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Thomas Banchoff

Beyond the third dimension

Some people claim to be able to visualise space with more than 3 dimensions, but for most of us the fourth dimension represents inaccessibility and mystery. This book explores the progress which has been made in reducing the mystery by showing how higher dimensions may be visualised. There is the usual comparison with Flatlanders visualising three dimensions, but the book also looks at other ways of presenting higher dimensions such as contour maps, 'unfolded' versions of polytopes (higher dimensional polyhedra) and perspective drawings. I would recommend this book to anyone who wants to get a better grip on what higher dimensions actually mean.

I have made my own attempts at visualising the 4th dimension, and I had hoped that this book would help me with this task. Unfortunately, although it does well at reporting what has been achieved in the subject, I didn't feel that it did enough to help the readers themselves to visualise higher dimensions. One of the problems with covering many different areas is that none is covered in much detail. For instance there is a short example concerned the presentation of multidimensional data, but not much in the way of practical advice for those with similar data to deal with. So the book is fine if you want an educational but easy to read work with plenty of impressive pictures, but if you want advice on how to create such pictures yourself then you should look elsewhere.  |  Chronon Critical Points  |  Recent Science Book Reviews