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

by Rudy Rucker (Author)

28 customer reviews

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In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.

Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library)

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Editorial Reviews

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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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Product details

Series: Princeton Science Library
Paperback: 368 pages
Publisher: Princeton University Press; Revised 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: 28 customer reviews
Amazon Best Sellers Rank: #896,908 in Books (See Top 100 in Books)
- #56 in Books > Science & Math > Mathematics > Infinity
- #383 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #745 in Books > Science & Math > Mathematics > History

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Mitch Cohen

Great book

June 15, 2015

Format: PaperbackVerified Purchase

A gift -- the recipient was delighted.

0Comment One person found this helpful. Was this review helpful to you?

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anon2001

Underrated popular mathematics classic!

November 3, 2010

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.

0Comment 12 people found this helpful. Was this review helpful to you?

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Katherine A. Allred

Where to begin? This is "Gödel, Escher, ...

April 17, 2017

Format: PaperbackVerified Purchase

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.

0Comment 2 people found this helpful. Was this review helpful to you?

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A Fillon

Interesting Book

September 2, 2016

Format: PaperbackVerified Purchase

I found most of the reviews on this book to be spot on. If you have an interest in infinity and a fairly good understanding of basic college level mathematics, you can get a lot out of it. I don't believe it is as accessible as most popular science books but the subject is a deep one and its hard to consider it properly without going deep into some tedious thought processes. I think I would have enjoyed this book more if the author spent more time talking about the philosophical implications of the mathematics and how the mind reacts to the idea on infinity.

0Comment 4 people found this helpful. Was this review helpful to you?

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William D. Fusfield

One of the Top Five Science Books Ever!

May 10, 2011

Format: Paperback

As a university professor I read zillions of, frankly often quite dreadful, mathematics and physics and astronomy books. I read this one when it first came out in 1982. It really bowled [or Booled?] me over even then, and every time I've picked it up since I find something new and clever I hadn't given full thought to before. It is a MUCH better introduction to transfinite numbers than the also still quite good book by the late David Wallace Foster [if I've ordered names those correctly]. When I say it's one of the five best science books ever written, I am not exaggerating, provided, of course, that you have a basic grasp of Calculus and a touch of "naive set theory" and basic analysis under your belt, which if you got through high school or college you probably do. Rucker's non-fiction books are always excellent. His fiction doesn't interest me as much, but some of the stories have interesting conceptual leaps etc.
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.

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Most recent customer reviews

very patient and helpful.

a present , good seller. Very well. the speed is so amazing. Thin and sharp. Well excellence. Great product.

Published 6 months ago by Isabel Ernest

Some annoying errors in Kindle edition

I won't comment on the content of the book, but I would like to comment on the Kindle edition that I bought.Read more

Published on April 21, 2014 by urbanix

if you like infinity, read it

Imagine searching for notions and uses of infinity in a wide range of intellectual disciplines and then weaving them together into a pretty fabric that can be understood by a...Read more

Published on August 11, 2012 by bearieq

Mind Bending

Of course a book about infinity is going to be mind bending. As I have read it, I am continually amazed by the various approaches that Dr Van Rucker takes in approaching this...Read more

Published on July 28, 2012 by Amazon Customer

Rucker v/s Stillwell (Roads to infinity)

Rucker does a good job in Chapters 2, 3 & 5, on transfinite numbers, paradoxes, the one/many problem, truth, nameability...Read more

Published on July 2, 2011 by André Gargoura

Is this statement true: 'this book is a collection of mistakes'?

The modern theories of the infinite were invented by Georg Cantor, though there's no notable starting date, as they emerged in a series of papers.Read more

Published on June 26, 2010 by Rerevisionist

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...Read more

Published on September 6, 2008 by J.S.

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,...Read more

Published on August 28, 2008 by AH-SAN WONG

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