Professor Stewart’s Hoard of Mathematical Treasures
PROFILE BOOKS 2010, 320 PAGES PRICE (PAPERBACK) £8.99 ISBN978-1-846-68346-6
Professor Stewart’s Hoard of Mathematical Treasures is the latest collection of puzzles, jokes and mathematical snippets by Ian Stewart, FRS, CMath FIMA, Professor of Digital Media at Warwick University. This collection is a sequel to his very successful Cabinet of Mathematical Curiosities and there is no drop in quality from the previous work. Over many collections (some from his column in Scientific American) Professor Stewart has developed an engaging and irreverent style featuring lots of puns and a series of recurring themes. Cats, for example, have often featured in Professor Stewart’s books, and in this volume there’s a discussion on how a falling cat manages to conserve angular momentum whilst twisting to land on its feet. This is then followed by a discussion on why buttered toast always falls face down (which is arguably an example of cosmological fine-tuning) and of course this then leads to a discussion on what would happen to a dropped cat with a slice of buttered toast on its back. Most people would be tempted to propose this as an anti-gravity mechanism, but Professor Stewart, amusingly, gives a more ‘rigorous’ treatment based on the cat-to-toast mass ratio.
This is what I liked about the book. Even on topics you think you are familiar with, Professor Stewart can be relied upon to take matters in an unexpected new direction. For example, I have an interest in astronomical calculations, which is well served in the book, and I wasn’t expecting to learn much new on a section on gravitational resonances. Yet Professor Stewart surprised me by introducing the extraordinary possibility that one of the rings of Neptune is clumped because of a 42:43 [sic!] resonance with the shepherd moon Galatea. And who would have thought that one could come up with a remarkably accurateestimate for π by averaging measured angles in a collection of bright stars which are assumed to be points randomly distributed across the sky).
You never know if a puzzle is there solely as a pleasant diversion, or as a springboard to introduce deeper mathematics (a pleasant diversion in itself, of course). For example, the solution to the simple puzzle of going from SHIP to DOCK, changing one letter at a time, leads to a fascinating discussion of the size of spaces of transformable words, which can be predicted using graph theory, and the importance of word chains such as SHOT-SOOT-SORT which allow the positions of vowels to be swapped and so connect islands of transformable words. Even if you have solved a puzzle, it’s still a good idea to read the solution, which usually introduces new ideas.
Finally, Professor Stewart isn’t afraid of using mathematics to illuminate some of the burning issues of the day. In a longer piece entitled ‘Global Warming Swindle’ Professor Stewart effectively skewers the claims made in the Channel 4 program ‘The Great Global Warming Swindle’ about global temperature changes leading rather than trailing CO2 production. Professor Stewart points out that, not only is this predicted by climate models, but also that it’s irrelevant. We need not be unduly concerned with the response of the climate to long-term changes in solar flux, which we have no control over, but we should certainly be asking what the response is to a step change in CO2 production, such as we have introduced in recent decades. A simple model illuminates his thesis. This is popular mathematics at its best, illuminating complex issues for non-specialists (such as myself) and cutting through plausible but specious arguments. Similar pieces cover the threat of asteroid Apophis (how come we know what date it might hit the Earth, but not what year?), and how statistics such as hospital mortality rates can be have non-intuitively when the population is sub-divided. These articles deserve a wider audience – especially among politicians.
So I’d recommend the book. Most mathematicians will find plenty of interest within it. But I suspect it would make an even better gift for interested non-mathematicians, who would gain a strong flavour of the range and versatility of our wonderful subject.
Mike Frost MIMA
Mathematics Today April 2012
Professor Stewart's Hoard of Mathematical Treasurers can be purchased at Amazon.co.uk