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by A. K. Dewdney (Author)
A mind-bending excursion to the limits of science and mathematics
Are some scientific problems insoluble? In Beyond Reason, internationally acclaimed math and science author A. K. Dewdney answers this question by examining eight insurmountable mathematical and scientific roadblocks that have stumped thinkers across the centuries, from ancient mathematical conundrums such as "squaring the circle," first attempted by the Pythagoreans, to G?del's vexing theorem, from perpetual motion to the upredictable behavior of chaotic systems such as the weather.
A. K. Dewdney, PhD (Ontario, Canada), was the author of Scientific American's "Computer Recreations" column for eight years. He has written several critically acclaimed popular math and science books, including A Mathematical Mystery Tour (0-471-40734-8); Yes, We Have No Neutrons (0-471-29586-8); and 200% of Nothing (0-471-14574-2).
Front Jacket
BEYOND REASON
In the past tow centuries, we have witnessed an unparalleled expansion in scientific and technical horizons. But with our longer view of things, the horizon is now interrupted, here and there, by walls. With our newfound knowledge and technical abilities has come an understanding of the limitations of science and technology. Beyond Reason provides a mind-bending exploration not into what is doable and knowable-but what is undoable and unknowable.
Temporary barriers to understanding are sometimes swept away by knowledge, each advance revealing new vistas. But some barriers appear to be permanent. Author A.K. Dewdney explores these grand limitations that stand like gr5anite walls around our scientific and technological enterprise. these are not the barriers of ignorance, but knowledge. It is perhaps only ignorance that prevents us from traveling thought time; Certainly no theory yet p5rohibits the possibility. Yet the presence of chaos in our atmospheric system implies rather strongly that we shall never predict the weather much better than we do now.
Beyond Reason explores these barriers and the theories that give them form and substance. We shall apparently never travel faster than the speed of light, nor shall we ever build a perpetual motion machine that performs useful work. After laying the foundations of each theory, illuminated by stories of the scientists who didcovere4d them, A.K. Dewdney then goes on to ask "What if"? Is there a way out? Are there no secret passages through these walls?
Divided into sections that cover inductive and deductive science, Beyond Reason explores the theories and caveats behind:
- Unknowable Particles. Why the detailed behavior of any quantum system-Whether consisting of electrons, photons, or atomic particles-cannot be described or predicted by any mathematical law.
- Unpredictable Systems. Why there are some classical systems (such as the weather or planetary systems) the long-term behavior of which cannot be predicted by any computer.
- Unprovable Theorems. Which theorems 9 true mathematical statements) will never be proven? Gödel's theorem says they exist.
- Impossible Programs. How it is that some problems with simple yes/no answers will never be answered by a computer, no matter how it is programmed.
- Intractable Problems. Why will some problems, even when they can be solved by a computer, nevertheless take forever to solve? Cook's theorem points the way.
Back Jacket
PRAISE FOR A.K. DEWDNEY'S PREVIOUS WORKS
200% of Nothing
"It is impossible to read this timely, important book without enjoyment and eye-opening enlightment." -Martin Gardner
"In today's world 'innumeracy' is an even greater danger than illiteracy, and is perhaps more common.... I hope that this wise and witty book will provide cures where they are possible, and warnings where they are necessary. It's also a lot of fun. I can guarantee that 100 percent." -Arthur C. Clarke
Yes, We Have No Neutrons
"We need more books like this-especially if they're this much fun to read."-Wired
"Written with wit and a touch of pathos-and sure to please science lovers." -Publishers Weekly
The Planiverse
"It's not everyone who gets to design a universe from scratch but A.K. Dewdney has done just that."-The Boston Globe
"Once you have been captivated by the two-dimensional Ardean world, the problems facing its difficult technology haunt you, begging for more solutions. Arde easily becomes a puzzle without end." -The New York Times
A Mathematical Mystery Tour
"Dewdney spins an absorbing narrative...an amenable introduction to a difficult subject." -Publishers Weekly
Author Biography
A.K. DEWDNEY, PH.D., is the author of several critically acclaimed math and science books, including A Mathematical Mystery Tour; Yes, We have No Neutrons; and 200% of Nothing, all from Wiley. He was a member of the computer science department at the University of Western Ontario and at the University of Waterloo for a combined period of thirty years before retiring. In 1996, he became an adjunct professor of biology at UWO. For eight years, Dewdney was the Computer Recreations columnist for Scientific American magazine.
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