Inventor Book Reviews

Archimedes' Bathtub

by David Perkins, 2000, 292 pages, $24.95 paper, ISBN 0-393-04795-4.  Published by W. W. Norton.

Inventors differ from the average person because they practice an art and logic that enables them to make breakthroughs in solving problems which ordinary reason and common sense fail to solve.  This author selected as a prime example of such insightful thinking the oft told story of how Archimedes, some 2200 years ago, determined if the king's crown was made of pure gold.  As you may recall from elementary school, as Archimedes lowered himself into his bathtub, the water rose and an insightful thought occurred to him.  He realized the volume of the irregularly shaped crown could be determined by how much water it would displace and with knowing the density of pure gold he could establish what the crown should weigh for its volume.

The book is devoted to answering the question of how breakthrough thinking works.  Many examples of such thinking are given and analyzed.  The author notes five stages or steps that many breakthroughs seem to follow: "Long search, little apparent progress, precipitating event, cognitive snap, and transformation".  He cites Leonardo's helicopter and the Wright brothers as examples.

He offers Edison's search for a practical light bulb filament as an example of the long search process.  He notes that Edison called his systematic scanning process "draghunt".

The author uses the Great Klondike Gold Rush of 1897-1899 to illustrate four basics that underlie breakthrough thinking.  He calls these the "wilderness of possibilities, the clueless plateau, the narrow canyon of exploration, and the oasis of false promise.  He applies these four "Klondike logic" elements to many examples of problems requiring breakthrough solutions.  He suggests how detecting clues, reframing, and decentering can put an end to going in circles.

To avoid being dry and abstract, the book contains many simple puzzles that illustrate how these analogies and techniques can be applied.  Some will amuse you and some may infuriate you.  We, as humans, tend to look only for the reasonable solution and miss the "unreasonable".

The book also looks at several of the familiar idea producing and creative problem solving techniques such as brainstorming and techniques not as not as well known such as bisociation, Synectics, and the triarchic theory of intelligence.  He examines both their positive and negative aspects.

The author compares how mother nature has solved problems with human solutions.  For example, how by evolution the insects and birds have achieved flight.

Much effort, through the years, has been devoted to trying to understand how insightful thinking takes place and how it might be acquired.  For example, in 1927, a German psychologist studied the familiar observation that we remember unsolved problems better than we remember solved problems (Zeigarnik effect).  Why do impasses seem to circulate in our memory banks and can we utilize this trait better?

The author calls attention to the fact that "knowing too much for your own good" can be a villain in problem solving.  A mental set may prevent trying different approaches.

In fairness, the author also examines the point of view that some scientists hold that sudden discovery is really a myth and that sequential reasoning is the proper technique.  The author concludes "...the cognitive snap is alive and well in the world of science, as in other worlds". Archimedes'Bathtub

Puzzle lovers will be delighted to see the classic nine dot problem has two solutions whereby one straight line can connect all nine dots instead of the usual four straight lines solution!

The author has a Ph.D. in mathematics and artificial intelligence, yet his book can be read by a high school student.  This book will be a real delight to anyone who has ever tackled difficult and "unreasonable" problems.  It can be read as recreation or as a serious approach to understanding the mysterious phenomena of sudden in-sight.