In order to understand this twenty-two chapter book (first published in the mid-1880s) by Edwin A. Abbot (1838 to 1926), you have to understand what is meant by the word "dimension," a word in the book's subtitle "A Romance of Many Dimensions." A dimension is any measureable distance such as length or width. So something that has one dimension has only one measurable distance, something that has two dimensions has two measurable distances, and so on. You also have to realize that there are geometrical forms that can be drawn in these dimensions. Thus a line is such a form that only has one dimension, a triangle is such a form that has two dimensions that appears flat and non-solid, and a sphere is such a form in three dimensions that appears solid. (Another name for three dimensions is space.)
Part one (twelve chapters) of this book gives us a glimpse of the two-dimensional land where the narrator, Mr. "A. Square," comes from. This place, called "Flatland," is inhabitated by two-dimensional beings of which Square is one. These beings no nothing of "up" and "down." Square tells us details of Flatland society such as its resident's domestic life and its political turmoil. It is a place dominated by such things as a rigid social hierarchy, sexism, and closed-mindedness.
Abbot was a Victorian and his description of Flatland is meant to be a parody (using wry humor and biting satire) of English Victorian society. Abbot seems to have fun mocking the upper classes of the 1880s in his book. I found that much of what Abbot says can be applied to modern society.
As an example, Square tells us of the social hierarchy that exists: "Our women are straight lines. Our soldiers and lowest classes of workmen are Triangles with two equal sides [called an Isosceles triangle]...Our middle class consists of Equilateral or equal sided triangles...Our professional men...are Squares...and five-sided figures, or Hexagons, and thence rising in the number of their sides till they receive the honorable title of Polygonal, or many-sided...Finally when the number of sides becomes so numerous...that the figure cannot be distinguished from a Circle, he is included in the Circular or Priestly order; and this is the highest class of all."
Part two (ten chapters) of this book is very interesting since Square tells us of his visits to "Lineland" (a land of one dimension), "Spaceland" (a land of three dimensions, a land Earthlings are used too), and "Pointland" (a land of no dimensions). Readers will find that they will have to adjust their thinking every time the two-dimensional Square visits a world of different dimensions. For example, when Square meets "Sphere" (of Spaceland), the reader will have to "see" Sphere as Square does--in two dimensions. The end of this part has Square realizing that three (and perhaps more) dimensions exist and trying to tell his fellow close-minded Flatlanders this.
My favorite sentence in part two occurs when Sphere makes an unexpected visit to Square's home (and Square doesn't know who Sphere is, fearing that he is a burglar). Square says, "The thought flashed across me that I might have before me a burglar or cut-throat, some monstrous irregular Isoceles, who by feigning the voice of a Circle, had obtained admission somehow into the house, and was now preparing to stab me with his acute angle."
Abbot, besides being a writer and educator, was also a theologian. So are their any spiritual or metaphysical aspects to this book? The answer is yes but this is not always obvious. For example, when Sphere makes his first unexpected visit to Square's home, he slowly seems to materialize in front of Square. Thus Sphere seems to be a supernatural, supreme being and Square refers to him as "your Lordship." Another example is Sphere sees Square as "a fit apostle for the Gospel of the Three Dimensions."
This book is written in Victorian English that may be difficult (for some) to comprehend at first. But I found that as I progressed further into the book and got used to this type of English, it becomes much easier to comprehend. The sketches found throughout the book also help immensely in getting across what Abbot was attempting to convey.
This book raises a number of questions, some of which are as follows:
(1) Why does our universe have three dimensions and not two or four?
(2) In what ways does our three-dimensional universe affect its physical, chemical, and biological properties?
(3) Do universes that have two, four, five, or more dimensions exist?
(4) If other universes of different dimensions do exist, then are there beings in these other dimensions?
Finally, for those who want a good non-fiction account of possible other dimensions, I recommend Dr. Michio Kaku's book "Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10TH Dimension" (1994).
In conclusion, this is a unique book that sparks your imagination and raises certain questions. Be warned though! By reading this book, you may become one in "a race of rebels who...refuse to be confined to [a] limited dimensionality."
on January 6, 2013
An odd book. This is the thought that dominated the back of my mind throughout the first half of the story. The second half really picks up and makes this a worthwhile read, and a strong teaching tool for people interested in physics and contemplating the ideas of other dimensions. It's quite an interesting book, one that's had a lasting impact, I think because of its ability to communicate a difficult idea for human to imagine.
I came across this book in a lecture about mathematics, as a suggestion to help listeners understand the idea of other dimensions. It was a great recommendation, as the book served this purpose. I've been studying physics on my own, casually, for a few years now, and this is the type of book that really helps me move along in my understanding. I'm not looking to learn everything, or become a physicist, but merely learn for interests sake and because much of the basics add to my understanding of life. In this respect, Flatland is a great read.
Parts of the book were difficult, not because they were hard, but they were a bit boring...maybe tedious concepts to grasp. Maybe it was the parts about societal standing that seemed to lack some, but several curious ideas rose out of this aspect to the story (one of which is the role of females and their similarity to higher status beings). I'm not sure in the language had anything to do with it, but it is possible. It's an easy read, but still a little removed from our own common use of English. The ending was powerful, however, and some of the concept explanations are very clear, and very easy to understand and potentially useful as review material. It's little wonder that this book has lasted so long.
on October 10, 2003
Do not miscast this wonderful little book as being merely "sci-fi". Two-dimensional "worlds" exist within ours, if only in a somewhat pragmatic sense. If we imagine some "thing" intellective within such a world, then we have little difficulty seeing that our humble narrator, Mr. A. Square, might be such a world's most insightful oddball. The book is a classic exposition in basic geometry, but it is more than this. Abbott uses mathematics to make some very telling observations about human minds and psychologies.
Edwin Abbott (1838-1926) was a clergyman and a math geek. He was an educator, an expositor of English literature and New Testament studies, a notable headmaster, and the author of something like 40 books on widely varied themes. Today you will probably have a difficult time finding any of his other volumes, but Flatland is said to have never been out of print since it was first published in 1884.
No need to retell A. Square's big adventures here, other than this bit of dialog between our two-dimensional thinker and his three-dimensional visitor/teacher (Square is given to thoughts of still higher-dimensional worlds):
"SPHERE. But where is this land of Four Dimensions?
[A. Square]. I know not: but doubtless my Teacher knows.
SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable."
Abbott offers his allegory of physical and conceptual limits with an economy of word and thought that is nothing less than extraordinary. A great many volumes, five to ten times as large, conclude having said far less than this little parable. Read it. You will take from it what you are willing to take. If you find little or nothing here, you are indeed a citizen of Flatland.
on April 28, 2000
Flatland is one of those pseudo-scientific novels that has since become a piece of the scientific canon in the same way that Alice's Adventures in Wonderland has; when attempting to explain theoretical physics to a class, and at a dead-end, a professor is most liekly to turn to an analogy from Flatland. Which makes sense. Flatland is the story of A. Square, a resident of the two-dimensional Flatland, and how he comes to understand that there are universes in every dimension. Previous to this, the idea of any universe but his own two-dimensional universe was unthinkable; by the end of the novel, he is positing the existence of a great, infinitely-dimensional being-- god. This is not surprising; Edwin Abbott was a theologist first and foremost. What is surprising is how modern eyes have seen this tale, and it gives us a perspective on the endless debate as to whether the author's belief about his story is the final and "right" one.
Abbott meant his book as a treatise on theoretical physics-- if at all-- in only a minor way. According to Abbott himself, his main goal in the writing of Flatland was to produce a kind of "satire of manners" on Victorian England. And, given what little I know of the ways of life in Victorian England, he seems to be right on the money. But what do I know? Abbott's assertion is backed up by the structure of the novel, certainly; the first hundred pages of this small (hundred fifty page) tome are devoted to the customs and mores of Flatland. How stinging a criticism they are of the values and mores of Victorian England is not for me to say. Thus, those of us who are not historians are left with the final fifty pages, and the impact of the first hundred pages upon them (which, aside form the knowledge gained therein, is minimal); and, at least as far as the physicists go, the book has metamorphosed into a trestise on theoretical physics.
I'm not a theoretical physicist, either, but I've always been interested in mathematics in a sort of hobbylike way, and the math presented in Flatland is good, solid theory that also happens to be thought-provoking. Seeing how A. Square's realization of how the third dimension works dawns on him, and seeing how Lord Sphere explains the mechanics of the third dimension to A. Square, it is easy to take those arguments and make them to postulate a theoretical fourth dimension (albeit one that is impossible to visualize, at least within the narrow scope of my mathematical knowledge) and its supercubes with sixteen points and eight faces, and the like.
The point is, however, we seem to have taken a minor part of the book's appeal to its original audience and made that its full appeal today. We still think it's good (or it wouldn't still be in print a hundred sixteen years after its release, no?), but we think different aspects of it are good. The opinions of the artist have passed on, and the work itself remains in a different perspective.
on January 26, 2009
I read the product description, and the book interested me. For 2.25, why wouldn't I purchase it? For a book that I wasn't expecting much from, it certainly suprised me. It was interesting learning about the world in which the flatlanders, and other dimensional beings lived. Although to me there were obviously flaws in some of the things the author said, it was generally really well done. I for one was impressed, and it certainly made me think about how possible other dimensions would behave and move around. I would reccomend buying it if you were thinking about it. Its cheap enough, just go for it!
on February 29, 2004
I bought this book on a whim because it was so cheap, and I rather enjoyed it, despite it being a very short book. At the minute, it is circulating among my friends.
The first part deals with the social structure and mores of the flatland society. I've heard that it's a critique of the way life was set up when the book was written, but I can't confirm that. It describes a world where women are seen as worthless nobodies who are dangerous without really noticing, and where people are judged and placed in social classes based merely on their appearance (more specifically, how many sides they have).
The second part is why you should buy this book. It is the tale of what happens when one of the members of this two-dimensional society is taken and shown how life is lived in worlds of one, zero, and three dimensions. It is this part of the book which is absolutely fascinating, and convinced me that I will never be able to envision a fourth spatial dimension.
I highly recommend this book as a singular novelty, and a very good read.
on January 13, 2004
I just finished reading "Flatland" by Edwin A. Abbott and I'm not entirely sure what to think. While this book challenges the imagination of the reader with the possibilities of any number of dimensions, I found the language of the book a bit harder to wade through. While only around 100 pages, I feel it took me a longer time to read it than a longer, modern fiction, as the language is a bit older, complete with whence, thou shalts, and so forth.
However, I still think this is a worthwhile read, as the ideas are still applicable, especially with modern physics and with string theory claiming that more dimensions do indeed exist. I encourage you to pick it up if you're at all interested in mathematical curiousities and having your knowledge of 3 dimensions pulled and twisted a bit. Also, the social structure of a two-dimensional society is extremely interesting.
The first part of the book describes the world of Flatland, a world restricted to two dimensions and the society contained therein. In this world, each human is a shape, and irregularity is highly condemned. Women are straight lines and the highest class of society is filled with circles, or many sided polygons. Our author is a square, who describes to us the ways of life in Flatland, from how to recognize each other (as every shape would appear as a straight line seen edge-on), to how the laws of nature grant that successive generations may gain a side, thus rising on the social ladder. Also, he tells of the history of Flatland, during the trying times of the "Universal Colour Bill" and the "Suppression of the Chromatic Sedition."
In the latter part of the book, our square friend tells us of his vision of Lineland, whose inhabitants are confined to one dimension. Sadly, he cannot convince the Lineland monarch of the existance of another dimension. The next day, however, he is visited by a sphere from Spaceland. Through much demonstration and persuasion, the Sphere finally convinces the square of the existence of a third dimension, by bringing him into it. Sadly, after the sphere departs, and the square is again restricted by Flatland, he is unable to convince his Flatland companions of this miraculous third dimension. He is sentenced to a life in prison, taunted by a knowledge of an extra spatial dimension, yet forbidden by his two-dimensional world from ever entering it again.
on July 22, 2003
A. Square is a rather exceptional member of Flatland, a world that only has two dimensions. He not only dreams about a one-dimensional world, but also dares to question the limitation of having only two dimensions. Being a polygon himself, he will never truly understand the magic of Spaceland, but his unbound imagination lets him travel beyond what others call their 'space'. When he finally succeeds in going "Upward, not Northward" he gets convinced that he has a message to give to the other members of Flatland. But will the others accept his prophecy?
Flatland is a truly remarkable piece of literature. Not only makes is philosophy and mathematics accessible for the common reader, it also gives evidence of Abbott's visionary mind. Written in 1884 this book introduces the readers to concepts that will prove to become very 'hot' more than 100 years later. Mathematicians of today who have no theory about the number of dimensions are almost considered to be unfaithful to their science.
This is simply a must-read for everybody who likes to fantasize about dimensions and what the world would look like if we could see beyond our known dimensions.
on January 11, 2003
"Flatland: A Romance of Many Dimensions," by Edwin A. Abbott, is a marvelous tale that I regard as a pioneering piece of science fiction. According to the introductory note in the Dover edition, Abbott was an English scholar and clergyman, and the book was first published under a pseudonym in 1884. The book is enhanced by the author's own delightful illustrations.
"Flatland" is told in the first person by an intelligent square who lives in a fantastic two-dimensional world. He describes in fascinating detail his own world of Flatland, going into such topics as architecture, war, genetics, medical arts, law, and family values. Particularly fascinating is his account of his society's rigid stratification by class and gender. The square tells of his visions of zero- and one-dimensional worlds, and of his life-changing contact with the three-dimensional world.
Abbott succeeds in a task attempted with varying success by generations of science fiction writers since him: he creates an alternate world which is utterly alien, yet disturbingly familiar--a world that is complete and consistently compelling. "Flatland" could certainly be read as a satire of Abbott's own world; parts of it are laugh-out-loud hilarious. Whimsical yet possessing a biting edge, this is a brilliantly conceived and wonderfully written book. For a companion text, try A.K. Dewdney's "The Planiverse" (also about contact between two- and three-dimensional worlds); also try Aldous Huxley's "Brave New World" (an equally intriguing view of a stratified sci-fi culture).
on December 15, 2002
What is there to say about Flatland? It is certainly a creative attempt at trying to familiarize people with the concepts of dimensionality. It is not nearly as enlightening as some reviewers have made it out to be, though there are a couple of great endearing ideas that will stick with you.
Unfortunately, what starts off as a great book quickly becomes mired in tedium. Part of the tedium stems from the vast difference between 19th and 21st century cultures. Abbott works hard to describe a society for one-dimensional or two-dimensional beings based on his own Victorian era. Unfortunately it is written in such a way that the difference in values between our two eras adds confusion rather than enlightenment to the message of the book. We can't identify with the society, and that identification is crucial to the usefulness of the story. Second, there is entertaining fiction, and then there is ad-nauseum details which detract from the plot. His penchant for tangents (pun intended) reminded me of how boring the Iliad could be at points.
The book receives an A for originality. As for simplifying weighty concepts and making the matter entertaining, it receives only a passing grade. It is so far entangled in a social scheme that is outdated as to detract from the overall enjoyment.