Beyond Reason: Eight Great Problems That Reveal the Limits of Science (Hardcover)

by A. K. Dewdney (Author) "IT IS NOT POSSIBLE TO BUILD A MACHINE THAT RUNS FOREVER WITH NO SOURCE OF ENERGY, YET PRODUCES USABLE ENERGY..." (more)
Key Phrases: own description tape, quantum curtain, constructable number, Fermat's Last Theorem, New York, Principia Mathematica (more...)

Editorial Reviews

From Publishers Weekly
Dewdney (A Mathematical Mystery Tour), best known for the Scientific American column "Computer Recreations," which he wrote for eight years, sets an impressive goal for himself: "to discover how physical reality depends on mathematical reality, and to examine how mathematical reality manifests itself." He attempts to do this by outlining four problems in the physical realm and four in the mathematical realm that he believes can never be solved. The topics he discusses are largely of great interest to science and math buffs: perpetual motion, the speed of light, Heisenberg's uncertainty principle, chaos theory, squaring the circle, unprovable but true mathematical theorems, "simple" problems that no computer program can solve, and the fact that some mathematical problems would require an infinite amount of computer time to solve. In his chapter on chaos theory, for example, Dewdney does a very nice job of explaining why we will never be able to predict the weather accurately more than four days in advance. The problem throughout the book, however, is that he alternates between colorful prose or explanations of basic terms (such as "primary number") and relatively dense mathematics (transcendental and transfinite numbers), never settling on who the appropriate audience for this study might be. B&w illus.
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

From Booklist
Inventors and engineers have invested centuries of effort trying to build a perpetual-motion machine. They have never succeeded, but without their valiant attempts, a particularly piquant chapter would be missing from this new book on scientific impossibilities. Science-writer Dewdney teases illuminating logic and formulas from the despair of physicists who wish to predict how electrons will dance, from the frustration of computer programmers who want to resolve certain types of yes-no questions, and from the embarrassment of meteorologists who would like to predict next week's weather. Rigorous enough to challenge intelligent readers but not so daunting as to overwhelm the nonspecialist, the investigation of each impossibility clarifies the barriers that forbid further progress along certain theoretical paths, limning the conceptual boundaries of science and even reflecting the limitations inherent in the structure of human rationality. Still, Dewdney concedes a catalogue of scientific impossibilities may just provoke some maverick to do what the greatest scientists have always done: enlarge the limits of the possible. Bryce Christensen
Copyright © American Library Association. All rights reserved

See all Editorial Reviews

Product Details

• Hardcover: 240 pages
• Publisher: Wiley (April 23, 2004)
• Language: English
• ISBN-10: 0471013986
• ISBN-13: 978-0471013983
• Product Dimensions: 9 x 6 x 0.9 inches
• Shipping Weight: 15.5 ounces (View shipping rates and policies)
• Average Customer Review: 2.2 out of 5 stars See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #1,125,073 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

3.0 out of 5 stars A Tough Slog, August 31, 2006

By	Nathan W. Casebolt "nwcasebolt" (Valencia, CA United States) - See all my reviews (REAL NAME)

"Some of the integers z will appear inside their corresponding subsets f(z) and some won't. If we take the set of all integers z that are not members of f(z) and place them in a special set W, we can ask a very serious question about W: To what integer does W correspond under this scheme? If we write that integer as w, we can ask if w belongs to W. If w belonged to W, then w would not be a member of f(w) by the definition of W. But wait! This is a contradiction, since W=f(w). On the other hand, if w were not a member of W, then w must lie in f(w) (i.e., W), another contradiction" (p. 143).

If that paragraph makes you giddy with glee, then you'll love Beyond Reason by A.K. Dewdney. I found such paragraphs less delightful, but it does illustrate my recurrent experience with this book: the nagging feeling that just a little closer reading will unlock what he's trying to say. Dewdney mixes layman's prose with mathematical abstractions, and the resulting book is like a girl who won't say yes or no. She's just interesting enough to make the frustration feel worth it (at least for a while).

I'm not a mathematical wizard. While I scored very highly in reading comprehension and language skills on the ACT, my math scores barely passed the threshold of acceptability (think of an airplane chipping its undercarriage on the peak of a mountain). I passed high school algebra and geometry with tears and travail, and never wanted to know anything about calculus or trigonometry beyond how to spell them. Dewdney makes me wish I'd worked harder at it. Not only because I might have a shot at fully grasping the nature of the problems he presents, but also because he's opened my eyes to the importance of mathematics in understanding our universe. As he writes on page 2, "We still have to account for the amazing success of mathematics as a description of physical reality. The precision of so many theories of physical reality may hint at a deeper truth, that mathematics is a major structural foundation of our universe."

Thus is introduced the premise of these eight chapters, exploring what appear to be the mathematical barriers that hem us into this three-dimensional reality. Since we're on the topic of structure, the book is divided into two halves. Part One deals with the mathematical realities that tell us we will never (1) build a perpetual motion machine, (2) surpass the speed of light, (3) predict the behavior of quantum particles, or (4) predict the long-term behavior of dynamical systems (e.g., the weather). Part Two deals with more abstract mathematical limits, telling us that we will never (5) square the circle, (6) prove every true mathematical theorem, (7) compute the answer to every yes or no question, or (8) compute every mathematical problem.

At the end of each chapter, Dewdney includes a short section entitled "Is There a Way Around It?", exploring the theoretical possibilities of surmounting these apparently insurmountable barriers to knowledge. This is the caveat hanging over the book like the Damoclean sword: will it still be relevant a century or two from now, or will we have uncovered deeper and broader mathematics that will reveal the key to passing through these barriers?

I found the book's main fascination in the concept that mathematics describe the boundaries of the universe. In other words, the history of mathematical discovery has been like a man in an empty space slowly lighting candles to explore his surroundings. That is, until he lights a candle that reveals a doorless wall. Then he finds another, and another, and yet another. He realizes there is a profound structure surrounding him, but he can't see what the structure is. As for what lies beyond the structure...well, no amount of imagination can see through walls.

In summary, Beyond Reason is a tough slog unless you're mathematically sharp. However, it has given me a glimpse (however unsatisfactory my vision) of the boundaries on our existence, which is like getting to touch God's fingerprints. That alone is the worth the furrows left from scratching my head.

11 of 13 people found the following review helpful:

4.0 out of 5 stars Obviously for a Specific Audience, September 27, 2004

By	J. Socol "MathMajor" (E. Lansing, MI) - See all my reviews (REAL NAME)

Dewdney's book is very interesting, challenging, and is, admittedly, a tough read. You might need ready access to Google to look up some of the terms he uses. But for the most part, anyone who took high school math and physics should be able to understand it. I'd recommend it to college and graduate students, and math and physics instructors. It has its down points, but on the whole is a very intriguing look at some of the problems afflicting all our logic.

10 of 22 people found the following review helpful:

1.0 out of 5 stars Very Confusing, May 3, 2004

By A Customer

The title of this book compelled me to try it as it sounded fascinating. However, I found it to be very difficult to understand for the average reader. Dewdney frequently introduces terms that he assumes the average person will understand. In most cases that is true, however there are a few times when it isn't. Furthermore, rather than relying on simple examples or other illustrations, he uses very difficult and elaborate examples. His writing clearly shows that he is a scientist and writing for an audience who has a significant background in science. I tried reading each of the 8 problems and came to the same conclusion. Writers like Bryson or even Hawking are much better at taking complex science and math and making them understandable to the layperson.