The book under review titled Beyond Reason - 8 great problems that reveal the limits of science by A.K. Dewdney is an excellent book.
The author was the 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!
His research in unknowable particles, unpredictable systems, unprovable theorems, impossible programs and intractable problems reflects in this well written book.
In eight chapters the scientist's mind explores the following eight great problems that limits the science:
1. It is not possible to build a machine that runs forever with no source of energy, yet produces usable energy.
2. It is not possible for matter or energy to travel faster than the speed of light in a vaccum.
3. The detailed behaviour of any quantum system, whether it consists of electrons,photons or atomic particles cannot be predicted by any mathematical law or computer program.
4. There are some classical systems (such as the weather or planetary motions) the long term behaviour of which can not be predicted by any mathematical law (or computer)
5. It is not possible using only rule and compass, to construct a square equal in area to that of a given circle.
6. There are some theorems (true mathematical statements) that we will never be able to prove.
7. There are some yes/no questions,perfectly well defined, that no computer no matter how fast or powerful can answer.
8. There are some mathematical problems that computers can solve only by taking an exponential amount of time.
In the first chapter Dewdney deals with the impossible perpetual motion.
He quotes a very rare Sanskrit book on astronomy, Siddhanta Chudamani, which describes a self-turning wheel.One of the slokas describe a self turning wheel. It states that if the wheel was properly supported, it would run for ever!
Nobody has tried to construct this wheel, so far! The other chapters deal with the other problems in detail.
Each chapter of the book explains in detail the mathematics involved in these eight problems which limits the science.
A list of reference books along with an index is very useful for the readers.
I strongly recommend this book for the people who are interested in Science and Religion. 224 pages of fun!
Dewdney's other books, A Mathematical Mystery Tour, The Planiverse, Yes, We have no neutrons, 200% of nothing were all well received by the scholars.
