Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

3/15/2012

Book of the Fallacy: A Training Manual for Intellectual Subversives Review

Book of the Fallacy: A Training Manual for Intellectual Subversives
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Madsen Pirie's The Book of the Fallacy: A training manual for intellectual subversives is a highly entertaining introduction to logical mistakes or fallacies. There is no end to human error and folly, and Pirie's short treatment of the 50 most egregious fallacies is both instructive and entertaining. I will try to order the text through Amazon's out-of-print service, but also have access to one at the local library. It is a pity that the book has gone out of print. There are many newer books on the market, dealing with similar material, but this is the most accessible I've experienced.

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Those tricks of logic or language used to persuade people into accepting false beliefs are gleefully exposed.

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2/06/2012

A Gardner's Workout: Training the Mind and Entertaining the Spirit Review

A Gardner's Workout: Training the Mind and Entertaining the Spirit
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It is most certainly not an exaggeration to say that more people have learned more mathematics at the literary knee of Martin Gardner than from anyone else. His columns in Scientific American and subsequent collections in book form have been an inspirational and educational experience for millions. When he "retired" from writing the column, he was succeeded, not replaced.
Since his departure from the duties of writing regularly for Scientific American, he has kept busy writing occasional articles for many different publications. He also stays active in following advances in mathematics and how it is taught in the American society. This book is a collection of many of the mathematical articles as well as some of his comments regarding how mathematics is currently taught.
While reading the book, I was once again placed in awe of his ability to state the mathematical experience in clear terms. One point follows from another with little or no extraneous fluff. There are many writers of technical books who adopt the style of adding in cutesy dialog that supposedly makes it easier to understand. In keeping with his personality, Gardner simply explains it and is done. It is very refreshing to read material in this form.
The topics are generally recreational in nature, although some, particularly those about artificial intelligence (AI) are philosophical. He dismisses the success of the chess playing computers as an insignificant special case. This is true, but he misses what should be the real point of Deep Blue defeating Gary Kasparov. The fact that it took such a computational monstrosity that does only one thing and years of programming to defeat Kasparov shows us how efficient the human brain is and how difficult it is to mimic human intelligence.
The remaining topics, such as magic squares, tiling, dissections and word play all sum up recent advances in the field. My favorite essay is one that details how to program magic tricks on a computer. The strategies used are very simple and show how easy it is to perform tricks that seem impossible.
I thoroughly enjoyed the book and consider it a necessary read for anyone interested in recreational mathematics. An entire generation has arisen since Gardner ceased his regular writings and I encourage all math teachers to examine his essays for material to use in their classrooms. They are the best explanations of mathematics you can find and it has already been proven that they light a fire of enthusiasm for mathematics.


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For many decades, Martin Gardner, the Grand Master of mathematical puzzles, has provided the tools and projects to furnish our all-too-sluggish minds with an athletic workout. Gardner's problems foster an agility of the mind as they entertain. This volume presents a new collection of problems and puzzles not previously published in book form. Martin Gardner has dedicated it to "all the underpaid teachers of mathematics everywhere, who love their subject and are able to communicate that love to their students."

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