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Flatland: A Romance of Many Dimensions

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This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status. Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.


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This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status. Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.

30 review for Flatland: A Romance of Many Dimensions

  1. 4 out of 5

    Robert

    When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire. Second, its point, even about i When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire. Second, its point, even about itself, is still as apropos today as it was then. We still do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements very seriously infinite numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions. Ultimately, this is a book about keeping an open mind. A really open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea. We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of conceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way. rgb

  2. 5 out of 5

    Stephen

    Take a classically styled, 19th century satire about Victorian social mores…dress it up in dimensional geometry involving anthropomorphized shapes (e.g., lines, squares, cubes, etc.)…bathe it in the sweet, scented waters of social commentary…and wrap it all around humble, open-minded Square as protagonist. The result is Flatland, a unique “classic” parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Sinc Take a classically styled, 19th century satire about Victorian social mores…dress it up in dimensional geometry involving anthropomorphized shapes (e.g., lines, squares, cubes, etc.)…bathe it in the sweet, scented waters of social commentary…and wrap it all around humble, open-minded Square as protagonist. The result is Flatland, a unique “classic” parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I’m recommending the book, I’m really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow “goodreaders.” So...um...math. Let’s get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don’t want people going all …and dashing away in a panic. Rest easy and increase your calm, the math is very minor. It’s really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. Damn, that didn’t sound good either….just trust me, you won’t need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book. However, with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional “Sphere” is explaining a universe containing only one dimension to our two-dimensional protagonist, you should….IMMEDIATELY…DISCONTINUE…READING…until you have: 1. burned some incense, 2. poured a big tumbler of whiskey, and 3. eaten a few “peyote” brownies, because the SHIT is about to get… PLOT SUMMARY: Written in 1884, the story is told by “A. Square,” who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society. Yep...the Flatlanders are chauvinists. The book begins with “A Square” describing his life as part of the “professional class” and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality. Later, “A Square” dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them. What follows is a fun, but somewhat confusing discussions during which “A Square” tries to explain the two-dimensional world to the king of Lineland. Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe…whiskey…peyote…now. Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, “A Square” returns to Flatland to teach the wonders of such “enlightened” dimensions to his fellow flatlanders, the result of which is… …nope…no spoilers here! THOUGHTS: As I sit here, sober and “mostly” peyote free, I think I enjoyed the “ideas and concepts” of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I’ve the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by. Overall, I liked the book. I think it’s worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it’s actually a novella, you can get through it quickly without a large time commitment. 3.0 stars. Recommended!

  3. 4 out of 5

    Cecily

    Imagine losing or gaining a spatial dimension Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute Action Lab video, explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to And He Built a Crooked House, which in turn, reminded me of a book I’d heard of, Flatland. Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both. And He Built a Crooked House, by Robert Heinlein This is an early short stor Imagine losing or gaining a spatial dimension Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute Action Lab video, explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to And He Built a Crooked House, which in turn, reminded me of a book I’d heard of, Flatland. Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both. And He Built a Crooked House, by Robert Heinlein This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction. Quintus Teal is a young architect who thinks of a house as “a machine for living, a vital process, a live dynamic thing”. His big idea is to use the fourth spatial dimension to “put an eight-room house on the land now occupied by a one-room house. Like a tesseract”. He goes on to explain a lot of geometry, and I would have been bemused if I hadn’t already seen illustrations of what a tesseract, aka hypercube, would look like. We’re all familiar with a cube and its net: Then add a dimension for a hypercube and its net: For more of an explanation, see video links at the end of this review. Teal achieves his dream “by using strong girders and folding money” and takes his friends, Mr and Mrs Bailey to see it. “That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation. But four dimensions don’t fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that Escher drew. Flatland, by Edwin A Abbott About a 2D world and published in 1884. This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations. The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere. In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. “Delicate females” are are mere lines, “wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory”, but Abbot himself was a priest and headmaster who believed in women’s education, including at university. The second half has more of a story: “my initiation into the mysteries of Space” and “the Gospel of Three Dimensions”. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that’s unimaginable and heretical in Flatland. The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is “a Line of Lines” and a sphere is “many Circles in one”. However, Abbott’s love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc). Image: “The Weeping Woman”, in which “Picasso used cubist forms of fragmentation to depict the face in a series of angular planes”. (Source) Clearly explained information about 2D and 4D To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways. • The fourth dimension explained, via second and third, in six minutes, HERE. • Hypercubes explained and illustrated, without sound, in five minutes, HERE. • Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, HERE. • Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, HERE. • Animation of the story of Flatland, made in 1965, eleven minutes, HERE. • Carl Sagan explains Flatland and goes on to the fourth dimension, in nine minutes, HERE. The two stories • You can read Flatland, free, in a variety of digital formats, on Gutenberg, HERE. • You also can find the text of And He Built a Crooked House online. Image: “Mr Osborne, may I be excused? My brain is full.” (The Far Side, by Gary Larson) See also • If it’s all too much, there’s Norton Juster’s delightful picture book, The Dot and the Line, which I reviewed HERE. I included illustrations and a link to an Oscar-winning animation. • Malcolm wrote two short stories about very high-tech homes in The Martian Chronicles, which I reviewed HERE. Usher II is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. There Will Come Soft Rains starts off almost slapstick, but takes a very tragic turn.

  4. 4 out of 5

    Michael Finocchiaro

    A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dim A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dimensions and when the protagonist returns to Flatland and tries to explain Spaceland, he is imprisoned as a heretic. The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.

  5. 5 out of 5

    Ahmad Sharabiani

    Flatland: A Romance of Many Dimensions, Edwin A. Abbott Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. The story describes a two-dimensional world occupied by geome Flatland: A Romance of Many Dimensions, Edwin A. Abbott Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium. On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points". These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so. In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ... عنوانها: «پـَختِستان»؛ «افسانه ی دو بعدی»؛ «سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه»؛ نویسنده: ادوین ابوت؛ تاریخ نخستین خوانش سال 1997میلادی عنوان: پـَختِستان؛ نویسنده: ادوین ابوت؛ بازنگری و مقدمه از: یانش هوفمان؛ مترجم منوچهر انور؛ تهران، روشنگران و مطالهات زنان، 1375؛ در 195ص؛ شابک 9645512433؛ چاپ دیگر تهران، کارنامه، 1388؛ در 172ص؛ شابک 9789644310799؛ چاپ دوم 1393؛ موضوع بعد چهارم - از نویسندگان بریتانیایی - سده 19م عنوان: افسانه ی دو بعدی؛ نویسنده: ادوین ابوت؛ مترجم: جلال جامعی؛ شیراز، لورا، 1387، در 192ص؛ شابک 9789648851366؛ عنوان: سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه؛ نویسنده: یک مربع (ادوین ابوت)؛ برگردان: آهنگ کوثر؛ شیراز، نوید شیراز، 1397؛ شابک 9786001927768؛ پَختستان: رمان بُعدهای بسیار، رمان کوتاهی از الهی‌دان و استاد دانشگاه انگلیسی، «ادوین ابوت» است، که نخستین‌بار آن‌را در سال 1884میلادی با نام مستعار نویسندگی «یک مربع» منتشر کردند؛ در این کتاب از دنیای خیالی «دوبُعدی پَختستان»، برای نشان دادن فرهنگ سلسله‌ مراتبی «انگلستان» دوره ی «ویکتوریا» استفاده شده‌ است.؛ این نگاره بیشتر یک تمثیل عبرت‌ آموز است، تا یک داستان؛ و نیز نقدی تند و گزنده، از ساختار اجتماعی و سیاسی جامعه ی روزگار خود، و ارزش‌ها، و روابط انسانی در آن است؛ «ابوت» برای اینکه نشان دهد، انسان‌ها در این دنیا از نظر افق دانش و بینش، در چه قفس تنگی گرفتار هستند، از جهانی خیالی با باشندگانی دو بُعدی سود برده است.؛ این باشندگان دارای شکل‌های هندسی «مثلث»، «مربع»، «پنج‌بر»، «شش‌بر» و «بالا و بالاتر» تا «دایره‌» هستند، که ناگزیر در سطح می‌زیند.؛ نویسنده و راوی داستان، یک مربع است، که این دنیا را شرح می‌دهد.؛ «پَختستان» در زمان انتشار خود، مورد توجه قرار نگرفت، پس از انتشار نظریه ی نسبیت عام انیشتین، این کتاب دوباره به یاد همگان افتاد، چرا که در آن به مفهوم «بُعد چهارم» نیز اشاره شده بود.؛ در مقاله‌ ای تحت عنوان «اقلیدس، نیوتن و انیشتین»، که در شمارهٔ دوازدهم ماه فوریه سال 1920میلادی مجله ی «نیچر» منتشر شد، از این کتاب نام برده شد، و «ابوت» را از یک نظر همچون پیامبری دانست، که در آن زمان به درک اهمیت زمان، در شرح یک پدیده، آگاه بوده‌ است.؛ انتشارات «هارپرکالینز» در سال 1983میلادی، نسخه‌ ای از این کتاب را با پیشگفتار «آیزاک آسیموف» منتشر کرد.؛ عنوان «پَختستان» را، مترجم نخست این کتاب، جناب «منوچهر انور»، برای آن برگزیدند، که از واژه ی فارسی «پَخت» به معنای «پهن» و بی‌برجستگی، و پسوند ستان تشکیل شده‌ است.؛ تاریخ بهنگام رسانی 27/05/1399هجری خورشیدی؛ ا. شربیانی

  6. 4 out of 5

    Gene

    When it comes to genre this book is in its own: let me call it satirical math. It anybody can come up with a better term, I am opened to suggestions. The story takes part in a flat country (universe?) where everything has only width and height - in other words, in a flat surface, like a picture. All the women in the country are straight lines and men are equilateral polygons - the more sides, the higher the status in their society. The top guy has so many sides he is indistinguishable from a cir When it comes to genre this book is in its own: let me call it satirical math. It anybody can come up with a better term, I am opened to suggestions. The story takes part in a flat country (universe?) where everything has only width and height - in other words, in a flat surface, like a picture. All the women in the country are straight lines and men are equilateral polygons - the more sides, the higher the status in their society. The top guy has so many sides he is indistinguishable from a circle for all practical purposes. The hero of the tale is a Square. His story consists of two parts. The first part describes his flat country and boy, did Edwin A. Abbott went full satirical on Victorian society! The second part discusses an interesting mathematical topic. Have you ever wonder what it would mean if we have fourth dimension in addition to our three? The author tries to explain it by analogy: our poor Square got to visit 3-D world and he is completely unable to grasp the idea of third dimension. Still, at least some concepts are understandable. Is the tale highly original and imaginative? Yes, without any doubt. Was it written under some drug influence? Probably, considering the availability of them during the time the book was written. Is it worth reading? The answer is, it depends. What was your reaction to the word mathematics during your school year and (possible) college? If upon hearing it you would start heavy sweating, your heart would develop some serious arrhythmia, and you face would turn an intriguing shade of green - turn around, start running, and do not stop until you are on the other side of the Earth from the book. Also in this case please subtract two(!) stars from my rating. If on the other hand you were at least decent in math and are curious how it can co-exist with satire, go ahead and read it. It is short and free (from Project Gutenberg). You do not even have to be on acid to enjoy it.

  7. 4 out of 5

    Apatt

    “I used to be a renegade, I used to fool around But I couldn't take the punishment and had to settle down Now I'm playing it real straight, and yes, I cut my hair You might think I'm crazy, but I don't even care Because I can tell what's going on It's hip to be square” Huey Lewis And The News - Hip To Be Square According to IMDB, several film adaptations have been made of Flatland, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can’t imagine a more appropriate t “I used to be a renegade, I used to fool around But I couldn't take the punishment and had to settle down Now I'm playing it real straight, and yes, I cut my hair You might think I'm crazy, but I don't even care Because I can tell what's going on It's hip to be square” Huey Lewis And The News - Hip To Be Square According to IMDB, several film adaptations have been made of Flatland, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can’t imagine a more appropriate theme song than the above Huey Lewis And The News number. Flatland is set in a two-dimensional world and narrated in the first person by a square (or “A Square” as appears on the original edition’s book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians. Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square’s adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no time, probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it. Flatland is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don’t want to consider (screw the hypotenuse, man!). However, for Flatland I don’t mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows: “Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. 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.” So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird! I really enjoyed Flatland, it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read Flatland before you flatline. Notes: • Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding. (link) • There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story. • There is one error in the book where Square mentions a cellar: “So I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.”. You can't have a bloody cellar if you only have two dimensions and you can’t “fall through” anything. • Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards! • The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (͡° ͜ʖ ͡°) • I initially thought this book was a collaboration between two abbots. Quotes: Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name. In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience. Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life? You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions—how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration? Hipster Square

  8. 4 out of 5

    Dan

    This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel. Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them. The story itself consists of a two dimensional world (Flatland), in which there are This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel. Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them. The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear. In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own. This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time." This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.

  9. 5 out of 5

    Duane

    I give it an extra star for it's originality, it's uniqueness. The concept was genius, Abbott was probably a math genius himself. However, as a work of literature it does not hold up well. It has a shadowy similarity to Gulliver's Travels, but falls well short of that Swift classic. I give it an extra star for it's originality, it's uniqueness. The concept was genius, Abbott was probably a math genius himself. However, as a work of literature it does not hold up well. It has a shadowy similarity to Gulliver's Travels, but falls well short of that Swift classic.

  10. 4 out of 5

    Kinga

    This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better. Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off a This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better. Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it’s to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a ‘peace-cry’ when out and about, in case anyone missed the wiggling bum. Seriously children, don’t do drugs. It makes you write things like that. The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that’s how a creature from 3D world would see it. You’re looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience. The same way we can’t actually see the third dimension but we can tell it’s there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him ‘tricks’ that the third dimension allows him to do, Square is just as incredulous. Even though the mathematics tells him there must be another dimension (and another, and another), he can’t quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it’s been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it’s gone.

  11. 5 out of 5

    Nandakishore Mridula

    At the outset... the 5 stars are entirely subjective. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did. I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same pr At the outset... the 5 stars are entirely subjective. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did. I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.) We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm. Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic. There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits. Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious. In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension). Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story. Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life. Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it. Since it is available online free from Gutenberg, I suggest everyone to give it a try.

  12. 5 out of 5

    Jon Nakapalau

    I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math. I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math.

  13. 5 out of 5

    Carol She's So Novel꧁꧂

    For the most part I hate maths, other than stats & arithmetic, but I loved this absolutely mad book! My copy didn't come with the line drawings, but they are available on http://www.geom.uiuc.edu/~banchoff/Fl... I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe! I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may ha For the most part I hate maths, other than stats & arithmetic, but I loved this absolutely mad book! My copy didn't come with the line drawings, but they are available on http://www.geom.uiuc.edu/~banchoff/Fl... I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe! I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me & trig friends! Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny. I didn't.

  14. 4 out of 5

    Coffee&Quasars

    3.5 stars. This is a very personal rating. I think I would’ve enjoyed this far more if I’d read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew. This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry 3.5 stars. This is a very personal rating. I think I would’ve enjoyed this far more if I’d read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew. This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.

  15. 4 out of 5

    Paul

    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... 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...

  16. 4 out of 5

    Charles van Buren

    Very strange Review of free Kindle edition ASIN: B0083ZRQR4 124 pages I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage ab Very strange Review of free Kindle edition ASIN: B0083ZRQR4 124 pages I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND: “All work is 3-D,” said Martin. We stared at him. He looked at me. “Remember that book Flatland you made me read?” “I didn’t make you read it.” “When a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that’s the same as making me read it.” “But you liked it, right?” “Yeah, because it made me feel smarter than the guy who wrote it.” “How so?” asked Sharice. “He says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.” “You could see them from the top,” said Susannah, “and from that vantage point, you could also see how many sides they have.” “No. To see them from on top, you’d have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn’t even know other men existed.” “They would when they bumped into them,” she said. He shook his head and placed two pennies on the table, sliding them until they touched. “These pennies can bump into each other because they have sides. But imagine them without sides. I don’t mean just really flat. I mean no side dimension at all. The men in Flatland can’t bump into each other because they have no sides.” “Why do you keep calling them men? Aren’t there women in Flatland?” “Sure. The author says they are straight lines. ”She shook her head. “Sheesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.” “Right. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can’t see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.” “He says something else about women,” I noted. “Because of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can’t remember it happening.” Sharice stared at me. “And you made him read that?” “For the math part. I knew he was smart enough not to believe the stuff about women.” “He was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn’t have sides …wait, they can’t see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.” “See,”I said, trying to move beyond my having forced a misogynist book on Martin, “You’re also smarter than the author.” I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it. No illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.

  17. 5 out of 5

    George

    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. 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 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.

  18. 5 out of 5

    Wee Lassie

    This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters. This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters.

  19. 5 out of 5

    Liam O'Leary

    My 4th best read of 2020. An incredible, timeless book. Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean. It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and My 4th best read of 2020. An incredible, timeless book. Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean. It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and we count when we care about and can demonstrate that it can be counted by more than one observer. Counting is also a subject decision insofar as we attribute a value to the variable counted, and a meaning to what its counting could mean. 'What counts has been counted'... in a nutshell? It also demonstrates that mathematical models can model social systems. The strength of mathematical models of social systems is that they avoid any obvious sociocultural bias and so enables things that would normally be socially censored to be claimed as theoretical propositions. In short, it enables discourse about stereotypes and demonstrates the possibility of universal social or moral values. I feel a lot of the social norms of Flatland still apply today, in a way. The importance of Spaceland I think is to demonstrate how it is nearly impossible to mathematically, or universally, demonstrate evidence of realities outside of measurable reality, because they begin and end in the subjective experience of the individual. Which is used as an argument both for and against religion. I think Flatland as a theological text favours spiritual belief in its lowly depiction of atheism or 'man as God' in Pointland as a less diverse system, geometrically speaking. I guess in a way it's calling existentialists navel-gazers insofar as they take their perception to solipsistic levels that is perhaps theologically speaking commits the blasphemy of 'self-as-a-God'. This shows why Flatland is so brilliant — it can simply, concisely and thoroughly show a complex understanding of human nature — such as how theists fail to explain their conviction, and atheists fail not to reject any conviction that conflicts with their original sense of perception. Most people don't get get that far in a debate in an hour let alone in less than 100 pages! Ok... I think I've made my point. I think most people read this as some 'goofy maths' essay, but I see it as a social commentary that somehow covers the archetypes of society and the perception of reality in less than 100 pages and is somehow still ahead of its time a century later.

  20. 5 out of 5

    Alice

    5* A world where every character is a shape, but only seen on a side view so everybody looks like a straight line. That's why the would is called flatland because everything is in 2 dimensions. THIS IS THE BEST BOOK I HAVE EVER READ! 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 5* A world where every character is a shape, but only seen on a side view so everybody looks like a straight line. That's why the would is called flatland because everything is in 2 dimensions. THIS IS THE BEST BOOK I HAVE EVER READ! 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: "Place a penny on the middle of one of your tables in Space, and leaning over it, look down upon it. It will appear a circle. 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 Women are Straight Lines. 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. Our Middle Class consists of Equilateral or Equal-Sided Triangles." "The thought flashed across me that I might have before me a burglar or cutthroat, some monstrous Irregular Isosceles, 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." HERE'S A FREE LEGAL LINK FOR THIS BOOK SO YOU DON'T GET A VIRUS: (The author has been dead for 100 years of course it's legal.) https://www.gutenberg.org/ebooks/97

  21. 5 out of 5

    Roy Lotz

    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? 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 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? 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 and skip the reviews. So I’ll keep my remarks brief. 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. 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. And this question of shapes is important in Flatland, as one’s status depends on one’s shape, with irregulars being the lowest and circles the highest. So was Abbott implying that, when we educate our own youngsters, most of this “education” consists in merely teaching them to navigate our own social hierarchy? 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? Incomprehensible. And how would the prospect of three dimensions seem to a two-dimensional creature? Nonsense. 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.

  22. 4 out of 5

    Jemppu

    Quite obnoxiously dated in certain regards, but does have lasting demonstrations on principles of dimensions, and some apparent gems in analogy, too. The following quote in particular stood out to me; if not for the intended purpose, but seemingly quite perfect as a description of the limitation in expressing and interpreting our true selves the best we can through variation of languages and cultural differences. "When you entered the realm of Lineland, you were compelled to manifest yourself to t Quite obnoxiously dated in certain regards, but does have lasting demonstrations on principles of dimensions, and some apparent gems in analogy, too. The following quote in particular stood out to me; if not for the intended purpose, but seemingly quite perfect as a description of the limitation in expressing and interpreting our true selves the best we can through variation of languages and cultural differences. "When you entered the realm of Lineland, you were compelled to manifest yourself to the King not as a Square, but as a Line, because that Linear Realm had not Dimensions enough to represent the whole of you, but only a slice or section? In the same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but can only exhibit a slice or section of me, which is what you call a Circle." ____________________ I read this as the designated book for Paul Stamets on startrek.com's "24 Classic Sci-Fi and Fantasy Books To Read Based On Your Favorite Star Trek Character"; a pairing which I would surely have a plenty more in me to ruminate about (than what is expressed in the brevity of the reading updates); turns out this might indeed be quite the perfect match.

  23. 5 out of 5

    Jan-Maat

    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. 3D creature proceeds to blow 2D creature's mind by exposing him (view spoiler)[ indeed gender apparently is trans-dimensional (hide spoiler)] to 1 dimensional world, who however in turn refuses to accept the possibility of 4, or more D , world (s). 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. 3D creature proceeds to blow 2D creature's mind by exposing him (view spoiler)[ indeed gender apparently is trans-dimensional (hide spoiler)] to 1 dimensional world, who however in turn refuses to accept the possibility of 4, or more D , world (s). 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.

  24. 5 out of 5

    JennyCash

    Published in 1884, this is meant to be a satire on Victorian culture but it's also just a math nerd's dream. Very cleverly done. The first half is the history and explanation of Flatland. The second half is the opening of the mind of A Square to understand a third or even fourth dimension. Published in 1884, this is meant to be a satire on Victorian culture but it's also just a math nerd's dream. Very cleverly done. The first half is the history and explanation of Flatland. The second half is the opening of the mind of A Square to understand a third or even fourth dimension.

  25. 4 out of 5

    Jafar

    This book is just brilliant. Written by a British mathematician in 1881, it’s a short fantasy novel about life in two dimensions. 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. Written by a British mathematician in 1881, it’s a short fantasy novel about life in two dimensions. 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 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. I don’t know about the political beliefs of the author. 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). 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. People in Flatland cannot even imagine a third dimension, like we can’t imagine a fourth spatial dimension. Imagine that you’re 2D and a sphere from a 3D space passes through your plane. 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. A 3D entity can see and touch the inside of your body (from above, but you don’t know what above is). If you’ve locked away things in your 2D safe, the 3D guy can pick them up from there and put them in front of you. 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.

  26. 5 out of 5

    Timothy Urgest

    This may be allegory and/or satire, but I was hella bored. Chapter 1 is genius. The rest did nothing for me. Concept > execution.

  27. 5 out of 5

    David Sarkies

    Prepare to Have Your Head Hurt 7 July 2018 – Brunswick Heads Well, this is a strange little book, but then again it did remind me a lot of Gulliver’s Travels, at least with the first part, because in the second part it starts to get really strange. Mind you, while there are some things in this book that I didn’t think quite worked, but we need to remember that what Abbott is doing here (or should I actually refer to the real author – A. Square) is trying to imagine a world of two dimensions, and Prepare to Have Your Head Hurt 7 July 2018 – Brunswick Heads Well, this is a strange little book, but then again it did remind me a lot of Gulliver’s Travels, at least with the first part, because in the second part it starts to get really strange. Mind you, while there are some things in this book that I didn’t think quite worked, but we need to remember that what Abbott is doing here (or should I actually refer to the real author – A. 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, what we are talking about here are regular polygons, the irregular ones are considered to be deformed, and if they aren’t killed, they are basically locked away. 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). Anyway, this is a land where knowledge is tightly controlled, and the only way to determine somebody’s shape (because they basically only see each other as lines) is to be educated in the ways of depth perception. This is something that is only taught to those higher up the social ladder. There was a time where colour was introduced, and this actually resulted in a civil war because it meant that everybody was able to know other’s shapes simply by looking at their colour. 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. Then there is another problem that some of these private schools aren’t necessarily objective in their curriculum. 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. Sure, you might be lucky and find yourself in a suburb that has a pretty good school, but that isn’t the case with everybody, particularly if they grow up in a poor or working class neighbourhood (as was the case with me). 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. Which sometimes makes me wonder whether the reason our governments are progressively underfunding our public education system is to basically keep people stupid. Well, there are arguments in favour of that, particularly if you aren’t taught to critically examine everything the mainstream media is feeding you. 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. However, with the rising costs of university (and one of the reasons that is happening is because we are also demanding all of the bells and whistles along with the education), many people are starting to miss out, and aren’t developing that ability to question what they are hearing, and what they are being told. 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. Well, it seems the answer is ‘with great difficulty’. One thing we should remember is that Abbott was writing before Einstein decided to join space with time and make time a dimension. Look, I’m not entirely sure if we can view time as a dimension in the same was as we view our other dimensions. 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. Even then, with the fifth dimension, that being probability, it only splits off into an infinite number of probabilities, it is not as if an infinite number of probabilities converge into that point as well (or do they, but then again you wouldn’t know it, would you). 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. This is where Abbott’s arguments really come into play. 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). I would say that we are actually more open minded these days, but honestly, I would beg to differ because we still go out of our way to shut down arguments that we really don’t like. 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.

  28. 5 out of 5

    Harry Whitewolf

    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. Simply brilliant. 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. Simply brilliant.

  29. 5 out of 5

    Celia

    Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884. This is a book that should appeal to any math major. In fact, a good friend said she had to read it in high school for geometry class. I consider myself a lover of geometry; it was one of my favorite subjects in high school. This book presents geometry in a new way. (At least it was so to me.) Flatland is a 2 dimensional universe, right? Still, if viewed from the c Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884. This is a book that should appeal to any math major. In fact, a good friend said she had to read it in high school for geometry class. I consider myself a lover of geometry; it was one of my favorite subjects in high school. This book presents geometry in a new way. (At least it was so to me.) Flatland is a 2 dimensional universe, right? Still, if viewed from the correct perspective, it can seem one dimensional. If you don't believe me, read the book!! I did copy this one paragraph from the book. It does give a good synopsis of the entire book: “Look yonder,” said my Guide, “in Flatland thou hast lived; of Lineland thou hast received a vision; thou hast soared with me to the heights of Spaceland; now, in order to complete the range of thy experience, I conduct thee downward to the lowest depth of existence, even to the realm of Pointland, the Abyss of No dimensions.” So Pointland: 0, Lineland: 1, Flatland: 2, Spaceland: 3... dimensions, that is. Loved the book. Took me down Memory Lane to High School. 4 stars Note: a book only a math major could love!!

  30. 5 out of 5

    aPriL does feral sometimes

    'Flatland' is amazing. 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. Square. To understand the concepts that these surprisingly charming fantasy characters who live in a two-dimensional world illust 'Flatland' is amazing. 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. Square. 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 360 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. 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. Gauss what? I like it! 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. Additionally, for many Victorians including Abbott, the new scientific discoveries about physics, especially about the possibility of a fourth (and more) dimension, revived a lot of theories about whether discovery of this dimension was the solution to where heaven and/or spirits might live. A pop culture grew up around the new kinds of proto philosophical- and mathematical-based social sciences. Abbott manages in about 100 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.

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