PDF Download Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library), by Rudy Rucker
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Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library), by Rudy Rucker
PDF Download Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library), by Rudy Rucker
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Review
"Rudy Rucker's Infinity and the Mind is a terrific study with real mathematical depth." (New Yorker)"Rudy Rucker, set theorist and science-fiction author, has continued the tradition ... of making mathematics and computer science accessible to the intellectually minded layperson.... Infinity and the Mind is funny, provocative, entertaining, and profound."---Joseph Shipman, Journal of Symbolic Logic"Attempts to put Gödel's theorems into sharper focus, or at least to explain them to the nonspecialist, abound. My personal favorite is Rudy Rucker's Infinity and the Mind, which I recommend without reservation."---Craig Smorynski, The American Mathematical Monthly"[Rucker] leads his readers through these mental gymnastics in an easy, informal way." (San Francisco Chronicle)"A captivating excursion through the mathematical approaches to the notions of infinity and the implications of that mathematics for the vexing questions on the mind, existence, and consciousness." (Mathematics Teacher)"It is difficult to find any aspect of infinity that is not explored in this compelling book. . . . This memorable book is one to be kept on an accessible shelf after reading it: it will not leave the reader unaffected." (Journal for Research in Mathematics Education)"Infinity and the Mind can be read and enjoyed by experts and nonexperts alike. Rudy Rucker is a talented logician who draws on his talents as a science-fiction writer and cartoonist to convey his ideas. This makes for not only a solid, accurate, and informative book but also a good read."--Thomas Tymoczko, Smith College"Informal, amusing, witty, profound. . . . In an extraordinary burst of creative energy, Rudy Rucker has managed to bring together every aspect of mathematical infinity. . . . A dizzying glimpse into that boundless region of blinding light where the mysteries of transcendence shatter the clarity of logic, set theory, proof theory, and contemporary physics."--Martin Gardner
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From the Back Cover
"Infinity and the Mind can be read and enjoyed by experts and nonexperts alike. Rudy Rucker is a talented logician who draws on his talents as a science-fiction writer and cartoonist to convey his ideas. This makes for not only a solid, accurate, and informative book but also a good read."--Thomas Tymoczko, Smith College"Informal, amusing, witty, profound. . . . In an extraordinary burst of creative energy, Rudy Rucker has managed to bring together every aspect of mathematical infinity. . . . A dizzying glimpse into that boundless region of blinding light where the mysteries of transcendence shatter the clarity of logic, set theory, proof theory, and contemporary physics."--Martin Gardner
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Product details
Series: Princeton Science Library (Book 26)
Paperback: 368 pages
Publisher: Princeton University Press; EXPANDED EDITION edition (November 21, 2004)
Language: English
ISBN-10: 0691121273
ISBN-13: 978-0691121277
Product Dimensions:
6 x 1 x 9.2 inches
Shipping Weight: 1.1 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
26 customer reviews
Amazon Best Sellers Rank:
#978,154 in Books (See Top 100 in Books)
Where to begin? This is "Gödel, Escher, Bach" for actual math people. You might call it instructions for a precise mysticism, though that barely touches what it really gets into.
I won't comment on the content of the book, but I would like to comment on the Kindle edition that I bought. Some figures are hard to read, and there are several typographical errors, such as mathematical symbols missing (for example the expression (s=t & t=r) -> s=r on page 272, is just (s=t & t=r) s=r in the Kindle edition. One place, a 1 is replaced by ], and one place the lemniscate - quite an important symbol in a book on inifinity - is replaced to separate circles (the ones used for degrees). These were even split across lines. Some = have been converted to :. It seems as the kindle edition is made from scanning and OCRing the print edition, without proofreading. The errors are not so numerous or hard to spot that it made the book significantly harder to read, but they are an annoyance. I would recommend the print edition.With technical books containing many formulas and figures, the kindle preview should always contain some sections with such elements.
The book is as described.
A gift -- the recipient was delighted.
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.
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.
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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