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Infinity and the Mind: The Science and Philosophy of the Infinite
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 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 Godel's incompleteness theorems. His personal encounters with Godel 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.
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 Godel's incompleteness theorems. His personal encounters with Godel 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.
368 pages, Paperback
First published January 1, 1981
106 people are currently reading
2432 people want to read
About the author
Rudy Rucker
194 books581 followersRudolf 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.
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Displaying 1 - 30 of 50 reviews
July 25, 2015
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 brilliant. However, more mathematical rigor and detail in some areas (for example, when dealing with hyperreal numbers) would have made the book more structured and readable.
Other parts of the book (such as infinite divisibility of matter, curvature of space etc.) are necessarily obsolete, given the age of the book.
The author occasionally gets a bit too mystical for my tastes (maybe these dips into mystical territory are a reflection of the "New Age" BS that characterized the intellectual climate of the period when the book was initially written), and in doing so he not just abandons the constraints of scientific inquiry, but also those of properly developed, disciplined philosophical discourse; but it must be said that, overall, this is a very nice book, which treats holistically the concept of infinity from different perspectives, and which provides lots of food for thought.
December 1, 2008
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 that if the reader has followed and understood the concepts so far you have another chance to exhaust your reasoning powers on these, because with infinities there are things that cannot be logically, mathematically or scientifically described fully. Rucker argues that many of the ideas about infinity are not rationally and deductive, but mystical an intuitive. This makes a book that is an active and entertaining mental wrestling match. It also makes it a stimulating, thought provoking, and potentially mind expanding read.
May 7, 2016
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.
January 18, 2021
I read this as a senior in high school which is a good age to contemplate Cantor's Transfinite mathematics. It is accessible to someone with High school math. Surprisingly as paradoxical set theory and Cantor's paradise seem it is very accessible and who doesn't want to think about nay become the wayfarer of infinite space. Good stuff opens with the possibility of infinite space and argues it is probably a reality as well. Then explores Cantor's paradise in a down to earth way with some cartoons to boot. Good stuff mind-expanding.
https://www.youtube.com/watch?v=X56zs...
https://www.youtube.com/watch?v=X56zs...
November 26, 2018
2.5/5.0
September 23, 2012
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.
January 1, 2010
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 a number of misprints in my edition - that was an early one, perhaps even first, though.
Overall, lots of interesting ideas, somehow not as thought-provoking as I had felt it could be ... But I would still recommend it, to philosophically minded (with a bent for playful puzzles) mathematicians , mainly.
Some passages and even some ideas were a bit obtuse/confusing, e.g. the concept of (circular) scale, which I only half understood. Quite a number of misprints in my edition - that was an early one, perhaps even first, though.
Overall, lots of interesting ideas, somehow not as thought-provoking as I had felt it could be ... But I would still recommend it, to philosophically minded (with a bent for playful puzzles) mathematicians , mainly.
October 6, 2013
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 point, any kind of point, to show up. It never did.
August 23, 2012
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.
September 24, 2012
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.
December 21, 2007
bit slow and dry at times. But fascinating topic
March 23, 2019
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 be a revelation.
Infinity and the Mind, a brilliant journey through Godel’s Theorem and mathematical proofs of the Infinite, lively and full of intriguing games and exhilarating, surprising thought problems, struck me as a graduate student with a force of vision which reshaped all my thinking; and resonates still, like a bell, ringing.
Infinity and the Mind is as important to higher math as Darwin's Origin of Species is to biology or Hawking’s' A Brief History of Time is to cosmological astronomy. Only Gregory Bateson’s Mind and Nature: a necessary unity, has changed and illuminated me as much. Working through his puzzles will change both yourself and how you relate to and conceptualize your reality, like a spell of transformation.
His other nonfiction includes The Fourth Dimension: A Guided Tour of the Higher Universes, Lifebox, and Mind Tools: The Five Levels of Mathematical Reality.
And there is his fiction; strange, hilarious, improbable, fantastical. First among his masterworks is Turing & Burroughs, a wonderful alternative history of two of my personal heroes that can stand as the equal of any other literary work of our time alongside Pynchon's Gravity's Rainbow, Vonnegut's Cat's Cradle, the Metamorphosis of Kafka, and the glorious novels of William S. Burroughs himself.
In As Above, So Below: A Novel of Peter Bruegel, Rudy Rucker once again maps a subversive allegory of the artist as visionary and revolutionary in a brilliantly imagined world.
A prolific writer, in the belles-lettres tradition of Flaubert, his books pour forth an entire alternate life as if an invisible scribe were recording events as they happen, both real and imaginary; Rudy Rucker is really two people, this mythic living hero and his invisible scribe. Which is the shadow cast by the other I cannot say; read therefore: Spaceland, The Hacker and the Ants, The Big Aha, Mathematicians in Love, Jim and the Flims; and the three novels of the Transreal Trilogy; White Light, The Secret of Life, and Saucer Wisdom.
If his novels are multidimensional and strange, fear not; Rudy Rucker explains himself and his literary theory and method of Transrealism in a manifesto on his free online page which collects the short fiction also published in Complete Stories:
http://www.rudyrucker.com/transrealbo...
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 be a revelation.
Infinity and the Mind, a brilliant journey through Godel’s Theorem and mathematical proofs of the Infinite, lively and full of intriguing games and exhilarating, surprising thought problems, struck me as a graduate student with a force of vision which reshaped all my thinking; and resonates still, like a bell, ringing.
Infinity and the Mind is as important to higher math as Darwin's Origin of Species is to biology or Hawking’s' A Brief History of Time is to cosmological astronomy. Only Gregory Bateson’s Mind and Nature: a necessary unity, has changed and illuminated me as much. Working through his puzzles will change both yourself and how you relate to and conceptualize your reality, like a spell of transformation.
His other nonfiction includes The Fourth Dimension: A Guided Tour of the Higher Universes, Lifebox, and Mind Tools: The Five Levels of Mathematical Reality.
And there is his fiction; strange, hilarious, improbable, fantastical. First among his masterworks is Turing & Burroughs, a wonderful alternative history of two of my personal heroes that can stand as the equal of any other literary work of our time alongside Pynchon's Gravity's Rainbow, Vonnegut's Cat's Cradle, the Metamorphosis of Kafka, and the glorious novels of William S. Burroughs himself.
In As Above, So Below: A Novel of Peter Bruegel, Rudy Rucker once again maps a subversive allegory of the artist as visionary and revolutionary in a brilliantly imagined world.
A prolific writer, in the belles-lettres tradition of Flaubert, his books pour forth an entire alternate life as if an invisible scribe were recording events as they happen, both real and imaginary; Rudy Rucker is really two people, this mythic living hero and his invisible scribe. Which is the shadow cast by the other I cannot say; read therefore: Spaceland, The Hacker and the Ants, The Big Aha, Mathematicians in Love, Jim and the Flims; and the three novels of the Transreal Trilogy; White Light, The Secret of Life, and Saucer Wisdom.
If his novels are multidimensional and strange, fear not; Rudy Rucker explains himself and his literary theory and method of Transrealism in a manifesto on his free online page which collects the short fiction also published in Complete Stories:
http://www.rudyrucker.com/transrealbo...
January 24, 2020
This was a fairly deep investigation of the nature of the infinite. Much like the infinite, the book offered finite descriptions of that which is truly Infinite. There are some genuine insights on the nature of sets, different sizes of infinity, together with interesting paradoxes and puzzles.
If you have already read Godel Escher Bach, then you can skip this book since it covers the same topics but describes them with more technical jargon.
Some quotes I enjoyed:
-God is an intelligible sphere, whose center is everywhere and whose circumference is nowhere.”
-By the classic work of the logician Thoralf Skolem, we know that for any finite description of N one might come up with, there will be a different set N* that also satisfies the description. So it is quite literally true that what is really meant by the “…” is inexpressible
-In Cantor’s words, “A set is a Many that allows itself to be thought of as a One
-It would seem, in particular, that God should be able to form a precise mental image of Himself. Insofar as the Mindscape is God’s mind, what I am saying is that one of the objects in the Mindscape should be the Mindscape itself.
-In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible
-As long as I identify with my body and my rational mind, I cannot conceive of my u 0 ; but it is not hard to envision my u 0 if I identify with the Absolute. This does not lead to the usual type-theoretic regress, because someone who is merged with the Absolute is in a position to “name” each and every natural number at once.
-No finite system can generate arbitrarily complex patterns. No finite system can understand everything. No finite system can define truth.
-Man will never know the final secret of the universe.
-It should be possible to form a complete theory of human behavior, i.e., to predict from the hereditary and environmental givens what a person will do. However, if a mischievous person learns of this theory, he can act in a way so as to negate it. Hence I conclude that such a theory exists, but that no mischievous person will learn of it.
-There is no contradiction between free will and knowing in advance precisely what one will do. If one knows oneself completely then this is the situation. One does not deliberately do the opposite of what one wants.”
If you have already read Godel Escher Bach, then you can skip this book since it covers the same topics but describes them with more technical jargon.
Some quotes I enjoyed:
-God is an intelligible sphere, whose center is everywhere and whose circumference is nowhere.”
-By the classic work of the logician Thoralf Skolem, we know that for any finite description of N one might come up with, there will be a different set N* that also satisfies the description. So it is quite literally true that what is really meant by the “…” is inexpressible
-In Cantor’s words, “A set is a Many that allows itself to be thought of as a One
-It would seem, in particular, that God should be able to form a precise mental image of Himself. Insofar as the Mindscape is God’s mind, what I am saying is that one of the objects in the Mindscape should be the Mindscape itself.
-In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible
-As long as I identify with my body and my rational mind, I cannot conceive of my u 0 ; but it is not hard to envision my u 0 if I identify with the Absolute. This does not lead to the usual type-theoretic regress, because someone who is merged with the Absolute is in a position to “name” each and every natural number at once.
-No finite system can generate arbitrarily complex patterns. No finite system can understand everything. No finite system can define truth.
-Man will never know the final secret of the universe.
-It should be possible to form a complete theory of human behavior, i.e., to predict from the hereditary and environmental givens what a person will do. However, if a mischievous person learns of this theory, he can act in a way so as to negate it. Hence I conclude that such a theory exists, but that no mischievous person will learn of it.
-There is no contradiction between free will and knowing in advance precisely what one will do. If one knows oneself completely then this is the situation. One does not deliberately do the opposite of what one wants.”
July 18, 2019
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 do we all feel the same pain, but that pain doesn't go away just because nobody's feeling it. He also believes in what he calls the Absolute Infinite, which is something like the set of all sets and something like God, but which he thinks can't have any property unique to it or else it would be nameable or comprehensible or something like that. It's a wild ride at places, and these pretty hefty claims don't have nearly as much support as you'd expect them to.
It loses a star for mutilating the views of some of my favourite philosophers. He attributes to Hume on scanty evidence a belief in something like the mindscape, which I think is wildly incongruent with Humean bundle theory. Of Wittgenstein, he asks: if all meaning is governed by rules, wouldn't we expect to be able to form a complete list of all the rules? To which I think the answer is "Not if you'd read Wittgenstein, you wouldn't."
It loses a star for mutilating the views of some of my favourite philosophers. He attributes to Hume on scanty evidence a belief in something like the mindscape, which I think is wildly incongruent with Humean bundle theory. Of Wittgenstein, he asks: if all meaning is governed by rules, wouldn't we expect to be able to form a complete list of all the rules? To which I think the answer is "Not if you'd read Wittgenstein, you wouldn't."
March 26, 2021
I read this as a senior in high school which is a good age to contemplate Cantor's Transfinite mathematics. It is accessible to someone with High school math. Surprisingly as paradoxical set theory and Cantor's paradise seem it is very accessible and who doesn't want to think about nay become the wayfarer of infinite space. Good stuff opens with the possibility of infinite space and argues it is probably a reality as well. Then explores Cantor's paradise in a down-to-earth way with some cartoons to boot. Good stuff mind-expanding.
https://www.youtube.com/watch?v=X56zs...
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following reviews
June 14, 1985 – Started Reading (Other Paperback Edition)
June 24, 1985 – Finished Reading (Other Paperback Edition)
May 12, 2020 – Started Reading
May 13, 2020 – Finished Reading
January 17, 2021 – Shelved (Other Paperback Edition)
January 18, 2021 – Shelved as: american-history
January 18, 2021 – Shelved
January 18, 2021 – Shelved as: cold-war
January 18, 2021 – Shelved as: european-history
January 18, 2021 – Shelved as: general-science
January 18, 2021 – Shelved as: late-twentieth-century
January 18, 2021 – Shelved as: mathematics
January 18, 2021 – Shelved as: philosophy
January 18, 2021 – Shelved as: physics
https://www.youtube.com/watch?v=X56zs...
2 likes · Like ∙ flag
following reviews
June 14, 1985 – Started Reading (Other Paperback Edition)
June 24, 1985 – Finished Reading (Other Paperback Edition)
May 12, 2020 – Started Reading
May 13, 2020 – Finished Reading
January 17, 2021 – Shelved (Other Paperback Edition)
January 18, 2021 – Shelved as: american-history
January 18, 2021 – Shelved
January 18, 2021 – Shelved as: cold-war
January 18, 2021 – Shelved as: european-history
January 18, 2021 – Shelved as: general-science
January 18, 2021 – Shelved as: late-twentieth-century
January 18, 2021 – Shelved as: mathematics
January 18, 2021 – Shelved as: philosophy
January 18, 2021 – Shelved as: physics
January 15, 2023
Before I read this I had read a review that said it was Gödel Escher Bach for people that actually studied math and logic so I was immediately sold. It didn't quite live up to that hype but there were still some very promising chapters in here.
Based on the first couple chapters I thought this was going to be a journey into infinity in all aspects (space, time, math, consciousness, etc.) But it really just struck me as examining the same paradox of self-reference from a CS, physics, logic, and philosophy perspective.
When I was a fresh 18 year old, learning about transfinite numbers for the first time is what initially got me interested in philosophy and logic. So to read Rucker's crystal clear explanation of counting to the different levels of infinity was an absolute gem. Likewise, with his chapter about his conversations with Gödel at Princeton. I am so fascinated by the man's academic work that I hardly ever considered him as a human, with a personality. It was honestly quite emotional.
There were some subsections where I just had to accept that the material was far over my expertise, but the book is written so that not understanding 1 section does not affect the rest of your enjoyment.
Based on the first couple chapters I thought this was going to be a journey into infinity in all aspects (space, time, math, consciousness, etc.) But it really just struck me as examining the same paradox of self-reference from a CS, physics, logic, and philosophy perspective.
When I was a fresh 18 year old, learning about transfinite numbers for the first time is what initially got me interested in philosophy and logic. So to read Rucker's crystal clear explanation of counting to the different levels of infinity was an absolute gem. Likewise, with his chapter about his conversations with Gödel at Princeton. I am so fascinated by the man's academic work that I hardly ever considered him as a human, with a personality. It was honestly quite emotional.
There were some subsections where I just had to accept that the material was far over my expertise, but the book is written so that not understanding 1 section does not affect the rest of your enjoyment.
August 1, 2023
I have probably read this book, cover to cover, at least 5 times. Having just purchased the hardback version I am about to read it through again. This is a seminal work and the best book on the subject of the Infinite that I have read to date. When you come to realise that the Absolute Infinite - the Ein Sof - if it exists - is indistinguishable from God - then the book takes on even more significance.
I feel a strong affinity with Rucker, as he writes in the Preface, "but at the time I thought I was still roughing out a start. I didn't realise it was a high-water mark; and that I would never again think so deeply about the philosophy of mathematics". I know that feeling so well :)
I feel a strong affinity with Rucker, as he writes in the Preface, "but at the time I thought I was still roughing out a start. I didn't realise it was a high-water mark; and that I would never again think so deeply about the philosophy of mathematics". I know that feeling so well :)
March 15, 2024
This is for sure an excellent book (probably, but I did not understand the majority), and I loved the first third of it. Then it becomes utterly difficult to read - plenty of formal mathematics (set theory, anyone?) - and I quit, or rather: started skipping the incomprehensible parts that became successively more prominent as the book went on.
It was a mind bending read, but I wish I could have taken away more of it.
So if you want entertainment, avoid this book. If you have the mathematics background plus the time and spirit to study this book including solving problems and exercises at the end of each chapter - go for it.
It was a mind bending read, but I wish I could have taken away more of it.
So if you want entertainment, avoid this book. If you have the mathematics background plus the time and spirit to study this book including solving problems and exercises at the end of each chapter - go for it.
May 27, 2021
This book is something that introduced me to things that would be a lifelong preoccupation, Infinity, Cantorism, the foundational crisis of mathematics, set theory, Godel. These are long-held furniture in my head. I think I read this in the 1980s and it was one of the first I came across. I suppose Godel, Escher, Bach was also a biggie and the John D. Barrow books also were an influence but this was arguably the first book I came across on these topics and it is a good place to start.
August 26, 2017
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.
January 21, 2020
This is a classic popular book on set theory and a lot of really deep questions on the world and our mind. But it’s not your average science popularising book, as it goes also into the maths (in the appendixes but not only there), so be prepared to a brain-teasing read requiring lots of attention, and you’ll be rewarded with an excellent experience.
December 14, 2024
على الرغم من حماسي الشديد لهذا الكتاب انطلاقًا من عنوانه ثم ما ذكر في النبذة، إلا أن قراءتي له أصابتني بخيبة. ربما رفعت سقف التوقعات؟ لا أعلم. لكن المحتوى في معظم أجزاءه معقد وممل جدًا ويسهب إسهابًا تضيع معه الفكرة الأساسية. وأرى أن محتواه لكتاب آخر لا يتواءم والنبذة المذكورة.
المرافق لقراءته من بحث واطلاع كان ممتعًا أكثر من قراءة الكتاب ذاته.
+ قفزت على بعض الفقرات والفصول.
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September 18, 2020
This book went way over my head. It was way too technical for me and I barely understood a quarter of it. There were a far parts that I followed and found interesting but the majority of it was mathematical equations that I could not follow.
December 6, 2021
Don't read anything else until you've read this. By the time you've finished you will have enhanced and rewarded all of your past best reading and life experiences and will enhance and reward all your reading and lifes experiences to come.
June 28, 2017
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.
April 16, 2020
Might be five. I have no way of knowing.
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January 4, 2021read most of
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February 12, 2021a bit mind challenging
August 16, 2022
Really enjoyed the discussion in this book. It gave me some good intuition for the definition of ordinal and cardinal numbers.
May 1, 2024
mind-bending but a bit too mystical towards the end
Displaying 1 - 30 of 50 reviews