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The Infinite Book: A Short Guide to the Boundless, Timeless and Endless

3.91 of 5 stars 3.91  ·  rating details  ·  603 ratings  ·  44 reviews
Infinity is surely the strangest idea that humans have ever had. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Can you do an infinite number of things in a finite amount of time? Is the Universe infinite?

Infinity is also the place where things happen that don't. What is it like to live in a Universe where nothing is
Paperback, 352 pages
Published November 3rd 2005 by Vintage (first published January 1st 2005)
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As I started studying Calculus more and more it made me a lot more curious about the nature of infinity. 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. Then, to top it off, I had my mind further blown by discussing infinite dimensions in Linear Algebra. Needless to say, I had infini ...more
Well, the good thing is, I managed to finish this book in a finite amount of time. At one point it looked unlikely.

Its not a bad book at all (in fact its quite good), but its a book written by a mathematician, with the assumption that mortals readily understand the meaning of words like 'topology' and 'singularity'. The only places where the book loses its grip is where the author succumbs to this trap.

Having got that out of the way, there are a number of things I liked about this book. First an
Bob Anderson
This book is a joy to read, with subjects that range from the strictly mathematical to the philosophical, physical and literary realms. Its chapters are split into sections, each of which has some quote from history or literature on the nature of the infinite, each of which is engaging (although my favorite quote on the touched-upon subject of the finitude of life, Prospero’s “and our little lives” is only briefly glimpsed with its phrase “our revels now are ended”, delivered in situ near the cl ...more
Benjamin Wallsten
Review taken from my blog,The Virtuosos.

Infinity. What is it? What is it not? Why should anyone care about something so intangible?

For many people. infinity is just a word that they’ve been taught means, “without bound; forever; bigger than anything; beyond comprehension.” It’s usually associated with mathematics, especially math of a “higher order,” like Calculus. And it seems intuitively familiar despite an utter lack of understanding for the most part.

Barrow takes the everyday view of infinit
The resourceful manager had begun by finding room for one extra guest in a full hotel, then a room for an infinite number of guests in a full hotel, but now he is being asked to find room for an infinite number of travel parties, each of which contains an infinite number of guests. What can he do? They will start arriving soon!
After a slightly meandering opening chapter or two this book starts getting going with "Welcome To The Hotel Infinity", an introduction to Cantor's fantastic diagonal proo
M.G. Mason

Infinity. How often do you think about it? I mean really think about the idea that something could go on forever? Have you thought about what the end of the universe might look like? Or whether there is a physical boundary to it? If there is a boundary, what is beyond it? More universes? Are they infinite?

What about the infinitely small? An atom’s radiation, for example, will never completely disperse, it will get smaller and smaller, halving each time while never reaching zero. This too is infi
The first half of the book concerns the evolution of mathematical theories underpining the ideas in the second half which considers the implications to the physical universe,and the possibilities that may arise.
The text is subdivided and illustrated in an abundant manner,which makes for fairly easy going and it reminded me of "Fermat's Last Theorem" or "A Brief History of Time" in its assumption of the intellect of its readership.Things did start to get mathematically taxing when he was discus
This book was really interesting: a discussion about ideas about infinity - history, paradoxes, implications, conditions of... It's a concept I took for granted. If space weren't infinite, then what would be on the other side, where it ends? Where would numbers end? Where would time end?

Most of the book is written for the layman with a basic knowledge of mathematics and some in the principles of physics. But the beginning rehashes some of this, so even if your knowledge were rudimentary you'd ge
John Barrow a professor of applied mathematics has written a fascinating, but rather meandering exploration of infinity. Particularly the concept of infinity in three flavors sheds light on the development of thinking about infinity. He suggests that there are three types of infinity: mathematical infinity, physical infinity, and absolute transcendental infinity. Mathematical infinity is the concept associated with concepts in mathematics. Physical infinity is the infinity found in nature like t ...more
Most people think "infinite is just some really big amount". In reality, infinite is neither an amount, nor "really big". This is a great pop-sci book on infinites, presenting them in both mathematical and physical (and even in philosophical) sense. I recommend it to everyone who is interested in mathematics or science.

Those who have a good grasp of high school maths and physics may want to check only the last four chapters.
Relaxed and brief review of commonplace topics around the concept of inifinity, including references to the usual suspects in infinity-land: Cantor, Gödel, Turing, Einstein, and a bunch of greek philosophers.

Infinity is sometimes just an excuse to talk of other topics, mainly cosmology. A litle too much wandering around philosophical and religious issues for my taste, but nevertheless very interesting for the historical perspective. Ive enjoyed the worthy notes and references.

Very advisable lect
The first few chapters cover the philosophies of antiquity about infinity (Aristotlean, Christian etc.), so they are a bit boring and feels irrelevant. But their inclusion is justified by the fact that the author wants to include the development of ideas about infinity from the very beginning.

Then things start to pick up. The author covers a vast range of topics related to infinity: paradoxes, Cantor's set theory, and the (in)finitude of the universe.

But the best part of the book is some of the
Affronta il tema più grande e complesso del tutto, l'infinito. Un saggio di filosofia, arricchito in alcune parti da teorie sui numeri.

Dalle concezioni e dalle idee dei filosofi dell'antichità sull'infinito il testo esamina la rivoluzione matematica ed il suo apice nelle teorie di Cantor, approfondendo la guerra fredda che i matematici hanno combattuto tra loro riguardo l'introduzione degli infiniti nella matematica.

Non mancano interi capitoli dedicati a teorie numeriche, teorie visionarie sull'
Argomento affascianante ma ostico.
Abbastanza semplice e comprensibile la scrittura.
Ci sono punti che proprio non capisco, ma complessivamente è molto ben scritto.
Steven Williams
I found the book fantastic. Very well presented. Held my attention from beginning to end. I read it in three days. Once again Barrow came up with a keeper.
Chelsea Ursaner
I enjoyed this book a lot more than I thought I would given that it has no story or characters. It is, exactly as it says it is, an exploration of the concept of infinity as it has been explored in philosophy, mathematics, literature, religion etc over the years. It’s very well organized and I liked the pictures and thought experiments. Plus you get a bunch of mini introductions to famous minds that have worked on the puzzle of infinity. However, he also goes too far out sometimes and lost my at ...more
John Stifter
Very interesting read. It is a good introduction to the concept of a super task.
Adrian Paleacu
one of the best book ever
Popular form of Math book.
Misleading title.

Very good book though. It's an intelligible introduction to the subject; never digging too deeply into the underlying maths and pleasingly free of jargon.
David Joseph
That this is the most easily accessible account of the "Universe of Discourse" can be easily argued and easily demonstrated and infinitely so.

It is elegant and artful.

You don't need to know any math at all to deeply appreciate the ideas that are explicated. A person just needs to have a working knowledge of plain English.

This is written at about, oh, Flesch–Kincaid Grade Level 8?

This is just a fine example of a little sumpin' for everybody.

Killer good!

This book was pretty good, though a little repetitive at first. However, it made me realise how much more there is to infinities and it's really hard to truly grasp what infinity is. There are even different levels of infinities! The book later goes on to even examine whether or not we are in a computer simulation, topics on immortality, and finally time travel. I recommend this book to those that are curious about what could be out there.
Really like the book, great history and anthology of infinity.

I could have done without all of the philosophy and astronomy, I was looking for more of a mathematical book. Great book in all.
Nicholas Diluzio
Barrow's book manages to sum up "infinity" in a finite manner without going into too much detail.
A fun little exercise in the history and applications of infinity. Unfortunately, this book suffers from what I expect is the same in all layman guides to high-level mathematics, cosmology and astrophysics: any simplifications of these topics will leave more questions unless you take it all the way.

Regardless, it certainly was an enjoyable and accessible read.
Mbuso Yende
Man has not seen God's eye-view on the concept of infinity, we can only approach it from one side, but here is a thought: if we have to traverse in opposite directions beginning at the same point, aren't we approaching infinity from both sides?...just a thought...the book has many thought-provoking ideas and concepts - a definite recommendation!
Evan Donovan
Apr 06, 2007 Evan Donovan rated it 2 of 5 stars  ·  review of another edition
Recommends it for: readers of popular science/math books
Shelves: recent-reads
Not as engaging as I'd hoped. The writing is surprisingly bad in some places. I have a feeling the author was rushing when he wrote it. I did learn some interesting things from it, I just wish that they'd been presented better and that the book was better organized.
mayfly wake
very ambitious in scope, so much that it seemed a bit scattered. i still enjoyed it though, definitely gave me a lot to think about and some lucid explanations of things that i haven't understood from other sources.
AJ Ostrow
If you enjoy abstract theorizing about mathematical concepts and relating them to the human experience in analogies, or just enjoy mathematical theories and the history behind them, this book is for you. I liked it.
Jul 13, 2007 Peter rated it 5 of 5 stars  ·  review of another edition
Recommends it for: All
Brilliant look at the concept of "infinity". Heady, no? The "big" infinity is nothing new, but it's the "little" infinity that blows my mind; how do you keep making smaller and smaller breaks in something? Whoa.
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John D. Barrow is a professor of mathematical sciences and director of the Millennium Mathematics Project at Cambridge University and a Fellow of the Royal Society.

He was awarded the 2006 Templeton Prize for "Progress Toward Research or Discoveries about Spiritual Realities" for his "writings about the relationship between life and the universe, and the nature of human understanding [which] have c
More about John D. Barrow...

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