Flatterland

by Ian Stewart, Perseus Publishing, $14.00,
ISBN 0-7382-0675-X, www.perseuspublishing.com, 2001

For many years, we have told the story of Flatland written in 1884 by Edwin Abbott. Flatland is the story of a man who lives in a two-dimensional world in which everything has width and height, but no thickness. It then describes what happens when a sphere crosses Flatland and the man in Flatland tries to understand what a sphere is about. Our use of this story has been as Abbott wrote it, to understand the nature of God--a being not limited to the three dimensions that make up our world. Other people have used Abbott's work in other ways, but everyone has agreed that he moved us to think about how foolish it is to try to confine our thinking to the world in which we live and not realize that there can be other dimensions out there that challenge anyone's imagination and thinking.

Ian Stewart has modernized Flatland. The story starts with Vikki, the great-great-granddaughter of the man who lived in Flatland and was visited by the sphere. Vikki finds an old notebook written by this man and tries to expand her thinking into dimensions beyond her own. Instead of the sphere that interacted with the hero in Flatland, Vikki comes in contact with Space Hopper who can guide her from one mathematical space to another. Space Hopper has two horns and a head that is an oblate sphere, so when he crosses Flatland head first, the horns leave two little circles, then the two circles with a circle between them for the top of his head, which then changes to one large oval.

With this introduction we read Vicki's diary as she is conducted through various dimensions in an "Alice in Wonderland" style. Stewart is a gifted and imaginative writer, and he brings the reader through various theories about everything from black holes to wormholes to hyperspace and 10-dimensional entities. Famous scientists in cosmology and quantum mechanics are woven into the story, so we read about "the domain of the Hawk King" clearly in reference to Steven Hawking. One chapter is titled "Cat Country" and takes us into Schroedinger's cat. The Feynman Diagram is discussed as a "Planithuthian who was doodling pictures of world lines of particles...." The planithuthian was named Richardfeynman, and planithuthians are three-dimensional beings.

Those with physics backgrounds or with familiarity with the modern discussions in quantum mechanics and the various theories of dimensional relationships will find this book clever, entertaining, and helpful. Some of the theories discussed are dubious, but that makes for challenging reading. Those without some background in these areas will find it bewildering. It will be useful to discussions about the nature of God, but at a level that will challenge all readers. It is not an apologetic book and has no discussions about God or spiritual things. It is useful, however, in understanding the foolishness of maintaining that all we can know is what we perceive through our senses, and also in understanding how a being in a higher dimension can function in a lower one.

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