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

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 pFor 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.

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 [...]

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 [...]

A fantastic book covering the endless scope of infinity. This is my first book of John D Barrow and I'm looking forward to reading his other books. He covers a diverse range of topics related to infinity and the arguments for and against it from both a mathematical sense as well as a physical sense. A good book for amateur knowledge gatherers with references to thoughts and sayings by famous physicists, astronomers, theologists and the like. Would recommend for anyone looking to understand the b [...]

A comprehensive explanation of different paradoxes infinity brings us. It may be not a book for scientists, but it surely is for us amateurs of knowledge.

An interesting book that defines infinite and explains some mathematic paradoxes. Easy to understand for the most part.

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 vie [...]

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 in [...]

Sull'infinito si può dire di tutto, e ancora di più. Ognuno quindi può scegliere quali punti trattare con più attenzione, a seconda della sua indole. John Barrow in questo libro ha scelto fondamentalmente la strada che è il peccato di orgoglio per chi ha una formazione prettamente scientifica, cioè buttarsi sul filosofico. Il risultato è un'opera che non contiene troppa matematica, e quindi si può leggere senza troppi problemi, ma poi si perde in considerazioni dubbiose o erronee. Tanto [...]

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 n [...]

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 discuss [...]

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 [...]

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 get i [...]

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 [...]

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 [...]

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. I´ve enjoyed the worthy notes and references.Very advisable l [...]

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 [...]

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 sul [...]

This was a really detailed and explaining book about infinity. It talks about infinity in multiple different ways, it talks about infinity paradoxes, infinity in math and number theory, the relative infinity. It even talks about hotel infinity, a word problem like hotel with infinite rooms. Personally, I found it interesting and fun to read. It was a bit confusing at times and was hard to keep up with everything the book was saying, however it was still good. I would recommend it to anyone who e [...]

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.

Un po' ripetitivo - sempre che non sia il primo libro di Barrow o affini che si legge; in quel caso, infatti, è un ottimo avvicinamento a una comprensione della matematica e di alcuni aspetti della fisica contemporanea molto diversa da tutto ciò che si insegna (purtroppo) a scuola - almeno nella maggior parte dei casi. In effetti, lo consiglierei agli insegnanti, tanto per farsi venire delle idee originali e coinvolgenti :)

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.

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.

A broad discussion about the notion of "infinite" ranging from mathematics to physics, philosophy and speculation (for example, "what would happen if we lived infinite lives?"). The book is OK, but I personally found it too superficial, too broad, and too speculative. Also, I would have enjoyed a deeper analysis of the notion of infinite in mathematics.

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 thoughte book has many thought-provoking ideas and concepts - a definite recommendation!

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.

An excellent book covering all aspects of infinity: math, science, history, ethics, philosophy and theology. Too much ethics, philosophy and theology for my taste, but an excellent intro to the breadth of the topic. Barrows is an excellent writer.

Took me a while, as it was quite maths-intensive in spots, but very well worth the read indeed. One of my favourite non-fiction works. Mr Barrow's prose can be enchanting; he ought to try his hand at fiction.

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.

Absolutely fascinating! The author provides beautiful descriptions of thoughts about the infinite - be it in science, mathematics, philosophy, or religion; and provides easy-to-understand descriptions of theories that surround the concept of Infinity. 10/10 would recommend.