For all the talk of the amazing geometry contained within crop formations, finding one current book which explains all the key aspects has been difficult – until now. The new book ‘Crop Circles – The Hidden Form’ by Nick Kollerstrom is an important education in the rudiments of cerealogical form and is reviewed here by ALLAN BROWN…
I first heard Nick Kollerstrom talking about the geometry of crop circles at the ‘Great Green Gathering’ several years ago. In a very understated and modest style, armed with nothing more than a handful of slides, Nick set about rearranging the contents of my head. It being too dark, too late at night, and too, well - it was a festival - I didn't have a chance to write down the pearls of wisdom that Nick was imparting. The following morning I remembered few of the details, but was left with an overwhelming sense of wonder at the astonishing mathematics the circles contained.
I next bumped into Nick when I gave my first public talk on the geometry of crop circles at a Southern Circular Research meeting in the autumn of last year. I was most delighted to see Nick turn up, especially as he had taken the trouble to brave the train and travel down from London to hear what I had to say. It was on this occasion that I had my first glimpse of a manuscript that was ultimately to become ‘Crop Circles - The Hidden Form’, the book I currently have open in front of me. Even with my first cursory glance at that manuscript I knew that I was looking at an extremely important piece of work and was disappointed to discover that despite the efforts of the Centre for Crop Circle Studies, who were initially trying to publish it, Nick was having trouble getting it into print. I even contemplated trying to raise the money myself, but in the end let the idea out to pasture.
Then completely out of the blue, and to my great delight, Andy (Thomas) phoned me up and asked whether I'd like to review Nick Kollerstrom's new book. I don't know who found whom, but Wessex Books, who have already released a book on crop circles entitled ‘Crop Circles - An Introduction’, have stepped in and brought Nick's work to fruition.
Nick Kollerstrom is a mathematician and, more to the point, he teaches mathematics. Even more to the point, he's a mathematician with vision enough to apply his knowledge to a subject that most in academia wouldn't touch with a bargepole. It is this unique combination of qualities that make this such an important book.
The format is very simple and user friendly. It is broken down into twelve small chapters, most no more than three or four pages long, each illustrating a particular aspect of crop circle geometry.
In the first chapter, Nick outlines his vision of 'Hypermaths', an integrated system of knowledge that preserves beauty and "demands that Delight and Wonder should be the guiding principles". This sets the tone of the book. I know from speaking to Nick that he would love to see mathematics being taught to children through the framework of crop circle geometry, and even though this book isn't particularly aimed at children, I can see this becoming a standard text book in more enlightened times.
Each chapter contains numerous photographs and diagrams that help illustrate the various points raised, and by the time you reach the end of the book you have covered the Vesica Pisces, the Triune Patterns, Squares and Cubes, Pentagrams and Pentagons, Sixfold Symmetry, The Heptagon, Fractals, Spirals, and a host of other surprises.
I think the real strength of this book lies in the fact that everyone from the 'mathaphobic' to the 'mathaholic' is going to find nourishment within these pages. Its warm, friendly and succinct style gently illuminates a feature or aspect of a formation that, once recognized, makes you totally reassess the level of intelligence and ground-breaking inventiveness that has gone into their design. And this, to me, is the one of the most astonishing aspects to the crop circle phenomenon - that so much completely original and hitherto unseen geometry should be casually strewn across our fields. There are formations featured in this book that were probably only ever seen by a handful of people; perhaps only a single survey or aerial photograph attests to their existence at all, and yet they contain a mathematical feature that may never have been seen before. Yet so prodigious is the talent and inventiveness of the designer(s) that it appears of little consequence whether or not we recognise these jewels of mathematical wisdom woven into their designs at the time. Several years can pass before someone may recognise an element to a design that lifts it from the mundane into the sublime, yet the formation just quietly came and went, without fanfare and fuss. How much have we already missed?
This is what Nick has set about to achieve in this slim, yet full volume. He has quietly studied the mathematics of the formations in a scholarly fashion, resisting the temptation to speculate on the mechanism or origin of their appearance. This book contains some really wonderful mathematics and profound observations that are going to take time to come to terms with. This is the sort of book you spend time with, over many months, and I suspect my copy (which I have already bought, as Andy is trenchantly clinging onto the review copy) will not be far from my side over the soon-to-be-upon-us winter months.
Not only do I heartily recommend this book, I think it's of great importance that we familiarise ourselves with its content. While some may turn to the wonderful work of the BLT team for their 'proof' as to the genuineness of this phenomenon, I would also unreservedly hold up Nick's writings. Read 'em and weep!
CROP CIRCLES – THE HIDDEN FORM, by Nick Kollerstrom, Wessex Books 2002, 64 pages, ISBN 1-903035-11-2, £6.99. Available from UK bookshops or by mail order from:
Wessex Books, 2 Station Cottages, Newton Toney, Salisbury, Wiltshire, SP4 0HD, UK. Tel: 01980 629349.