The Power of Logical Thinking

This is one book that can really change your outlook and your life. Its first sections are largely based on replies Marilyn vos Savant made to the statistical puzzles her readers submitted to her "Ask Marilyn" column in "Parade" magazine. However Marilyn has added a lot of new insights to the responses she gave over the years. Many of her explanations of the math involved in these problems are counter-intuitive and therefore very surprising. They make us reassess a whole range of real-life situations we've probably been misjudging most of our lives, to our daily detriment. That's what makes this book so riveting - and so important. The book starts with what has become the on-going cause celebre of "The Monty Hall Dilemma." Some years ago, a reader innocently asked about the best strategy to employ on the "Let's Make a Deal Show" when guessing which of three doors hid a valuable prize. Marilyn's answer provoked a firestorm of protest. Many of the people who most vehemently disagreed with her answer were mathematics or physics professors. Marilyn's original answer was correct, and finally, after many rounds of point and counter-point, she managed to convince most of her critics. However, people continue to explore the implications of her statistical analysis. Some have even found imbedded in Marilyn's answer to this question a challenge to the way experiments in the field of quantum mechanics have traditionally been interpreted. The discovery of the nature of reality could hinge on an understanding of "Let's Make a Deal" strategy! Portions of this continued exploration into the problem's implications are presented in the book's first chapter and in a lengthy Appendix. Another example of one of Marilyn's very surprising (and in this case, very comforting) statistical proofs is presented in her section on interpreting the results of medical tests. It turns out that if you test positive for some disease or condition, even having used a presumably very accurate assay - the chances are still very small that you actually have that disease. Most doctors don't come close to realizing this. They assume that one positive test result is close to proof of your having the disease, and they often proceed accordingly with aggressive interventions. By following Marilyn's reasoning and advice on this topic - you could save your life. Then in the last section of the book, Marilyn provides insights into many of the statistics politicians invariably throw around to "prove" that the other guy ran the Country into the ground, while their own Party ushered in an unprecedented period of prosperity. Although this book was written in 1996, it is surprisingly relevant to the 2009 recession. Most of Marilyn's advice about how to appraise politicians' figures regarding wages, unemployment, and purchasing power, might seem to come from a strong conservative perspective. However, whatever your politics, I think you'll find it hard to refute most of her conclusions. The one

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 the 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.

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.

If you want to understand how our minds are sometimes fooled into believing or assuming things that are not true, read this book. If you want to broaden your range of understanding, read this book. It is interesting and informative. The explanations that help you to understand the lapses of logic are very easy to understand.