Product Description

A century-old classic of British letters that charmed and fascinated generations of readers with its witty satire of Victorian society and its unique insights, by analogy, into the fourth dimension.

Product Details

• Amazon Sales Rank: #6483472 in Books
• Published on: 1999-11-16
• Binding: Mass Market Paperback
• 156 pages

Amazon.com Review
Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only two in your life, these are the ones. Taken together, they form a couple of accessible and charming explanations of geometry and physics for the curious non-mathematician. Flatland, which is also available under separate cover, was published in 1880 and imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. The further mathematical fantasy, Sphereland, published 60 years later, revisits the world of Flatland in time to explore the mind-bending theories created by Albert Einstein, whose work so completely altered the scientific understanding of space, time, and matter. Among Einstein's many challenges to common sense were the ideas of curved space, an expanding universe and the fact that light does not travel in a straight line. Without use of the mathematical formulae that bar most non-scientists from an understanding of Einstein's theories, Sphereland gives lay readers ways to start comprehending these confusing but fundamental questions of our reality.

Review
"The best introduction one can find into the manner of perceiving dimensions." -- --Isaac Asimov in the ForewordA

Review
One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world.
(The Washington Post Book World )

Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions.
(Victorian Studies )

This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition.
(Zentralblatt MATH )

Customer Reviews

An excellent edition of a classic - extended
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.

Unimaginable Dimensions
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.

The book that started it all for higher dimensional analysis
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.