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

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.

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.

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.

The book is as described.

A gift -- the recipient was delighted.

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. It really bowled [or Booled?] me over even then, and every time I've picked it up since I find something new and clever I hadn't given full thought to before. It is a MUCH better introduction to transfinite numbers than the also still quite good book by the late David Wallace Foster [if I've ordered names those correctly]. When I say it's one of the five best science books ever written, I am not exaggerating, provided, of course, that you have a basic grasp of Calculus and a touch of "naive set theory" and basic analysis under your belt, which if you got through high school or college you probably do. Rucker's non-fiction books are always excellent. His fiction doesn't interest me as much, but some of the stories have interesting conceptual leaps etc. 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.

Rudy Rucker deals with the concept of Infinity in regard to our mental conceptions and the structure of reality. The question is whether or not the concept of Infinity makes sense, and then the relation of finite thought and human consciousness relates to the possibility of infinites in the structure of reality.Rucker is a professor of Calculus and centres this discussion in the History of Mathematics stemming from the ancient Greeks. For the Greeks there was no distinction between mathematics and philosophy. He takes a mathematical approach, but converses fluently in the disciplines of Quantum Physics and Philosophy.I classified this book as Epistemology (the Philosophy of Knowledge) because the central concept is the meaning and definition of Human Consciousness. In this regard Rucker probes the meaning of consciousness and the relationship of the individual mind to the concept of Universal Mind.The title includes Infinity, because the investigation considers all aspects of the ultimate or Absolute. So at the root of this is the question of whether it makes sense for anything to be Infinite. Is there such a thing as Infinity? Are there multiple infinities? Involved is the question of whether the human mind can conceptualize an infinite thought, or is every human thought a finite thought?The reason this is a question of Epistemology is that one must consider how we know, and what a finite mind can know. Thus Rucker looks at the question in terms of many disciplines of knowledge. Basically, we are asking whether it is possible for something in the universe (one mind, and its thoughts) to know the Absolute or Ultimate reality, of which it is a part!Another term for the discipline commonly dealing with this problem is Theory of Mind. Before Rucker's book, I had not looked at the concepts of Theory of Mind and the Philosophical question of the Absolute and the One-Many debate in a mathematical perspective before. This latter entails the concept of whether there is some ultimate unity to the universe, including the recent question of multiple universes, and whether the Absolute is sentient, as an active God or relatable entity.Rucker points out that any ultimate question, posed in terms mathematical, theological or otherwise, is a mystical question. He references concepts of Zen Buddhism as well as classical Western Philosophy and Christian theology. He lays a firm foundation for the problem in a historical format by reviewing the ancient Greek concepts.Taking this mathematical approach, Rucker's discussion of set theory helps to clarify the issues involved when we consider whether humans, as finite entities, can conceptualize the ultimate. He deals with the relationship between thoughts and concepts and the external objective world. Set theory and its refinements, which Rucker discusses in terms of the history of their development, provide a way of objectively evaluating whether there can be infinite.Rucker lays out the formulas in geometry and calculus, but discusses the implications from practical and theoretical perspectives in science and theology. I did not camp out in the mathematical formulas, but could generally follow the arguments. But the philosophical implications and the factors discussed in the practical and theoretical scientific disciplines was very helpful. Rucker uses very practical life-situations and analogies to provide a reality for these concepts, which can seem ethereal and abstract.One of the practical aspects is a whole chapter critically evaluating ideas of Artificial Intelligence, "Robots and Souls." He asks whether an artificial intelligence can become self-developing to the stage comparable to human consciousness. He ruminates on the relationship of artificial intelligences to human consciousness.Rucker reviews the creative and ground-breaking theories and writings of Kurt Gödel, a mathematical philosopher in the 20th century. Gödel conclusively established the concept of Infinity. Rucker reports on personal discussions he had with Gödel, who was a mystic and philosopher. They discussed the concept of Universal Mind and the existence of mind beyond body.It was also interesting to see this perspective on the Theory of Mind, various concepts of the Absolute, and critical analysis of the possibilities and limitations of human conception, as written almost 25 years ago, and see that most of what is known and considered now was active knowledge back then.The critical analysis Rucker provides was helpful for a fresh perspective on the methods mathematics brings to metaphysics arising from Particle Physics and the Cosmogony arising out of Theoretical physics on the astronomical level.

Amazon is selling this for Kindle format, BUT its only for android and NOT a Kindle !!

Great

very good

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 !

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.