Super Crunchers: How Anything Can Be Predicted by Ian Ayres, John Murray, 2007, 272 pp, hardcover £16.99, ISBN 0-719-564638. Audio book, Hodder Murray, 2007, ISBN 0-719-524622.
How do you choose the best title for your new book? Which stocks and shares should you purchase in order to guarantee the best return? Can a disease be diagnosed by a computer? Is it possible to know that you have bought your airline ticket at the lowest price? The answer to all these questions, and more, is super crunching.
Super crunching is the new way for businesses to make decisions based on recognising patterns in past data rather than through intuition and personal experience. For example, instead of choosing a wine by taste, it is possible to construct an algorithm that will decide which year is most likely to produce an exceptional vintage. One such algorithm has been based on winter rainfall, average growing season temperature and harvest rainfall. Mathematically speaking it is not hard to see that, when formulated correctly, this approach will often produce good results. Similar algorithms have been designed to predict which films will become tomorrow’s blockbusters and which trading rules to use when investing in the stock market. Obviously mathematical modelling, statistical analysis and data mining have been around for a long time but what makes super crunching super new is the enormous quantity of past data that can now be analysed in a comparatively short space of time.
When faced with the decision concerning choice of book title, the author, lawyer and economist Professor Ian Ayres conducted a randomised trial. He took the three prospective titles: ‘The End of Intuition’, ‘Why Data-Driven Decision Making is the New Way to be Smart’ and ‘Super Crunchers’ and set up a test on Google. Within days he established that people searching for topics linked to data mining were more likely to click on adverts for ‘Super Crunchers’ than either of the other two titles; possibly an unsurprising result. Thus Super Crunchers has been the product of super crunching.
The initial chapters are jam-packed with examples of research that the author has carried out using these randomised trials to form predictions. They are described in such a way that could not fail to excite anyone who has an interest in predicting outcomes. The beauty of this book is that it doesn’t need to go into detail concerning the different algorithms and statistical processes used by the modern generation of data miners, but rather it explains the concepts surrounding the problem in ways that can be easily understood. Personally I would have appreciated a little bit more mathematical content but I am sure that’s missing the point. We seem to live in a very anti-statistical society: newspaper reports continually misinterpret statistics and the general public seems loth to use them in any meaningful way. Now we have a book devoted to statistical analysis that hardly mentions it!
Only in the final chapter are standard deviations and means mentioned and this is merely in the context of a heart-warming anecdote concerning Ayres’ nine-year-old daughter, Anna, who appears to use them unprompted in order to make informed decisions. Surely this provokes the response ‘if a nine-year-old can understand this, then so can I’.
As the examples progress they become more political and concern areas such as education, health and insurance. It is clear that without appropriate guidelines the wrong questions can be asked and data mining can be used to back up erroneous claims. One claim that Ayres cites in some detail is the assertion that more guns lead to less crime and he goes into some detail as to why this research failed to find the correct answer. Finally the rather more negative aspects of data mining are touched upon – is our every move being watched and evaluated and where will this lead? The reader is left with a mixture of emotions – amazement at the scope of these fairly simple, logical algorithms and randomised tests, yet distinct uneasiness at the Orwellian nightmare we seem to be heading into.
Making Mathematics with Needlework edited by Sarah-Marie Belcastro and Carolyn Yackel, AK Peters Ltd, 2007, 200 pp, hardcover US$30, ISBN 978-1-56881-331-8.
As an artist working within a computing and maths department I am probably the perfect customer for this book, combining as I do a flair for needlework and clothes design and a more than passing interest in maths. Because of the mix of disciplines, however, I initially feared I might be its only customer. Each chapter is a combination of a mathematical paper and a corresponding needlework project with additional teaching ideas; the maths is written by and for mathematicians, the project for craftspeople: how many of us are there who are at home in both worlds?
Choosing a chapter at random, entitled ‘only two knit stitches can create a torus’, I seize needles and wool and start reading. A seemingly oblique overview about the problems of being a left handed knitter develops into a set of questions about the different possible ways of constructing a knit stitch. Slowly this becomes the ‘mathematics’ section (but warned by the subheading ‘mathematics’ I know to put that hat on). Initially it is hard to shrug off the ‘knitter’ in me who baulks at a seemingly over-complicated explanation of what can be demonstrated in moments with needles and wool, but I am soon charmed by the way that the laying out in mathematical terms of a process I know by heart can inspire a confident sense of knowledge. The support of previous practical experience is so strong that when invited to "pick up yarn and knitting needles in order to verify the following observations" I feel no need to do so. This supports the claim of the book that practical exercises with thread and fabric construction can provide an education in visualising mathematical ideas and the possibilities of geometrical shapes. I’m afraid my fascination was more in terms of enjoying the comprehensive mathematical descriptions of processes I’ve enjoyed and explored for years.
I won’t pretend that the maths is easy. The support of a friendly mathematician would be a bonus at several moments, but the craft sections offer the constant reassurance of a practical viewpoint. We are offered the chance to make: a Möbius quilt, a bi-directional hat (Diophantine equations), a Sierpinski shawl (self-similar crochet), a torus, a symmetries sampler, algebraic socks, Fortunatus’s purse, a pillow of braid equivalence, a Holbeinian graph (graph theory of Blackwork embroidery) and (last but not least) hyperbolic pants! I plan to make them all, but I think the publisher is lucky in my streak of craft-based curiosity. Perhaps the real market for this book is a particular moment in education when the application of maths to real world problems can become a fascination.
When I read that it grew out of the American Mathematical Society Special Session in Mathematics and Mathematics Education in Fiber Arts held in 2005 in Atlanta, Georgia, the structure and content of the book seem a natural and inevitable consequence of their purposes. It was still hard to decide who amongst my friends might have liked it as a Christmas present.
Collaborative Learning in Mathematics: A challenge to our beliefs and practices by Malcolm Swan, National Institute of Adult Continuing Education, paperback £24.95, ISBN 981-1-86201-311-7; hardback £44.95, ISBN 978-1-86201-316-2.
Some years ago I attended a session on mathematics education at a British Mathematical Colloquium. One of the questions put to the panel came from a PhD student, who said that she was hoping subsequently to become an academic in a university maths department, and asked how she could get training in teaching while working on her PhD. As I recall, the chair’s response was something like "Why would someone who wanted to become an academic be interested in teaching?"
Well, of course university mathematicians are interested in teaching (and the advent of the National Student Survey can only increase that interest). But much of the educational literature is generic and mathematics seems to be different from other subjects. This provocative new book by a specialist in mathematics education examines how one learns mathematics, showing (through illustrative examples, including video clips on the accompanying CD-ROM) how mathematical pedagogy can be learner-centred rather than teacher-centred, and emphasising the value of collaborative discussion. Its focus is at GCSE level, but there is much that is worth considering at all levels. Swan discusses research about teachers’ and learners’ attitudes to mathematics: when I took some of the questionnaires he discusses into an undergraduate class, the result was the liveliest and most productive discussion I’ve ever experienced with mathematics students, as they argued about how they learn mathematics and how the different approaches they had experienced had helped their learning.
This very readable book has led me to appraise and question how I teach, and I feel that I and my students have benefited considerably as a result. I cannot recommend this book too highly.