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We take these limits of functions to get the derivation process, we look at area with integration by summing infinitely small pieces under a curve, and then we look at the divergence and convergence of a series with limits to see what these things do at infinity. Don't get me wrong, it's definitely relevant). Cosmology being a major one, but he also brings us through some of the more "pop culture" elements (if I dare call them that). I found this utterly fascinating and Cantor did some impressive work with infinity.Naturally Barrow ups the ante as the history gets to more modern day applications. Don't worry, if you're not a mathematician you can still grasp the general concepts discussed in this book. Needless to say, I had infinity on my mind.
However, I wanted a more informal book to read to pass the time. Studying the formal texts is fun, but can get tedious.Barrow's book "The Infinite Book" is exactly what I was looking for. As I started studying Calculus more and more it made me a lot more curious about the nature of infinity. I would even rank this as a rather exhilarating read. (I'm actually getting sick of reading about this, it feels like just about every math book I read discusses Zeno. Anyway, some of the more interesting stuff comes when he gets to discussing Cantor's history. Barrow approaches the subject in an excellent way and not in a way where I think non-mathematicians will feel put aback by the arcane discussions.
With that in mind you take a walk through the history of infinity and how it touches human curiosity. Then, to top it off, I had my mind further blown by discussing infinite dimensions in Linear Algebra. Such as strange movies that involve things like an infinite game, which are now movies I intend to track down and watch. One of the great aspects of this book is that Barrow brings through a bit of the history of infinity. Natural he makes reference to Zeno's Paradox. Some of this material may be beyond some readers, it was a little beyond me at times, but I wouldn't say it was so overwhelming I got totally lost in what was being discussed.If you're at all curious about the nature of infinity, then I highly recommend this book. After reading this I am definitely interested in reading other books by Barrow and I would definitely recommend this to anyone interested.
The Book starts off pretty well, very interesting, brings up unique stories, concept and theories on infinity. Half way through the Book, everything is already said, and begins to repeat itself (like infinity). The book speaks too often about the universe and its implication in regards to infinity. In conclusion starts good and then drops some, but very thought provoking, and enjoyable.
Barrow is one of my favorite authors, and his lucid explanation of fascinating topics is always a pleasure.
This is a marvelous book. He goes deep into the subject -- this is by no means a superficial treatment -- yet never loses an attentive reader. Infinity is a tough concept to wrap your mind around, but Prof. Barrow makes it as understandable as anyone possibly can. His brilliant final chapter, dealing with the theory of time travel, will knock your socks off. Barrow has a nice wit, and as a special bonus he has seeded the text with some intriguing Briticisms that were new to me, but happily understandable from the context.
This concept has a precise definition in mathematics and since the times of Cantor we know that there are various degrees of infinity, one of the most interesting problems being whether there in an infinite between the cardinal of the natural numbers and that of the real numbers, the so called continuum hypothesis, which was proven to be undecidable in the usual Zermelo-Frankel-Choice axioms of set theory.In recent times, cosmologists, whether those adopting the inflationary scenario or those favouring the cyclic universe, are pondering whether the universe is infinite in space and possibly eternal in time (although some believe it had a beginning about 14 billion years ago, but may never end).So the topic of the book is pertinent to our age.Naturally, the idea of infinite is also related to the idea of God, although this is not a scientific subject, but possibly a philosophical one.The first part of the book is a hystorical review of the concept of infinity, from Zeno and Aristotle to Kant and Cantor, via St. Naturally, the limit on how fast information can spread will probably preclude us from knowing whether the universe is infinite unless we can get some degree of confidence on some basic theory that predicts this infinity.The book also discusses interesting problems regarding the impact on ethics of inmortality and the possibility of clones in an infinite universe (Vilenkin has explored also this idea in one of his books). So the question remains, how we happen to live in such universe that has made it possible for life to appear (at least in the Earth, possibly in many other planets) and to develop a self-conscious and inquisitive species by means of which the universe interrogates itself. Instead, superstring theory has landed with a whole landscape of possible universes. The question of the possible topologies of the universe is discussed, although we do not know yet the answer. A very entertaining chapter is the one about the Hotel Infinity and all the challenges that the manager meets, quite successfully and that would be impossible in a hotel with only a finite number of rooms.
The second part of the book deals more with physics and cosmology, things like the singularities at the center of black holes. It is interesting to learn that an English astronomer of the 16th century already proposed that the universe is infinite. This book discusses infinity. I found very interesting the 4-body configuration discovered by Xia in 1971 that , according to Newton's theory , sends the 4 bodies at infinite distance in finite time. Another example is the graph in page 190 which suggests that expansion of the universe is decelerating, contrary to recent data of supernovas). Physicists have changed their views on the universe in the last 30 years when it was hoped that The Theory of Everything would be mathematically unique and would determine one universe. Einstein's general relativity doesn't allow this, so that infinities did appear not only in quantum mechanics, but also in newtonian mechanics.One of the important conclusions of the book is that the human race is not necessarily equipped to know all things that are true about the universe.
Unhappily , the drawing in the next page will confound the lay reader because the radius is pictured at 14 billion light years. Augustine. The diverse answers are tabulated in page 186. The important distinction between the observable universe and the universe as such is made in page 139 where the radius of the visible universe is stated to be 42 billion light years (which seems to be the correct figure if we take into account the expansion of the universe since the light emitted 14 billion years ago has reached us). (There are also some other minor mistakes in the book, which would have been avoided by a careful reviewer before publishing. It also has another chapter on virtual reality "à la Matrix" (simulated universes) and it also discusses the possibility that advanced civilizations are capable of cultivating universes, the way we grow cornfields or build cities.Another of the subjects discussed by the author is that of machines capable of supertasks. "We have no special right to expect that all truths about the Universe can be tested by observations that are within our reach: that really would be an anti-Copernican outlook" (page 198).The book is an eye opener for those readers not familiar with the role of infinity in the mathematical and physical sciences, but if you look for definite answers about these difficult problems you will not find them here (not in other books, of course).
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