User Reviews
Rating: really liked it
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.
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Rating: really liked it
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!
Rating: really liked it
Imagine losing or gaining a spatial dimensionLiving 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.
Rating: really liked it
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.
Rating: really liked it
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
Rating: really liked it
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.
Rating: really liked it
“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
Rating: really liked it
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.
Rating: really liked it
I will start my own brief multi-dimensional romance on this book - but dangerously, perhaps, exploring elements of my own experiences out into Spaceland that led me back, like Abbott, to my home-sweet-home of Flatland - with a caveat that I am a rather odd duck.
Being born with ASD didn't help at all.
We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says - the Jeu Suprême - as all reality curls up comfortably at its Ironic Edges.
But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville.
So my apologies at the outset to my GR friends who were math majors.
No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!
***
As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there.
Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland.
That sophistication fed my nascent knowledge.
So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur.
Yikes.
Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland!
***
An awakening refused leads back to simplicity, as Abbott found -
And it's where I am now writing this:
In "a state of simplicity (which cost me) not less than EVERYTHING."
And won me Flatland forever...
Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.
Rating: really liked it
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.
Rating: really liked it
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.
Rating: really liked it
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.
Rating: really liked it
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.
Rating: really liked it
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.
Rating: really liked it
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...
