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Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library) EXPANDED EDITION
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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.
Review
"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
"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
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
About the Author
- ISBN-100691121273
- ISBN-13978-0691121277
- EditionEXPANDED EDITION
- PublisherPrinceton University Press
- Publication dateNovember 21, 2004
- LanguageEnglish
- Dimensions6 x 1 x 9.25 inches
- Print length368 pages
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With technical books containing many formulas and figures, the kindle preview should always contain some sections with such elements.
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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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 !
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.




