- - Wednesday, October 31, 2012


By Edward B. Burger and Michael Starbird
Princeton University Press, $19.95, 168 pages

“The 5 Elements of Effective Thinking,” by distinguished mathematics professors Edward B. Burger and Michael Starbird, is not only inspirational and engaging but also educational and immensely practical. As the title suggests, the book details the implementation of the authors’ five elements of thinking and learning: Understand deeply, make mistakes, raise questions, follow the flow of ideas and allow yourself to change. “The 5 Elements of Effective Thinking” is replete with sound advice and fresh ideas while drawing on historic examples to substantiate the efficacy of putting the elements into practice.

In the first chapter, “Grounding Your Thinking: Understand Deeply,” the authors provide pertinent illustrations of deep understanding that produced profound advancements from the experiences not only of familiar past luminaries such as Newton and Picasso, but potential future luminaries such as the authors’ own students. The chapter wraps up with the advice, “Understanding simple things deeply means mastering the fundamental principles, ideas, and methods that then create a solid foundation on which you can build.”

Peppered throughout this slim volume are motivating gems such as this one by Winston Churchill: “Success is the ability to go from one failure to another with no loss of enthusiasm.” This quote appropriately introduces the book’s second chapter, an explanation of the second element, “Make mistakes,” or don’t be afraid to fail in order to succeed eventually.

Early in their book, the authors briefly quote George Polya, a very influential mathematician of the 20th century. In his popular 1954 book, “How to Solve It: A New Aspect of Mathematical Method,” Polya introduced a four-phase general approach to problem-solving that has similarities to “The 5 Elements of Effective Thinking.” Polya’s final phase involving “looking back” contains portions of Element 3 of the 5, “Raise questions.”

The recommendation of the fourth element, to “follow the flow of ideas,” highlights the role of continuity in deeply understanding, advancing through mistakes and asking questions to increase your own knowledge of a subject. Examining the history of an invention — for example, the light bulb — can help cement the history of an idea to its present and potential future applications. Also, learning the flow of any subject “makes each part far more stable and meaningful.” Furthermore, stopping when a solution to a problem is obtained or a need is fulfilled is the wrong action. The authors counsel, “We must get in the habit of seeing each advance as putting us on the lower slope of a much higher peak that has yet to be scaled.”

Finally, the first four elements are of no use if they are not practiced and do not produce a change in the practitioner. Thus, the authors refer to change as the quintessential element, and sometimes radical change is required. Warren Buffett is quoted in this regard: “In a chronically leaking boat, energy devoted to changing vessels is more productive than energy devoted to patching leaks.”

“The 5 Elements of Effective Thinking” is in no way a political volume. However, near the end of the book, this sage advice is offered, which can be applied to the upcoming election: “When the American Founding Fathers imagined a democracy that would reflect the will of the people, the people they envisioned were thoughtful, independent-thinking citizens who would understand the issues of their day and would turn their own clear wisdom to making sound decisions for the benefit of society.

“Surely more than ever the world needs thoughtful voices — voices that can ignore the bombast and heat of shallow excitement and focus instead on thinking calmly and sensibly about long-term goals and consequences.”

For our own sake and for others, citizens in all walks and stages of life need to do a better job of thinking and learning. The benefit is for all. As encouraged by the authors, the “modest habit of effective thinking will help you accomplish things you never dreamed possible.”

Anthony J. Sadar is a certified consulting meteorologist and science educator. He is author of “In Global Warming We Trust: A Heretic’s Guide to Climate Science” (Telescope Books, 2012).

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