Mind Tools: The Five Levels of Mathematical Reality

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. (April 16)