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Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library) Paperback – November 21, 2004

4.2 out of 5 stars 25 customer reviews

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Editorial Reviews

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

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
  • Paperback: 368 pages
  • Publisher: Princeton University Press (November 21, 2004)
  • Language: English
  • ISBN-10: 0691121273
  • ISBN-13: 978-0691121277
  • Product Dimensions: 1 x 6 x 9.2 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (25 customer reviews)
  • Amazon Best Sellers Rank: #433,011 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
I've read a few of Rucker's other nonfiction books (his fiction is another topic entirely), and I think this one is still his best. I bought and read it when it was new and I'm about to buy a replacement copy.

The "book description" on this page touches briefly on one of Rucker's key points: "the transcendent implications of Platonic realism." This is well put, and the remarks above correctly relate this point to Rucker's "conversations with Godel." Godel was a mathematical Platonist -- that is, he believed that mathematical objects are real in their own right and that the mind has the power to grasp them directly in some way.

Rucker gets this right, unlike some other better-known interpreters of Godel who have co-opted his famous Theorems in the service of strong AI. Rucker, too, thinks artificial intelligence is possible, but for a different reason which he also here explores: he takes the idealistic/mystic view that _everything_ is conscious in at least a rudimentary [no pun intended] way, and so there's no reason to deny consciousness to computers and robots. Heck, even rocks are conscious -- just not very :-). (I don't know whether Rucker would still defend this idea today or not. At any rate, for interested readers, a more elaborate version of panpsychism is developed and defended in Timothy Sprigge's _The Vindication of Absolute Idealism_.)

These and other speculations are the jewels in a setting of solid exposition. Rucker is powerful in general on the topic of set theory, which he takes to be the mathematician's version of theology. And his discussions are a fine introductory overview of the various sorts of infinity, including but not limited to mathematical infinities.
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Format: Paperback
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...
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Format: Paperback
I know very little about any of the subjects discussed in this book, although I do have a degree in philosophy of science, and I liked this book a lot.
I can't believe I made it through 7 years of senior school and 2 years of degree level maths and nobody ever bothered to tell me about infinity, transfinite numbers, set theory and its relationships with, and underpinning of other branches of mathematics in a way I could understand rather than simply regurgitate. Rucker on the other hand manages to do this in 362 pages.
I slso found the stuff about Godel and the impossibility of complete formulisms very useful, not only philosophically, but also just for my own peace of mind.
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Format: Paperback
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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Format: Paperback
Firstly, please ignore the silly one and two star reviews. They seems to be written by
cranks. For reasons unknown to me Set Theory seems to attract cranks who get very upset
by the work of Georg Cantor and the "diagonal method" in particular.

This book should be on all bookshelves of popular accounts of mathematics.

Infinity and the Mind is a superb popular account of Set Theory as an approach to
exploring the concept of infinity. I know of no other book like it. It is quite accessible
to anyone who has studied high school mathematics. The book tackles deep issues of
mathematics, logic and philosophy. Rudy Rucker explores topics such as Godel's Theorems,
paradoxes of Set Theory, orders of infinity (large cardinals), artificial intelligence,
the logical foundations of mathematics and much more. The maths is pretty rigorous too
for a popular work.

The author is well qualified to write on the subject. As well as doing research in
Set Theory he has, incredibly, interviewed Kurt Goedel himself shortly before he died.
An account of his discussions with Goedel is included in the book.
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