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Title: Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library)
ISBN: 0691121273
Author:
Rudy Rucker
Publicate Date: 2004-11-01
Publish: 2004-11-01
List Price: $22.95
Average Customer Rating: 4.0
Format: Paperback
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Amazon Lowest New Price: $14.81
Amazon Lowest Used Price: $13.50
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| Customer Review: |
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1: Infinite Amount of Math
I've always been facinated with the concept of infinity. Having been a math minor I figured the math wouldn't be all that bad; however, after the first 100 pages, the book became 'Infinitly Bored out of my Mind'. Anyone without a PhD in math, looking for a philosophical read on infinity and infinity paradox, can safely skip this book.
Pro - It has a pretty cover
Con - Anything beyond the cover
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2: Rucker's personal notes on the Infinity problem
I was first introduced to this book by a mathematical philosopher friend in 2001. Immediately I was drawn into the book, because it dealt with many subjects I'd been thinking, such as how there are more real numbers than natural numbers, how infinity comes in different sizes, and how the mere existence of infinity is to be questioned. Soon I got lost in all the numbers and had to put the book down a few times until the summer of 2006.
Rucker's writing was more like personal notes he wrote for himself than a well-constructed thesis on the subject. And here are some of my own personal notes about this book.
Chapter one reviews the history of infinity, and introduces the concept of mindscape. Years ago I was excited about the idea of mindscape, but after I had the fortune to see the Reality as a whole, I found this idea rather intuitive and basic. I was happy to see the mention of the Absolute as part of the discussion of Infinity.
Chapter two is about all the numbers. Again soon I became confused with the names of different infinities. Unless one can tightly grab onto the endless symbols Rucker introduced incessantly throughout the chapter (and the book) one would have a difficult time follow the text. Also his figures are ill-labeled. I don't think I am missing much by skipping some of the paragraphs. I also skipped the two excursions because they are even more technical.
Chapter three is titled "The Unnameable", and Rucker discussed the Berry Paradox and discussed the reality of Truth, among other subjects. It's interesting to see how systematically and detailed he talks about the logic of "This sentence is false", and even distinguishes it from "This sentence is not true". I skipped the more technical section of Richard's Paradox, assuming it is along the similar line of the truth discussion. I was glad to find out that Rucker is also a Borges's fan (I only wish I could write reviews of books and movies as clearly and originally as Borges). From Borges's story about the Library of Babel--the library of all possible books, Rucker introduced a clever tool--to code each book into a natural number. Furthermore, the whole universe can be coded into a natural number, and thus we can think about the infinity nature of the universe the way we think about numbers.
Chapter four is about robots and souls, but the more interesting part is the three conversations Rucker had with Godel. I was happy to know that Godel is a mystic, partly because I am becoming more and more identified with the label mystic.... Godel has found. Rucker is still seeking.
Chapter five is on the One and the Many, the most philosophical chapter of the book. Rucker probably does not have the One figured out, but it's interesting to see how he compares the One and the Many in a rational way.
Rudy Rucker wrote this book in 1982. Perhaps he has reached another stage in his search. Despite of many inadequacies I found in this book, it nonetheless has showed me fascinating new ways of thinking about the universe. For this I am grateful. I would rate this book 4 out of 5 stars.
p.s. I feel I am much slower than 5 years ago. I don't seem to be able to comprehend complex systems as effortlessly as I used to--perhaps a sign that my brain power is declining?
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3: Infinity and the Mind
This book is packed full of a lot of good information on infinity. However, the author's philosophical position on infinity is a bit extreme, outside the mainstream of mathematical thought today.
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4: Misleading
Rucker had finished writing this by June 19, 1981, as his preface says. Yet, he has the naivete (or perhaps the gall) to say something inane like "Set theory is, indeed, the science of the Mindscape. A set is the form of a possible thought." on p. 41. Since Zadeh published his landmark "Fuzzy Sets" paper in 1965, and Black and others had written similar ideas years earlier, along with multivalued logicians like Lukasiewicz developing possibly infinite-valued logics as far back as the 1920s, one would think that Rucker would be informed or wise enough than such statements. It appears otherwise. I find it curious that Rucker also knew Godel who did work in multivalued logics, but basically Rucker doesn't acknolwedge multivalued logics as even possible forms of thought.
As for the comments about Mr. Rucker qualifying as an intellectual descendent of Hegel, they simply don't hold water. Rucker denies the property of contradiction (it is not the case that A and not A hold). Hegel accepted it and sought some other way to do logic than Aristotle's logic.
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5: Reclaiming the Greek Heritage: A Modern Mathematical Philosophy
Rudy Rucker deals with the concept of Infinity in regard to our mental conceptions and the structure of reality. The question is whether or not the concept of Infinity makes sense, and then the relation of finite thought and human consciousness relates to the possibility of infinites in the structure of reality.
Rucker is a professor of Calculus and centres this discussion in the History of Mathematical stemming form the ancient Greeks. For the Greeks there was no distinction between mathematics and philosophy. He takes a mathematical approach, but converses fluently in the disciplines of Quantum Physics and Philosophy.
I classified this book as Epistemology (the Philosophy of Knowledge) because the central concept is the meaning and definition of Human Consciousness. In this regard Rucker probes the meaning of consciousness and the relationship of the individual mind to the concept of Universal Mind.
The title includes Infinity, because the investigation considers all aspects of the ultimate or Absolute. So at the root of this is the question of whether it makes sense for anything to be Infinite. Is there such a thing as Infinity? Are there multiple infinities? Involved is the question of whether the human mind can conceptualize an infinite thought, or is every human thought a finite thought?
The reason this is a question of Epistemology is that one must consider how we know, and what a finite mind can know. Thus Rucker looks at the question in terms of many disciplines of knowledge. Basically, we are asking whether it is possible for something in the universe (one mind, and its thoughts) to know the Absolute or Ultimate reality, of which it is a part!
Another term for the discipline commonly dealing with this problem is Theory of Mind. Rucker I have not looked at the concepts of Theory of Mind and the Philosophical question of the Absolute and the One-Many debate in a mathematical perspective before. This latter entails the concept of whether there is some ultimate unity to the universe, including the recent question of multiple universes, and whether the Absolute is sentient, as an active God or relatable entity.
Rucker points out that any ultimate question, posed in terms mathematical, theological or otherwise, is a mystical question. He references concepts of Zen Buddhism as well as classical Western Philosophy and Christian theology. He lays a firm foundation for the problem in a historical format by reviewing the ancient Greek concepts.
I had never looked at these questions from a mathematical approach. His discussion of set theory helps to see the issues involved in considering whether humans, as finite entities, can conceptualize the ultimate. He deals with the relationship between thoughts and concepts and the external objective world. Set theory and its refinements, which Rucker discusses in terms of the history of their development, provide a way of objectively evaluating whether there can be infinite.
Rucker lays out the formulas in geometry and calculus, but discusses the implications from practical and theoretical perspectives in science and theology. I did not campout in the mathematical formulas, but could generally follow the arguments. But the philosophical implications and the factors discussed in the practical and theoretical scientific disciplines was very helpful. Rucker uses very practical life-situations and analogies to provide a reality for these concepts, which can seem ethereal and abstract.
One of the practical aspects is a whole chapter critically evaluating ideas of Artificial Intelligence, "Robots and Souls." He asks whether an artificial intelligence can become self-developing to the stage comparable to human consciousness. He ruminates on the relationship of artificial intelligences to human consciousness.
Rucker reviews the creative and ground-breaking theories and writings of Kurt G??del, a mathematical philosopher in the 20th century. G??del conclusively established the concept of Infinity. Rucker reports on personal discussions he had with G??del, who was a mystic and philosopher. They discussed the concept of Universal Mind and the existence of mind beyond body.
It was also interesting to see this perspective on the Theory of Mind, various concepts of the Absolute, and critical analysis of the possibilities and limitations of human conception, as written almost 25 years ago, and see that most of what is known and considered now was active knowledge back then. The critical analysis Rucker provides was helpful for a fresh perspective on the methods mathematics brings to metaphysics involved now in Particle Physics and the Cosmogony now entailed by Theoretical physics on the astronomical level.
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