The Power of Logical Thinking: Easy Lessons in the Art of Reasoning...and Hard Facts About Its Absence in Our Lives

Marilyn Vos Savant is known for her provocative articles in Parade Magazine and also gets publicity for her high IQ (a little too much publicity). But what really made her world famous was the reaction to her solution to a reader's question about a probability problem. Her answer was simple and direct but received the wrath and scorn of many mathematicians that thought she had blundered. This problem is now called the Monty Hall problem and discussion of it can be found in statistical journals and introductory textbooks. I use it in my elementary statistics classes to arouse the interest of my students.
This book is about the way that most people make decisions in their daily lives without logical thinking. Counterintuitive problems like the Monty Hall problem bring this home. Marilyn had confidence in her answer and stuck to her guns when many argued against her using only their degree credentials as support of their position.

Personally, I participated in the debate. When I read her article and saw my fellow mathematicians and statisticians condemning her, I wrote to her with an argument in her defense. Alas, she got so many letters that mine did not appear in her column. She seemed to delight in publishing more of the nasty critical letters than the ones in her defense. I guess she felt capable of defending herself inspite of her lack of an advanced degree in mathematics or statistics.

At this point I think she is milking it a bit as the same problem or a slight variation of it continues to show up in her column from time to time.

This book has a wonderful theme and it is played out in three parts, 1. how our mind plays tricks on us, 2. how numbers and statistics can mislead and 3. how politicians exploit our innocence. Many of the examples are not original and this terrritory, especially topic number 2., has been well covered by Huff and others dating back to 1954. But the coverage of US Presidential campaign of 1992 with all its distortions of economic data is new , interesting and thought provoking. That section alone is worth the price of the book.

Personally I bought it more for the detailed account of the history of the Monty Hall problem in her column and the even more interesting appendix "The Monty Hall Dilemma: To Switch or not Switch" by Donald Granberg. In addition to providing a rigorous account of the mathematical assumptions that lead to Marilyn's solution as teh correct one, Granberg did survey research to try to understand how people solve such problems and why they stick to erroneous solutions inspite of the excellent counter-arguments.

Though it did not have good critics, I decided to give it a go anyway. I was really expecting an essay on thinking and quite a structured text. In my mind, I formed the opinion that it would start with Parmenides or Socrates and after talking some thinking history, jump into some thinking theory commenting some bad thinking (fallacies, biases, etc). The title "Essay" made me think that.

To the contrary, the text is "just" a collection of a few of her postings in the Parade magazine and controversial opinions about them.

I have read lots of thinking books from De Bono, Buzan, Ehrenberg, Alder, Sharon Begley, Damasio, Francisco Rubia, etc. so don't take me wrong, I am quite a fun of the subject.

From my point of view this book is not good for teaching thinking nor provides further insight about the subject. You might only be interested if you are looking for examples of bad thinking. It can be instructive if you want to gain a deeper thinking approach, but your thinking is not guided anyway so I could not see its value.

I kind of had the feeling (just guessing) that the Editor might just have used the attention brought around the Monty Hall problem to put together some articles and answers to them in a book.

Marilyn vos Savant has been a favorite of mine for some years now, so when I saw this book available used at a local bookstore, I readily picked it up (in nice condition, no less!). This book is filled with excellent examples of logical fallacies and counter-intuitive word problems.

An example that comes to mind: a man walks up a mountain hike, stopping for lunch and time to enjoy the scenery. What are the odds that the next day, walking down, that he will be at the very same place at the very same time (assuming he leaves and arrives back at the same time)? The surprising answer? One hundred percent. The proof, visualized? Imagine a ghost walking up the path the same way the man went up at the same time he leaves to go down. They *have* to meet up at some point, and that will be the place and time. Amazing.

Other examples, more applicable to real life, include the odds of a false positive in a drug test (fifty/fifty) and the misuse of the average in determining average pay for a company. To someone who is not educated on logic and numbers, this is a fascinating and groundbreaking look at how our intuition is completely wrong most of the time.

For anyone interested in using their minds (logic, reason, rationalism) this book is definitely worth a read!

After a basic introduction to some logical fallacies such as the statistical implications of some drug tests, this book moves to the now famous Monty Hall problem. This seemed like a simple problem on the surface. On a game show you are given the choice of three doors behind one of which is a fabulous prize. You pick one and afterwards the host turns around one of the wrong door. Then he offers you to keep the door you originally chose or to change doors. Do you stay or change? This simple problem caused a great deal of controversy and numerous letters after Marilyn Vos Savant stated that it would be better to switch. Her explanation is here as well and letters from various scholars as to why she was wrong. Turns out, she was right.
With that background to catch your interest (and it does so very well) she then moves on to other topics and how statistics can be used to support just about any position. Of particular fascination are the ways in which our intuition leads us to one conclusion but logic and mathematics prove that conclusion to be wrong. As a good example, she covers politics and how the political engine uses our intuitional errors and statistics to prove both sides right!
I will have to say that she does a good job of explaining the problems and conclusions in a style that even someone who does not understand mathematics very well can still comprehend. There are several other books that cover similar topics and if you like this one then you might also try them. I loved Innumeracy and found it fascinating to read through.

Marilyn Vos Savant is known for her provocative articles in Parade Magazine and also gets publicity for her high IQ (a little too much publicity). But what really made her world famous was the reaction to her solution to a reader's question about a probability problem. Her answer was simple and direct but received the wrath and scorn of many mathematicians that thought she had blundered. This problem is now called the Monty Hall problem and discussion of it can be found in statistical journals and introductory textbooks. I use it in my elementary statistics classes to arouse the interest of my students.

This book is about the way that most people make decisions in their daily lives without logical thinking. Counterintuitive problems like the Monty Hall problem bring this home. Marilyn had confidence in her answer and stuck to her guns when many argued against her using only their degree credentials as support of their position.

Personally, I participated in the debate. When I read her article and saw my fellow mathematicians and statisticians condemning her, I wrote to her with an argument in her defense. Alas, she got so many letters that mine did not appear in her column. She seemed to delight in publishing more of the nasty critical letters than the ones in her defense. I guess she felt capable of defending herself inspite of her lack of an advanced degree in mathematics or statistics.

At this point I think she is milking it a bit as the same problem or a slight variation of it continues to show up in her column from time to time.

This book has a wonderful theme and it is played out in three parts, 1. how our mind plays tricks on us, 2. how numbers and statistics can mislead and 3. how politicians exploit our innocence. Many of the examples are not original and this terrritory, especially topic number 2., has been well covered by Huff and others dating back to 1954. But the coverage of US Presidential campaign of 1992 with all its distortions of economic data is new , interesting and thought provoking. That section alone is worth the price of the book.

Personally I bought it more for the detailed account of the history of the Monty Hall problem in her column and the even more interesting appendix "The Monty Hall Dilemma: To Switch or not Switch" by Donald Granberg. In addition to providing a rigorous account of the mathematical assumptions that lead to Marilyn's solution as teh correct one, Granberg did survey research to try to understand how people solve such problems and why they stick to erroneous solutions inspite of the excellent counter-arguments.