Flatland (Illustrated)

I first read this book in High School many, many years ago. It was a treat to read it again as an adult. The humor, irony, social comment, wonderfully stilted Dickensian language and logic were mostly lost on that drifty teenager but really enjoyed this time around.

"Flatland" is a great, short piece of writing that will bend your brain in pleasant ways. Written in 1884, it is as much a commentary on society at the time as it is a thought experiment on dimensional perception. This particular version, however, is junk. Don't waste your money! The text is all there, but the illustrations are missing. The quality of the printing is pretty bad as well; the book feels more like a pamphlet.

There are plenty of good versions out there; this isn't one of them.

It was a fun re-read, I read it first about 100 years ago while in high school. Published in 1884, it usually gets categorized as Science Fiction, but it’s a social satire that skewers Victorian mores, especially how women were viewed by that society. And it examines dimensions. The main character is a 2 dimensional square who has a glimpse of the 3rd dimension, which sets him thinking in a new way.

It’s a pleasant little story.

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.

I am a mathematics student and the idea of multiple dimensions is familiar to me but it was still very interesting viewpoint. I strongly recommend this book to everyone who likes to think out of the box.

This is an awesome read, have read it a couple times before this version was available, it is great - however in the free kindle version there are no illustrations - it still is amazing but just need to use imagination a little more!

This edition is terrible on the Kindle. There's all sorts of extra line breaks that make it difficult to read. There's also no table of contents. Buy the MobiPocket version for the same price. It's a much better format

I personally enjoyed how the book laughed at the society of the time, but I think it missed a bit of speed and plot. Still, it gave a huge amount of background and logical basis, which I think is good

Book is a classic that perhaps opened the path to modern considerations of the study of dimensions by many. AND the study of Specificity resulting from the intersect of dimensions. And a sly commentary on society at the time.

A good book and especially interesting in an election year. It's an allegory of course. We all live in a Flatland world, too. Politicians and priests tell us about our world of two dimensions – a world where they try to control our thoughts. And for thousands of years it hasn’t worked so well. Millions of dead people attest to it.

Wouldn’t we all be better off – and wouldn’t life be easier if we could pursue our personal goals in business and in relations with people and with family without the distractions of (especially) politics and taxes?

The first half of the book can be a little boring – unless you really love geometry. After that it gets more interesting. "Flatland" would be a good recommendation for teenagers who might want to explore alternatives to traditional mores -- where morality and rationality prevail instead of religion and politics.

A great book, full of great ideas, wonderfully executed and really thought provoking. Where was this hiding when I was young! Read it!Flatland: a romance of many dimensions

This is an excelent primer on line, plane and spactial geomerty. no math just the ideas put in a way that anyone can understand. If you read it as fantasy to small children they will grasp the concepts and it will give them a great leg up in there later life. P.S. It is also a great story

P. P. S. I know the spelling sucks ;)

I had been intending to read this book for years, ever since I first heard about it. Something about the concept really appealed to me. The idea of a story that takes place (mostly) within a 2D world was something that I just couldn't envision. Of course, I had a few incorrect assumptions about what was going to happen within the relatively small confines of this experimental piece.

To make things short, I was quite disappointed in this tale. There were definitely some imaginative pieces going on, and once Abbot moved away from explaining how Flatland works and got into the story proper, things did get a bit more interesting, but all in all, this is really a rather lame attempt at describing something that is rather difficult to describe.

There is, however, a wonderful satire piece at the heart of this tale, one that shows how easy it is to close oneself off from thinking outside of the confines of one's own world, even when in the midst of expanding the world for the person who is trying to expand yours.

All in all, this is a very imaginative piece that shows a lot of promise, but probably doesn't deserve quite the respect it has gotten over the years.

Too much time spent on explanation and not enough on character and story development. The author obviously thinks readers are too dumb to understand the concepts. Maybe so, but if that's the case, why bother writing the book in the first place. Also, yet another attempt at early 20th century caste guilt dredging. Getting a little care worn at this point.

I dont understand how it was subtitled a A Romance as it is anything but. However, given when it was written and how so much of this thinking evolved into our current theories of the multi universe, it is worthwhile reading for those who love physics and thought experiments.

Every young math student should read this book. And every budding philosopher. It speaks to life as few others, perhaps Animal Farm. A must read again if it has been a while. It is a short but worthwhile read. It can be read aloud easily.

This entertaining little tome provides an excellent foundation for understanding dimensions. It could be of great use to math and physics instructors in getting this concept across to students. For the one Flatlander who experienced Spaceland, it demonstrated the consequences of non-conformity. Perhaps, this was a statement about the nineteenth-century society in which the author lived. Are there any Spacelanders who have experienced the 4th dimension? Do they wish to come forward?

I was introduced to this book at a teacher's conference and looked forward to reading it. However, the book, while a wonderful idea, does not come out as intended. The concepts become difficult to follow with all the education needed to understand Flatland. The actual story seems rather anti climatic. All that work on A Square's part...for what?

I downloaded one version of Flatland for the Kindle which said it was illustrated, but all I saw where each illustration was supposed to be was what looked like placeholders. This version is beautifully formatted, with illustrations and table of contents. More than worth the $0.99.

A good book, and a testament to the job of the researcher to attempt to explain their findings when there is no precedent for them. The book seems simplistic, but covers quite a wide breadth of topics, ranging from caste structures, to family values, to the historical clash between ecclesiastical orders and the pursuit for higher knowledge. My only criticism is that the book is a bit shorter than I'd like.

the product came in dependable the store prime fashion and was pleasing ,to read. the story the writer takes you through helps you understand his intent. over all it is a very good book, anybody intrested in math, science, or fantasy should read this bood

I had a very hard time with the old fashioned style of language in this book. The first two thirds of the book were very hard to get through. It was hard to understand, as well as boring. It took the first two thirds to set up the background of the story. Once I made it to where the story actually started, it was easier to read. The language was still very old fashioned, but the story helped to get past it. All in all, I don't think I would recommend this book.

I was wasting my time reading it. it seems an exercise in something. I did not want to hang around to find out. My free copy had no illustrations. Can't imagine that that would improve it. If it is to teach math...math alone is much more interesting because when you master a concept there are more to build on.

I read this book over 20 years ago for extra credit in 10th grade geometry. It has the effect of compressing your mind like a spring, (into 2D) then releasing it. What I got was a different meaning than most. And that is...this could explain "where" Heaven and Hell are. If our 3D existance is a subset of 4D or higher as the book suggests, then it "fits" for an answer to a rather basic question of faith in God.

I was wasting my time reading it. it seems an exercise in something. I did not want to hang around to find out. My free copy had no illustrations. Can't imagine that that would improve it. If it is to teach math...math alone is much more interesting because when you master a concept there are more to build on.

I read this book over 20 years ago for extra credit in 10th grade geometry. It has the effect of compressing your mind like a spring, (into 2D) then releasing it. What I got was a different meaning than most. And that is...this could explain "where" Heaven and Hell are. If our 3D existance is a subset of 4D or higher as the book suggests, then it "fits" for an answer to a rather basic question of faith in God.

Don't buy this version, there are plenty of others, including free downloads. The formatting of this book is broken such that there's a forced line break every other line, making the text annoying to read. Get one of the others that is properly formatted and don't waste your money on this one.

Flatland may be famous, the message may be good, but as a story it's terrible. The first half of the book (I'm not exaggerating-- it was 52%) is an infodump. Complete backstory explaining how Flatland actually works. But then, nothing actually happens in the 'story' after that anyway. The main character visits 2 other lands as the author attempts to teach us how we have to try to see things from a different perspective, or from a different angle because there might be more to the universe than we can currently see. Nice sentiment. I agree with that (it's always bugged me that scientists say life couldn't exist on Mercury, for instance, simply because nothing from Earth could survive there), but if you're going to sell/ describe something as a story, then make it interesting. Make something actually happen. Have some conflict that has us wondering what's going to happen.

And for all the people saying it's a lesson in geometry... What? Just because it has some shapes in it doesn't mean it's teaching you something about geometry.

I heard about this story about 10 years ago and have been wanting to read it since because it sounded interesting. That 10 year wait is the only reason I finished it-- that and an increasingly despairing hope as I read that something was going to happen. Well, something did happen... It ended, and I was grateful.

This edition is essentially unreadable and not representative of traditional printings. It's printed directly from the digitized (and free) copy from Google Books and has clearly had NO editing work done. The book is filled with references to figures that were not included, mangled words, and seemingly random breaks and markings in some spots. This would be fine for a free digitized text online, but is entirely unacceptable for a paid-for product, especially a short book that would be similarly priced in a physical store.

The book is great. I have purchased dozens of copies in the past for my students. This E-tailer has poor communications practices: no notification that the product was shipped, no tracking method, no notice as to which carrier the product was shipped with, no notice that the recipient received the shipment (the purchase was a gift sent to another address.)

I had hoped to enjoy this book as I normally enjoy the books I choose to read. But I did not enjoy reading this book. The language is dated and hard for me to follow. The topic although initially interesting quickly becomes lost in a morass of useless detail. The only thing that I can point to as a benefit of having read it is the reassurance of the social progress that humanity has made such that so many of the concepts in this book are so foreign such as to make this book almost unable to be understood by a layman. A person who is much more familiar with the 19th century than I will undoubtedly enjoy this book more than I did.

Heard about the book on NPR and Big Bang, sounded like it might be a good read, wrong. If you read the first 3 pages you pretty much have read the whole book. It rambles on and on repeating itself without saying anything.

Prior to reading this novella, I absorbed a great deal about it from the zeitgeist. It's referenced quite often and it was one of those books on my List of Shame, having never read it. However, after completing my read-through, I was sorely disappointed.

I would like to caveat that although I gave this book a poor review, you should read it. I think it's an important work, despite its abysmally poor execution.

As a thought experiment, this novella offers absolutely stellar fare. As a story, meaning a collection of words that abides by the elements of plot, Flatland fails utterly. The premise of the main conflict of the book is ground-breaking; it deals with a 2D entity's reaction when confronted w/ the heretical idea that a higher dimension exists above him. However, the author's expansion on this premise is poorly done and I did not find it engaging, even over the course of such a short work. The author makes several errors that killed this book, at least for me.

The author wastes no time in committing his first sin; more than the first half of this book is an info dump that is meant to orient the reader to the 2D world and satirize Victorian culture; however, these sections say very little that could not have been summed up in a few pages. For example, do we really need to read across 10 pages of an 80 page book about how colors were outlawed b/c they stir up revolution? No we don't, satire or not. Instead how about taking a paragraph and explaining how the 2D entities move about their world; something that the author purposely omitted, along w/, to paraphrase him, several other thousand inane issues that are of no consequence. As another example, do we really need to take up so much space describing how the Flatland women are essentially brainless morons who require neither education nor stimulation beyond child rearing? Again, no we don't. Whether or not Abbott is satirical or sincere in his views on women is immaterial. He dedicates pages to useless information that impacts the story in minute ways. He also contradicts himself in his digressions regarding women; I am unclear on whether this is done on purpose or not. He states, "[women] shall have no memory to recall, and no forethought to anticipate..." and yet several pages later we see females participating in political maneuvering. So which is it Abbott, are they mindless walking wombs, or are they intelligent creatures who are simply looked down upon by the men folk? If you're pointing out the paradox of women being so influential in Victorian society, yet being viewed so dimly by its men-folk, then you did a poor job emphasizing this point and it just came across to me like you simply weren't following the thread of your own writing. In my particular case, these sections of the book did very little other than create a feeling that I was reading a work so far out of its time that the material being referenced was meaningless.

Another aspect of the author's writing that threw me was the way in which he makes disconcerting switches in language choices. At times, the main character uses modern English (modern even by the standards of 1884), while at other times he seems to channel his inner Ye Olde Gentleman and starts tossing about thees and thous. I don't have an issue w/ this in itself; but upon closer inspection, we find that there is no rhyme or reason to the author's choice of which tone the character takes. Sometimes he uses modern language w/ people of higher status than himself, sometimes w/ those of lower rank; the thees and thous are similarly thrown about at random. This flip-flopping back and forth took me out the story a bit.

Lastly, there really isn't much structure to be found here. We have roughly 40 pages of info dump as I mentioned earlier, followed by 30ish pages of story, followed by a non-ending that does very little to provide any kind of resolution to the story. I realize that the gems of this novella are not found in its deep character development or rich story; but the characters and events of the story are pushed to the side to such a degree that it makes me wonder why the author even bothered to include them at all. This novella could have just as easily used nameless characters and settings. I think this version would have been a stronger book, since it would presumably not have required the author's clumsy attempt at characterization, nor would it have required his unnecessary social commentary that bogged down the novella we actually have.

I made it about 40 pages and gave up. At first I enjoyed the description of the flatland but it didn't move fast enough. If you understand the concepts by page 10 then I can attest that the next 30 pages are just like rereading the first 10, 3 more times. Maybe there is something later in the book that is a mind bender but I can say the first third of the book is pretty elementary.

This book is outdated. Like another reviewer said, it is a book of its time. I bought it because it was supposed to present creative and interesting mathematics. It didn't. The math concepts wouldn't be new to 5th graders. The book tedious!

Flatland requires more imagination than I was willing to come up with; please note that I never watch sitcoms any longer because they always let me down in the laughter/satisfaction department. Your experience may vary.

Flatland, a delightfully odd science fiction novel, was originally published in 1884. English author Edwin Abbott Abbott wrote the book under the pseudonym of A. Square. The story is narrated by an actual square, an intelligent geometric figure who lives in a universe of only two dimensions. Speaking to an audience of third-dimensional readers, the Square introduces us to his flat-plane world, describing in detail not only its physical characteristics but also its societal and political structure. The result is a strange combination of geometry lesson, social commentary, and utopian parody.

With no conception of height, only length and width, the inhabitants of Flatland can only see each other as straight lines and must distinguish each other through hearing, touch, and visual techniques acquired through training. This is very important because the society of Flatland is built upon a strict social hierarchy. Circles, or Priests, are the highest social strata, while the lowly workers and soldiers take the form of very acute isosceles triangles. The higher the number of sides and the wider the angles that compose a figure, the greater his intelligence and the higher his social standing. Women, unfortunately, are not even factors in the class struggle, as they always take the form of straight lines. Through his description of this fictional society, Abbott wryly criticizes England’s restrictive class system. When in this satirical mode, the book entertains with an absurdism reminiscent of the sci-fi satire of Voltaire’s novel Micromegas. The humor is so dry at times that in some cases, like the extreme chauvinism with which women are discussed, it’s difficult to tell whether Abbott intends to be funny or not.

Flatland is based around an ingenious idea, but the execution is not always all it could be. Though only composed of 155 sparse pages, the book feels long-winded. At times reading through Abbott’s convoluted prose is like trying to run through molasses. Particularly in the first half of the book, he spends a lot of verbiage in making his points and often goes off on annoying digressions. The second half of the novel is much better. The Square describes his visit to the one-dimensional Lineland and his attempts to explain Flatland to the inhabitants there. Then he relates how he originally became aware of the third dimension when he was approached by a sphere from Spaceland. Here the geometry takes precedence over the satire, and the book is better for it, as Abbott illustrates the difficulty in comprehending dimensions above and beyond those which we experience with our senses. The book ends on a high note as Abbott delves deeper and deeper into the philosophical implications of multi-dimensional geometry. On the one hand, the Square and his third-dimensional awakening stands as a sympathetic surrogate for those who claim to have experienced religious revelations. On the other hand, the spirituality of those revelations are called into question as possibly being sensory experiences of geometrical dimensions higher than our own. Once again, how much of such speculation is intended to be serious or humorous is unclear.

For the mathematically minded, the contemplation of fourth-, fifth-, or higher-dimensional worlds is a perplexing but fascinating pursuit. Though the relevance of some of its social satire may have worn off with the end of the Victorian Era, Flatland can still speak to those with an interest in such abstract intellectual exercises, and it does so in a way that is both provocative and amusing.

I'm YEARS late in reading this book. I first spotted it on the shelf of one of my high-school math teachers, and I thought it looked interesting and asked if I could read it. He sadly declined, saying "you won't like it, it's pretty sexist." Over a decade later, as an adult, I finally got my hands on a copy of it... and while I wouldn't call it an entertaining read exactly, it's certainly VERY thought-provoking. And I have to disagree with my old teacher -- it's not so much sexist as it is a scathing commentary on misogyny (and eugenics, and class separation, and religious suppression of scientific advancement...). And somehow it manages to pack all this social commentary in with a fascinating exploration of various dimensions, and just how higher and lower dimensions would look to an outsider.

"Flatland" follows A. Square, the square-shaped inhabitant of the titular Flatland. He spends the first half of the book detailing the nature and culture of his world, and seems content with his lot in life -- he may not have as many sides as one of the noble class of multi-sided polygons or the priestly Circles, but at least he isn't a brutish Triangle or a female Line. His world is upended one night, however, when he dreams of a world of two dimensions, inhabited by Lines... and later, when a visitor of the third dimension, the enigmatic Sphere, appears in his home, he learns the truth about his world. There are higher and lower dimensions than the two-dimensional Flatland, and as he visits these mysterious worlds he learns that some astounding truths have been hidden from him by the government of Flatland. He decides it's time to spread the truth... but his crusade has terrible consequences, and Flatland society will do anything to keep him quiet...

If you pick this up expecting it to merely be an entertaining story, you'll probably be disappointed -- there's not so much a story here as there is an exploration of what a 2D universe might be like, and how higher and lower dimensions would appear to one from this sort of universe. On one level it works as a sort of introduction to basic geometry and to inter-dimensional thinking, and is fascinating reading to anyone with a mathematical knack. Even the legendary Isaac Asimov has praised this book as "the best introduction one can find into the manner of perceiving dimensions." (Quote his)

On another level, however, author Edwin Abbott wrote this book as a scathing commentary of his time period. The culture of Flatland is horrifically sexist and racist, dismissing both women and polygons with less than four sides as somehow less than "human" and stupid, vicious brutes... but in all honesty, this isn't much different from Victorian-era thoughts of the day, which thought very little of women, the lower classes, and people of different races. And the thought of the Circle-priests deliberately withholding information on the higher dimensions isn't much different from how religious leaders have suppressed scientific advancement for centuries -- something that plagues our society even today.

While the story itself is rather lacking, this novel is still a surprisingly creative exploration of mathematics and dimensions... and a biting commentary on the prejudice and misogyny of its time. When my teacher called it "sexist," I have to wonder if he just missed the satirical part of it, or if he thought a high-school student wouldn't understand satire. Regardless, it's still a worthwhile read, both as mathematical creativity and as a fascinating social commentary that still resonates today.

The first time I heard of the book Flatland was about 15 years ago when a friend asked what I thought a hand would look like if I were a two-dimensional being. He described one possible experience, if a 2D being were on a flat surface but looking "upward", a hand coming toward it might appear to be five circles increasing in size, with no clear indication that the were 3D fingers attached to a very real 3D hand.

I loved the thought experiment and we discussed matters of limited perception for some time, with him finally recommending Abbott's classic novella. It was a few years later when I finally read it for the first time. I was on a flight from Tucson to Detroit and finished it before we landed. It stuck with me and I've returned a few times since, most recently last week.

The story is told in the first person by A. Square, a cleverly named 2D being that exists in Flatland. The book could almost be considered two distinct stories. The first part is a detailed description of life in Flatland, which is dominated by a rigid hierarchy based on the number and regularity of angles one has. This part of the book is said to be a satirical look at Victorian England and its elitist structure and legal and social institutions. It is incredibly witty, especially told from the perspective of a square who finds the rules and habits, even the most barbarous and cruel of them, quite natural and beneficial.

The descriptions of life in (or rather on) Flatland are analogous to much more than just Victorian England. It's a geometric allegory to the horrifically tyrannical society praised by Plato in his Republic. It also has a very Darwinistic, mechanistic flavor in terms of individual progress being the result almost entirely of biological progress with each successive generation. There is also an especially cutting description of teachers and schools that I very much enjoyed.

The second part of the book is what has made it a classic and popular among math geeks, physicists, and philosophers. It describes the Square's discovery of other dimensions. First in a dream he descends to Lineland, where only a single dimension exists and the denizens and King are incapable of understanding him when he tries to convince them that he exists in two dimensions rather than one. They experience him as a point on a line that appears and disappears as her moves side to side.

This dreamtrip to Lineland precedes the Square's excursion to Spaceland and provides a brilliant backdrop and analogy both for the character and the reader. There is something very powerful buried in the sequence of events: he must first descend, go lower or more basic as it were, in order to ascend to something greater and more complex. The secrets of Spaceland are only (barely and with great difficulty) comprehensible to A. because of his ability to analogize his descent into Lineland and see from his perspective how limited to understanding of Linelanders was. First go within in order to go without.

The Sphere that visits him and brings him into Spaceland reveals how things appear from his 3D perspective and wows the Square with new vistas. They descend even further into a dimensionless Pointland briefly, which is one of the most captivating passages in the book. The journey as a whole is reminiscent of the fabulous scene at the end of the movie Men in Black, where the camera zooms out so far as to reveal our entire galaxy to be contained within a marble being tossed in a game by some great galactic creature.

The Square, being newly enlightened by all this, proceeds to speculate on the existence of additional dimensions. The Sphere, seeming so wise when revealing to the Flatlander a third dimension, is baffled and stubbornly resistant to the possibility of additional dimensions beyond his own, an excellent example of how the newly learned are often better at finding even deeper truths than those for whom knowledge is old habit.

A few minor observations that stuck out to me in this reading:

Things banned in Flatland include any house or building with acute angles, because from the vantage point of a Flatlander all shapes appear as lines until felt up close and therefore a sharp angle could seriously injure someone who bumped into it. From their perspective, this prohibition seems perfectly reasonable. But if they only had greater knowledge and perspective to see the additional dimensions of reality, no angle no matter how acute could pose a threat. Isn't this the way all strict prohibitionism works?

In Flatland a being can distinguish shapes not only by feeling them, but also through sight. Since everything appears as a line the only thing that makes sight recognition possible is the presence of fog. If, say, a Pentagon was coming toward you in Flatland even though it would appear as a single straight line you could see it's leading angle more brightly than it's sides, receding into the fog as it were. This is important because an irregular shape might be dangerous, whereas a near-circle would command great respect and deference. The book provides a fuller and clearer description of sight recognition, but I was struck by a simple analogy. Given our limited powers of perception, we often require various forms of "fog" in order to distinguish one person from another and see their true nature. When approached in a fogless environment, people may appear to have equal angularity and an equal number of sides at least until we become intimate enough to "feel" them. But fog - hardship, challenge, difficulty - provides a backdrop against which the unique shapes of each being can be distinguished.

There is so much in this book to ponder and explore. The existence of dimensions we are currently incapable of perceiving not least among them. But the lesser appreciated social and political satire in the first half of the book deserves exploration and discussion as well.

Go check it out. Let it take your mind "Upward, but not Northward".

Author shows us an imaginary land, civilization of beings that are inferior to humans.

Into the book you realize that it is teaching humans how limited, low on the evolutionary scale we are, our thinking is limited by beliefs, many false and robotic action. Book shows where we are as compared to higher, more evolved beings, worlds.
Our view is limited, just as the flat lines, shapes in the beings, things in the lower world described in this book.

We can open our minds, grow and evolve.

I was referred to this book through reading; My Big TOE - The Complete Trilogy by Thomas Campbell.

Am learning and hope to grow from the knowledge in both books and many others he refers to.

As I grow older I realize the time I wasted that could have been used in developing the spiritual side; have read of certain practices that prolong life, some that conquer death and illness. People like Jesus, other saints... are at that level, have that ability.

I am not. But it doesn't hurt to start at my present level and work toward that positive and entertaining goal. Its work at times, but it’s worth it. The results are permanent. Something that cannot be taken from you.

Robert Monroe (Journeys Out of The Body and other books mentioned meeting a being that was hundreds, (maybe thousands, I have to find the paragraph) of years old. A very advanced human. When asked how he hides his identity, age; he-she replied; I just keep changing jobs.

The earth is round. But many of our minds-thoughts are limited as would be as a flat surface.

This book is free as public domain. But is definitely worth having an original in your hand. Look for the antique, unaltered.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

In "Flatland", Edwin A. Abbot uses fiction to provide a unique understanding of dimensions. Rather than start with a three-dimensional subject and descend "downward," he starts in the "middle," with a two-dimensional square in Flatland that first visits a one-dimensional world called Lineland before "ascending" to the three-dimensional world of Spaceland. Abbot's narrative technique is quite effective in setting up his explanation of spatial geometry, though the first part of his story suffers from many of the biases and prejudices of his day. The first half of the book, and much of the second half, is replete with blatant misogyny and an approving portrayal of eugenics. Though Abbot's work plays a significant role in speculative fiction, he could not escape the views of his own time even as he invented new worlds. This work will interest fans of speculative fiction and those looking at the history of science fiction, but is unpalatable to modern sensibilities.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Flatland: A Romance of Many Dimensions, published in 1884, is Edwin A. Abbott's social satire and Christian apologetic. As a Cambridge mathematician, theologian, and schoolmaster, Abbott had a lot to say about his Victorian society and about being open-minded to the supernatural. He does this from the point of view of a humble square that lives in Flatland, a world of only two dimensions.

For the first half of the book ("This World"), the square explains the demography of Flatland, all the while offering hilarious social satire. He begins at the lowest social stratum (women, who are straight lines) and ends with the king, who has so many sides that he's indistinguishable from a circle. Low-class men, such as soldiers, are isosceles triangles with sharp acute angles. Since the brain is the size of the smallest angle, these men are stupid, but their sharp angles provide offensive weapons. Anyone who has an angle under 60° is a serf. Women, of course, have no angles, which means they are brainless and irrational (and Abbot provides plenty of tongue-in-cheek evidence for this fact). But women have a mouth on one end, and it can effectively be used as a dagger. When viewed from the back, a woman is hard to notice since she is seen only as a point, thus she must sway her bottom back and forth to alert others of her dangerous presence.

Pretending that he's merely explaining Flatland society to his readers in "Spaceland," Abbot mercilessly mocks his era's class structure, fashion, aristocratic marriage and parenting practices, the education system and school board politics, and government. All of this is done in a reasonable-sounding lecturing tone:
Obviously then a Woman is not to be irritated as long as she is in a position where she can turn round. When you have them in their apartments -- which are constructed with a view to denying them that power -- you can say and do what you like; for they are then wholly impotent for mischief, and will not remember a few minutes hence the incident for which they may be at this moment threatening you with death, nor the promises which you may have found it necessary to make in order to pacify their fury.

In the second half of the book ("Other Worlds") the square explains his vision of a one-dimensional realm called "Lineland" where he meets the king of Lineland who can't imagine Flatland, a world of two dimensions. The square thinks this is amusing, so he torments the belligerent king by using the second dimension to speak to the king from above, to magically pop in and out of the King's view, and to offer predictions about who is approaching the king from afar (image in review at FanLit). With his omniscience and omnipresence, the square bewilders the king of Lineland.

Upon his return to Flatland, the square is confronted by a sphere from our Spaceland of three dimensions who, poised in the third dimension, can view all of Flatland. To the Flatlanders the sphere looks like a circle of changing diameter, and to Linelanders he seems to be only two lines (see the image at FanLit). The sphere can pop in and out of Flatland and Lineland as he wills, can see inside (and even manipulate) houses and bodies, and can make predictions about the future based on what he sees from his viewpoint. Our square, who harassed the king of Lineland for his inability to imagine Flatland, is now flummoxed at the thought of a dimension he can't perceive, but he believes it because he has witnessed the sphere's power and he remembers his analogous encounter in one-dimensional Lineland. When the square tries to preach this new teaching, though, he meets resistance from unbelievers.

The metaphor, of course, is that we in Spaceland, being confined to only the dimensions we are able to perceive, can't imagine more dimensions in which other beings exist and may be able to visit, view, or manipulate us. This idea isn't at all new to me, but I found Abbott's explanation to be a very convincing line of reasoning and, perhaps, a way to imagine what it must be like to be God. Flatland is best known, by the way, as a treatise on dimensionality and is considered by scientists to be prophetic in its use of unseen dimensions to explain physical phenomena.

Flatland is available in the public domain, but I chose to listen to Blackstone Audio's recent version which is four hours long and read by Robin Field. The audiobook does not come with Edwin Abbott's drawings, but I had no trouble imagining them because they're thoroughly described by Abbott in the text. However, it's easy to refer to them in public domain sources if you wish. I loved Robin Field's narration and, even though the material seems heavy, I didn't have any problem following along. I did, however, have to maintain constant focus just to translate all of the geometric metaphors into social analogies during the first section of the book. For that reason, Flatland is hard work, but immensely rewarding. I thought it was brilliant.

Very interesting book. It is based on math, but is also social commentary. Anyone with a mathematical bent that enjoys Animal Farm should read. A square in Flatland first explains his universe which is of course a plane. The number of sides a figure has determine its status with circles being supreme beings. Of course, females are lines no matter the class and are nearly unthinking creatures. Soon the square has a vision of something called a sphere and the sphere teaches him about three dimensions of which our friend is to spread the gospel to his neighbors. He of course fails but learns lots along the way. The prejudices of course translate into Victorian morals of the author's time. REally enjoyable

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

A square living in a two-dimensional plane explains his ingenious world, and his revelatory introduction to lands of fewer--and more--dimensions. I have fond memories of reading this book as a child, but this was my first time revisiting it since then--and it was quite an experience. What I remembered best is a brillaint, unique concept, and that's still there: there's nothing else out there like Flatland, a world that appears utterly alien but is in fact too well-realized to be unfamiliar. It's ingenious, and a delight to rediscover. Yet this slim volume offers more than that idea alone. About half the book is given over to infuriating social satire, which I'd forgotten about completely. The satire isn't always obvious as such: Flatland's society has an extreme view of the misogyny, classicism, and essentialism present in our own (and particularly in Abbott's Victorian era), but the sad truth is that it's not a grand exaggeration--and it's presented so blandly that it reads more like an unfortunate relic of prejudice than any sort of social commentary. As such, I worry that the satire may go over the heads of younger readers (I can't remember if it went over mine) and would be taken at face value; regardless, it feels almost out of place--not that it doesn't have moments of keen, even painful, insight, but it is quite disparate from the fascinating physics lesson that fills the rest of the book.

To wit, the other half of the book is a novel exploration of dimension, verifying and exploring the existence of four or more dimensions by exploring two and fewer. It may not render comprehensible the incomprehensible, but it's a strong argument for some sort of world greater than the one we know. Meanwhile, the dimensions explored by our narrator the square are fascinating. Abbott succeeds by taking his concept to its furthest extent: the lines and shapes have unusual societies which are greatly influenced by the nature and limitations of their worlds, surprisingly simple diagrams help the reader to enter these unusual lands himself, and Abbott often anticipates--and then answers--the questions and doubts that surround his strange ideas. He takes what seems to be a pure mathematical novelty and renders it from a dynamic, convincing first-person perspective--and while it remains just one imaginative interpretation of the issue at hand, it's a brilliant one and a great read. Abbott's voice can tend towards stilted and dated, but Flatland's combination of breadth and brevity nonetheless make it compelling. This may not be precisely the book that I remember, but it provides what I loved and remembered best: something ingenious and brilliantly realized, something intriguing and delightful and thought-provoking. I take more issue with Flatland now than I did then, but I find it fascinating above all and so recommend it despite lingering reservations.

Edwin Abbott wrote this work in 1884 as a political satire on Victorian culture. I first heard of it through a reference made by science educator John Clayton. The concept of an entire civilization living in a 2 dimensional world and unable to fully grasp the concept of 3 dimensions is a wonderful analogy for human beings attempting to understand the divine nature of God; especially the trinity. We can become insistent in our demands that nothing can exist outside of our sensory perceptions. Or, we open our minds to the possibility that there does exist something beyond our understanding that has been revealed to us in ways we could grasp.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

I was hesitant about reading Flatland, due partly to its age, but mostly to my negative relationship with math. However, due to its shortness, and my fascination with higher and lower dimensions, I picked it up and haven’t had a decent night of sleep since.

Flatland tells the story of a 2-Dimensional Square, living in what can only be described as the 2-Dimensional equivalent of Victorian England, which is pretty much hitting the nail on the head, because the book is meant to be a critique of the era, but I feel it’s so much more than just that.

The descriptions of the lower and higher dimensions were so flawless and well thought out, I didn’t even notice the fact that my edition had no illustrations (something other people seem to be complaining about, but you can easily find them online), as I easily grasped the concepts. The two main ideas I had going into this book; not liking math but enjoying dimensions, proved to be a fascinating mind-set. First of all this book has very little to do with “traditional math” in the sense of 1+4 or 67-53, or even finding the hypotenuse of a triangle, rather focusing more on basic geometry and anthropomorphizing beings of higher and lower dimensions. As someone who has scoured the web for fascinating stuff on dimensions outside of our own, I was quite surprised to find that this book is probably the most fascinating thing I have come across on the topic. In fact I spent quite some time making sure that this wasn’t a recent publication, as I had difficultly believing something this “enlightened” could have come out of an era as oppressive as the Victorian.

Despite not conforming to traditional mathematical concepts, I feel that if this book was taught to me back in school, I think my marks would have sky-rocketed, because finally math was interesting. Obviously I would kick and scream at first, thinking that it’s not bad enough I have to do equations, now I have to also read a book about it. But it would have all been worth it, and I’m sure other students would agree with me.

There is, however, one downside, which I would go as far as to say is a deal-breaker with this book; the nightmares. From the moment I opened the book, I was infected. Most of the dreams I’ve had since reading Flatland have, to some degree or another, involved travel between different dimensions. This may sound really awesome at first, but it’s also quite taxing. And it’s not just in sleep; I’ve missed countless slides at college because I’m too busy making sketches on my notepad of squares and lines and tesseracts. It even seeps into my meditation practice, and tends to be the place my mind most frequently wanders. I know psychologically this all means something very important, but I haven’t gotten to that module in college yet.

Overall I highly recommend this book, as it is short enough to finish in as little as two or three sittings, and it’s fairly easy to digest, even if you aren’t well versed in different dimensions. As long as you are okay with having visions of worlds beyond this one, you will be just fine.

This novel is a short classic that was written by a school headmaster as both an educational tool as well as a criticism of victorian society.

The novel follows the life of A. Square. Square is a lower middle class inhabitant of a 2 dimensional world. The polygon world and its politics are explained in the book as well. The square is visited by a 3 dimensional being (a sphere) and is taken to point land (1 dimensional) and is also taken to see the hidden inner workings of his own society.

The work is a commentary not only on mathematics, but is also a commentary on British society, repression of women, repression of the lower class, slavery, euthenasia, social dominance as well as religion (the sphere can symbolize educational or spiritual enlightenment). While this may all sound boring as hell, dont be fooled, the story line is fascinating and the plot is great. Additionally, the ending is a real killer! You wont be disappointed in the ending here!

Definately buy this book as it is a literary classic. The math behind it is very elementary and is easy to understand. It should be noted it had to be written this way since Abott could not come out and directly criticize the monarchy without being politically quited.

Definately buy this book and read it. This is a great piece for in depth literally analysis for class as there is tons of social commentary in it. Great plot, hidden meaning, awesome ending.. you cant lose!!

Edwin Abbott's "Flatland" is a story that can be read as many things: as an Orwellian satire on The State, as a contemplation of dimensions (even ones we do not know yet), as a philosophical variation of Plato's Cave, or simply as a delightful sci-fi story.

Flatland is broken up into two parts. The first sees our main character (a square who is a mathemetician - how cute!) telling us - those who live in "spaceland" - about the ins and outs of flatland. He teaches us both about how life is lived as a two dimensional object, explaining such things as how one can recognize by sight a squre from a hexagon without being able to see the angles. Also, the square explains how flatland's class and government system works: how women, for instance, are inferior to men and do not attend school, how polygons are superior to lowly squares and triangles, and how the circles make the laws.

It is this first section that is both a savy critique on government and the then prevailing social mores. Also, this seciton is fascinating from a mathematical point of view, answering questions that the astute reader is bound to have. (How, for instance, is sight possible in two dimensions?)

The second section of the book is where stuff gets even more intersting. This is the section where our square mathemetician both finds himself (in a dream) having to explain the concept of a second dimension to a "linelander", and is visited by a "spacelander" who must try to convince our "flatlander" that a third dimension is possible.

This section is most interesting from a philosophical perspective. How, for instance, is it possible to explain a third dimension to one who only knows two dimensions? To the flatlander, terms like "up," "down," "above," "below," "vertical," (etc.) have no meaning as they presuppose knowledge of a third dimension. That is, can a spacelander use "two diemsional language" (language presupposing no familiarity with any but two dimensions) to explain a third dimension? (Edwin Abbot thinks he can, but the astute reader will notice Abbott's linguistic fallacy in how he brought this about!)

At any rate, it is this part of the book that can also be seen as a variation on Plato's Cave. (Plato's Cave analogizes us to people looking at the back wall of a cave open at the other end, who see only shadows of objects outside the cave, but who are convinced that what they see is the real things.) That is, "Flatland" very beautifully articulates the idea of someone realizing that what they assumed was a complete view of reality was only a partial view of reality. And now, the flatlander bears the burden of trying to convince other flatlanders that the reality they take for granted as "all there is," is, in fact, not a complete view of reality at all.

Can he do it? Will he run into the same linguistic stumbling block already spoken of? More interestingly, if the "linelander" was wrong in assuming only one dimension, and the "flatlander" was wrong in assuming only two dimensions, might the "spacelander" be wrong in assuming only three dimensions, and so on? And how, if possible, could we find out?

These questions and more are artfully and skillfully broached in Edwin Abbott's mathematical classic "Flatland." Even if all you want is an intersting science fiction book, "Flatland" will do the trick. But for those who want a great "thinking" novel, "Flatland" is an outstanding choice!

Yes, many young people have been required to read Flatland against their wills. Yes, many people have missed the real point of the book. This book stretched the mind and imagination in ways that are fun and challenging. The author might not have been entirely serious in writing the book, but nonetheless provided serious food for thought.

I believe Flatland is an excellent (and quick) reading experience for minds in the formative stage, a stage I recommend maintaining throughout life. The book's theological implications were the most important to me. I had always wondered where heaven might be, how God can see inside us, and what the spirit is made of. I do not know if extrapolating the Flatland concepts into a fourth (or fifth) physical dimension reflects ultimate reality, but it provides a sufficiently possible and plausible explanation to remove rationalist objections.

The 3-D sphere that intersects the plane of reality provided the "Aha" moment. The sphere embodied perfection and could mysteriously appear and disappear. Explaining the view from above the plane to a flat square is as difficult as explaining the spiritual realm to a person unable to envision beyond the world seen with the eye. A greater-dimensional being floating above the plane can see inside the geometric shapes, reach inside their skins without intersecting their boundaries, think far more complex thoughts, and take them out of their limited reality to a better place they could not have imagined. If a Flatland person had no thickness, he would have no volume by our reckoning, and therefore no real existence. If there is a spiritual dimension and a person has no thickness in that direction at all, then he may not really exist either.

We have learned to adjust to modern concepts of reality that are no longer Euclidean and Newtonian. Perhaps we need a view of creation that is not limited by unfounded presumptions of limited dimensionality. After you ponder the concepts of Flatland and extrapolate them to your life, I wonder what new thought may form.

+++++

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."

+++++

The persecution of individuals is an abhorrent way of life in some lands. To be repressed simply for preaching a new view of things. To be imprisoned for your beliefs. I am thinking, at this moment, of one individual in particular who has had to suffer the humiliation of life without parole simply because he chooses to see things in a different way. Should the fact that this person is merely a square (four equal sides and corners) be any kind of an impediment towards our full understanding of him? As a recent convert to three-dimensional worlds, the author of "Flatland" (given, originally, as merely A. Square) describes his own two-dimensional existence as best as he is able. It is hoped that perhaps by publishing this petite memoir of his world and experiences he may shed new light on his predicament and perhaps even win a follower or two.

The world of Flatland (as opposed to our own multi-dimensional Spaceland) is a simple one. In it, the more sides an individual has, the (supposedly) greater intelligence and influence. Therefore it stands to reason that circles (which is to say, many sided polygons) rule as priests and all hexagons, squares, triangles, etc. hope to someday ascend or let their children ascend to that most worthy class. Women, sadly, are given short shift. They appear as lines (though the narrator does concede later on that they are perhaps more accurately described as very thin Parallelograms. The narrator goes on to describes how shapes in Flatland recognize one another, what their lives are like, and even gives a bit of brief historical background regarding the great Chromatic Sedition that almost made all shapes equal under the eyes of the law and society. The square then recounts the adventures he had when, in a dream, he approached Lineland and then was visited by a sphere preaching the gospel of the Spaceland. With the discovery of a third dimension the square is given to preaching about this new place to his fellows and, for his efforts, is summarily arrested and cast into prison from whence he writes this book.

"Flatland" was originally published in 1884, a fact that places some of its odder elements into (ha ha) perspective. Appended with a Preface that accompanied its second revised addition, the "author" (A. Square) responds to those critics that accuse him of classism and sexism. The square admits that years in prison may have, since the publication of the book, given him greater insight into both women AND his "betters". Just the same, it's difficult for a reader today to hear that women are "consequently wholly devoid of brain-power, and have neither reflection, judgement nor forethought, and hardly any memory" and not feel a little put out. On the other hand, we're dealing with some serious satire here, and we should treat the book accordingly. In general, it's a delight. Paving the way for such modern classics as "The Phantom Tollbooth" or even "A Wrinkle In Time" (the latter making at least one direct reference to "Flatland"), the book is a satire in the finest sense of the word. The narrator is, undoubtedly, unreliable which makes the entire book just that much more enjoyable. Author Edwin A. Abbott put an extraordinary amount of effort into this story. As is often the case with authors that slum in fiction, children's literature, or works of humor (right off the top of my head I'm thinking of Gilbert & Sullivan and Sir Arthur Conan Doyle), "Flatland" was written as a bit of fluff and ended up (whether Abbott liked it or not) as the author's best known work.

Though a lovely concept, this book is perhaps best read by teens and adults rather that kids. I'm not saying that there won't be the spectacularly brainy ten year old who's a fan of both Math AND English and speeds through this book like butter. I'm just saying that such a child is in the minority and that you probably shouldn't foist a tale that contains such sentences as "Now, all our lines are equally and infinitesimally thick (or high, whichever you like): consequently, there is nothing in them to lead our minds to the conception of that Dimension". You get the picture. One fact I discovered to my own delight was that this book does not, in fact, require a firm grasp on geometry. It couldn't hurt, and I'm sure you'll get quite a lot more out of it than if you've heard of angles or circumferences, but it's not a prerequisite for enjoying this tale. As long as you've a certain amount of imagination and a will to suspend disbelief, you should be in the clear.

The Saturday Review of Literature once said that Flatland was, "One of the best things of its kind ever written". This seems to me to be somewhat backhanded praise since very few "things of its kind" HAVE ever been written. And shouldn't it be unequivocally be pronounced the best by default alone? To my mind, the book's well worth the reading. It deserves its praise and should be remembered amongst the best of the fantastical satires ("Gulliver's Travels" for example). It's a short book too, so you've really no excuse for not reading it. A delightful dip into the unknown.

As a math major, I really enjoyed this book. It introduced the concept of multiple dimensions without sounding too much like a textbook, and romanticized geometry without straying too far from actual facts.

I thought the personification of the shapes and lines and points was very well done. I especially enjoyed the sections where A. Square explains how two dimensional shapes see, hear, move, and live. Although it could be slow at times, it really helped to visualize how creatures of other dimensions might behave. Especially those of a fourth dimension, since we live in a three dimensional world.

The book is highly conceptual, and while I think that someone who isn't well versed in math or theory could enjoy this book, I think that someone with at least basic understand of shapes, dimensions, and theory would come away with more. I would give this book a 4/5 though, and recommend it to all of my nerd friends, and anyone who might be interested in learning a little something about math through a fictional medium.

This book is often recommend by theoretical physicists and mathematicians (most often mathematicians involved in hyperdimensional topology) to their students.

It was written by a Shakespeare scholar in Britain more than 100 years ago. The reason it is recommended by theoretical physicists, etc., is it provides the reader with a framework for understanding and trying to visualize dimensions above or beyond our ordinary four-dimensional world (length, width, heighth, space-time).

It deals with a two dimensional world with two dimensional beings and what happens when a third dimensional being interacts with a two dimensional world and what the two dimensional beings would see. It also does this in terms of a one dimensional being and one dimensional world interacting with a two dimensional world and two dimensional beings (or structures).

This book written with apparently some intent on commenting on Victorian England and its values (with what appeared to me to have some misogynistic comments within it), was otherwise an enjoyable book and really does provide a good analysis on multi-dimensional view points and visualizing or imagining hyper-dimensions.

If you are interested in advanced theoretical physics, hyperdimensional geometry or topology or mathematics, this is a very interesting book and may be useful. If you are just interested in a good unique science fiction story, I would highly recommend this. This is not an (explicit) math or science book - so you won't find any explicit mathematics (i.e., no math is required).

Excellent.

This was another oldie I found on my bookshelf unread and then found out it is free on goodreads. I will definitely be taking advantage of the free classics on goodreads.

This book is highly conceptual and the first half is very slow, but it really makes you think. I enjoyed the breaks I had between reading this book in which I could contemplate how a 2 dimensional being would comprehend a third dimension or how I could possibly comprehend a fourth.

The first half describes the two dimensional world in which the protagonist lives. The social structure is definitely dated. This novel is very sexist, but it may have been the norm at the time.

The second half of the novel describes the square protagonist's adventure into the three dimensional world and his resulting evangelizing. This part was more enjoyable to read than the first.

I give this novel a 3/5 because of the slow start and the dated vocabulary and structure. If you are a math nerd or like to think about crazy ideas, you will really enjoy this.

I heard about this book in a chemistry course I took in college I think it was. Several years later I had the chance to read it. I am very glad that I did.

Not only does this book give a reader a new perspective in looking at space and maybe even time, but might also be extended to give a new perspective on almost anything. It may show us that at least in many cases, it is how you look at something that can determine what you see.

In any case, the book helps readers get an intuitive idea of what 4 (or maybe more as well) spacial dimensions mean. That is not as easy a thing as you might think. Give it a try before you read the book and see. I think that I got at least a glimpse as I neared the end of the book.

The author used a method of showing how worlds with fewer than three spacial dimensions might operate, and how a higher dimension being would be perceived by them and vice versa. This concept was used in many respects in Rucker's more recent book SPACELAND - also worth a read if the subject interests you.

I have read that Flatland was also originally meant to provide some social commentary, but this may be in large part lost on us today as times have changed I guess. Or maybe not?

The book is short and not that mathematically challenging if at all. Give it a try and I promise you will learn something.

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.

This is a book, indeed a fable, that was exquisitely designed to expand the mind. By showing how incomprehensible a three-dimensional world would be to two-dimensional entities, Abbott opens the door, and the mind, to speculation on higher dimensions. That is why the principles of this story are summarized in virtually every text dealing with the 4th dimension.

I believe Abbott framed this tale primarily to serve as a philosophical and mathematical justification of spiritual and "heavenly" subjects. After all, if a Sphere seemed a supernatural entity in Flatland, would not a 4th Dimensional entity seem so to us? I suspect that Mr. Abbott was also a Freemason, since the "regular progression of science from a point to a line, from a line to a superficies, from a superficies to a solid" is the way Freemasonry explains the process by which the Deity brings the four levels of existance into being. Actually, this is a neo-platonic teaching device that can be traced through the literature of the Renaissance, via medieval Spain, to Alexandria....
An examination of Theosophical Society literature from this period will also show a fascination with the 4th dimension as an explanation for spirit phenomena. Personally, I believe that this train of thought is still a quite valid analogy.
I found this book a joy to read, but then, I was trained in classical Euclidian geometry and formal proofs as a boy. I understand that such training is quite extinct in most modern public schools....

Flatland is a two-dimensional unvierse, inhabited not by people as we know them, but by shapes - triangles, polygons, circles, etc. The narrator, A. Square, introduces the readers to the customs, class distinctions (based on geometric shape), male and female roles, how to tell one another apart, and on general life living in a world of only two dimensions. Square's life is turned upside down when, on the eve of the new millenium, a strange visitor literally drops into his home. This visitor - a Sphere - has chosen Square as his apostle to teach the two-dimensional masses about how more to life there is beyond their flat world view.

At first glance, this comes across as a novel about higher math: geometry, 2- and 3-dimensions, the possiblity of higher cimensions after the third, etc. Author Edwin Abbott examines and illustrates what life would be like living in such flat world, in which everyone resembles a straight line - whether the "person" is a circle, a triangle, or a square - because only one side of them can be seen. On a deeper level, though, Abbott offers a scathing parody of Victorian society. (After all, the book was first published in the late 1880s.) Class distinction based on birth is rampant. The "lower" beings, such as isocoles triangles and irregular shapes, live in shame and are looked down upon by society. They will never attain the good paying jobs or respectability that those shapes with more sides have. Women are seen as merely lines, very dangerous to society, though, so they must be kept uneducated. Their main purpose is to help their male counterparts achieve higher and higher status through breeding.

Quite a remarkable book for its time.

You start appreciating the beauty of this work once you understand the context in which it was written and once you realize that it was written in the 19th century by a teacher for pedestrian consumption. The folks back then were probably not throwing around the word 'Dimensions' in everyday conversations as we do today.

It would be an exaggeration to say that I shed three dimensional tear drops for our Square, the Galileo of the two dimensional world who had to face the Inquisition led by the Circles and Polygons. But I hope he will take solace in the fact that I'm now a thorough convert to the Gospel of Infinite-Dimensions. Though I do have to admit there is an occasional relapse during my showers, when I find myself singing along with the monarch of the PointLand:

"Ah, the joy, ah, the joy of Thought! What can It not achieve by thinking!
Its own Thought coming to Itself, suggestive of Its disparagement, thereby to enhance Its happiness!
Sweet rebellion stirred up to result in triumph!
Ah, the divine creative power of the All in One! Ah, the joy, the joy of Being!"

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.

This is a book, indeed a fable, that was exquisitely designed to expand the mind. By showing how incomprehensible a three-dimensional world would be to two-dimensional entities, Abbott opens the door, and the mind, to speculation on higher dimensions. That is why the principles of this story are summarized in virtually every text dealing with the 4th dimension.

I believe Abbott framed this tale primarily to serve as a philosophical and mathematical justification of spiritual and "heavenly" subjects. After all, if a Sphere seemed a supernatural entity in Flatland, would not a 4th Dimensional entity seem so to us? I suspect that Mr. Abbott was also a Freemason, since the "regular progression of science from a point to a line, from a line to a superficies, from a superficies to a solid" is the way Freemasonry explains the process by which the Deity brings the four levels of existance into being. Actually, this is a neo-platonic teaching device that can be traced through the literature of the Renaissance, via medieval Spain, to Alexandria....
An examination of Theosophical Society literature from this period will also show a fascination with the 4th dimension as an explanation for spirit phenomena. Personally, I believe that this train of thought is still a quite valid analogy.
I found this book a joy to read, but then, I was trained in classical Euclidian geometry and formal proofs as a boy. I understand that such training is quite extinct in most modern public schools....

It is hard to imagine such an intense combination of science, creativity and spirituality all rolled into one. The book is not an easy read but definitely a fascinating one. The creation and description of a two dimensional society in such great detail leaves one full of amazement. The idea of introducing an additional dimension, incomprehensible to people of two dimensional world as an indicator of our own limitations in realizing and recognizing what lies beyond or within our world is very touching. The "Upward not northward" notion, that the Square so tried to explain and preach could perhaps best be translated to "inwards not outwards" for us in our own world.

Although this book was written in the time when Hinton and his pseudo-analyses of higher dimensions ruled the popular masses (mostly as a semi-plausible explanation of the existence of ghosts), it delves a lot deeper into the nature of things, and, as noted above, even delivers a forceful parody of the society.
The author of the book is a Square, a perfectly flat creature that lives in a flat society in an ideally 2D world. His four equal sides (irregulars are always killed or imprisoned due to the confusion of recognizing an irregular figure from looking at its side) give him the status of lawyer (the number of sides denotes the social rank). His amazing visions and visitation give this flat and narrow-minded individual the understanding of the worlds outside his own.
First is the visit to Line Land, where all persons are lines of different lengths and vision is limited to a single spot. Naturally, bypassing anyone is a geometric impossibility, but, strangely, the denizens of that land live happy lives.
Next is the visit of mysterious Lord Sphere, who, due to the lack of dimensionality, has to resort to manifesting himself as his cross-sections which the square can see. He delivers to the Square the Gospel of Three Dimensions, and, when the complacent Square refuses to comprehend, Spherer pulls him out into 3D (i.e. puts him at an angle to his own flat space).
Finally, we are given a view of Point Land, inhabited by but a single creature of no dimensions and no coprehension of others beside it, hearing all and attributing all to its own grace and might.
The book is extremely sarcastic and acidic: a 2D woman is a straight line, invisible when seen head on ( and lethal if met headfirst due to her sharpness), and is always reduced to constantly emit her Peace Cry. Color is forbidden because it causes too much confusion. Criminals are those whose sides are not equal. Etc. etc., etc.
Read this book and stop to think from time to time - this is the sort of book that rewards thought.

I read this book because it came up in several conversations I have had recently about higher dimensions and also because it showed up in some reviews of modern physics (quantum physics) books that I have considered reading.
The book is just over 130 years old, but is still a fairly easy read. It includes some social commentary on life in Victorian England, of which I care very little. The meat of the book for me is in helping the reader to pontificate the existence of higher dimensions by showing how crazy the idea of two dimensions would seem to a line and how ludicrous the idea of three dimensions would be to a shape that exists on a plane.
The book likely will not help you to picture hyper dimensions, as doing so requires a dimension which we have not yet discovered and may in fact even be too profound for us to fathom. That being said it is still worth a read if you wish to expand your mathematical understanding of dimensions or as a warm up to trying to understand some of the concepts presented in quantum physics.

Like many readers and reviewers, I heard of Flatland long before I got around to reading it. I expected it to be conversational in tone, but all about the geometry of one, two, three, and four dimensional space. To my surprise, the book is as much about the foibles and prejudices of England's class-based society as it is about the explanation of contemplating more dimensions than one can directly perceive. While it has valuable insights on both dimensional space and class politics and mobility, as well as a light, humorous, conversational tone, the mix is an odd one, and ultimately a combination that is bound to be a bit disappointing to those reading it solely for the math and those reading it solely for the social commentary. A good, ground-breaking book, clearly ahead of its time, but neither a light, pleasant read nor especially deep on the substantive topic. Still, a short, intriguing read for those who like to think about abstract concepts, both mathematical and political. Recommended. Donald J. Bingle, Author of Forced Conversion and GREENSWORD: A Tale of Extreme Global Warming.

Much has been said about how Edwin Abbott's "Flatland" is a fun and thought-provoking mathematical fiction novel, introducing readers to dimensionality by personifying geometrical shapes. As a high school math teacher, I first read it planning on using it in my class to teach geometry. However, almost as interesting and its mathematical observations are its metaphors and, in my opinion, satires of Abbott's 19th century society.
All inhabitants of the novel's world, dubbed Flatland, are polygons, the narrator being a square. Flatland features a strict caste system, with a polygon's class being determined by his number of sides. A square is higher on the social order than a triangle, for example, yet lower than a pentagon. The rulers, or priests, are circles. Well, actually they are polygons with very many sides, approximating a circle. The lowest figures in Flatland are women, who are straight lines. One can interpret this fictional social order in a number of ways, including accusing Abbott of being classist and sexist. I happen to see this as a critique, even a satire, of our (spaceland's) social order, replete with classism and sexism. "Flatland" also spoofs eugenics and political short-sightedness, so there's plenty to choose from.
After introducing Flatland's social order, the narrator describes a journey he takes to lineland and spaceland, which offers a great way of looking at dimensionality, even for mathematics laypersons. I'd advise reading it slowly or even more than once to be sure your mind grasps all the interesting narrative and dialogue.
Mixing a clever introduction of mathematical concepts with an element of social satire, "Flatland" is well worth reading, even for those who are normally averse to anything that has to do with mathematics. While I still plan on using this novel to teach geometry, perhaps I'll also infuse some social justice issues into my lessons.

Flatland is a well-written, timeless satire. Author, Edwin Abbott, was an educator, theologian, and mathematician who lived and wrote during the Victorian Age with all its narrow-minded weirdness. That might seem sufficient reason to run, not walk, away from purchasing this book. Two reasons though to buy and read it: Best reason first, it is thought-provoking and requires the reader to imagine a --perhaps-- different realm and mode of existence. Second, the message is relevant even now when Western societies, as a whole, rarely question the critical social importance of quality, universal education.
How easy is it though to let our thinking become just as two-dimensional when we are contending with an intransigent "other" or seemingly immutable status quo?
Flatland is an engaging read that is short enough, and rich enough, to warrant rereading. Remember, Ladies, it IS a satire authored by an educator and father who valued his daughter as an intelligence superior to the education and opportunities which would be available to her and women like her.

The justly famous Flatland by Abbott stands out for several reasons
1. Its old Victorian style writing which is written from the somewhat "distant observer" viewpoint with the accompanying Englishness to go with it. It is full of social mores of the time (1884) such as the role of women in society or the very specific roles of the "lower classes" and those of the higher levels of society. Included also in this is the social graces themselves where his "feeling" inserted into the book as a means of differentiating various shapes is really a metaphor for the almost repugnant consequences of a meeting between a peasant and a member of the Aristocracy. As such the book is a superb example of he Victorian Age.
2. Another aspect, maybe not so much mentioned, is the fact that the book presents a fine example of the fact that people are trapped by their own culture/upbringing, this time dealt with through the idea of a 2 dimensional being not being able to comprehend 3 dimensions. Apart from the fact that the mind is not able to get around the concept of dimensions higher than the usual 3 I believe the book was intended maybe even accidently to support the idea of a prison of your own culture. However Abbott goes on to show that people are infinitely adaptable and there are ways to meet these seemingly insurmountable challenges. Again a path breaking book when looked at from this angle, who before Abbott would have considered such a view.
3. Finally the book presents many wonderful examples of the illumination of strange concepts not even considered in ordinary life through the vessel of the trek of the square who attempts to grasp his new world with the aid of a sphere.
A wonderful little book containing hitherto unexpected insights.

In the imaginary world of Flatland, everybody is some kind of geometry shape. Flatland has two dimensions, which we call length and width. There is no third dimension, which is the height. If I were in Flatland, I probably would have been a square, like the narrator of the story. If I were a square, I’d be smarter than a triangle. My brother would be a triangle. Like the narrator, I believe that I have one more side than a triangle. I would like to have more sides and larger angles, so that I would be more important in Flatland, but I just have four sides. The more sides and angles that someone has, the more they would be better and smarter. The bigger your angles, the smarter you are, and the circles rule.
Triangles are lowest in society, because they only have three sides. The steeper your angle and narrower your base, as a triangle, the dumber you are. The dumbest ones in the triangle group are the criminals. The criminal class is used for teaching school children their manners. The children practice greetings on the criminal triangle, which is chained up, until the triangle is worn out and dies. Then the triangle class is required to replace them. Girls are treated badly. They are considered to be dumber, because the women are straight lines. They have only one side. They can be dangerous if they become angry, because they can pierce right through anyone, so all the other shapes try to control them. They have no hope of improving. Sadly, they just have to live with keeping one side. They are not considered smart, because there isn’t enough room for brains. If they could remember longer that they never can improve, the writer thinks they would be upset.Through a special marriage, children can have more sides than their parents. The main square, the lead character, has two sons that are pentagons, because they have five sides. His grandsons have six sides. It means that they are smarter yet. If you have a family, they become more important, if each generation has one more side. In Flatland, there are many details about how everyone lives, which are very interesting. The towns, the laws, why colors were banned, and the special rules that women must obey are what the square talks about. When the writer was visited by a being, which had three dimensions, the climax of the story appears. This is where he discovers another world. Then something you’ll need to read about in Flatland will tell you what happens to him. When you read Flatland, it makes you think about why some people are born different than others, and how dangerous it can be to be different when no one wants to believe it’s true.

Even though this was written around 1880 it still is one of the most creative science fiction books I have read. This is a real mindbender. Edwin A. Abbott made me realize in his novel how narrow minded I actually am even though I consider myself a very open minded person. I came away from this book realizing their are more dimensions out their that science has yet to discover. This book also has a hidden message in the book that most people are completely ignorant about the world around them. They think they know it all and have no desire to educate themselves further than the little education they already have.
People believe in myths and assumptions and are ignorant and don't bother to seek the real answers in life. This message was very powerful to me and an important lesson. This author was concise, wasn't wordy like so many sci-fi/fantasy authors now, and didn't fill the book with nothing but metaphors and similies, and got right to the point in his writing. It took me the same time to read this book as it takes me to read most of the long wordy sci-fi/fantasy novels out their now. When a 700-900 page novel takes the same time as a 150-250 page novel to read that means that 900 page novel is of very poor quality.

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.

I just finished the book, and let me say this: just because it is talking about polygons and n dimensions does not make this book a math book! This book is first and foremost a book on philosophy and a social satire, and secondarily a book on religion.

Why?

Well, the long running theme is the socio-economic class system of Flatland, which is not simply unjust, but more accurately elitist, and misogynist. Polygons are just metaphors; well-off people get better off more quickly for every successive generation, and low poor working class people are stuck in a perpetual circle of poverty but always wishful to achieve higher status in the next generation.

The trips to Lineland, Pointland, and Spaceland illustrate the stubbornness of mankind and the irony of that stubbornness. After his dream that Lineland people and Pointland person are too stupid to accept Flatland, Square himself was regarded as too stupid to accept a higher form, i.e. the Spaceland. The Sphere, in turn, refused to accept an even higher form just after he admonished the Square for refusing to accept a higher form to him.

Granted, the details on geometry and polygons and the line on 4th dimension are pretty well-written, but such focuses are brief in this 81 pager, and briefer still when their metaphorical powers are accounted for. Don't just read the words. For a classic like this, one must read between the lines.

Flatland is subtitled "A Romance of Many Dimensions." I wouldn't call this book is "Romantic" in either the original or the modern sense of the term, but it certainly does include many dimensions. . .
And much more. With this one little book at the centre, one can discuss a wide array of topics: literature (late 19th century British satire), history (relate the satire to Victorian society), mathematics (beyond what you get from your typical proof-laden geometry class), physics (String Theory fits nicely), art (the influence of such mathematics on artists such as Dali and Escher), theology (pythian theology: God as The Being of Infinite Dimensions), and even a little climatology (how does it rain in a two-dimensional world?).
The first part of Flatland is an extensive description of life in a two-dimensional society. This is where most satirical elements can be found, but you don't have to know about British Victorian-era society to benefit by learning to view
physical reality more perceptively. How often would you ordinarily stop to consider what the social interactions and the houses and the weather and the class structure and so forth of a two-dimensional world might be? In addition to gaining a new appreciation for planar geometry, you will learn how very fortunate you are to have the extra dimension--but what if someone other entity is thinking the same about. . .
In the second part of Flatland, things really get spicy from the mathematical/physical/philosophical perspective. If you thought the preceding material was mind-expanding, just wait until A. Square travels to Sphereland, Lineland, and (my favorite) Pointland. This engages your brain in a way that no ordinary, prosaic math book can. Everything is explained in a manner that is easily understandable--but at the same time impossible to comprehend. You'll know what I mean when you try to apply the transition from Pointland to Lineland to Flatland to Sphereland to a like voyage to a fourth spatial dimension, and it seems like you should be able to do so, but you can never quite visualize the next dimension. You simply CANNOT. But, oh, what a savory intellectual treat it is to try!
Flatland does not have a plot--at least not until the very end, which is the book's most enduring satirical moment. How sad that this is based in reality. (It is also much like something one might read in. . .dare I say. . .a dystopia.)
If you really want an intellectual trip, contemplate temporal dimensions in a like manner. Yummy. . .
. . . but Abbott poses an even greater enigma: why is it that Flatland residents with the most acute angles are the most mentally obtuse (and vice versa)??
~pythia~

This is not a romance in the modern sense. It's more a dystopian tragedy and satire.

I first heard of it when researching fiction stories that incorporate math. I love Anno's Mysterious Multiplying Jar and Sir Cumference: And the First Round Table (A Math Adventure). This is quite a bit drier than those more recent books, as well as being intended for an older audience. I listened to it while working on a mind-numbingly boring project. If I'd attempted the book in other circumstances, I'm not sure I would have made it through, but I'm glad I did.

Much of the book is taken up describing Flatland and what it's like to live there (spoiler: not so great.) This is interesting from an academic stand point, but not a dramatic one. Toward the end when the action finally started and during the conclusion I was rooting for the Square main character (guess how that worked out.)

As an author, I know how difficult world building is. I've been working on a science fiction piece lately and it's incredibly challenging. Even with the book I have out, [...]where only one detail of our world has been altered, I found it incredibly difficult to portray it accurately. Abbott did a very good job with this. I don't think I'd read it a second time, but I'm glad to have read it once.

Flatland by Edwin A. Abbott was originally published in 1884 and is proof that great stories survive the test of time. It's a mind-bending adventure starring a protagonist that lives in a two-dimensional world. The story is filled with humor, romance, and satire. Flatland is a captivating and delightful invitation to free our thinking from the artificial constraints we constantly impose on it.

Certainly the saving graces of this little gem are its brevity and Abbot's creativity. Much more of the descriptions of life in Flatland would have bordered on tedium. However, the explanation for the banishment of color in Flatland was very clever and one of the better parts of the story. As it is, it's a humorous, demure satire in the Swiftian vein whereby the protagonist, A. Square, teaches us about his world, has a series of adventures, and learns lessons about life (and mathematics) along the way.
I question its value as a teaching tool, though. I fear the Victorian niceties employed in the exposition will seem stilted and nigh unbearable to today's younger audience, especially if assigned as schoolwork. But, I think those who already grasp the mathematics involved (basic geometry) will enjoy it. Also, A. Square's unabashed enthusiasm and thirst for knowledge are qualities one would happily encourage in students.
My favorite part of the whole book has got to be the visit to the King of Pointland. The way Abbot so succinctly portrays humanity's capacity to ignore evidence that does not conform to preconceived notions, then force the facts to fit long established beliefs is a stroke of genius. In Pointland, ignorance really is bliss.
This little tale definitely provided excellent entertainment for the price I paid here at the store. If it sounds interesting to you, I suggest putting it on your wish list, and then adding it to the next purchase you make (your wallet will barely feel it).

Back in the nineteenth century, the book was described both as being "fascinating" and "mortally tedious". I can see how both apply. For the most part, the book is amusing. It follows the world of A. Square who is, as his name indicates, a square. The first section of the book describes the world of the square, Flatland. The inhabitants range from the women who are straight lines, to the working isosceles triangles to the grand priest, a polygon of a great many sizes that he appears as a circle. The society boasts of a strict hierarchy where figures of greater sides are thought as smarter and better than the rest. The book describes how the shapes recognize each other. The book even goes into detail about a social upheaval where colour was introduced. If any section could be described as tedious, this part would be. However, picturing the actual society was indeed, very entertaining and amusing but at times, certain facts seemed insignifcant.
The second half of the book devotes itself to describing the discovery of other dimensions by A. Square and the consequences of him trying to attempt to explain these discoveries to his world. This part of the book would be the part considered prophetic and charming. First, A. Square stumbles upon one dimensional world. Then accompanying a sphere, he visits a third dimensional world and then a zero dimensional world (a point). Through his discoveries, he even contemplates universes of higher dimensions, the fourth and the fifth and so forth. Eventually his efforts to spread the knowledge end in vain with social ostracization.
The book truly shines in the detail of its description of the different worlds. In language, it could be described as somewhat bland, and stiffnecked but the worlds it describes are truly fascinating. Plus this book is a classic sci-fi and if you ever want to read more about hyperspace and so forth, many non-fiction books refer to Flatland.

If you're obsessed with math but need a break from equations and formulas, pick up a copy of Edwin Abbott's Flatland and go to town. Published over a century ago, this book illustrates the faults of politics and nobility as it explores the delicate relations between the inhabitants of Flatland. As the book progresses it diligently explains the factors of the known dimensions, and the obstacles that separate them. This book is a great read for anyone who loves history, math, and a good laugh.

This book follows a square that is set in his ways about the world. As an inhabitant of Flatland, this square ranks as a "Professional" or "Gentleman". He is joined by every other imaginable regular figure, and all have their place in the world according to their shape. The chain of nobility begins with women, who are, as Abbott repeatedly mentions, "straight lines". Following the women are Isosceles Triangles, who make up the army and servant class. Next come Equilateral Triangles, followed by Squares, Pentagons, Hexagons, and the rest of the regular Polygons follow suit. At the top of the pyramid rests the Priestly Circles, along with Polygons made up of so many thousands of sides they appear to be circles. Each level is smarter than the previous, starting with women who are like goldfish in their mentality, and ending with the Circles who occupy the highest roles of society. The second way Abbott connects the generations is highly entertaining for me, so I'll just leave that treasure for you to discover on your own.

Abbott has a lot of fun in creating the geometric figures' way of life. For instance, he has made recognition of another figure possible by sound, sight, and touch. The women have to take special precaution due to their dangerous shape. Abbott goes to the extreme when describing their circumstances, which I believe to be rather humorous.

The second part of the book follows the Square as he is shown dimensions that are unimaginable as well as down right silly in his perspective. He's shown Lineland, the world of one dimension, in a dream. Later a figure appearing to be a magical circle shows him the way to Sphereland, the world of three dimensions. Lastly, the Square is shown the world of Pointland, a place of no dimensions consisting of simple dots. Each world evokes a different response from the Square as his mind is opened to the various spaces surrounding him.

All in all, the book was a fun read. The best part to me was Abbott's many explanatory diagrams. However, being a female I was severely disgruntled by the low intelligence and mockery of women. I did find peace in knowing that our sharp points could be the weapon of ultimate destruction, as ironic as that may be. The line of nobility definitely revealed the books age, and also evoked several strong feelings I have towards equal rights. I love how I was connected to the troubles and controversy of an older era while learning about present day mathematics. Honestly, if you are a person with strong opinions who loves to argue, this book will give you and your book club things to talk about! One factor that kept me zoned in throughout the story was the reoccurring mention of the phrase "straight line". This redundant fault of Abbott's was a rather comical feature for me, and I have to say it was interesting to see how many times it popped up.

This book is a fun way to view the world as it exists in two dimensions. The flashbacks to historical ideals make for a highly political and controversial read that will surely keep the reader interested. Once Abbott starts explaining the multiple dimensions and their connections, the book becomes a whirlwind of that "I know what I mean but I just can't explain it" feeling of frustration and determination. If you or anyone you know enjoys geometry, controversial issues, and puzzles, this book is sure to be a hit.

For hundreds of great reviews of young adult books by young adults themselves, be sure to check out notrequiredreading.com.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

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.

I can see this book being interesting to two types of people.
First, the book is based on geometrical concepts to create a vision of Flatland. The descriptions of how to visualize different dimensions and the question of higher dimensions are simply explained. I believe someone who knows nothing about math would find the explanation satisfactory.
Second, the book is a satire of Victorian society. It's important to remember that the author does not actually think women are inferior, just that he is mocking the world around him. I also found an interesting passage where the author describes how the inhabitants of the southern latitudes (e.g., Africa) are savages because their air inhibits the ability to distinguish shapes. This compares to the northern latitudes (i.e., London) where fog allows better sight. Trust me, it will make sense when you read it.
This is just one of the examples of satire in the book. I thought the book was excellent and can easily be read in a few hours. Plus, it costs a buck..

Flatland: A Romance of Many Dimensions is an 1884 novella written and illustrated by Edwin A. Abbott. Here, a square that lives in a two-dimensional world relates his experiences there along with his travels in one- and three-dimensional worlds.

The social classes of the country of Flatland are described in such a way as to lampoon the Victorian social hierarchy. Every inhabitant of Flatland is devoted to climbing the social ladder; order is prized more than liberty; women belong to a lower class of their own. Abbott here is not particularly subtle in his criticisms, and one must imagine that the narrow thinkers that accused Abbott of misogyny really must not have been paying very close attention (these are the nineteenth-century analogs of people who think Stephen Colbert is really a conservative).

This dated aspect of the tale may not have particular relevance for a modern audience, but Flatland still has plenty of value. Abbott's one- and two-dimensional worlds are impressively imaginative and quite well thought-out. Flatland is immersive, and along the way, Abbott manages to work in a number of profound thoughts on existence.

Flatland's lasting legacy is its discussion of dimensions. Just as Abbott takes the reader through the two-dimensional square's travails in comprehending a third dimension, so the reader is challenged to imagine a fourth. And Abbott does an excellent job of this, whether one considers this fourth dimension as time (as per general relativity) or an extra aspect of space (this is quite a bit harder to imagine). It also works if you consider the tale an allegory for God and the spiritual realm (Abbott was a rather prodigious theologian), which is not by any means a stretch given the "preaching" done in the story. In any case, it's marvelously thought-provoking.

On the whole, Flatland is a well-imagined, well-reasoned, stimulating work.

Even after 110 years, Flatland is a fascinating book. We are
introduced to life in Flatland -- a 2-dimensional world --
through the eyes of a scholarly square, a respectable gentleman.
He teaches us the ways of Flatland, and then takes on a mind-blowing
adventure into the third dimension and beyond.
Through the Square's discovery, we expand our view of our own
world. We begin to wonder if we, the human race, are like inhabitants
of Flatland, blissfully unaware of all that we cannot see. We wonder
if we might even be as the King of Lineland, mightily ruling
our fragile Earth. We question the validity of our perceptions of
the world.
Reading Flatland requires full concetration, due to Abbot's dense
prose, but the results are spectacular. Take a look at Flatland
and expand the dimensionality of your universe.

This book was written by a theologian, not a math professor, and it's not about geometry. The author uses geometry to create a parable that was intented to help open the mind of the reader to spiritual reality.

What happens when a lowly square receives a revelation of a higher dimension of reality from a sphere, and then tells the other flat shapes what happened to him? He gets presecuted and thrown in prison. Does that sound vaguely like something that might happen in our world and has happened over and over again in history?

Anyway, it seems our Westen Civilization is getting flatter all the time. Read this book, and gain some insight into our human condition, and some funny insights into the culture of Victorian England. How can you miss at this price? This book really is a classic.

It is the second time I read this book, and it got me hooked again, with its geniality. The same time it talks about geometry, it also talks about politics, society patterns and interpersonal relationship. It is no doubt the work of a genius, as it was written so long ago and is still up to date and very accurate.