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Infinity And The Mind: The Science And Philosophy Of The Infinite (Penguin Science)

3.99  ·  Rating details ·  689 ratings  ·  37 reviews
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 Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpret ...more
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Published May 29th 1997 by Penguin (first published 1981)
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3.99  · 
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 ·  689 ratings  ·  37 reviews


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WarpDrive
Mar 27, 2013 rated it really liked it  ·  review of another edition

A quite interesting, intellectually challenging, vibrant book which describes the concept of infinity both from mathematical (transfinite numbers) and philosophical standpoints.

Some ideas, like the concept of "Absolute Continuum", are very interesting; several subjects (like Godel's incompleteness theorems, Set Theory and its foundational importance in mathematics and in other disciplines, the Continuum Hypothesis, Godel's Neoplatonic philosophical approach to mathematics) are absolutely brillia
...more
Chris Dietzel
May 07, 2016 rated it it was amazing  ·  review of another edition
I read this years ago and have been meaning to get back to it again for round two. At the time, it was one of the first books I had read that really opened my mind to how mathematics, physics, and philosophy are intertwined in every day life and with how our minds process information. The best part of it is that I very easily get in over my head with this type of subject matter but 'Infinity and the Mind' was presented in a way that even I could understand what was being discussed.
Bruce
Nov 30, 2008 rated it really liked it  ·  review of another edition
In the 1981 preface Rucker writes, “This book discusses every kind of infinity: potential and actual, mathematical and physical, the ontological and the mundane.” The main line of argument is mathematical. Rucker uses physics, philosophy and theology as illustrations and examples of mathematical concepts. He also uses mathematical formulas, diagrams and cartoon to illustrate concepts in other disciplines. The five chapters all conclude with a collection of puzzles and paradoxes. This assumes tha ...more
Peter Mcloughlin
This book written in the seventies is something I read as a teenager in the 80s and is one of my all time favorite non-fiction books. This book explores infinity a concept that has always been with humans but was revolutionized in the late 19th century by Georg Cantor. Cantor showed that the infinity of the natural numbers is the smallest of (wait for it) an infinite number of larger and larger infinities. Cantor opened up a paradise in the words of one mathematician that we shall never be banis ...more
Ísabel
I liked this book for the particular aspect of trying to give a popular account on large cardinals (like the inaccessible and Mahlo cardinals and more) - it achieves this goal quite well, but perhaps only for mathematically predisposed persons... The idea of Absolute Continuity was also intriguing to learn (although I already knew about Knuth's surreal numbers).
Some passages and even some ideas were a bit obtuse/confusing, e.g. the concept of (circular) scale, which I only half understood. Quite
...more
Jason
Aug 23, 2012 rated it it was amazing  ·  review of another edition
Great read from either the mathematical or mystical point of view on the infinite.I had read this back in high school then again later in the early 90s. I figured it was time to pull some cobwebs out of my noggin so I ordered this fine work again.
John Fink
Sep 23, 2012 rated it it was amazing  ·  review of another edition
This was, for me, a life-changing read. Although very technical and mathematically rigorous, it is an appropriate challenge to undertake for any Critical Thinker. If you thoroughly comprehend what Rudy is trying to lay out, your paradigms will get a make-over by the time you're done.
Daniel
Jun 21, 2016 rated it it was amazing  ·  review of another edition
This book exceeded my expectations. It's mathematical rigor sprinkled with the occasional psychedelic fever-dream and wild, uninhibited-yet-sometimes-convincing thought experiment. It's great.
Vince
Sep 19, 2012 rated it it was ok  ·  review of another edition
Not something I would really want to read cover to cover but fun to jump around between various topics. Very technical and sometimes a bit erratic in how topics are introduced and explained.
Kristen
Dec 20, 2007 rated it really liked it  ·  review of another edition
Shelves: non-fiction, science
bit slow and dry at times. But fascinating topic
Jay
Mar 23, 2019 rated it it was amazing  ·  review of another edition
Rudy Rucker, on his birthday March 22
Author of one of the very few books that changed how I think, Rudy Rucker is a mathematician who also writes fictionalized autobiographies and histories using science fiction tropes; hallucinatory, sublime, filled with scientific references and social observations, curiouser and curiouser.
A wizard of numbers and their philosophical meanings, he spins stories which may or may not be fictions in the usual sense; and the discovery of his nonfiction works can
...more
Zorn Rose
This is really fun and his discussion of Godel is one of the best I've seen. He doesn't shy away at all from speculation, though. I found it difficult at places to work out what had been comprehensively worked out by mathematicians and what he took himself to have found out through mystical comprehension. His wild speculation was pretty fun to read once I recognized it for what it was, though. He thinks thought and feeling are forms of exploring a shared non-physical mindscape, so that not only ...more
J.
Aug 25, 2017 rated it it was amazing  ·  review of another edition
I recently returned to this text after many years with new appreciation for its bold (and still largely unrivaled?) attempt to introduce the concepts of large cardinal theory to the general reader, bypassing unnecessary barriers to entry into the discussion of this intrinsically philosophically important topic.
Anju Mai
Jan 14, 2018 rated it it was amazing  ·  review of another edition
This book was so good I want to buy it for myself and reread it.
Steve Gutin
Jun 27, 2017 rated it really liked it  ·  review of another edition
I had to skip some of the math, not being a mathematician myself, but Rucker is such a fascinating writer that I got a lot out of it. Some great stuff in there for sure.
Jarrodtrainque
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 ...more
Sinan
The book is leaning mostly on mathematical view point of infinities. Although some other types of infinites are mentioned in the book, such as physical infinities which struck my mind.
There is puzzles at the end of every chapter but they are not merely new information, most of them are differentiations of the idea in that topic.
I cannot go without mentioning the paradoxes. They are everywhere in the book. 'Even in my comment, which is false' If the sentence is true then my comment includes a
...more
Unni Krishnan
An elegant book on the concept of infinite and it takes a lot to read and understand all the ideas presented in the book. The concept of the existence of multiple types of infinities was very new to me. And the way the idea of infinity was rigorously defined based on the set theory by Cantor and others was also very fascinating. I found the ideas from this very useful when I read some chapters of Principia Mathematica, especially the idea about the real numbers and why the infinity arising from ...more
Chin Jian Xiong
Dec 12, 2015 rated it really liked it  ·  review of another edition
Shelves: psychology-neuro
Nice introduction about various topics of Infinity that is willing to be quite rigorous (well, for my puny beginner head). A lot of stuff went over me, although I got the gist of it, but the part that really went over me was the part on the Richard Paradox and constructing reals, which I completely was just lost at. Hodstafter's explanation of Godel's Theorems in I Am a Strange Loop helped me to accommodate to the Godel parts here.

Of course I didn't read the lengthy extra math excursions at the
...more
Robert Dormer
I wanted to like this book, I really did. But what can you say about a book where the author writes, "we have now come to the end of this book" - and then proceeds to chug along for another twelve pages, plus two more supplemental chapters? I was expecting a book about the history and mathematics of this elusive and important concept. Instead, what I got was 300 meandering pages of cringe inducing philosophical speculations and mental masturbation. I kept waiting and waiting for some kind of poi ...more
Josh
Nov 24, 2015 rated it liked it  ·  review of another edition
I know that's what I should've expected, but there was too much math and numbers. It took too much effort to get my mind to wrap around concepts then after a while the concepts of infinity started to become repetitive.

*Infinities and indivisibilities - I just appreciate this string of words
*Finite but unbounded - my favourite part of the book in chapter 1 which help me put the 4th dimenesion into perspective
Mike
Apr 10, 2009 rated it it was amazing  ·  review of another edition
Best book I have read in a long time, not for the beach. However long plane rides are a good time to chew on this. It really gets your mind going - so in theory between any two points there are an infinite number of points, this is rather obvious, however if we think of time as linear, as we have been trained to do then in between any two moments there is an infinite amount of moments, and thus an infinite amount of time...This guys is the undisputed expert on infinity.
Misha
Apr 13, 2009 rated it really liked it  ·  review of another edition
Shelves: nonfiction, college
I read this in college, not for a class but just because it sounded interesting. I was an English major with a fondness for the ideas of science, but lacking the patience to try to understand the mathematics of it all. This book was engaging and accessible, and opened my mind to new concepts. I wish I could remember more of them.
Dave Peticolas

An overview of the mathematics and philosophy of the infinite.

This book touches on many subjects including the transfinite numbers, Godel's Incompleteness Theorems, the possibility of machine intelligence, the limits of human intelligence, the ultimate reality of mathematics, and the concept of the Absolute.

Timothy
Oct 21, 2016 rated it really liked it  ·  review of another edition
Enlightening walk through the most interesting facets of the philosophy of mathematics. Covers Godel's theorem, higher infinities, and exposes the reader to the development of mathematics from scratch (ZF set theory and alternative axiomatic systems). Features interesting discussions about the irreducibility of consciousness.
Collin
Sep 15, 2011 rated it liked it  ·  review of another edition
Shelves: put-down
Made it through the first two chapters, but in the end my inability to comprehend transfinite numbers held up any forward progress. Might revisit this one later as my mathematical sophistication improves.
Kate
Dec 08, 2010 rated it liked it  ·  review of another edition
What I understand is interesting.
Gary
Feb 12, 2008 rated it it was amazing  ·  review of another edition
Everything you want to know about infinity. Very thought provoking.
KidPolaroid
Mar 27, 2007 rated it it was ok  ·  review of another edition
Recommends it for: people willing to think for 2.2 hours about 3.4 sentences
I downloaded the reading list and problem sets for the MIT course entitled "Paradox & Infinity" and am slowly trudging through it. Really fun though.
Julian Smith
Long book, lots to comprehend.
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Rudolf von Bitter Rucker is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk genre. He is best known for his Ware Tetralogy, the first two of which won Philip K. Dick awards. Presently, Rudy Rucker edits the science fiction webzine Flurb.
“As Aquinas, the quintessential theologian, says: “The notion of form is most fully realized in existence itself. And in God existence is not acquired by anything, but God is existence itself subsistent. It is clear, then, that God himself is both limitless and perfect.”28” 1 likes
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