I have read many books on problem solving and breakthrough thinking. This is by far the most accessible. David Perkins is co-director of "Project Zero", an educational research group at Harvard Graduate School. He has a PhD in mathematics and artificial intelligence from MIT, so he is very qualified to be writing on this subject.
Perkins covers a lot of ground in this book and manages to explain his theory of problem solving from many different aspects using varied problems and examples.
The title refers to Archimedes and his breakthrough discovery of the displacement of water to calculate volume. This is the first example, which is drawn from this near mythological event. Perkins continues to delve deeper into how breakthroughs in thinking occur.
He outlines a series of steps that he believes are key to breakthrough thinking. These are abstracted from many different examples of breakthrough thinking. (Long Search, Little Apparent Progress, Precipitating Event, Cognitive Snap, Transformation).
From certain aspects this is the easy part, defining a set of steps that seem to be common in breakthroughs. The interesting part for a reader will be, can Perkins describe a series of steps that can define how the mind can actually achieve breakthroughs? Defining the steps always seems reminiscent of seeing the instructions for tying a bow tie, steps 1 to 4 seem reasonable, and then suddenly in step 5 you have a tied bow tie. But how do you get from step 4 to step 5 is always left a mystery that needs to be worked out. Obviously with a little fiddling, and knowing the end result, tying a bow tie, is a breakthrough that most people can achieve. But how to get from precipitating event to cognitive snap (or Eureka) is a little trickier to define. Is there really a series of steps to achieve breakthroughs?
Perkins spends the rest of the book, delving deeper and exploring this subject. He tackles some of the common pitfalls of thinking that can hamper someone's ability to solve a problem. Breakthrough problems by their very nature need to breakthrough current assumptions and thought patterns. Perkins uses the analogy of the Klondike gold rush to explore the principles further. How do you find a small amount of gold in a large area? Perkins feels this is analogous to finding solutions to breakthrough problems. He describes some common pitfalls, using this analogy (Wilderness of Possibilities, Clueless Plateau, Narrow canyon of exploration, Oasis of False Hope).
Perkins uses many puzzle examples throughout the book. Some of the puzzles are old, but still useful to explore. He defines the different kinds of puzzles, the ones that can be solved by a linear progression of thought, and then the second kind that needs a breakthrough in thinking (not always on a large scale), this is where linear logical progression will not reveal the answer. He uses the pitfalls as defined and shows how each of them can side track the puzzler from finding the solution.
At first, the nature of the Klondike analogy, seems to be too contrived and can be off-putting. But Perkins manages to demonstrate the different aspects of breakthrough thinking using it. The book is filled with puzzles that will be fun for anyone who loves puzzles. Perkins explores many aspects of thinking, delving into artificial intelligence and evolution. Sometimes I felt that some of the chapters were probably irrelevant, but on the whole, this book is very cohesive and manages to follow through a logical progression through the many facets of breakthrough thinking. It is very accessible, and its simple nature, could be mistaken for lack of substance. But there is a lot of information, and the reader will learn many techniques and can actually put together a set of steps to "help" them solve problems. Obviously it is not going to give a step-by-step manual to come up with the next "Theory of Evolution" but there is a lot of information here that can be used practically to help solve puzzles, and help solve real world problems. Perkins never succumbs to boasting that this is an exhaustive set of principles to achieve breakthroughs in thinking.
This is a very rewarding book, but if you are looking for a "how to" guide, you will not find it here. But you can extract many helpful insights from this book that will help you solve problems.
I highly recommend this book for anyone interested on breakthrough thinking.
Note: This is published in paperback under a different title "The Eureka Effect"
Note: This was initially published in hardback as "Archimedes in the Bathtub"