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

by Rudy Rucker (Author)

4.5 71 ratings

Part of: Princeton Science Library (52 books)

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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.

ISBN-10

0691121273
ISBN-13

978-0691121277
Edition

EXPANDED EDITION
Publisher

Princeton University Press
Publication date

November 21, 2004
Part of series

Princeton Science Library
Language

English
Dimensions

6 x 1 x 9.25 inches
Print length

368 pages
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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

Review

"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

Product details

Publisher ‏ : ‎ Princeton University Press; EXPANDED EDITION (November 21, 2004)
Language ‏ : ‎ English
Paperback ‏ : ‎ 368 pages
ISBN-10 ‏ : ‎ 0691121273
ISBN-13 ‏ : ‎ 978-0691121277
Item Weight ‏ : ‎ 1.1 pounds
Dimensions ‏ : ‎ 6 x 1 x 9.25 inches

Best Sellers Rank: #2,074,609 in Books (See Top 100 in Books)
- #93 in Mathematical Infinity
- #972 in Mathematical Logic
- #1,294 in Mathematics History

Customer Reviews:
4.5 71 ratings

About the author

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Rudy Rucker

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Rudy Rucker has written forty books, both pop science. and SF novels in the cyberpunk and transreal styles. He received Philip K. Dick awards for for the novels in his "Ware Tetralogy". His "Complete Stories," and his nonfiction "The Fourth Dimension" are standouts. He worked as a professor of computer science in Silicon Valley for twenty years. He paints works relating to his tales. His latest novel "Juicy Ghosts" is about telepathy, immortality, and a new revolution. Rudy blogs at www.rudyrucker.com/blog

Customer reviews

4.5 out of 5

71 global ratings

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Some annoying errors in Kindle edition

Reviewed in the United States 🇺🇸 on April 21, 2014

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I won't comment on the content of the book, but I would like to comment on the Kindle edition that I bought. Some figures are hard to read, and there are several typographical errors, such as mathematical symbols missing (for example the expression (s=t & t=r) -> s=r on page 272, is just (s=t & t=r) s=r in the Kindle edition. One place, a 1 is replaced by ], and one place the lemniscate - quite an important symbol in a book on inifinity - is replaced to separate circles (the ones used for degrees). These were even split across lines. Some = have been converted to :. It seems as the kindle edition is made from scanning and OCRing the print edition, without proofreading. The errors are not so numerous or hard to spot that it made the book significantly harder to read, but they are an annoyance. I would recommend the print edition.

With technical books containing many formulas and figures, the kindle preview should always contain some sections with such elements.

11 people found this helpful

Robert j palumbo

Reviewed in the United States 🇺🇸 on August 5, 2021

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Food for thought
Clear and well organized

One person found this helpful

Interesting Book

Reviewed in the United States 🇺🇸 on September 2, 2016

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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.

5 people found this helpful

Good interesting book!

Reviewed in the United States 🇺🇸 on December 23, 2019

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Good explanation of the concept of Infinity and the mathematics involved, including the work of Godel, Einstein, and Turing, and a host of others from the Vienna Circle, between the wars.

One person found this helpful

Katherine A. Allred

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

Reviewed in the United States 🇺🇸 on April 18, 2017

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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.

8 people found this helpful

Reviewed in the United States 🇺🇸 on April 17, 2018

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The book is as described.

Infinite Amount of Math

Reviewed in the United States 🇺🇸 on September 7, 2008

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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 'Infinitly Bored out of my Mind'. Anyone without a PhD in math, looking for a philosophical read on infinity and infinity paradox, can safely skip this book.

Pro - It has a pretty cover
Con - Anything beyond the cover

7 people found this helpful

Infinitely entertaining and deep

Reviewed in the United States 🇺🇸 on July 19, 2022

Great read by a sharp and playful mind.

Top reviews from other countries

'The' Burton

Self serving and ultimately pointless maths for the sake of it

Reviewed in the United Kingdom 🇬🇧 on July 11, 2010

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I was a little concerned when 'Infinity' arrived looking like an old maths books; unfortunately it reads like one too. It's all very dry and Rucker lasts about five pages before assaulting us with equations in the middle of the text, with no introduction and incomplete keys to explain all the variables. This is quickly followed by some patronising statements about simple maths, i started to question if Rucker knew who he was targetting this book at. Not a good start.

Following this up with some sweeping generalisations about the big bang and relatively, cherry picking the concepts which suit his cause and side-stepping proper explanations with statements along the lines of, 'I don't have time to justify my beliefs, so just believe them.' If i wanted that attitude I'd go to church thanks. This is a weak composition of ideas based on flawed logic, massive assumptions and out-dated ideas such as: There's no mention of the Planck length, or the fact that the rate of expansion of the universe is accelerating, (which makes his musings on the concept of a closed universe moot). Rucker appears - to me - to sit on the fence on too many theories, making me believe he's unsure himself.

It's less about infinity and the mind, more about finding flaws in our language and maths, creating paradoxes that only serve to point out the weaknesses inherent to these systems. There's also far too much algebra that breaks up what little flow there is, without serving much purpose and it reads like a mathmaticians diary of the world, which is not interesting. The philosophy (and there's a lot) is circular, unprovable and i disagreed with most of it. The end of chapter questions did not stimulate thought, i could answer them immediately, and they are for the most part, ridiculous. And don't even get me started on 'cardinal' numbers; no matter how vast they may seem, if you can write it down - let alone imagine it - it's not infinite, okay? The only question it made me ponder was; if this book is boring now and my opinion didn't change, no matter how many times i re-read it, is it infinitely boring? I think so.

5 people found this helpful

André Gargoura

Rucker v/s Stillwell (Roads to infinity)

Reviewed in France 🇫🇷 on July 2, 2011

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Rucker does a good job in Chapters 2, 3 & 5, on transfinite numbers, paradoxes, the one/many problem, truth, nameability... And in exploring the many routes towards the unattainable/inconceivable absolute...

His treatment of transfinite & large cardinals, in Excursion 1, is more complete than Stillwell's.

His treatment of Gödel's incompleteness theorems, in Excursion 2, is more detailed but totally unstructured as compared to Stillwell's exposition (via Emil Post's & Gentzen's discoveries...).

BUT, but, if you haven't been exposed to books such as Smullyan's, Stillwell's on various topics such as sets, ordinals, cardinals, ZFC, NBG, class/set differences, finite/transfinite induction & recursion, foundation, rank, constructible sets, independence of the continuum hypothesis... then Rucker's skimming over those concepts will appear confusing.

As for the philosophy side, Rucker's book is packed with interesting details and it would have taken a Hofstadter to structure the whole lot, into what could have become a fascinating exposition... Alas, not everyone is a Hofstadter .

Finally, concerning presentation and readability : sections are not numbered, let alone paragraphs which are overpacked ; figures are "thrown" in the text, unrelated ; proofs are half achieved, are not even stated as proofs ; conclusions are loosely tied to proofs and theorems, when they are...

If that's how Rucker teaches, then I feel really sorry for his students !

One person found this helpful

Albert

Three prefaces worthwhile

Reviewed in Canada 🇨🇦 on June 23, 2014

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The current release with the additional prefaces is worthwhile in comparison to the original. This book is a good starting point for the uninitiated into the work of Godel or Woodin.

Ilan

Awesome book

Reviewed in Canada 🇨🇦 on September 18, 2019

Verified Purchase

Great

hamoodi

Five Stars

Reviewed in the United Kingdom 🇬🇧 on December 17, 2014

Verified Purchase

very good

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