A Brief History of Infinity: The Quest to Think the Unthinkable [Paperback]

Brian Clegg (Author)

Book Description

Publication Date: September 12, 2003

'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' - Douglas Adams, "Hitch-hiker's Guide to the Galaxy". We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us 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, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Editorial Reviews

Review

Here [Clegg] has done an excellent job of making the most complex concepts accessible while allowing their mystery to continue to shimmer just out of focus. --Kirkus Reviews

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

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. --Laurence Phelan, The Independent

About the Author

Brian Clegg studied physics at Cambridge University and is a Fellow of the Royal Society of Arts. He has written a number of popular science books including A Brief History of Infinity, Light Years, The God Effect and Before the Big Bang.

Product Details

• Paperback: 288 pages
• Publisher: Constable (September 12, 2003)
• Language: English
• ISBN-10: 1841196509
• ISBN-13: 978-1841196503
• Product Dimensions: 7.6 x 5.1 x 0.7 inches
• Shipping Weight: 8.5 ounces (View shipping rates and policies)
• Average Customer Review: 2.6 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #1,209,711 in Books (See Top 100 in Books)

More About the Author

Brian has written a number of popular science books, including Ecologic, The God Effect, on the most remarkable phenomenon of the quantum world and Before the Big Bang. Other titles include A Brief History of Infinity and Inflight Science, which explores the science that's all around you and outside your window when you are on an airplane.

Along with appearances at the Royal Institution in London he has spoken at venues from Oxford and Cambridge Universities to Cheltenham Festival of Science, has contributed to radio and TV programmes, and is a popular speaker at schools. Brian is also editor of the successful www.popularscience.co.uk book review site and is a Fellow of the Royal Society of Arts.

Brian has Masters degrees from Cambridge University in Natural Sciences and from Lancaster University in Operational Research, a discipline originally developed during the Second World War to apply the power of mathematics to warfare. It has since been widely applied to problem solving and decision making in business.

From Lancaster, he joined British Airways, where he ran teams including Emerging Technologies, amongst the most eccentric but talented staff in the company, who researched technologies from fingerprint recognition to electronic cash. This emphasis on innovation led to training with Dr. Edward de Bono, and in 1994 he left BA to set up his own creativity consultancy, running courses on the development of new ideas and products, and the creative solution of business problems. Clients include the BBC, the Met Office, British Airways, GlaxoSmithKline, Sony, The Treasury, Royal Bank of Scotland and many other blue-chips.

Brian has also written regular columns, features and reviews for numerous publications, including Nature, The Guardian, PC Week, Computer Weekly, Personal Computer World, Innovative Leader, Professional Manager, BBC History, Good Housekeeping and House Beautiful. His books have been translated into many languages, including German, Spanish, Portuguese, Chinese, Japanese, Polish, Turkish, Norwegian, Thai and even Indonesian.

Customer Reviews

Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

3.0 out of 5 stars Be sure you know what you're buying!, July 31, 2010

By 

Paul Weiss (Dundas, Ontario Canada) - See all my reviews

This review is from: A Brief History of Infinity: The Quest to Think the Unthinkable (Paperback)

Perhaps I should state what I think should have been made a little more obvious. Clegg's "A Brief History of Infinity" is not a mathematics book. It is definitely a history book. In fact, it outlines the history of man's struggle to come to grips with the exceedingly complex and devilishly bewildering concept of infinity. Of necessity, of course, it touches on matters mathematical but the meat of this book is the history.

A BRIEF HISTORY OF INFINITY delves into man's contemplation of matters infinite from the earliest days of its discussion by Greek philosophers, to St Augustine's theological musings of creation, to Leibniz and Newton battling over bragging rights for the creation of calculus, to Cantor's transfinite numbers and even to the implications of infinity in quantum physics.

Having noted that the book is more focused on history than mathematics, it's definitely worth pointing out that the mathematics would still be daunting for a complete neophyte. That said, my hope was for somewhat more mathematics and a little less of the historical background. For example, I found the section on Leibniz and Newton's battles with Bishop Berkley over infinitesimals quite dreary and plodding.

But, the misunderstanding as to the exact nature of the book can probably be laid more my doorstep. A more careful examination of previous reviews and the marketing info on the book cover would have better informed me as to what I was stepping into.

Recommended.

Paul Weiss

12 of 14 people found the following review helpful:

4.0 out of 5 stars Enjoyable Excursion into the Realm of Infinity, August 5, 2006

By 

Michael Wischmeyer (Houston, Texas) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: A Brief History of Infinity: The Quest to Think the Unthinkable (Paperback)

A Brief History of Infinity - The Quest to Think the Unthinkable by Brian Clegg is a good introduction for the layman to the historical development of the concept of infinity. Clegg's book is a good book, but not an exceptional one. I found the first half to be less engaging, as perhaps the sections on Greek mathematics and the historical development of calculus were too familiar. The second half is much better, especially the discussion of Cantor's transfinite numbers. On balance, A Brief History of Infinity rates four stars and should appeal to a wide audience.

Clegg touches on a wide range of topics, often exploring unexpected connections and tangential matters. Sometimes his side trips are diverting and enjoyable, but at other times I found these digressions to be overly distracting. (The discussions on quantum physics seemed unnecessary; there so many good books for the layman available.) But to be fair, infinity is a broad topic and other readers may well find Clegg's far ranging approach to be stimulating and enjoyable.

Clegg addresses in a credible fashion Galileo's investigations of infinity, the battle between Newton and Leibniz (and Bishop Berkeley too) over infinitesimals, Cantor's transfinite numbers, and Robinson's non-standard analysis. These non-technical discussions are neither too superficial, nor too vague.

For readers willing to delve deeper into the mathematics of infinity, I highly recommend The Philosophy of Set Theory - An Historical Introduction to Cantor's Paradise by Mary Tiles. This is not an easy book as it primarily targets advanced students in philosophy and mathematics. Nonetheless, it is within reach of a persistent reader. Some sections can be read stand-alone; three mid-chapters (Numbering the Continuum, Cantor's Transfinite Paradise, and Axiomatic Set Theory) are outstanding and in themselves are worth the price of this book.

Going a step farther, a math major might wish to tackle Georg Cantor's Contributions to the Founding of the Theory of Transfinite Numbers. I particularly recommend the Dover reprint of the same title as it contains a lengthy introduction by the mathematician Philip E. B. Jourdain.
There is yet a third book to consider, one that has the same title as Brian Clegg's book. A Brief History of Infinity by Paolo Zellini (translated by David Marsh) "explores every aspect of infinity, distilling the wisdom of philosophers, artists, mathematicians, and theologians over the millennia". Less mathematical than my other two recommendations, Zellini's work is nonetheless quite challenging. It provides a detailed examination of philosophical issues underlying the concept of infinity.

4 of 4 people found the following review helpful:

3.0 out of 5 stars To infinity and beyond ................., June 14, 2006

By 

Mr P R Morgan "Peter Morgan" (BATH, Bath and N E Somerset United Kingdom) - See all my reviews
(REAL NAME)   

This review is from: A Brief History of Infinity: The Quest to Think the Unthinkable (Paperback)

There is almost a pun in the title: how can you have a brief history of infinity? However, this book by Brian Clegg is part of a series, so it is stretching bounds of probability to suggest that the whole series is named just to get a pun in a title! I have not read any of the others in the series, but from their titles, they seem to be of a historical nature, rather than concepts and ideas. The sub-title of this volume is also interesting: "the quest to think the unthinkable". That statement gives a key to the book. What does the notion of infinity give us?

For me the first 100 pages of Clegg's book do not really work. It is both slow, and nebulous. However, after that, it opens up, and gives a good narrative of the progress towards the unreachable. Strangely, that is not just the infinitely large, but also the infinity small. Somehow "proper" numbers are sandwiched between the immeasurable at either ends of the spectrum. Clegg falls on the side of the usefulness of ideas, rather than the sheer understandability. Calculus, in both the Newtonian and Leibnizian forms, is introduced as "something that works". It was only later that the need for infinitely small is eliminated from calculus - by then this mathematical tool had been very useful in solving many real problems.

After the slow labouring start, the volume CAN be a beginner's guide to the subject, but is probably not be for the faint-hearted. It will help your understanding if you are familiar with ideas from modern mathematical thinking. If not, the notion of there being different `levels' of infinity can come as rather a jolt. How can two numbers, both of which are not countable, be different? How can there be the same number of odd numbers as there are of odd-and-even numbers? It is not surprising that the man behind set theory, Georg Cantor, lost his sanity when investigating the infinitely large.

In essence, the book covers so much more than just infinity. It really does go "to infinity and beyond". Infinity is a strange idea, but one that underlies many of the advances that have taken place since the start of the 20th century. Advances in number theory, cosmology, physics and atomic physics can be better understood if a basic understanding of infinity is grasped. Clegg covers these parts well.

The title was not a pun. However, Clegg does not disappoint in his last sentence. "When it comes to infinity, the possibilities are, perhaps inevitably, endless". I suppose he had to say that, didn't he?

Peter Morgan, Bath, UK [...]