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Edwin Abbott's "Flatland: A romance of many dimensions" is a philosophical novel, trying to explain the possibility of there being many dimensions that we as three-dimensional beings are unaware of.
We meet our protagonist, A. Square, who finds himself in Flatland, a place populated by beings of one dimension. These beings are effectively invisible to each other when they stand still, so they have cleverly evolved a way of moving which swishes their back ends from side to side to enable them to move forwards and be seen. Mr Square, who obviously does not need to wiggle his back end, is a source of great astonishment, and the one-dimensional beings are frightened and perturbed by him.
The idea is that there could be dimensions of which we are unaware and which we could not comprehend. In that respect this book is a lot like Swift's Gullivers Travels - an analogy to explain a complicated philosophical problem. Does it succeed? Yes, in that it is thought-provoking and interesting, but since the ideas it's explaining are so hard to comprehend it's maybe not a book for everyone. It is a fantastic book of its type, though, and short enough to be an easy read. Recommended.
When wondering what to use my hard earned DooYoo amazon voucher on I decided to do some research to find a book that I was gonna really love. I ended up here at Edwin Abbotts Flatland, and my god am I glad I did.
Edwin Abbott (a victorian school master during the second half of the 19th century) was not a writer I'd encountered before and although the book seemed incredibly short at a mere 80+ pages I just couldn't resist taking on a book that tackled a subject that is central to my understanding of the world and that is the concept of higher dimension.
The book not only offers interesting ideas about creatures and worlds in different spatial dimensions but at the same time offers a light hearted look at victorian social structure.
The book is set in flatland, a 2 dimensional world. The main protagonist in the novella is square, he is a geometric square and as such ranked socially quite highly amongst his piers. Acute triangles are at the bottom of the pecking order (actually women are the bottom of the pile im afraid, with acute triangles slightly above), members of the clergy and aristocracy are many sided shapes with the idea of a perfect being (or god if you will) as being perfectly circular. No member of flatland is a perfect circle but the king and high priests have so many sides that they appear almost circular.
One night A.Square is approached by a being who claims to be from a world of three dimensions.In keeping with the theme of shapes the being is a sphere. As Square is restricted to 2 dimensions, the physical view our narrator has of the spherical being (fixed within his 2 dimensional frame of reference) is that similar to a woman (i.e a straight line). As the being moves his 3d form through 2d flatland he displays properties similar to an acute triangle (a very low class or put another way someone not to be trusted in Flatland society) and eventually a member of the aristocracy. Finally after much misinterpretation, as square struggles with the confines of using 2 dimensional vision to see a 3 dimensional object, the being appears to square as a perfect circle.
(imagine if you were in 2 dimensions, you would see the cross section of a sphere as a straight line, it would take the delicate and trained knowledge and social skills of a flatlander to assertain the class of the being. As it would be incredibly impolite and a social no-no to "feel up"a potentially higher class stranger to ascertain his angles, this makes gauging social position an art form in flatland which is taught in academies to the more well off inhabitants.)
Trying to describe how flatlanders tell people apart from their limited perspective is impossible within such a review, it takes E.Abbot 40 or so pages to cover this topic (also it would ruin part of the charm of the book to give away it's secrets here). But on reading the book it is clear that our flat little friends have to rely on complicated systems to tell eachother apart, the difference between a straight line (a woman in their society) and a near circle (clergy or royalty) to us three dimensioners is obvious, but a flatlander would see both initially as being almost identical straight lines.
They have to come up with clever mechanisms as well as much closer and thorough visual inspections with which to determine the shape (and therefore class) of different persons. Imagine accidentally greeting a member of the clergy in the same manner as you'd greet a member of the lower classes, socially this simply would not do.
Anyway back to A.Square and his realisation that he is in the presence of what his society would perceive as a perfect being or god.
The being then takes our narrator on a tour of a world with 1 dimension (Lineland), no dimensions (i.e a single point) called Pointland. On seeing these fascinating ne worlds our narrator then humbly challenges the perfect being and implores him to entertain thoughts of a four dimensional world and indeed a fifth ans six and so on. The sphere is disgusted by the idea, stoically spouting his own dogmatic diatribe that the third dimension is the highest with none above it, at this point Abbott challenges the arrogance of his fellow victorians (and indeed pokes a little fun at them), it is an arrogance that is still inherrent in some today. The idea that we are the top of the chain and that there are no creatures above us. It's an idea that is understandable to a point, we have no proof of higher beings, but as this wonderful book shows our perception of the world can sometimes be wrong or incomplete.
Science Writer Isaac Asimov described flatland as "The best introduction one can find into the manner of perceiving dimensions." and I agree with this entirely. I think many people equate this kind of topic with science fiction or worse, abstract spiritual nonsense but If you're like me and have a keenly scientific interest about higher spatial dimensions in a literal, proveable way then this book is a charming and easy going introduction to these concepts as well as just being a fun and engaging read. It doesn't offer scientific or mathematical proof of the existance of higher space/time dimensions it just allows the reader to ruminate on the topic from a fun and interesting stand point.
I love this book so much and I really hope my review will encourage you maybe to go out and read it, you can get it really cheap on amazon (i think sub £2 secondhand) and it's available from your local library.
I love mathematics - I studied it at university and now I teach it, so little novelties like "Flatland" always pique my interest.
When Borders bookshop went into administration, during its last days it offered a ridiculous 90% off reduction, so a good trawling of the already-depleted shelves was in order.
Wedged between two fat tomes I found the Dover Thrift Edition of "Flatland", a thin novella I had never heard of before and was very unlikely to put back on the shelf for two reasons: the blurb began with 'This masterpiece of science (and mathematical) fiction...', and the fact that the RRP was only £1.90.
With 90% off, I paid a pauper's sum of 19p - bargain!
"Flatland", a story of living triangles, squares, hexagons and circles living on a plane, is a novel of two parts, the first of which is long and tedious, while the second part isn't much better.
The problem is that the book hasn't aged well.
Originally written in 1884, this is written from a late Victorian point of view, including all of the usual language pomposity, completely unrealistic dialogue and ridiculously horrendous views towards women.
"Flatland" is probably one of the most intentionally sexist books I've ever read.
"...as they have no pretensions to an angle, being inferior in this respect to the very lowest of the Isosceles, they are consequently wholly devoid of brainpower, and have neither reflection, judgment nor forethought, and hardly any memory."
In Flatland, women are but straight lines who are incredibly difficult for the male polygons to actually see - flatlanders can only see a straight line, which may offer different shading according to the shape facing it.
If a straight line is seen from its end, all the flatlander would see is a point, which could be exceedingly difficult to spot before there's a deadly collision!
The story itself is told from the point of view of a square looking back on his adventures.
The first half of the novella is a description of the world and is lumbering in its effort to detail and explain, while the second half pertains to his interaction with Lineland (one dimension), Pointland (zero dimensions) and Spaceland (three dimensions), and his efforts to convince others of his findings.
It's one of those novels, sadly, where the wealth of ideas outweighs the performance, where the fantastically thought-out world of Flatland is encumbered with lengthy descriptions, very little character interaction and plot, and grating dialogue.
"Fool! Madman! Irregular!" I exclaimed, "never will I release thee; thou shalt pay the penalty of thine impostures!"
Look out, that's square's corners are pointy!
However, "Flatland" does have its plus points, and this comes in the effective explanations of how higher dimensional beings interact with lower dimensions, how a square can be perceived by a one dimensional being, or how a sphere would be seen as a side-on circle by 2D creatures.
It is perhaps not a thought exercise one would ever really consider, but it is certainly an interesting idea to consider and mull over.
"Flatland" is never an entertaining read, but with its use of diagrams (all drawn by the author) it makes for an original reading experience and one that is difficult to forget.
The novella has been adapted into several animations, of which perhaps the Michael Sheen-voiced 30 minute version is the better (and also perhaps the most instructive) version.
[The book can be purchased from play.com for £5.99 (at time of writing), including postage and packing]