruz · Rating 3 out of 5]

El título ya lo dice todo. No son acertijos, sino más bien ideas, situaciones teóricas que conducen a paradojas relacionadas con varios campos: números, geometría, probabilidades, tiempo, etc. Son bastante sencillas (algunas son algo más complicadas, las referidas a probabilidades, por ejemplo, por ser más contraintuitivas) y están como siempre fabulosamente explicadas por Martin Gardner, que era un crack de la divulgación matemática. Además, para algunas propone maneras de «visualizar» la teoría con la ayuda de juegos de cartas, monedas o papeles recortados, que son truquillos muy adecuados para acercarles las matemáticas a los niños.

Una cosa que me fastidia de esta edición es que en la página de créditos ponen el nombre de todo el mundo menos el del autor de las ilustraciones interiores, que tienen un aire casi cutrecillo y demodé (también es que son de los años 70), pero que me han resultado muy graciosas. Al final he logrado enterarme de que son de un tal Jim Glen, del que poco más he averiguado. Cualquier información sobre él será bienvenida (y que RBA le diese crédito en alguna futura reedición, eso también).

[Cheryl · Rating 4 out of 5]

Bad blurb - the hardcover is anything but pocket size, and there are no riddles in any common sense of the word. These are puzzles & provocations. They're aimed at youth who need just a little nudge to realize that they want to become mathematicians. It reminds me very strongly of the books that I enjoyed back in the day when I imagined I could get into higher math like topology and non-Euclidean geometry. Stuff happened, and now the best I can do is extend my understandings of probability and statistics. Anyway, this book introduces all of those different maths, and more, through brain-teasers, outlines of classic paradoxes, and other 1-3 page illustrated mini-lessons. Would that all children & teens had a teacher as lively & engaging as Gardner, or at least one who used his works in their math classes.

Gardner's Annotated Alice in Wonderland is also a delight, and I picked up a stack of his works from the university library so, if you're interested, watch for my reactions to them in these coming weeks.

Find a card or square scrap of stiff paper. Write on one side "The statement on the other side of this card is true." On the other side, write "The statement on the other side of this card is false." Set it out on the counter or coffee table. Watch reactions of those who pick it up.

I appreciate the shout out to Anno's Alphabet and other books by Mitsumasa Anno, and to science fiction writers including Fredric Brown and his What Mad Universe.

This prompts me to try again to read Gödel, Escher, Bach: An Eternal Golden Braid. I will however not look at the bibliography for fear of adding unavailable (due to age) titles to my wishlist.

A paraphrase: "To a statistician, coincidences are extremely probable. There are lots and lots of ways that a coincidence of *some* sort can arise in the course of all the events & interactions of a day. What we forget is that for each coincidence, there are*many more* possible ones that did *not* occur."

Get a grid of 20X20 graph paper, two colored pencils, and a coin (or a paint program other random binary number generator). Sequentially color in squares on the paper according to whether the red was cued by 'heads' or the green was cued by 'tails.' Note the clumps. Reassess your understanding of "random."

And, yes, I still want more fun w/ probability & statistics, so if you have titles to recommend please do comment!

[Robu-sensei · Rating 5 out of 5]

[Warning: This review may contain an unexpected tiger. You won't know where the tiger will be until you encounter it. Now you know the tiger can't be the last word, because then it wouldn't be unexpected; having read all the words but one without finding the tiger, you would know the tiger was next before you actually saw it. By the same logic, the tiger couldn't be the penultimate word, either, because if you read up to the third-to-last word, you'd know the tiger would come next, and you'd expect it. You can extend this line of reasoning to prove that the tiger can't be anywhere within the review.]

Martin Gardner, mathematician and former Scientific American "Mathematical Games" columnist, compiled this treasury of curious and entertaining paradoxes in logic, mathematics and probability. The collection includes some famous conundrums, such as Zeno's Paradox, Pascal's Wager, Simpson's Paradox (in the form of a search for swingers at a singles' club) and the Gambler's Fallacy. Examples are illustrated TIGER with crude but hilarious drawings (some of which originally appeared in a series of filmstrips (anyone remember filmstrips? the soundtrack beeping to tell you to advance the frame? the projector's light bulb, hotter than the sun's surface, always just about to explode?) about paradoxes). This book is lots of fun for accomplished and aspiring nerds, but is also a good first introduction to infinite sets and (very) basic probability theory.

[Javier Santaolalla · Rating 3 out of 5]

Buena recopilación de paradojas MATEMÁTICAS. Resalto esta palabra y la pongo en mayúsculas porque sí, no a todo el mundo le gustan las matemáticas. Y yo creo, y esto es algo a debatir, que si NO eres amante de la física o la biología, bien puedes disfrutar un libro de divulgación sobre física o biología; pero encuentro algo complicado que alguien a quien no le llamen las matemáticas, aunque sea un poco, pueda disfrutar de un libro de matemáticas.
Dicho esto, el libro trata sobre paradojas en diferentes bloques: lógica, geometría, probabilidad, estadística,... y las apoya con una explicación. Muchas de ellas son impactantes, algunas son más simples, otras dejan indiferente, pero en general, es buena recopilación y un buen ejercicio mental.
¿Qué es una paradoja? Desde luego algo que hace pensar y que genera discusión. Prueba a leerlas y compartirlas con amigos o familiares, verás qué delicioso se vuelve.
¡A disfrutar!

[Remo · Rating 5 out of 5]

Maravilloso libro. Recuerdo haber devorado este libro a los 14 años. Recuerdo mi asombro al aprender sobre el hotel de Hilbert, que con sus infinitas habitaciones llenas de huéspedes era capaz de admitir a un huésped más (cada huésped en la habitación n pasa a la habitación n+1 y el huésped nuevo se queda con la habitación 1) e incluso admitía a infinitos huéspedes cuando las infinitas habitaciones estaban llenas (cada huésped de la habitacion n pasa a la 2n y quedan libres las infinitas habitaciones impares). Fue un descubrimiento, lo leí entero en la casa de la cultura de mi pueblo un día que me colé en la biblioteca porque me aburría. Grandísima introduccción a las matemáticas y al pensamiento abstracto.

[Manuel Alfonseca · Rating 4 out of 5]

ENGLISH: A great collection of logical and mathematical paradoxes. Anyway, Gardner made three mistakes:
1. On page 80, he says that The Plattner Story by H.G. Wells recounts the case of a man who on an interstellar journey suffers symmetrization..., but it was not an interstellar journey, rather his disappearance was the result of a failed chemical experiment. Gardner could also have quoted here Arthur C. Clarke's short story "Technical error," which is based on Wells's short story, but is more complete.
2. On page 109 (Pascal's Wager) he says that Pascal applied his wager to the Christian faith, which is not correct: he applied it to the existence of God.
3. On page 153 (The tachyonic telephone) he says in two places that tachyons "would go back in time", which is not correct, since for them time would be imaginary. See this post in my blog: https://populscience.blogspot.com/201...

ESPAÑOL: Estupenda colección de paradojas lógicas y matemáticas. Eso sí, Gardner cometió tres errores:
1. En la página 80, dice que The Plattner Story de H.G. Wells relata el caso de un hombre que en un viaje interestelar sufre la simetrización..., pero no fue un viaje interestelar, sino que su desaparición fue resultado de un experimento químico fallido. Gardner podría haber citado también aquí el cuento de Arthur C. Clarke "Technical error," que está basado en el cuento de Wells, pero es más completo.
2. En la página 109 (La apuesta de Pascal) dice que Pascal aplicó su apuesta a la fe cristiana, pero eso no es correcto pues la aplicó a la existencia de Dios.
3. En la página 153 (El teléfono taquiónico) dice en dos sitios que los taquiones "tendrían que remontar el tiempo", lo que no es correcto, pues para ellos el tiempo sería imaginario. Véase este artículo en mi blog: https://divulciencia.blogspot.com/202...

[Jack · Rating 5 out of 5]

The world is lesser without Martin Gardner in it.

Martin Gardner was a supremely intelligent mathematician with a real talent for explaining complex mathematical problems in a way that lay people could understand.

Gotcha! follows the same lines. It's kind of an odd book, in that the cartoony style is a little dated and it really looks more like a kid's book or a Young Adult book. Make no mistake, it's not, though young adults could certainly benefit and enjoy.

Gardner primarily approaches logical fallacies in this book. He uses the cartoons to walk you through exactly the wrong conclusion, then steps back and brilliantly deconstructs the argument so that you can see where your normal human condition fails you and why the unintuitive answer is the mathematically correct one. That said, he does it in a way that involves minimal math and only a basic understanding of logic and reason.

That's not to say the book is dumb or dumbed down. Nothing could be further from the truth. It tackles some very complex problems and some issues that have confounded mathematicians and logicians for centuries. Some of the problems don't even have an answer, and he even manages to walk you through why we've been unable to answer the question even though the answer seems obvious.

Overall, it's just a delightful book that's easy to read and leaves you much smarter than you were when you started it. There's not many books that can make such a claim.

[Anna]

A gift from my father in 1992.

[Paulo García · Rating 3 out of 5]

La información es agrupada en seis capítulos, cada uno alusivo a un área particular (lógica, números, geometría, probabilidad, estadística, tiempo). Se podría decir que mucho de lo presentado tiende a ser un problema mal razonado (de ahí lo contradictorio) y lo que estaba esperando eran situaciones más en el sentido de la paradoja de Rusell.

Se utilizan unas caricaturas en la presentación de los problemas, que en algunos casos no representan un apoyo a lo expuesto por el autor (en la rosquilla reversible, esta viene pintada de negro y no facilita el ver las regiones). Con varios de los problemas había tenido algún contacto previo por lo que no me representaron algo novedoso, aunque el autor los presente con alguna modificación en su enunciado (como lo indica, por ejemplo, en el tigre sorpresa o un curioso testamento).

Me parece valioso el listado de textos sugeridos al final del libro para ahondar más en la temática.

[Liedzeit Liedzeit · Rating 2 out of 5]

This is a previously unread book from my library. And I can see why. It should be a delightful book written by the great Martin Gardner. It contains short introductions to many paradoxes from different fields. It is like a little encyclopedia on paradoxes. And even if most of the paradoxes are quite well known one can learn a lot. For example how to determine whether you believe in free will or determinism.
But the book is completely ruined by the images. It is a physical pain to see these incredibly ugly drawings. And they are not even done by the 5-year-old grandson of Martin. But presumably by someone who got paid to do it.

[Miguel Covas · Rating 3 out of 5]

Gardner’s Scientific American articles fondly revisited.
Now, I just caught Mr Gardner in one slip: on page 160 he introduces a problem about finding a pea under one of three nutshells. The player chooses one nutshell and the game leader offers to upturn one of the remaining nutshells which will be empty. Then the player can change his bet. Gardner maintains that the player does not obtain new information from the upturning. As a matter of fact, the problem is a variant from the Monty Hall problem. After the upturning the player knows that the odds of the pea being under the not chosen nutshell are now 2/3…

Besides that slip, I also found that Gardner uses too often to redirect you to other books of him for further explanation about topics being discussed…

[Grace · Rating 4 out of 5]

I have had this book "forever" and have just now read it through. I could say I loved it except for two things:
1. After a while the many references to Gardner's other books, while helpful, began to feel like advertisements for those books.
2. The explanation of time dilation completely missed the paradox arising from relativity. There is no single "observer at rest". Observer's on the spaceship would see clocks on earth (if they could observe them) ticking more slowly than their own.

Still, the section on magic squares helped me to create a game for my grandson.

[Eric]

For this and "Aha! Insight": Books of paradoxes, fallacies, puzzles, and just plain fascinating ideas. Gardner has written hundreds of great columns on mathematical ideas for Scientific American, as well as a huge number of excellent books on math, science, pseudoscience, magic, and much else. These two are great books for that clever kid you know, age nine and up. They're almost a "best of" collection of many of the topics he's written about before in his columns, distilled down to their essence.

[Analuabc · Rating 4 out of 5]

Apesar de ter anos, este tipo de livros nunca deixa de estar actual. Muitos dos paradoxos aqui descritos continuam efectivamente a fazer parte da nossa vida, com ainda mais discussão e tentativas de resolução desde o lançamento original do livro. E muito ajuda a forma como são apresentados os temas. Engraçado que nesta versão que tenho ainda é usado o Escudo para o dinheiro.

[Volodymyr Andrusenko · Rating 5 out of 5]

I remember that this was my first acquittance with Martin Gardner's writing. I greatly enjoyed the book, it was entertaining and educational at the same time. After reading this book, I was specifically looking for all new works of this author. Simply the best author in recreational mathematics.
5 stars.

[Ily · Rating 4 out of 5]

Libro interessante e adatto anche a coloro che, con matematica e logica hanno poco a che fare! Getta le basi di queste due discipline attraverso una serie di spiegazioni ed illustrazioni sui paradossi più comuni.

[Isaac · Rating 3 out of 5]

Great list of concepts covered that should be able to inspire any curious mind, however I do feel like a few of the subtopics were brushed away quickly without greater detail. Some of the explanations can also be a bit vague.

[Inpul · Rating 5 out of 5]

当我在对数学还抱持着懵懂状态的时候，这本书给了我兴趣和启发。

[Diego Torre Bordes · Rating 3 out of 5]

“Para más información lea mi siguiente libro [...]” Como final a cada sección.

[Zanos · Rating 4 out of 5]

Es un libro breve y muy entretenido, con paradojas realmente interesantes aunque algunas queden sin un desarrollo apropiado. Es fantástico para leer en ratos libres y pasar un buen rato.

[Jose · Rating 5 out of 5]

Muy entretenido.

[David · Rating 5 out of 5]

Martin Gardner is one of my favorite math writers. His enthusiasm is very contagious. Great book for math lovers.

[Jennifer Jiang · Rating 5 out of 5]

very fun, thought-provoking but also light, great book!

[Clara Limón · Rating 5 out of 5]

Este libro mola tanto que case me arrependo de regalarllo á miña ex :v

[Alberto Amigo Gómez · Rating 4 out of 5]

Un libro muy divertido para los que nos gustan las matemáticas.

[Angel Jimenez · Rating 4 out of 5]

¡Un libro paradójico!

[Sarah Rigg · Rating 3 out of 5]

I've had this on my "to read" list for years and finally got around to checking it out. It amuses me highly that the book came out of a compilation of filmstrips Gardner had done around various logic puzzles. The book is full of illustrations, which makes some of the explanations a lot easier to follow than they would be otherwise. He groups the book into several sections and groups the paradoxes under headings such as "Number" and "Time." I knew quite a bit of the stuff about ancient paradoxes (Zeno's paradox, the sultan who leaves camels to his 3 sons) and paradoxes from set theory, but other stuff was brand new to me, and I really enjoyed the heck out of the topology sections. I recommend this to people who enjoy brain teasers or are generally interested in math, science, or philosophy & logic. You can see a few sample pages on this Boing Boing link:https://boingboing.net/2016/04/12/the...

[Fiver · Rating 4 out of 5]

Not to be overlooked by the casual reader who might not see themselves as the puzzling type, "Aha! Gotcha," is that rare breed of puzzlebook that has universal appeal. It's a book that focuses almost entirely on those special singularities in our minds where the standard logic of a situation breaks down to allow a loophole, a shortcut... a "Gotcha!".

The book jumps lightly from puzzle stories, to light math, to trivia, and a wide variety of applications and puzzle types. This buffet-style approach might dissappoint serious puzzlers (like me!) when they first pick it up, but what "Aha!" lacks in depth it greatly makes up for in charm and appeal. Each puzzle is drawn out using childish stick-figures to present a paradox or riddle, which is then explained and reviewed in prose on the following page. This book is just the sort of thing to keep your company occupied when they visit.


Puzzle books are a very difficult genre to review, because in many ways they are more like interactive games than sources of prose information. Even coffee-table landscape eye candy tomes can be roughly compared to other non-fiction reading, but puzzle books more often can be passed off as merely glorified flashcards. And as we all know, flashcards can't be reviewed, right?

[Paulo · Rating 4 out of 5]

Fantástica colección de paradojas, un mundo fascinante que te hace pensar, reflexionar y quedarte dándole vueltas para encontrar el sentido en situaciones completamente antiintuitivas.

No me han gustado mucho las explicaciones, que en algunos casos me han parecido insuficientes y en otros poco claros. Estos últimos dudo si será cuestión de la traducción que he leído o si será achacable a la redacción original del propio Gardner. Eso hizo que me plantease incluso en bajar mi valoración a 3 estrellas, pero al final la sensación que me ha dejado el libro es bastante buena, porque realmente he disfrutado leyéndolo. Y de eso se trata, ¿no? Así que tiene pegas como para ponerle 5, pero 4 bien las merece.

[Xènia Casanovas · Rating 5 out of 5]

Cuando ves este libro piensas que en tu vida te lo leerás. Y así es.
Yo tuve que leérmelo de forma obligada debido a mi Proyecto de Recerca de 2n de bachiller, ¡y no dudaría en volver a leérmelo! Siempre he considerado que el mundo de las paradojas es un sinfín de cuentos carentes de lógica o que, simplemente, te invitan a pensar. Estoy muy satisfecha de haber elegido este tema para mi proyecto porque me obligó a leerme este libro que, a pesar de mi afinidad por las paradojas, jamás en la vida pensaría que me lo iba a leer!