November 2007 January 2008

Book Reviews December 2007

Meta Math!:The Quest for Omega Gregory ChaitinAtlantic Books, 2005ISBN: 1843545241
cover
Mentioned in
Gdel's incompleteness theorem
Gregory Chaitin has done significant work on how computability is limited by complexity. In Meta Math!:The Quest for Omega he gives an account of some of his work aimed at the non-specialist reader. The book starts with his early fascination with Gödel's incompleteness theorem as well as his interest in computing, and in particular the LISP programming language. He explains how several of the philosophical ideas which seem to have arisen with the advent of the computer age, such as the universe being built out of information, were in fact thought of by Leibniz several centuries before. Continued..
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The Void Frank CloseOxford University Press, 2007ISBN: 9780199225903
cover In ancient times philosophers wondered whether it was possible to have a part of space with absolutely nothing in it. Aristotle decided that it was not - Nature abhors a vacuum. When Frank Close was young he also wondered whether nothingness was possible. In The Void he tells the reader how people have answered this question. He explains how it was found that a vacuum could be produced with a sufficiently good air pump. But then people began to wonder how light and gravity was transmitted through such a vacuum, and invented the luminiferous aether. Continued..
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The fabric of the cosmos Brian GreeneVintage, 2004ISBN: 0375727205
cover
Mentioned in
road to reality
Full Review
What are space and time. Although these are familiar concepts to us, they have always been a source of interest to philosophers and scientists, and in The Fabric of the Cosmos Brian Greene takes a look at the answers they have come up with. Thus he introduces special and general relativity, as well a quantum theory, in a non-technical way, and explains how chance and thermodynamics are related to the flow of time. He also looks at Bell's inequalities and experiments involving quantum entanglement and shows how all these things have revolutionised our ideas about space and especially time Continued..
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Fermat's Enigma Simon SinghFourth Estate, 1997ISBN: 1841157910
cover
Mentioned in
fermat undecidable
Note:This book also has the title Fermat's last theorem in the UK.

Andrew Wiles heard about Fermat's last theorem when he was 10 years old, and decided that he was going to prove it. He finally succeeded 30 years later. Fermat's Enigma by Simon Singh tells the story of this proof. Singh tells of how Fermat claimed to have a proof, and of how in the following centuries many people also thought that they had proved the theorem, only for a fault to be found in their work. The attempts did lead to a lot of interesting mathematics though. Thus Fermat's conjecture became more and more famous, and several prizes were offered for its proof. Continued..

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Why Beauty is Truth Ian StewartBasic books, 2007ISBN: 0465082360
cover Although symmetry seems to be predominantly a geometrical property, Why Beauty is Truth: A History of Symmetryshows that it really gained its importance in mathematics and physics via a different route - that of the solutions of polynomial equations. Ian Stewart starts at the time of the Babylonians, who were able to solve quadratic equations, and moves through the solutions of the cubic and quartic in the Renaissance. Hence we get to the work of Abel and Galois, who demonstrated the insolubility of the quintic by radicals. This was the start of group theory, and the rest of the book shows how this had much influence in later mathematics and physics. Continued..
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Godel's proof
Ernest Nagel and James R Newman
Routledge, 1958ISBN: 0415355281
cover
Mentioned in
Gdel's incompleteness theorem
Co-author
Nagel,Ernest
Gödel's incompleteness theorem has a reputation of being mysterious and difficult to understand. In Gödel's Proof Ernest Nagel and James R Newman give a clear explanation of the basics of the proof. They explain the background to the proof and in particular the search for a way of proving consistency of a system of axioms. They then exhibit a system where such a proof is possible - the propostional calculus. The book continues with chapters on the concept of mapping in mathematics, and on Gödel numbering, finishing off with the proof of the incompleteness theorem itself. Continued..
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The New Behaviorism John StaddonPsychology Press, 2001ISBN: 1841690147
cover Behaviourism - the idea that psychology should be based on correlating stimuli with behaviour, rather than postulating unobservable mental states - is generally thought to have died out in the 1960's. John Staddon thinks that it's demise was premature, and in The New Behaviourism: Mind, Mechanism and Society he puts forward his ideas for a revival. He feels that it was an accident of history that the behaviourists rejected the connectionist models of thought, which were then taken up by the cognitive psychologists. Such models were made possible by the increase in computer power, and Staddon explains how they fit naturally into the behaviourist ideas. Continued..
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The Whole Shebang Timothy FerrisWeidenfeld & Nicolson, 1997ISBN: 0297815180
cover
Mentioned in
stretchy space
In The Whole Shebang: A state of the Universe(s) report Timothy Ferris takes a wide ranging look at cosmology and related subjects. After a short overview of the history of cosmology, Ferris introduces the reader to general relativity, and so to the big bang. This is followed by chapters on the evidence for dark matter, on the occurence of large scale structure such as galactic clusters and superclusters, and on the evolution of the universe. Ferris then gets on to the small scale physics that is needed to understand the universe at its earliest moments. Continued..
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Godel's theorem : an incomplete guide to its use and abuse
Torkel Franzen
Peters, 2005ISBN: 1568812388
cover
Mentioned in
Gdel's incompleteness theorem
Gödel's incompleteness theorem is one of the most well known mathematical results, but unfortunately this has led to it being mentioned in highly inappropriate ways. In Godel's theorem : an incomplete guide to its use and abuse Torkel Franzen examines various ways that this theorem has been wrongly quoted, and tries to set the reader straight on what it is really about. He looks at what has been said about incompleteness in physics, in theology and of course in various postmodern ramblings. There is also a chapter criticising attempts to use the incompleteness theorem in the philosophy of mind. Continued..
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Utz Bruce ChatwinVintage, 1988ISBN: 0099770016
cover Bruce Chatwin had a long fascination with our urge to surround ourselves with possessions. Utz is his story of a man who did so more than most of us. Kaspar Joachim Utz came from the minor nobiltiy in Czechoslovakia. With the coming of communism, he ends up in a small flat in Prague, but is allowed to keep in it the collection of Meissen porcelain which he has accumulated. He has money in foreign banks and so has the possibility of building a new life (and porcelain collection) for himself in the west, but somehow he just can't bring himself to do it. Continued..
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The Artist and the mathematician Amir AczelHigh Stakes, 2006ISBN: 9781843440390
cover The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed . Amir Aczel's book has a strange title, but then the story of Bourbaki is rather strange. Originally a joke, the Bourbaki name became a focus for updating the syllabus of mathematics in French universities, and eventually grew into a huge project to rewrite mathematics from the bottom up. As such it had great influence in the mathematical world, bringing a new sense of rigor to the way mathematics is done, as well as leading to initiatives such as New Math in the USA. Continued..
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Simplexity Jeffrey KlugerJohn Murray, 2007ISBN: 9780719508114
cover Interesting things don't tend to happen in the simplest of systems, nor in the most complex, but somewhere in the middle. In Simplexity:The simple rules of a Complex World Jeffrey Kluger takes a look at this phenomenon, and how it applies to a wide range of topics. He starts with the problems we face when everyone is following the trends set by others, whether it's leaving a burning building or investing in the stock market. Later he examines the effects of scale in living things, and in particular how long they live, and see whether this can be extended from organisms to organizations. Continued..
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The Real Dr Strangelove Peter GoodchildWeidenfeld & Nicolson, 2004ISBN: 0297607340
cover Some people see Edward Teller as an evil figure, whereas others see him as a protector of democracy. In Edward Teller: The Real Dr Strangelove Peter Goodchild examines the reasons for this dichotomy. He gives information about Teller's early life, but much of the book deals with the years after the Second World War, when Teller was leading the development of the H-bomb, and when he supported the removal of Oppenheimer's security clearance. There is also information how Teller fared in the growing opposition to all things nuclear in the 1960's and 1970's as well as Teller's support for the SDI project in the 1980's. Continued..
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Moby Dick Herman MelvilleVintage, 1851ISBN: 9870099511182
cover I would guess that most readers of this review will know the story of Herman Melville's Moby Dick - how Ishmael signs on with the whaling ship Pequod, to find that it's captain, Ahab, only has one whale on his mind. What you may not know is how long the book actually is - nearly 650 pages. Melville is an expert story teller, but sometimes I got the feeling that he was padding out the book just for the sake of it, in particular the long sections giving various facts about whales. Continued..
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Models of Peano Arithmetic Richard KayeClarendon Press, 1991ISBN: 019853213X
Mentioned in
fermat undecidable
Goedel's incompleteness theorem tells us that no finite set of axioms can capture the essence of the integers - there will always be non-standard models of such a set of axioms. In Models of Peano Arithmetic Richard Kaye takes a look at such nonstandard models. The book is not for the fainthearted though - there's no gentle introduction, from the start it is full of highly abstract symbols. The book is aimed at aimed at postgraduates starting research into the subject, and assumes some previous experience of model theory. Continued..
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Mathematical Fallacies and Paradoxes
Bryan Bunch
Dover Publications, 1982ISBN: 0486296644
cover
Mentioned in
Gdel's incompleteness theorem
Mathematics may seem to be the embodiment of certainty, but in Mathematical Fallacies and Paradoxes Brian Bunch shows that you sometimes have to watch your step.In the first chapter he demonstrates that the circumference of a circle doesn't always seem to be 2πr, as well as proving that 1=0. This is followed by a look at the paradoxical nature of infinity, and a chapter on arguing by contradiction. Bunch then gets on to self reference and the paradoxes of set theory, leading up to a well written explanation of Gödel's incompleteness theorem. Continued..
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November 2007 January 2008