Product Description

Praise for Five Golden Rules

"Casti is one of the great science writers of the 1990s. . . . If you′d like to have fun while giving your brain a first–class workout, then check this book out."–Keay Davidson in the San Francisco Examiner.

"Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti′s gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." –Christian Science Monitor.

"Merely knowing about the existence of some of these golden rules may spark new, interesting–maybe revolutionary–ideas in your mind." –Robert Matthews in New Scientist (United Kingdom).

"This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." –Ben Bova in the Hartford Courant

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." –Rudy Rucker, author of The Fourth Dimension.

"With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." –John Allen Paulos, author of A Mathematician Reads the Newspaper.

Product Details

• Amazon Sales Rank: #367609 in Books
• Published on: 1997-10-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 235 pages

From the Back Cover
Praise for Five Golden Rules

"Casti is one of the great science writers of the 1990s. . . . If you′d like to have fun while giving your brain a first–class workout, then check this book out."–Keay Davidson in the San Francisco Examiner.

"Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti′s gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." –Christian Science Monitor.

"Merely knowing about the existence of some of these golden rules may spark new, interesting–maybe revolutionary–ideas in your mind." –Robert Matthews in New Scientist (United Kingdom).

"This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." –Ben Bova in the Hartford Courant

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." –Rudy Rucker, author of The Fourth Dimension.

"With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." –John Allen Paulos, author of A Mathematician Reads the Newspaper.

About the Author
JOHN L. CASTI is a resident member of the Santa Fe Institute and a professor at the Technical University of Vienna. He is the author of four other trade books, Would–Be Worlds (Wiley), Paradigms Lost, Searching for Certainty, and Complexification, as well as the two–volume Reality Rules, a text on mathematical modeling (also published by Wiley).

Customer Reviews

Fails in its mission to make difficult concepts accessible
To make difficult concepts accessible, inevitably you have to be economical with the truth. You have to remain aware of what your audience does and doesn't know, and what lies you have told. Maths teachers do this at every level, so there are some people who are well practised at it.

I had to reach for graduate-level textbooks to work out what Casti was trying to tell me. It ought to be the other way around.

This book is written at a level for the scientifically/mathematically literate reader. So he cannot be allowed to get away with the sloppiness I will now demonstrate.

Casti discusses the concept of convexity in relation to topological spaces, without telling us that convexity is an algebraic or geometric property, not a topological property. Moreover the non-topological nature of convexity is plain to the reader who has understood what went before, since straight lines are not an admissible concept in "rubber sheet" topology. The reader with a little mathematical education (many of the target audience) will further realise that convexity is a property of sets within a larger space, not of a space itself, so to refer to a "convex topological space" is a contradiction in terms.

To illustrate convexity (surely unnecessary for the target readership), he draws some convex and non-convex sets. But some of the non-convex sets plainly possess the Brouwer property that is asserted only for convex sets. There is no explanation of this contradiction. He then asserts that the Brouwer property is held by the surface of a sphere, a set which is non-convex and cannot even be topologically deformed to a convex set.

If the reader was to gain any insight into the Brouwer property, then surely it is to obtain an intuitive understanding of why Brouwer's theorem is true for the surface of a sphere but false for a ring. I would love to understand this. Casti does not even try.

The problems illustrated here are present, to a greater or lesser extent, throughout the rest of the book.