Best Barrow I have read
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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 :-))
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Has its limits
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"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!
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An easy read on a hard subject
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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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