Mind Tools: The Five Levels of Mathematical Reality (Paperback)

~ Rudolf Rucker (Author)

Editorial Reviews

From Publishers Weekly

Number, space, logic, infinitythese basic patterns seem to reflect essential features of our minds and of the world around us. By analyzing each of these building blocks from the standpoint of information (reduction of uncertainty), Rucker takes the uninitiated reader deep inside the world of modern mathematics. He moves from patterns in bathroom tiles to cellular automata or machines that can reproduce themselves. Sections cover the new science of fractals (fragmented, real-world shapes) and catastrophe theory, which deals with abrupt change. Mathematician David Hilbert's futile search for an all-encompassing mathematical system leads Rucker to navigate the shoals of symbolic logic, Godel's Incompleteness Theorem and Turing machines. The author's previous books include Infinity and the Mind and Software, science fiction about artificial intelligence.
Copyright 1987 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

From Library Journal

There have been many books written about mathematics for the nonmathematician. This one focuses on the most recent areas of mathematical research that are most closely related to the areas of computer science and artificial intelligence. Among the topics treated are fractals, logic, complexity, computability, and information theory. The subtlety of these fields requires the reader to bring a fairly solid background to the book. Rucker makes a good try at making these ideas simple and intuitive but some sections remain conceptually very difficult. On balance, this is a good book about modern mathematics for the informed reader willing to put in some mental effort. Harold D. Shane, Mathematics Dept., Baruch Coll., CUNY
Copyright 1987 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 328 pages
• Publisher: Mariner Books (February 1, 1988)
• Language: English
• ISBN-10: 0395468108
• ISBN-13: 978-0395468104
• Product Dimensions: 8.2 x 5.5 x 0.5 inches
• Shipping Weight: 9.6 ounces
• Average Customer Review: 4.3 out of 5 stars  See all reviews (6 customer reviews)
• Amazon.com Sales Rank: #267,109 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars Mind Tools, January 29, 2008

By	Adrian Dworniczak "Adrian D." (NY, USA) - See all my reviews (REAL NAME)

Rudy Rucker links mathematics to reality and explains 5 ways we can look at it: in terms of number, space, logic, infinity and information. The concepts explained are rather simple to understand and I'm pretty sure everyone will find some things they didn't know before. Later in a book he argues that "reality as information" may be the most correct view and our universe can indeed be a computational process.
I suggest people whose interest touches corners of math read the book, otherwise you may get bored.

19 of 28 people found the following review helpful:

4.0 out of 5 stars Basically good introduction to mathematical concepts, February 23, 1999

By	Dr. James V. Blowers "javeybee" (Chester, VA USA) - See all my reviews (REAL NAME)

In this book Rudy Rucker provides a novel way of classifying mathematical thinking - as number, space, logic, infinity, and information. He uses many standard examples and some more unusual ones such as classifying numbers as small, medium, large and inconceivable. It provides a good introduction for the general reader of mathematics, especially on the mathematical frontier, with such concepts as transfinite numbers, Goedel's incompleteness theorem, and cellular automata theory. It does have some errors, such as calling "Every sex act is sacred", "Every sex act is evil" imply "Some evil acts are sacred"; is a valid logical argument; not so. Consider this interpretation: "Every irrational integer is irrational", "Every irrational integer is an integer"; hence "Some integers are irrational". But in general I would recommend this book to the general reader.

6 of 9 people found the following review helpful:

5.0 out of 5 stars Mind (Expanding) Tools, January 18, 2002

By	Gordon Rios (Palo Alto, CA United States) - See all my reviews

Really nice survey of important ideas underneath the application of mathematics to real world analysis and understanding. Actually started a company based on one of his "someone should write a progam that ..." statements.