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Infinity and the Mind Paperback – May 15, 1995
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"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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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.
Now what are the four OTHER TOP FIVE SCIENCE BOOKS? Well, George Gamow's "Mr. Tompkins" books are pretty darn good but a bit dated in presentations. Stan Ulam's auto?-biography is good as well, As are the two books on the making of the A and H bombs. It was Ulam BTW who really figured most of it out. But those are not top fiver. "A Primer of Real Functions" by Ralph Boaz is great, as is the old ? Thomas Very Complete "Calculus" book. [In fact it was so complete you couldn't really get through the work even teach a three quarter series of courses with it. [Ah, such a noble task!] I remember they used it at Macalester College when I was there in the early 70s. They were very proud of using such an advanced text too, as they should have been. Try using the same books these days, and the students would probably immediately haul you off to the Provost and try to get you fired for giving them "thinking headaches." ... but I'm not getting starting to get bitter after 30+ years of teaching ... am I? Oops, one last thing, as great as Rucker's book is, even he doesn't provide several intuitively helpful conceptual images of the deeply mysterious "measurable cardinal" first discovered by Ulam BTW. It still all "infinite intersections and unions of sets, ultra-filters etc., if he even goes that far down the road. Though he does say something mind-expanding like "they are so much larger than all the cardinals that come before them that they sort of stand to Aleph infinity as Aleph Nought does to a large finite," or something like that. And, even in the 28 years since my first read, I still haven't found anyone, online or off, who can conjure up an intuitive picture of measurable cardinal for me ... oh why, oh why, do I bother to go on? "Man by nature seeks to know" is all Aristotle would say.