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Infinity and the Mind Paperback – May 15, 1995

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Rudy Rucker (Author)
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Rudy Rucker (Author)
4.2 out of 5 stars 26 customer reviews
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Product Details

  • Series: Princeton Science Library
  • Paperback: 352 pages
  • Publisher: Princeton University Press; New edition edition (May 15, 1995)
  • Language: English
  • ISBN-10: 0691001723
  • ISBN-13: 978-0691001722
  • Product Dimensions: 1.2 x 6.2 x 9.5 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #2,266,148 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

42 of 43 people found the following review helpful
Infinity made simple and understandable
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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42 of 44 people found the following review helpful
Rucker's best.
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.Read more ›
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25 of 26 people found the following review helpful
At the intersection of parallel lines...
By FrKurt Messick HALL OF FAMEVINE 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...Read more ›
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Most Recent Customer Reviews

Great book

A gift -- the recipient was delighted.

Published 5 months ago by Mitch Cohen
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 19 months ago 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
One of the Top Five Science Books Ever!

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. Read more

Published on May 10, 2011 by William D. Fusfield
Underrated popular mathematics classic!

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... Read more

Published on November 3, 2010 by anon2001
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, such... Read more

Published on August 28, 2008 by AH-SAN WONG

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