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John Barrow

The Infinite Book

The infinite can be an intimidating concept. In 'The infinite book' John Barrow takes a lighthearted look at the nature of infinity. He starts with the early objections to the concept - Zeno's paradox and the writings of Aristotle - and moves on to the work of Georg Cantor, when infinity became respectable. The book goes on to look at what it means for the universe to be infinite in space or time. Barrow demonstrates the paradoxes or infinite replication which would occur if either of these were the case , but also shows how they could explain why the part of the universe we live in seems to be so favourable for the emergence of life.

The final chapter of the book concerns the eternal life, looking at both the possibility of extending our lifes forever in this world, and the question of an afterlife. But would we know what to do with eternal life if we had it?

So who should read this book? Well I felt it was written for a general readership - no previous knowledge is required. However, Barrow does tend to jump from one subject to another, and I think that this might be confusing for those who don't recognise what he is discussing. Hence I would recommend it to those who have had at least a little previous exposure to the subjects covered.

Amazon.com info
Paperback 352 pages  
ISBN: 1400032245
Salesrank: 151598
Weight:5 lbs
Published: 2006 Vintage
Amazon price $10.85
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Amazon.co.uk info
Paperback 256 pages  
ISBN: 0099443724
Salesrank: 220320
Weight:0.62 lbs
Published: 2005 Vintage
Amazon price £6.99
Marketplace:New from £2.84:Used from £1.47
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Paperback 352 pages  
ISBN: 1400032245
Salesrank:
Weight:5 lbs
Published: 2006 Vintage
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Product Description
For a thousand years, infinity has proven to be a difficult and illuminating challenge for mathematicians and theologians. It certainly is the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment, reading an identical sentence on an identical planet somewhere else in the Universe.

Now Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories. From the paradox of Zeno’s arrow to string theory, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live. The Infinite Book is a thoroughly entertaining and completely accessible account of the biggest subject of them all–infinity.
 
Fascinating *****
Barrow is one of my favorite authors, and his lucid explanation of fascinating topics is always a pleasure.
 
Thinking about the unthinkable *****
This is a marvelous book. Infinity is a tough concept to wrap your mind around, but Prof. Barrow makes it as understandable as anyone possibly can. He goes deep into the subject -- this is by no means a superficial treatment -- yet never loses an attentive reader. 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.
 
The various faces of infinity ****
This book discusses infinity. 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. Augustine. 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. The question of the possible topologies of the universe is discussed, although we do not know yet the answer. 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). Unhappily , the drawing in the next page will confound the lay reader because the radius is pictured at 14 billion light years. (There are also some other minor mistakes in the book, which would have been avoided by a careful reviewer before publishing. Another example is the graph in page 190 which suggests that expansion of the universe is decelerating, contrary to recent data of supernovas). 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). 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. Instead, superstring theory has landed with a whole landscape of possible universes. 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? The diverse answers are tabulated in page 186.
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 . 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. 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. "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).



 
Infinite questions. ****
I have not been disappointed by any of John Barrow's book so far. He has a unique gift of writing with exceptional clarity about difficult topics. This is not a typical cosmology book, but large portion is devoted to beginning, shape and future of The Universe.
Like in his previous "Book of Nothing", author mixes philosophical and scientific musings about infinities (big and small) affecting theology, mathematics, cosmology, physics (TOE) and our existence.
I found Georg Cantor's life and his quest for understanding "absolute infinity" (God?) quite interesting and emotional. And check how Blaise Pascal argued about believing (or not) in God, because of infinite gain (or loss!!).
One truth emanates from "The Infinite Book": we are far, infinitely far from knowing the truth about everything (Immanuel Kant's rings the bell!). The more we learn the bigger infinite number of questions surface in front of us. Are we nearing the limits of knowledge? Professor John Barrow does not suggest it has come to this, but read about them and enjoy stretching your mind.
 
Light infinite ***
If you are interested in infinity and you are not familar with Cantor or Borges' "The Library of Babel", then you may be amazed by this book. Otherwise, you can find it too light. Probably good as a light summer reading.

Infinity is a fascinating subject, and I thought that this book would contain a lot of interesting information in its 300 pages. I have found many quotations, a lot of superficial theology and ethics, and little information on the concept itself. I missed more depth in handling the mathematical concepts.

Anyway, there is a very good part of the book (from my point of view) devoted to eternal inflation and simulated universes, especially for how the theories are introduced and chained. Even if it is not strictly related to infinity, it is the best part of the book. The chapter that describes Cantor's works is worth reading too.
 
Best Barrow I have read ****
I have read already several books from John D Barrow (Theories of Everything, Book of Nothing, Pi in the Sky), and I found some of them a bit vague and with some irrelevant chapters. To me, this one is the best one from Barrow I have read. The topic could have been discussed even more in depth, but overall, the book kept me turning pages from the beginningto end, and I have not read many better written popular science books. Even though there were some, therefore I give 4 of 5 :-))
 
Has its limits ****
"Well," I said to myself, as I picked up The Infinite Book for a bargain, finite sum of money, "this ought to last a while".

There are a number of playful paradoxes on the theme of "infinite" books, and indeed Barrow mentions one of them in a chapter of his own "Infinite Book", a short story by Borges, in which a man finds a book with an infinite number of pages, which means that absolutely all knowledge, both true and false, is contained within it ... the answer to everything is always there, somewhere, but once you've lost your page the chances of ever finding it again are mathematically nil. However, this "Infinite Book" reminded me of a different sort of imaginary "infinite book" - a mathematical paradox, in which every successive page of a book is half the thickness of the previous one, so when you flip the book over to look at the last page, the last page doesn't exist.

Just like this latter "infinite book", it seemed to me that the content of "The Infinite Book" started out in the early pages as challenging, hefty, engaging - and then starts to become more flimsy and insubstantial as it goes on. It's as if the author started out with a terrific idea for a book (and the early chapters, about Cantor's infinities and the heresy of infinity, make for engrossing reading) but then ran out of ideas and had to pad it out to book length with in some places, frankly daft chapters about Infinite Machines and Living Forever. Increasingly the reader is asked to accept statements that challenge not only one's intuition but also the foregoing text, unless of course the current theory is truly so esoteric that it doesn't make sense to the ordinary brain. For instance, computers, we are told, have doubled in power every couple of years or so on average since about 1900 "which has led some people to speculate that eventually there may be machines capable of performing an infinite number of calculations." Oh, right, okay, says the reader, and when's that going to happen? No answer is given us here. Elsewhere in his book, Barrow tells us that the existence of an infinite number of universes, apparently, "implies" that everything exists and is infinitely repeated. It's hard to see why, though, since we have already been introduced to the idea that the number "1" for instance, is never, ever, repeated again in the infinitely long series of whole numbers. Perhaps universes are counted as a different order of infinity. But it isn't clear. Another thing which slightly jarred was that, even though the existence of Infinity is still (the author tells us) a matter of philosophical speculation among mathematicians, the philosophy in this book seems to be pitched at a considerably lower level than the science ("endless" confused with "timeless" seemed to me like a bit of failed expository legerdemain). This is annoying, because presumably a book called "The Infinite Book" will be read by people with an interest in both camps.

Nonetheless Barrow writes well, and has also provided a very comprehensive bibliography for anyone wanting to read further about a fascinating subject, but despite its title, in the end this is a book that whets the appetite, rather than trying to cover the entire field of his subject - which would admittedly be a daunting undertaking!

 
An easy read on a hard subject *****
A very well written book which makes a hard subject deceptively easy. Very light on equations and the "frightening" bits of mathematics, very strong on well written explanations of why infinity isn't a number, and all that flows from that.

The quote on the cover says "popular science doesn't come much better than this", and for once I agree.


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