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


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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: 9.2 x 6.1 x 1 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: #173,890 in Books (See Top 100 in Books)

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


More About the Author

Rudy Rucker is a writer and a mathematician who spent 20 years as a Silicon Valley computer scientist. He's a contemporary master of science-fiction, and received the Philip K. Dick award twice. His 37 published books include novels and non-fiction books such as THE FOURTH DIMENSION. His cyberpunk series THE WARE TETRALOGY and his novel of the fourth dimension SPACELAND are favorites. His memoirs NESTED SCROLLS and ALL THE VISIONS offer uniquely skewed insights into our times. Recent books include COMPLETE STORIES and the novels TURING & BURROUGHS and THE BIG AHA. His new reprint collection TRANSREAL TRILOGY includes his classic novels THE SECRET OF LIFE, WHITE LIGHT, and SAUCER WISDOM. More info at http://www.rudyrucker.com

Customer Reviews

The book tackles deep issues of mathematics, logic and philosophy.
anon2001
There are two well written excursion chapters : one on Cantor's set theory and one on Godel's Incompleteness theorems.
S.Venkatesan
This book is a must read for anyone who has ever wanted to know more on this subject.
J. Fox

Most Helpful Customer Reviews

40 of 41 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on February 25, 2000
Format: Paperback
In many ways, infinity is the most abstract concept of all. Many of the advances in understanding how to manipulate infinities had unpleasant consequences. As the legend goes, the first one to announce that there are infinite non-repeating decimals was rewarded by being drowned. Georg Cantor, the first to prove that there are different levels of infinity, faced extreme criticism and ultimately went mad. Fortunately, Rudy Rucker provides a gentle introduction to this concept, one that can be read by most with the only consequence being enlightenment.
The entire range of infinities (what a phrase!) is covered in this book. From the simplest infinity (omega), to the multi-universe theories of quantum theory. All are put forward in a very readable style, although there are times when one must slow down and read very carefully if one is to understand. Rucker's encounters with Kurt Godel is a welcome contrast with the common depiction that he was a dry, humorless man. It is refreshing to hear that he laughed and had a sense of humor.
Many different test scenarios have been put forward to determine if a computer is indeed intelligent. At this time, I would propose that any machine that can understand the concept of infinity must be considered intelligent. Any human wishing to pass that test need only read this book. It should be required reading in all undergraduate mathematics programs.

Published in Journal of Recreational Mathematics, reprinted with permission.
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41 of 43 people found the following review helpful By John S. Ryan on August 9, 2000
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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24 of 25 people found the following review helpful By FrKurt Messick HALL OF FAMETOP 1000 REVIEWERVINE VOICE on June 5, 2003
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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