Mind Tools: The Five Levels of Mathematical Reality

From mathematics and computers to insights into the workings of the human mind, Mind Tools is a reflection of the latest intelligence from the frontiers of mathematical thought. Illuminated by more than 100 drawings, Mind Tools connects mathematics to the world around us. It reveals that the great power of mathematics comes from the fact that it serves as an alternative language for understanding things -- from one's hand to the size of infinity. Exploring such concepts as digital versus analog processes, logic as a computing tool, and communication as information transmission, Rudy Rucker presents the "mind tools" for a postmodern age.

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.

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.