Flatland (Everyday Handbook)

Flatland is THE must-read for anyone interested in getting a feel for higher dimensions. The book is extraordinarily readable and succeeds even with people that are afraid of mathematics. Abbott's charm lies in his ability to write simply and clearly about a topic that has its share of very unreachable, esoteric books. You fall into the story (whose plot is by no means secondary to the mathematical ideas), and before you know it you find yourself in contemplation of things like the fourth and fifth dimensions. The visual image that this book provides is a necessary step to envisioning and then understanding the idea of higher dimensions, even for those already versed in the mathematics of it. You never know, after you read this, you might even be willing to try your hand at things like Einstein's relativity. A little on the social aspects of the book: keep in mind that it was written in the very late 1800's. Hidden within the philosophical and mathematical ideas is a satire of the social climate of the times: how women, the military, the upper echelons of society, and just about everyone else were viewed. Flatland makes you think, and think deeply, on many different and sometimes unexpected levels.

If you are not familiar with Edwin Abbott's "Flatland", this is the edition to buy. If you are familiar with it (but presumably do not yet own it), this is still the edition to buy.

You've heard the classic criticism of a story is that it is "two dimensional". Well, Edwin Abbott's tale of an imaginary two-dimensional land adds a whole new twist to that phrase. Flatland, as he describes it, is about as rich as a two-dimensional story can be. And it is marvelously extended by its narrator's encounters with the unknown - the world of 3 dimensions. The challenges that narrator faces as he encounters the incomprehensible, quite closely mirror mine whenever I attempt to think about a 4th (or 5th or 7th) dimension. If you've faced the same struggle, you will be delighted by this book.

If you've ever wondered what a 4th dimension would look like, Flatland provides a lens through which you can imagine that extension of our 3D world. From here you can go on to read Rudy Rucker or Pickover or Hawkins - but this is the place to start your exploration of dimensions beyond experience. Abbot accomplishes this by describing the eye-opening extension of his narrator's 2D world when visited by a 3D apparition, a "sphere". His framing of the foundational issues through the experiences of what you'd expect to be the least interesting character in fiction are really quite engaging. The storyline, however sparse, is as interesting as the mathematics - albeit quite nineteenth-century'ish in tone.

Don't misconstrue Abbott's seemingly misogynist portrayal of women and of his class-stratified society. This element was intended to provide a third layer of sharp, Swiftian satire and critical commentary on the rigid social mores of his era. Abbot succeeds in this (but I, nevertheless, decided not to read it aloud to my 6th grade classes - worrying that they might not be attuned to this subtlety of tone.) Be forewarned.

The neat twist of this edition, the inclusion of Dionys Burger's 1983 "Sphereland", as an upside-down "second book", is quite a nice touch. Although I did not find Burger's stylings quite as engaging as those of Abbott, his extension of the mathematical ideas into non-Euclidian spaces is a nice introduction to that idea for non-mathematicians. Since it was intended as a standalone book, "Sphereland" commences with a detailed review of the "Flatland" story. This can be skipped without loss but is not a substitute for reading the original "Flatland", here, first.

Flatland is a timeless classic; a great book for the mathematician and non-mathematician alike.

Abbot was passionate about addressing a Christian concern that I share: differentiating mere superstition from the supernatural. Flatland was written with this in view: to make a parabolic case for the dynamic of the "higher order" of things and how it would thus relate to us. It is also hilarious social and spiritual satire. While often portrayed as a treatise on mathematics, the math was only the idiom. He was trying, by way of parable, to show the rationality of belief in the supernatural.

The first half of the book is a set-up for the second half where the action takes place. The first time I read it (age 17) I thought it was a bit tedious till I got to the middle. But the first half must be read for the MIND BLOWING second half to make sense. When older and on second read, the first part is now my favorite. For Abbot is not just describing Flatland, he is satirically lampooning Victorian culture, priggery and prejudice. To think how this book must have made people's blood boil back then, just as it does now!

As for style, Abbott has a way of constructing a phrase that is just plain delicious once you get into the flow of it. He waxes most eloquent (in the voice of the "square" narrator) when he is most absurd and wrong, and this--you must admit--is a little too close for comfort as well.

A friend of mine called me at 4am several years after I gave him Flatland, having finally read it straight through, and said "I think I now 'get' the Revelation!" I hope it has a similar encouraging effect on you--either by humorous, pithy satire or spiritual insight.

Flatland is a unique and brilliant treatise on a trifurcated level. It is a sociological statement, a mathematical statement and a religious statement all rolled into an incredibly astute 82 pages. The book centers mostly on the differences between a two dimensional world and a three dimensional world; but comments on society, law, prejudice, religion, and proselytizing.

The book especially points out the difficulty in envisioning a greater reality and a greater vision than is commonly observed by any individual in any dimension or society. The author's premise relates to things existing in a "plane geometry" world as opposed to a "Euclidian Geometric" three dimensional figure universe. The book carefully illustrates to one denizen of Flatland how the three dimensional world of space works and/or exists. Upon finally understanding the "Gospel of Three Dimensions" our protagonist goes on to try and apply the same arithmetic logic and geometric analogs to a fourth dimensional universe. Shouldn't there exist a fourth dimensional universe that allows an entity to look down upon the three dimensional universe with as much transparency as one can from three dimensions to two?

Alas, things become different in dimensions other than the first, a world of lines, the second, a world of shapes and the third, a world of objects. In the zero dimension, all things are a point. Mathematically we know that any number raised to the "0" power equals 1 and therefore, all things in the zero dimension resolve into one single omnipotent point. This condition would also exist in the fourth dimension; as those of us in the third dimension have no model to compare it to. Envisioning a fourth dimension, even with time as the fourth dimension is truly difficult or impossible for us in the third dimension.

Interspersed with this witty and intellectual dialogue are comments on society and its structure. He specifically comments multiple times of the degradation of women in society to the lowest social status. Only men are educated in Flatland. Interestingly, he paints a picture of an authoritarian society in which people are judged by their shapes and angles. This reflecting the Victorian societal values around him at the time of his writing.

Flatland is recommended to all those who seek to enlighten their view of the universe and of potential universes. It is especially recommended to those seeking higher knowledge of any type. Flatland is truly a multi-dimensional experience and worth every minute.

From the square character's world of two dimensions in Flatland to the Sphere's three dimensional Spaceland, one comes to recognize the role of dimensions in geometry and in thinking in Abbott's Flatland. Both a mathematical essay and a satire the book challenges readers to discover dimensions for themselves in an unusual story. Beyond the story of the square lawyer protagonist and his adventure with the Sphere is the satire on Abbott's English society. Women are depicted as lines with the power to destroy men with there sharp, pointed ends. They are forced to remain in a constant waving motion as a courtesy to men in order to remain visible. An interesting predicament surfaces when coloring becomes a popular practice in identification. Women from certain viewpoints appear the same color as priests, much to the priests' chagrin. In sum, the women appear to have an inferior role to the multi-sided men as women faced inequality in late 19th century society. Secondly, the shapes themselves present a hierarchy of society. From the irregular figures to the noble Circles, each shape has its own ranking and occupations. Moreover, each shape is subdivided into figures that have a higher status in the Flatland world. For example, the equilateral triangle is seen as superior to any of the other isosceles triangle with top angles of less than sixty. These shapes have little hope of progressing; hope lies in their offspring which may possess a more respected number of equal sides. This can be seen as an analogy to the lower classes struggle to achieve success in the society dominated by the wealthy or aristocratic. While the story of Flatland may be a mockery of Victorian England, its heart is its mathematical meaning. It serves as an interesting and understandable window into the subject of dimensions. From Lineland, which knows no left or right directions, to the abstract Fourth Dimension, where it is possible to look inside a solid object, readers are introduced to new ways of thinking not usually encountered in math class. Most importantly, the text of the book is not beyond the scope of someone with a casual interest in the topic. Anyone can appreciate the search for the meanings of dimension and truth in easy to comprehend analogies presented by the author. Another math topic addressed is the discovery of new ideas themselves. Abbott shows that math is a field where anyone with an interest has a chance to succeed just as the main character stumbles upon the meaning of dimensions from thoughts from his grandson. He pursues his hypothesis on the dimensions of Spaceland as well as develops the ideas for the Fourth Dimension on his own. Although he is imprisoned for his thoughts and attempts to teach others, the square keeps his theories, not letting the views of society interfere with his work. It is interesting that he faces this fate when trying to educate the public about the truth of their world and beyond. On the whole, Flatland is more than just a short book with intriguing mathematical ideas. It is an opening experience to the search from the truth behind the world through the subject of dimensions. While mocking the English , the book also introduces readers an odd world of shapes and figures. Lastly, math is encouraged even though it may go against the grain of society. Any book that introduces readers to a new way of thinking is worth reading.