Beyond Reason: Eight Great Problems That Reveal the Limits of Science / Edition 1by A. K. Dewdney
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/b>… See more details below
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.
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Table of Contents
Introduction: Where Reason Cannot Go.
Math in the Cosmos.
1. The Energy Drain: Impossible Machines.
2. The Cosmic Limit: Unreachable Speeds.
3. The Quantum Curtain: Unknowable Particles.
4. The Edge of Chaos: Unpredictable Systems.
Math in the Holos.
5. The Circular Crypt: Unconstructable Figures.
6. The Chains of Reason: Unprovable Theorems.
7. The Computer Treadmill: Impossible Programs.
8. The Big-O Bottleneck: Intractable Problems.
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