Edwin A. Abbott’s droll and delightful ‘romance of many dimensions’ explores this conundrum in the experiences of his protagonist, A Square, whose linear world is invaded by an emissary Sphere bringing the gospel of the third dimension on the eve of the new millennium. Part geometry lesson, part social satire, this classic work of science fiction brilliantly succeeds in enlarging all readers’ imaginations beyond the limits of our ‘respective dimensional prejudices’. In a world where class is determined by how many sides you possess, and women are straight lines, the prospects for enlightenment are boundless, and Abbott’s hypotheses about a fourth and higher dimensions seem startlingly relevant today.
There are those books that sit on your shelves for years, patiently waiting for you to come to your senses and devour them and this is just such a book. It brings together the joys of maths, philosophy and fun all in one easy and entertaining to read combination.
It’s a fantastic abstract journey, something akin to Gulliver’s travels or Allan Quatermain, giving you a chance to consider something totally alien yet immensely easy to visualise realities.
Taken at face value, this tale is a wonderful jaunt around a two-dimensional world in which you will get to understand such things as how the inhabitants can distinguish each other when they all appear as lines, as well as learning about the hierarchy, politics and history of Flatland.
For those of you who love a bit of subtext, the book is a razor-sharp satire on Victorian culture, its morals and ideologies. Naturally women get a raw deal, although Abbott, a supporter of Women’s rights makes some salient points throughout the book on the position and the almost parallel culture the two sexes led at the time. The politics of keeping the masses docile against the rich and the lack of a decent education system both come in for a fair bit of parody as well, the absurdity of such a system would be amusing were it not a mirror for real life. That all of the above still goes on in the world today is genuinely a chilling thought to my mind.
The book is broken up into two parts, part one contains the guide to this new world, realising a land of two dimensions where logic and perspective are strangely skewed but the rules remain consistent and coherent at all times. The characters in the story do lack depth but then again that is the nature of their universe and for a world that struggles with the concept of upward, and yet not Northward we shouldn’t be surprised.
Part two is where things get more epic, there is a look at the extremes of logic in one, three and even no dimensions, which is fascinating and vivid and leads the reader to speculate on how a fourth dimension would look to our eyes, trained as we are to seeing in three dimensions. It is worth noting that the Sphere, despite being a ‘higher’ being as it were, is still flawed and prone to the same weakness in logic that his fellow dimension hopper is and is not messianic figure as tradition on this plane dictates.
The same questions of further dimensions still tantalise us today and this book will engage and beguile the reader and leave them looking at things in a different way. I have one further point (oh come on, as if I would let the review go without that pun, although I have done well to get this far without using it) to make, the writing may not always be of the highest standard but the ideas contained will encourage forays into science books and maths literature. For those of you wishing to read something mathsy I recommend looking up Fermat’s Last Theorem, Lewis Carroll in Numberland and Euclid’s Window to name a few of the ones I enjoyed.