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A Brief History of Infinity

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Welcome to the world of Infinity.

We human beings have trouble with infinity. Philosophers and mathematicians have gone mad contemplating its nature and complexity - and yet it is a concept now routinely used by schoolchildren.

In this highly entertaining and stimulating history, Brian Clegg takes us on a tour of that borderland between the extremely large and the ultimate, from Archimedes counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite.

Full of unexpected delights, the history of infinity proves to be a surprisingly human subject. Whether it's St Augustine contemplating the nature of creation, Newton and Leibniz battling over the ownership of calculus or Cantor's struggle to publicize his vision of the transfinite, infinity's fascination remains the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Exploring the infinite is nothing more than a journey into paradox.

Read the first two chapters of Infinity FREE! Click here

Like something a little more compact and quick to absorb? You can get a quick fix with Introducing Infinity - a visual guide.

Listen to an interview on A Brief History of Infinity with the Skeptically Speaking radio show:

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A Brief History of Infinity does what it says on the tin. Anita Barnes, +plus Magazine

This curiously intriguing work might also, perhaps more poetically, have been dubbed 'the limits to infinity' or indeed, to quote Buzz Lightyear (as Clegg does), 'infinity and beyond'. Or both. For it doesn't take much delving to learn that infinity is full of paradoxes - and strange enough, according to Clegg, to have driven at least two great mathematicians over the edge into insanity. It is probably fair to say that unless you have a reasonably mathematical mind this book could take you there too. But that should not deter you, for there are great rewards in these pages. The concept of infinity inevitably involves built-in contradictions: Clegg's analogy of trying to work out the truth when someone says, 'I'm lying' gives a good idea of the mental twists involved. Yet it's also so simplistic that anyone can grasp its meaning - as long as you can grasp the meaning of 'finite' and the meaning of 'not'. Infinity has been a source for almost infinite speculation from the early Greek mathematicians onwards and has variously been greeted with awe, suspicion and denial; Clegg describes it as 'the interface between mathematics and reality'. And goodness knows maths needs one - he relates in some detail the enormous efforts which mathematicians throughout history have put into trying to solve conundrums largely of their own invention. One can't help thinking that the ancients had an inordinate fondness for inconsequential puzzles - yet often just as the reader is thinking 'does it matter?', Clegg shows us that indeed it does. Clegg, author of Light Years and The First Scientist, used to work for British Airways examining cutting-edge technologies and now runs his own creative consultancy business. Here he has done an excellent job of making the most complex concepts accessible while allowing their mystery to continue to shimmer just out of focus. We start to understand, perhaps, why the linkage of God with the infinite occurs in almost all modern religions, and yet why the church should have felt the need so often to stamp on closer investigation into scientific truths.
Kirkus Reviews UK

This was an entertaining and interesting book... All in all, Clegg did a great job on making this book an interesting and (relatively) easy read on a topic which is definitely fascinating. H, Mathematical Association of America Online February 2005

Clegg is immensely readable and manages to convey to a lay audience some of the key mathematical ideas concerning infinity... a success.
H. Geiges, Times Higher Education Supplement 13 August 2004

[T]he best book on the subject at a "popular" level I have seen... I love how Brian Clegg ingeniously expounds upon the concept of infinity challenging our minds to go beyond previously defined limits of the notion. Bizarre paradoxes, strange people and brilliant metaphors make the whole story move from the mundane to delightfully inspiring and I'm not really a fan of science.. Infinity : the quest to think the unthinkable is a trip to infinity and beyond!!. Undated

Clegg has an amiable, easy style; he chats us through complex ideas rather than lecturing to us. Like other good science populists (Isaac Asimov springs immediately to mind), he explores his subject through narrative and anecdote: hanging discussions of infinity onto their historical development puts flesh onto what might easily be dry bones in other writers' hands, and so we have a tour of fascinating personalities and slices of history, a subject breathed into life.

Brian Clegg has just had me revisiting areas of mathematics I haven't even considered since university. And I enjoyed it. Dr Keith Brooke Infinity Plus 22 December 2003

Clegg's book is engagingly written and includes several interesting biographical sketches, which animate the mathematics and give a good sense of the very human concerns that have helped to propagate the story of this (very inhuman?) concept... there is much to be learned from this book and much pleasure to be derived from it. Dr Adrian Moore London Review of Books 18 December 2003

Playfully mindboggling.
The Age (Australia) 13 December 2003

Believe it or not, this is a reader-friendly math book. Really! (Don’t move on quite yet, math haters!) Instead, it’s quirky history, all about the guys who went mad trying to determine infinity, and who eventually figured it out after all, not to mention what infinity ‘is’ as well. Great for a snowy Sunday afternoon when all there is to do is sit by a fire with a glass of port and ponder the imponderable.
Suzanne Falter-Barns The Joy Letter 3 December 2003

Author Brian Clegg takes us on an enjoyable trek through the history of infinity, from the earliest concepts through the middle ages and into the modern world of non-standard analysis and beyond. Readers of a non-mathematical persuasion can be assured that they won't be stretched too hard, though some of the ideas are hard to get hold of at first... Clegg does a good job of illuminating the subject through the powerful personalities that grappled with ideas of the infinite... But this is more than just a series of interesting biographical sketches, each of the episodes looks at the issues these mathematicians and philosophers were grappling with. The book is written in a friendly, chatty kind of way. ... It's a good read and should appeal to all but the most mathematically-resistant.
Pan Pantziarka Tech Book Report 28 November 2003

If I had to choose [from the books on infinity] I'd take Clegg… he is making it as simple as possible. One reason why Clegg is readable is that he likes to gossip about personalities. He tells us about Lancashire counting songs, of the assumptions, true and false, of the Pythagoreans, and how the Greeks, while being fixated on geometry, using an impossibly cumbersome system of numeration, and having no zero and no algebra, really did pretty well… the dazed humanist begins to see why Clegg calls his final chapter "Endless Fascination".
Frank Kermode, The Guardian 18 October 2003

Infinity can provide us with as many mind-bending paradoxes as special relativity or quantum mechanics, but it can also be grasped by anyone who intuits that, no matter how large a number is, you can always add one. ... As likely to quote William Blake or Douglas Adams as Newton and Einstein, he provides an accessible and, of course, open-ended overview of infinity as conceived of and wrestled with by theologians, mathematicians and philosophers, from Ancient Greece onwards... endlessly fascinating even for the rest of us.
Laurence Phelan, The Independent 21 September 2003

Provides a useful summary of almost everything we need to know about the history of infinity, and how to use it for fun and profit*... Covers the essentials in a usefully finite number of pages.
Daniel McBeal Focus Magazine September 2003

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