Rating: 
Summary: tough read
Review: Not an easy read. Compare it to training for a marathon, not fun at first but a new perspective of being evolves. It has taken me a good six months to read and reread and still parts I am shady on. I still am not totally finished with this book but recommend it.
Rating: 
Summary: Good job explaining infinity along various lines
Review: Rudy Rucker's book is one of the best introductory texts into the problems of infinity and understanding the problems inherent in dealing with an infinity. He covers quantum mechanics to some extend and the problem of an infinite number of parallel worlds which are created and collapsed on a near constant basis. There are many examples of how when dealing with infinities most of our logic deserts us and the very basis on which we understand things may not hold true. For example if you have two sets of numbers and one set has all integers and the other has the squares of all numbers possible then which set is larger? The set with the squares of all numbers is missing an infinite number of numbers (for example, 3, 5, 6, 7, 8, 10, etc) and so the one with all possible integers is larger since it contains all numbers. But since all numbers have a square then they are the same size. How can the be they same size and one infinitely larger than the other at the same time? When dealing with infinities those rules don't apply and there is no contradiction.
Mr. Rucker leads us on a wonderful trail of discovering how these things work on a philosophical level and how they all relate together. What sort of infinities exist and how does understanding infinities affect our concepts of philosophy are questions that this book attempts to work through. A thoroughly enjoyable read for those who would like to expand their way of thinking or who enjoy delving into concepts that defy logic while being totally logical.
Rating:
Summary: Good job explaining infinity along various lines
Review: Rudy Rucker's book is one of the best introductory texts into the problems of infinity and understanding the problems inherent in dealing with an infinity. He covers quantum mechanics to some extend and the problem of an infinite number of parallel worlds which are created and collapsed on a near constant basis. There are many examples of how when dealing with infinities most of our logic deserts us and the very basis on which we understand things may not hold true. For example if you have two sets of numbers and one set has all integers and the other has the squares of all numbers possible then which set is larger? The set with the squares of all numbers is missing an infinite number of numbers (for example, 3, 5, 6, 7, 8, 10, etc) and so the one with all possible integers is larger since it contains all numbers. But since all numbers have a square then they are the same size. How can the be they same size and one infinitely larger than the other at the same time? When dealing with infinities those rules don't apply and there is no contradiction.
Mr. Rucker leads us on a wonderful trail of discovering how these things work on a philosophical level and how they all relate together. What sort of infinities exist and how does understanding infinities affect our concepts of philosophy are questions that this book attempts to work through. A thoroughly enjoyable read for those who would like to expand their way of thinking or who enjoy delving into concepts that defy logic while being totally logical.
Rating:
Summary: At the intersection of parallel lines...
Review: Rudy Rucker, son of a cleric and mathematics whiz kid, produced this book on 'Infinity and the Mind' years ago, but reading and re-reading it, I continue to get insights and the chance to wrap my mind around strange concepts. 'This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.' This book was intended to be accessible by those without graduate-level education in mathematics (i.e., most of us) while still being of interest to those even at the highest levels of mathematical expertise. Even if the goal of infinity is never reached, there is value in the journey. Rucker provides a short overview of the history of 'infinity' thinking; how one thinks about divinity is closely related often, and how one thinks about mathematical and cosmological to-the-point-of-absurdities comes into play here. Quite often infinite thinking becomes circular thinking: Aquinas's Aristotelian thinking demonstrates the circularity in asking if an infinitely powerful God can make an infinitely powerful thing; can he make an unmade thing? (Of course, we must ask the grammatical and logical questions here--does this even make sense?) Rucker explores physical infinities, spatial infinities, numerical infinities, and more. There are infinites of the large (the universe, and beyond?), infinities of the small (what is the smallest number you can think of, then take half, then take half, then take half...), infinities that are nonetheless limited (the number of divisions of a single glass of water can be infinite, yet never exceed the volume of water in the glass), and finally the Absolute. 'In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.' At the end of each chapter, Rucker provides puzzles and paradoxes to tantalise and confuse. * Consider a very durable ceiling lamp that has an on-off pull string. Say the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed? Rucker explores the philosophical points of infinity with wit and care. He explores the ideas behind and implications of Gödel's Incompleteness Theorem, and leads discussion and excursion into self-referential problems and set theory problems and solutions. He also discusses, contrary to conventional wisdom, the non-mechanisability of mathematics. We tend to think in our day that mathematics is the one mechanical-prone discipline, unlike poetry or creative arts and more 'human' endeavours. But Rucker discusses the problems of situations which require decision-making and discernment in mathematical choices that no machine can (yet!) make. * Consider the sentence S: This sentence can never be proved. Show that if S is meaningful, then S is not provable, and that therefore you can see that S must be true. But this constitutes a proof of S. How can the paradox be resolved? This is a beautifully complex and intriguing book on the edges of mathematics and philosophical thinking, which is nonetheless accessible and intellectually inviting. You'll wonder why math class was never this fun!
Rating:
Summary: At the intersection of parallel lines...
Review: Rudy Rucker, son of a cleric and mathematics whiz kid, produced this book on `Infinity and the Mind' years ago, but reading and re-reading it, I continue to get insights and the chance to wrap my mind around strange concepts. `This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.' This book was intended to be accessible by those without graduate-level education in mathematics (i.e., most of us) while still being of interest to those even at the highest levels of mathematical expertise. Even if the goal of infinity is never reached, there is value in the journey. Rucker provides a short overview of the history of 'infinity' thinking; how one thinks about divinity is closely related often, and how one thinks about mathematical and cosmological to-the-point-of-absurdities comes into play here. Quite often infinite thinking becomes circular thinking: Aquinas's Aristotelian thinking demonstrates the circularity in asking if an infinitely powerful God can make an infinitely powerful thing; can he make an unmade thing? (Of course, we must ask the grammatical and logical questions here--does this even make sense?) Rucker explores physical infinities, spatial infinities, numerical infinities, and more. There are infinites of the large (the universe, and beyond?), infinities of the small (what is the smallest number you can think of, then take half, then take half, then take half...), infinities that are nonetheless limited (the number of divisions of a single glass of water can be infinite, yet never exceed the volume of water in the glass), and finally the Absolute. `In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.' At the end of each chapter, Rucker provides puzzles and paradoxes to tantalise and confuse. * Consider a very durable ceiling lamp that has an on-off pull string. Say the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed? Rucker explores the philosophical points of infinity with wit and care. He explores the ideas behind and implications of Gödel's Incompleteness Theorem, and leads discussion and excursion into self-referential problems and set theory problems and solutions. He also discusses, contrary to conventional wisdom, the non-mechanisability of mathematics. We tend to think in our day that mathematics is the one mechanical-prone discipline, unlike poetry or creative arts and more 'human' endeavours. But Rucker discusses the problems of situations which require decision-making and discernment in mathematical choices that no machine can (yet!) make. * Consider the sentence S: This sentence can never be proved. Show that if S is meaningful, then S is not provable, and that therefore you can see that S must be true. But this constitutes a proof of S. How can the paradox be resolved? This is a beautifully complex and intriguing book on the edges of mathematics and philosophical thinking, which is nonetheless accessible and intellectually inviting. You'll wonder why math class was never this fun!
Rating:
Summary: A passionate introduction to the theme of infinity
Review: The book mentiones : Infinity commenly inspires feelings of awe, futility and fear. Reading of the book makes one agree to it. The book is written for a reader who is philosophically curious and patient in reading. After introducting the various context ( spatial, temporal , physical) where one encounter the issue of infinity, the author explain clearly the debate of potential vs actual infinity. Here author points out about the Greek philosophical tendencies. Chapter two discusses the revolution brought by Cantor's works. He explains the concept using a lot of symbols, diagrams and illustrations. The reader is made to understand the notion of transfinite number. The chapter ends with an extract from his novel White Light which deals with the idea of the chapter. Next chapter discusses the kind of paradoxes one encounter in thinking the theme of infinity within modern mathematical logical framework. Chapter four discusses the implications of Godel's theorems in question of Robot consciousness. He gives details about his personal interactions with Godel. He mentiones about his dream about Godel the day before Godel's death. This is most humanistic chapter. Last chapter discusses the abstract philosophical reflections. There are two well written excursion chapters : one on Cantor's set theory and one on Godel's Incompleteness theorems. Every chapter has well thought puzzles and paradoxes section.
Rating:
Summary: Bozo, Chico, Harpo - An Eternal Moebius Strand Of Spagetti
Review: The first time I read this book I felt what I could only explain as a great disturbance in the Force: it was as if a billion washing machinces all became unbalanced at once and were suddenly silenced. As Rucker himself could only put it in his immortal fashion: "Imagine. Pursued by a tiny girl in a yellow dress, white ducks move deliberately across a green sward sloping down to stagnant brown water. How many ducks are there?" Fortunately there are many other mind bendingly philosophical statements in this work, such as "The word number can be construed as "That which makes us numb"". To lighten the dreary philosophical/academic tone of this tome, the book contains many good pictures of things like turtles standing on turtles standing on turtles (etc), a strange guy with ants crawling on his skin and a unicycle instead of feet, a couple of printers ink splotches obscuring important passages of text and so forth. All in all, despite the rather high level of incoherence of some of the chapters of this text, I think this book serves as an excellent reference on the subject of infinity for alchemists, metaphysicists, new age theologians and tax consultants.
Rating:
Summary: a mind-blowing trip to the infinite
Review: What is infinity? How do we train our minds to understand the idea? This one of the hardest questions to answer for non-professional mathematicians, and one that Rucker address superbly - and, believe it or not entertainingly in this excellent book. And once you think you grasped that, how about a higher level infinity? Next one? Infinite series of higher level infinities? Sound very scary, and it is. It takes an amazing capacity to explain these concepts to a (relative) layman, and Rucker has it in abundance. An exhilarating intellectual tour de force, perhaps comparable to climbing mount Everest - infinite number of times, with deep philosophical, and perhaps, religious connections, presented in a light, funny, and yet rigorous manner. The book also provides a history of the concept of the infinite, and interesting people who developed it. A must read for a curious mind.
Rating:
Summary: Stretching your mind has never been so fun!
Review: Yeah, its a book on math and a book on philosophy. Actually, it's a bit more. It's a book that uses mathematics as an approach to philosophy, but certainly not in a mechanist or reductionist fashion; after all, what's the last book by a mathematician that treated mysticism as a serious philosophy? Inside you learn about: what sorts of infinity there might be, why the ancients and medievals were uncomfortable with infinity, truth, randomness, transfinite arithmetic, Hilbert's Hotel, robots and souls, and quite a bit more. Bottom line-the mathematical discussions can be tough slogging at times, but are explained thoroughly and in fine detail, with wit and charm, and the whole constitutes one of the richest scource of ideas I have ever come across. A bargain at twice the price!
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