Mind Tools Pa

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.

Page 32 gives a chart which shows the evolution of the strands of mathematics from ancient times until the present. This makes the book.

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.

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.

This is an amazing book for teaching the concepts of mathematical logic, fractals, number theory, and information theory. I have never seen these concepts introduced in such an easy-to-understand fashion. I recommend it highly to anyone with an interest in these concepts. Near the end of the book, it does go a little overboard with the information theory and becomes hard to follow. Happily though, Rucker does a fairly good job of disproving the existence of god via information theory; for those of you prefer to see God in the numbers, here you will be shown that the opposite is the case.