Flatland: A Romance of Many Dimensions (Dover Thrift Editions) [ペーパーバック]

Flatland is a unique and brilliant treatise on a trifurcated level. It is a sociological statement, a mathematical statement and a religious statement all rolled into an incredibly astute 82 pages. The book centers mostly on the differences between a two dimensional world and a three dimensional world; but comments on society, law, prejudice, religion, and proselytizing.

The book especially points out the difficulty in envisioning a greater reality and a greater vision than is commonly observed by any individual in any dimension or society. The author's premise relates to things existing in a "plane geometry" world as opposed to a "Euclidian Geometric" three dimensional figure universe. The book carefully illustrates to one denizen of Flatland how the three dimensional world of space works and/or exists. Upon finally understanding the "Gospel of Three Dimensions" our protagonist goes on to try and apply the same arithmetic logic and geometric analogs to a fourth dimensional universe. Shouldn't there exist a fourth dimensional universe that allows an entity to look down upon the three dimensional universe with as much transparency as one can from three dimensions to two?

Alas, things become different in dimensions other than the first, a world of lines, the second, a world of shapes and the third, a world of objects. In the zero dimension, all things are a point. Mathematically we know that any number raised to the "0" power equals 1 and therefore, all things in the zero dimension resolve into one single omnipotent point. This condition would also exist in the fourth dimension; as those of us in the third dimension have no model to compare it to. Envisioning a fourth dimension, even with time as the fourth dimension is truly difficult or impossible for us in the third dimension.

Interspersed with this witty and intellectual dialogue are comments on society and its structure. He specifically comments multiple times of the degradation of women in society to the lowest social status. Only men are educated in Flatland. Interestingly, he paints a picture of an authoritarian society in which people are judged by their shapes and angles. This reflecting the Victorian societal values around him at the time of his writing.

Flatland is recommended to all those who seek to enlighten their view of the universe and of potential universes. It is especially recommended to those seeking higher knowledge of any type. Flatland is truly a multi-dimensional experience and worth every minute.

Although it isn't very long, Flatland does take a long time to read. This isn't because it is boring, or because it is hard to read, but because of the large amount of digestion one need's to fully comprehend (and to fully enjoy) this book. Even this book contains only 82 pages, it is by no means light reading. The book was originally released in 1884 under Abbott's pseudonym A Square. In the story we follow the journey of a square who lives in a land of two dimensions--a flat land. In it class, and ultimately intelligence, is determined by the amount of sides that a shape has. As the amount of sides a shape has decreases, we find that it also is more emotional and apt to cause destruction through their pointed corners. Women are depicted as straight lines, but one has to take into account the time that this book was published. One can also disregard the story as having any relations to anything in our society and enjoy it for what it is, a mind bending social criticism. In this tale we follow the aforementioned square through his everyday life. we learn what it is like to exist in only two dimensions. We learn of how rain falls form the north and disappears to the south and how gravity is a minute force that pulls to the south ever so slightly. We follow him through the government and through social classes, and the discrimination that comes with them. When his son talks of geometric impossibilities such as 23 (cubed) he has a dream of a lesser land than his, a land called line land. IN it there is not two but only one dimension of being. Through discussion with the kind of lineland, we are offered insight into why our hero the square cannot conceive of the third dimension. Later our hero is visited by a great being, a sphere that appears to him seemingly out of nowhere. This confuses the square very much, and even more when the sphere tries to explain how he passed into his dimension from the third. After heated debate, the sphere takes him and shows him the third dimension, turning our hero into an evolved form of him self, a cube. Form his higher vantage point the square is able to see the innards of those who reside in flatland. He receives tutoring from the sphere about this new dimension and all that it entails. He learns of how limited the field of vision is for those living in flatland, both literally and figuratively. With his previous limits of reality stripped and with his eye opened to the truth, the square quickly follows logic and asks to see the insides of the sphere, and wishes to ascend further into greater dimensions, fourth dimensions and fifth and onward and upward. The sphere is appalled by this heresy and send our hero back to the limited realm of flatland. Here he tries to convince others to be enlightened, but cannot find success. He has a second dream involving the dimension of pointland, no dimensions. The being inhabiting this land is of nothing and knows nothing but itself, which is nothing. There fore this being cannot be disappointed by anything, because it cannot conceive of anything other than itself. We can see the religious parallels to Hinduism and Buddhism here. The completely content creature is of nothingness, much like the state that Buddhists try to achieve, and the outward ranking by dimension not sides can be seen in Hinduism in the spiral path towards God that the Hindu believe they travel along passing from one point on the spiral to another with each passing life. In this land of math all of the lands are contained within each other, much like the rings of the spiral. Finally after this dream the square realizes the futility of trying to convince others through speech, and he feels he must do it through demonstration. Folks hear of his heresy and bring him to the court for the climax of the book. Whether or not the plot of the novel itself is very entertaining, the ability to get your head around concepts that can only be experienced through the mind is challenged thoroughly by this novel. It is a must read for anyone who thinks that they are well educated, as it will quickly tell you just where you stand, theologically, philosophically and mathematically.

Flatland is THE must-read for anyone interested in getting a feel for higher dimensions. The book is extraordinarily readable and succeeds even with people that are afraid of mathematics. Abbott's charm lies in his ability to write simply and clearly about a topic that has its share of very unreachable, esoteric books. You fall into the story (whose plot is by no means secondary to the mathematical ideas), and before you know it you find yourself in contemplation of things like the fourth and fifth dimensions. The visual image that this book provides is a necessary step to envisioning and then understanding the idea of higher dimensions, even for those already versed in the mathematics of it. You never know, after you read this, you might even be willing to try your hand at things like Einstein's relativity. A little on the social aspects of the book: keep in mind that it was written in the very late 1800's. Hidden within the philosophical and mathematical ideas is a satire of the social climate of the times: how women, the military, the upper echelons of society, and just about everyone else were viewed. Flatland makes you think, and think deeply, on many different and sometimes unexpected levels.