Flatland: A Romance of Many Dimensions

Alas, a few years ago, I should have said 'my universe': The Strange Case of Dr. Six Great Sherlock Holmes Stories. Alice's Adventures in Wonderland. Satan, Cantor and Infinity: The Lady or the Tiger?: Geometry from Euclid to Knots. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. From Geometry to Topology. Mathematics and the Imagination. Mathematical Fallacies and Paradoxes. An Adventure in Non-Euclidean Geometry.

Mathematics for the Nonmathematician. Mathematics and the Physical World. Quindi tranquilli, a Flatlandia ci ritroverete molto. Non incazzatevi troppo con Abbott se ce l'aveva con le donne. Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine. La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.

View all 4 comments. Jan 28, George rated it really liked it Shelves: Quite a charming allegory for the English society of the time, and boy does it show it's age. This is basically covered by everyone who reviewed this book, so I am not going to talk about that. What I noticed and I haven't seen anybody mention this yet, is the fact that at the time when this book was written Darwinian evolution has already grasped popular imagination. Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generat Quite a charming allegory for the English society of the time, and boy does it show it's age.

Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generation after that is achieved gets more sides until it reaches their version of perfection that is the circle. As I am aware people looked towards evolution with quite an optimism at the time and started envisioning utopias that will come to existence with careful work, selection and patience.

Just look at the squares enlightenment at the prospect of 3 then 4 and as many dimensions it can possibly go. Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts 4 dimensional cubes and glomes 4 dimensional spheres and not be rewarded. Both mindfuckery and awesomeness. Oct 18, Alice Cai rated it it was amazing Shelves: That's why the would is called flatland because everything is in 2 dimensions. It's so trippy and it's really funny too. I can't just give funny quotes though because you need to know the context from the beginning of the chapter and then the context of the chapter before that to get the humor.

Some quotes to give an idea of what the book is like: But now, drawing back to the edge of the table, gradually lower your eye thus bringing yourself more and more into the condition of the inhabitants of Flatland , and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table so that you are, as it were, actually a Flatlander , the penny will then have ceased to appear oval at all and will have become, so far as you can see, a Straight Line.

Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short often not exceeding half an inch that they form at their vertices a very sharp and formidable angle. Indeed, when their bases are of the most degraded type not more than the eighth part of an inch in size , they can hardly be distinguished from Straight Lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles, and by this name I shall refer to them in the following pages.

The author has been dead for years of course it's legal. The narrator, a shape living in a two-dimensional universe, has his thought-world turned upside down went he meets a mysterious being from a three-dimensional world. This notion of perspective and liberation from one's own perspective gives the work a The narrator, a shape living in a two-dimensional universe, has his thought-world turned upside down went he meets a mysterious being from a three-dimensional world.

This notion of perspective and liberation from one's own perspective gives the work a transcendent slyness and power as it offers a freedom beyond whatever the limited conceptions of the author were. Comes with illustrations showing the exciting worlds of triangles and such. View all 5 comments. Jul 28, Milica Chotra rated it really liked it. This Square hopes that his account "may stir up a race of rebels who shall refuse to be confined to limited Dimensionality": Also, in the first part of the book, Abbott cleverly uses geometrical concepts to criticize his own society e.

Bear in mind that "Flatland" was written in the 19th century, and if you like math, social critique and enjoy pondering the nature of the Universe or Multiverse - you'll like this book. A religious person might experience it on a different level, but I guess they'd like it as well. Aug 16, Paul E. What a fantastic little thought-experiment, only really half-disguised as a story. Through his witty little parable, Abbott manages to explore the physical, mathematical, societal, philosophical and theological without once spoon-feeding his readers OK, maybe there's a little bit of spoon-feeding in the earlier chapters.

It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years Oh, well; I suppose nothing's perfect Aug 24, Roy Lotz rated it really liked it Shelves: For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles?

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Or again, why blame a lying Isosceles, when you ought rather to deplore the incurable inequality of his sides? This is one of those delightful little books, so difficult to review because its charms require no toil to appreciate, and also because the book is so short you might as well read it an For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles? This is one of those delightful little books, so difficult to review because its charms require no toil to appreciate, and also because the book is so short you might as well read it and skip the reviews.

The charm of the book lies in its conceit, rather than its execution. Indeed, though certainly able, Abbott is not an expert writer; nor does he pretend to be. The genius of this book is in the simple beauty of its premise: What would life be like for a square living in a two-dimensional world?

Abbott wrings a remarkable amount out of this simple question. First, he gives us a satire of Victorian culture—perhaps the less enduring part of this work, though certainly keen and ruthless in its modest way. To me, the most interesting point Abbott makes in his satire has to do with education. The residents of Flatland spend all their time learning various methods to identify the shapes of others.

Flatland: A Romance of Many Dimensions

For if you are living on a two-dimensional plane, telling a square from a circle is no easy matter, as they all appear to you as flat lines. But of course, the more fascinating part of the work has to do with dimensions. How would the possibility of two dimensions appear to a one-dimensional creature? And how would the prospect of three dimensions seem to a two-dimensional creature? To the residents of Flatland, tales of cubes and spheres appear like so much absurd metaphysics.

Abbott uses this point to show how narrow is our mental framework, how completely blind we are to realities outside our everyday, commonsense world. Doing so, Abbott elevates this work from novelty to true art. For after satirizing the world we know, he gives us a glimpse of a world beyond. Mar 16, Jafar rated it really liked it. This book is just brilliant. People in this book live in a two-dimensional world.

They're not aware of, or can't even imagine, the third dimension. They have simple geometrical shapes like triangles and squares and other polygons. The higher the number of the sides, the higher the individual is in the social hierarchy. Those who have so many sides that they resemble a circle are priests. The land This book is just brilliant. The land is ruled by the Chief Circle. Squares are considered middle-class. Triangles are underclass and soldiers. The lowest status is given to women who are just straight lines.

He was either mocking the sexism and the rigid social order of the Victorian Britain, or he was a supreme reactionary. Life in two dimensions has its many challenges. As an example — everyone looks like a straight line. Shapes are recognized only when seen from above — in a 3D world. When you live on a plane and see everything on the plane level, everything is just a straight line.

The author goes to some length explaining how people can distinguish shapes similar to how 3D creatures like ourselves can have 3D vision.

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Life in Flatland is not as boring as you might think. A lot is going on. There are wars and revolutions too. The story is narrated by a smart Square who is visited by a Sphere from a three-dimensional world. It is only a point at first, then becomes a circle growing in size, then a circle shrinking in size, until it disappears. All the while, you have no idea where the circle came from and where it went to. There are countless fantastical things that the 3D guy can do in your 2D world — all magic to you!

Think of the implications for us if there is a fourth spatial dimension and something comes to us from the 4D space. Square is trying to imagine a world of two dimensions, and then taking the hero of the story on a trip to a one dimensional world, and in turn a three dimensional world. On Education The first part of the book basically describes the world of Flatland, which, as I mentioned, is a world of two dimensions.

In a way it is pretty difficult to imagine such a world, and how things would actually function considering that we tend to live in a three dimensional world. There have been suggestions that despite living in a three dimensional world, we only see things in two dimensions, but that is something that I would object to because, well, we happen to have something call depth perception that is if both of your eyes are functioning correctly.

The other thing that I found a little odd was how the children of the citizens of Flatland would progress up the social ladder, and while that may be the case when there is a system of universal education, this was not necessarily the case in a world without access to such education. This is where the social criticism of the book comes to fore. Flatland is an incredibly stratified society and the more sides you have, the higher up the social scale you happen to be, until you reach the point of a circle, where you pretty much have an infinite number of sides. However, my problem comes that when citizens of Flatland have children, their children will have one more side that their father women in Flatland are basically lines.

This is something that is only taught to those higher up the social ladder. Obviously, the higher orders won, and since that time colour, and any talk of colour, was banned. This is the thing about education, and that is that the more educated one happens to be, the more options that there tend to be open to them. However, the more knowledge one has, the more threatened those in power happen to be. This is why certain governments will go out of their way to actually ban books. In fact, despite the freedoms that we have today, there are still books being banned in our democratic societies, as well as attacks by certain elements of society against certain books, such as Harry Potter apparently it is designed to indoctrinate children into the Wicca cult.

Free and universal education was, and still is, a marvellous development, and actually worked to break down the structures of social classes. The problem is that these days state schools are being stripped of funding, so if you actually want a good education, then you have to pay for it. For instance, the school that I went to refused point blank to teach evolution because, well, it was a Christian school and in their minds evolution was wrong. I certainly felt the full wrath of that when I handed in a project on dinosaurs only to receive no marks whatsoever because I had written it from the viewpoint of the evolutionist.

Sure, while I accept that some people want to believe in a literal seven day creation, and that they want to scientifically prove that the world was created in seven days good luck with that by the way , the problem is that High School diploma exams tend to all test you based on an evolutionary basis, and good luck walking into first year biology subject and challenging the lecturer that evolution is wrong.

Yet not everybody can afford a good education, which means that a lot of people end up at state schools. There are a lot of really intelligent people that end up destroying their lives simply because they do not receive the same level of education as others, or they are dragged into the wrong social group than others.

Me, I was lucky, but not many other people are.

Flatland: A Romance of Many Dimensions

Which sometimes makes me wonder whether the reason our governments are progressively underfunding our public education system is to basically keep people stupid. One of the main reasons that a lot of left wing leaning individuals tend to be university educated is because that is where much of your critical thinking comes into play.

The nth Dimensions Now, Abbott was a mathematician, and in the same way that he is exploring education, he is also exploring concepts of higher mathematics. For instance, what would a society restricted to only two, or even one, dimensions be like. In fact, what if we took a two dimensional being into the third dimension — how would he react, and how would he be able to explain this extra-dimension that nobody in his world can experience. One thing we should remember is that Abbott was writing before Einstein decided to join space with time and make time a dimension.

For instance, in each of these worlds, everybody is experiencing time, which means time is a factor in each of these dimensions. So are they truly one, two, or even three dimensional worlds? The other thing is that we are all moving through time, from early to later. There is no way we can slow it down, stop it, or even reverse it.

Sure, there are theories, and of course movies like Back to the Future, but the reality is that it is still a force that we really do not understand. Secondly, if we did go back in time, would we even be able to get back to where we started, since by even going back in time we are changing the past, and thus creating a new future.

As such, we would then need a way to cross these time streams Sliders style to be able to get back to our original point of origin — thus we have the fifth and sixth dimensions as some people theorise.

As I mentioned, this book is probably more of a mathematical exploration of higher dimensions, and the possibility that they could exist. The suggestion here is that you can create a line from a point, a square from a line, and then a cube from a square. That brings us to our three dimensions. What do you get then if you extrapolate a cube from a cube — a tesseract. No, not the tesseract that happens to hold an infinity stone I suggest that they used the name because they though it sounded cool as opposed to actually knowing what it meant , but rather a four dimensional cube, as below: In fact, they even attempted to create a tesseract in Paris — the Grande Arch.

Well, only as good as you could do it in three dimensional space, but then again it is the same way that they create a cube on a two dimensional space. It is just that since we do not live in a four dimensional world, we simply have a lot of trouble experiencing, or even imagining, a four dimensional object. Mathematicians have long since rejected concepts because the idea either made their heads hurt, or it could not be replicated in real life. For instance, the concept of 0, negative numbers, fractions, and even the fact that there is more than one infinity and the guy that came up with that, despite all of his mathematical proofs, was laughed out of the profession and died in an insane asylum.

Finally, Abbott suggests that in Flatland, three dimensional beings could do things such as entering rooms that are locked, simply by going there through 3D space. This is a really interesting idea because it could have ways to not only explain the ghost phenomena, but also other spiritual ideas. Abbott was an ordained Anglican priest as well as a mathematician, and I could not help but think that his suggestion was that God, and in turn Jesus Christ, were in fact beings from a higher dimension how high is beyond me, but there is a suggestion in the Bible that God could exist outside of not only time, but of the sphere of probability in that not only does he see time, but like Dr Strange in Infinity War, is able to perceive every single possibility of every single decision and action ever taken.

This is why Jesus was able to appear in rooms that were locked, or even do things like walk on water. These days the idea of higher dimensions are being bandied around by scientists — super-string theory holds that there are 10, and there are some theories that suggest that there are many more — 26 for one theory I believe. However, a lot of this stuff does make, at least my head, hurt somewhat, and in the end many of these things probably just exist in mathematical constructs.

Feb 09, Harry Whitewolf rated it it was amazing Shelves: Don't be a square - read this book by A. Square; the author of this tale who describes the worlds of Pointland, Lineland, Flatland and Spaceland and the idea of other lands which mathematically and logically lie beyond the latter. This book has just joined the ranks of my all time favourite classics of original genius, such as Micromegas, The Little Prince and Ways of Seeing.

In fact, this book's better than those three combined. Nov 20, Amir Tesla rated it really liked it Shelves: Keep an open mind to the endless possibilities of life. Mar 30, aPriL does feral sometimes rated it really liked it Shelves: Dimensions are the point of the tale. And the line, the square and the solid cube. Sorry about being so oblique, but I often angle for a laugh at the beginning of a review, no matter how circuitous. The author Edwin Abbott Abbott with a wink and a smile introduces us to the science of geometry in the Victorian Age in this a cute story about A.

To understand the concepts that these surprisingly charming fantasy characters who live in a two-dimensional world illust 'Flatland' is amazing. To understand the concepts that these surprisingly charming fantasy characters who live in a two-dimensional world illustrate, I think you need to be either good in math or be a high school graduate. Nevertheless, if you have some mathematics education, this is a fun read which becomes something bigger on the inside. But I was very dubious, initially and I was afraid of a something coincident with the most boring math class I'd ever taken and too much eccentricity.

I circled my living room going around and around at least degrees, I think. Do I want to read 'Flatland', even for a monthly book club selection? A Victorian Romance, equal to no less than 0 in my estimation, about math? But, a distant chord projected tangentially into my attempts to square the circle and I realized I had transcended my doubts.

So, I reached a crossroads of sorts, an intersection in my thoughts. I devised a postulate for myself: I'm at a point between two directions - do I make a line towards the library, or use up valuable space on my Kindle downloading this book? Plus, I'm geometrically opposed to wasting my time. A pain, as if a ray was bisecting the plane of my forehead, warned me I was overthinking this. After all, an endpoint to reading is expanding my universe into different dimensions of ideas.

Flatland: A Romance of Many Dimensions (Illustrated) by Edwin Abbott Abbott

I'd function on a higher plane, I mused. So, after I folded myself into the curvature of my couch, I grabbed my Kindle and made the calculus of how I would squeeze in time to read this dense concept fantasy. The topologies of 'Flatland' Pointland, Lineland, Flatland and Spaceland were surprisingly easy to understand. I believe the biographers of Abbott who described the author as an outstanding teacher and writer are correct!

He also was surprisingly liberal for a preacher, standing up for women's rights and the extension of upper-class social freedoms to everyone. A pop culture grew up around the new kinds of proto philosophical- and mathematical-based social sciences.

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Abbott manages in about pages to tie in all of these social questions while his character A. Square tells us about his life and friends in a two-dimensional city. When he is visited by a sphere, a physical impossibility, it turns Square's mind hyperbolic. However, once the sphere shows him the wonders of his three-dimensional world, two of which being that as a Spaceland citizen, Sphere can see Square's intestines and take money out of safes in Flatland as easy as pi.

It seems three-dimensional creatures see straight into two-dimensions because there is no 'roof' to a two-dimensional world, only length and width. It would follow fourth- or other multi-dimensional beings could see into our three-dimensional universe, doesn't it? Boggles the brain proportionally to the black hole of ignorance one possesses before reading this The wonders of Flatland go on and on infinitely.

For example, Square's wife is a line, as are all women, and the King is a circle, as are all priests. Lower forms workmen, soldiers, middle-class are triangles and the noble classes above squares are pentagons and hexagons. Squares are professional men and gentlemen. Intermarriages can be arranged, and babies are born naturally upgraded into a higher rank. The more regular and sided an individual, the better the individual's class, so Equilateral triangles are of a higher class than Isosceles triangles.

Women are the lowest class which was a satirical device - the author actually believed in women's rights. Execution for crimes and rebellions, as well as knowing too much, are common politics in Flatland sounds very harsh to me, but then I can be quite obtuse. Frankly, I think there must be a transference of information between universes as anyone can tell you they have discovered me humming a Peace-cry often while cleaning my house.

I must admit I am in awe of the unusual symmetries between the deadly needling talents of two and three-dimensional women. I wonder at the timeless qualities of real and irrational human nature. My mind is a torus of spinning speculation, even turning inside out. This novel has no parallel in modern times, but it was a bit lacking in depth. Apr 19, Scarlet Cameo rated it it was amazing Shelves: Mar 18, Debbie Zapata rated it it was ok Shelves: I should not have tried to read this book.

I do not have a mathematical imagination. I only read it okay, tried to read it because GR friend Jaksen suggested it as a companion piece to a short science fiction story I recently read titled The 4-D Doodler. I liked the idea, and the blurb made the book sound clever.

But there were diagrams! And I felt like I was back in math class falling far far behind. I will probably be one of the few readers who enjoyed the first section of I should not have tried to read this book. I will probably be one of the few readers who enjoyed the first section of the book more than the second. The social commentary of the author's day couched in terms relating the society of Flatland was fascinating.

But then we went on to Part 2 and suddenly there I was lagging further and further behind. My little pea brain just couldn't handle anything beyond skimming after that. Neat idea and an interesting approach, but definitely not a book meant for me. My Math Phobia is too strong. It conquers even the best of intentions. View all 13 comments. Flatland Cover Dilema 3 25 Aug 25, April Group Read: Flatland a Romance of Many Dimensions 27 30 Jun 28, Flatland 1 6 Dec 13, Flatland - Buddy Read 22 44 Mar 28, A Romance of Many Dimensions 4 16 Feb 24, Edwin Abbott Abbott, English schoolmaster and theologian, is best known as the author of the mathematical satire Flatland He was educated at the City of London School and at St John's College, Cambridge, where he took the highest honours in classics, mathematics and theology, and became fellow of his college.

In he took orders. Mortimer as headmaster of the City of London School in at the early age of twenty-six. He was Hulsean lecturer in He retired in , and devoted himself to literary and theological pursuits. Abbott's liberal inclinations in theology were prominent both in his educational views and in his books. His Shakespearian Grammar is a permanent contribution to English philology. In he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus , Onesimus , and Sitanus Flatland was published in