I know of no subject in mathematics that has intrigued both children and adults as much as the idea of a fourth dimension -- a spatial direction different from all the directions of our normal three-dimensional space. Philosophers and parapsychologists have meditated upon this dimension that no one can point to but may be all around us. Theologians have speculated that the afterlife, heaven, hell, angels, and our souls could reside in a fourth dimension -- that God and Satan could literally be lumps of hypermatter in a four- dimensional space inches away from our ordinary three-dimensional world. Throughout time, various mystics and prophets have likened our world to a three-dimensional cage, and have speculated on how great our perceptions would be if we could break from the confines of our world into higher dimensions. Yet, despite all the philosophical and spiritual implications of the fourth dimension, this extra dimension also has a very practical side. Mathematicians and physicists use the fourth dimension every day in calculations. It's part of important theories that describe the very fabric of our universe.
- Arthur C. Clarke:
"I can't imagine anybody whose mind won't be stretched by this book -- but I only hope it isn't responsible for an outbreak of mysterious disappearances."
- Ian Stewart, Mathematics Awareness Center, University of Warwick:
"Pickover just seems to exist in more dimensions than the rest of us."
- Professor Paul J. Nahin, author of Time Machines:
"Cliff Pickover's new book is a perfect reflection of its author's imagination, an imagination so vast it MUST be hyperspacial itself! Three dimensions are simply not sufficient to explain Pickover's astounding breadth of knowledge on such arcane matters as spacetime wormholes, random walks, and the enormous science fiction literature dealing with the higher dimensions. The book is not loaded with mathematics (that's a plus!), but even the purest of mathematicians will find the ideas in it deep, and Pickover's discussions of them stimulating."
- Dr. Michio Kaku, author of Hyperspace:
"Whimsical, delightful, and always fun, Surfing through Hyperspace will tickle the imagination and boggle the mind. Hyperspace is where physics, mathematics, and science fiction collide. Pickover is our mischievous tour guide for the bizarre realm of higher dimensions, where common sense becomes obsolete. Surfing through Hyperspace teases us to imagine the unimaginable."
- Charles Ashbacher, Editor, Journal of Recreational Mathematics:
"There is no more difficult topic for the human mind to grasp than spatial dimensions beyond three. In this book, Clifford Pickover weaves a science fiction tale with embedded mathematical analysis that explains the fourth dimension in a unique and amusing way. The approach works well in a manner reminiscent of the classic work, Flatland, by Edwin Abbott."
- Publisher's Weekly, August 1999:
"Hyperbeings have kidnapped the president! Prolific Discover magazine columnist Pickover (Time: A Traveler's Guide) alternates expositions of math, physics and geometry with episodes of instructional science fiction while showing interested amateurs the mathematical and physical properties of higher spatial dimensions.
Familiar analogies from Edwin Abbott's classic Flatland link up with odder ones from Baha'i and Christian scriptures, The X-Files and the superstring theories of modern cosmologists, as Pickover explains how to trap a 4-D organism or why one twirl through a fourth dimension could turn you into your mirror image. Pickover's usual whimsy is in full force here as he focuses on what four-dimensional organisms could (or do) look like to us: 4-D lifeforms, he explains, could make any 3-D object vanish (or reappear) by lifting it out of (or dropping it back into) our 3-D space. And 4-D creatures with anatomies analogous to ours would probably look, from our limited perspective, like sets of floating, unconnected flesh blobs.
In the book's science-fictional sections, 'you' (a Mulderesque FBI agent) team up with a skeptic named Sally to investigate mysterious hyperbeings. These second person adventures seemed aimed at young readers, though they don't get in the way of more sophisticated ideas. Several substantial appendices describe puzzles and games related to hyperspace, while others explain related topics (like the mathematical entities called quaternions) or suggested further reading. Line drawings throughout."
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this page last updated 28 December 2002
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