Flatland: a journey to the discovery of many dimension

FLATLAND: A JOURNEY TO THE DISCOVERY OF MANY DIMENSION

Mathematic Reason and Imagination will help to reveal the Truth.

"Flatland: a romance of many dimensions" is one of the most worldwide known and

appreciated novels, which concern with Mathematics and Scientific subjects. Written by

Edwin Abbott Abbott and published anonymously in 1882, the book is even more read in

the present, when, after the appearance of new revolutionary scientific theories, the

problem of dimensions has become topical and necessary to understand the laws which

regulate our Universe. But Flatland isn't a mere treatise of Geometry, it is at first a story:

the fantastic, ironical, adventurous story of a world, absurd and paradoxical, but strangely

not too different from ours.

EDWIN ABBOTT ABBOTT: A LIFE DEVOTED TO CULTURE

Edwin Abbott Abbott was born in London in 1838, son of Edwin Abbott, headmaster of the Philological School in Marylebone. He        attended the St John's College in Cambridge, where he excelled in

both Classics and Mathematics. He was also very interested in

Theology and in 1862 he took orders. At the early age of twenty-six

he became the headmaster of the City of London School. He

reintroduced the traditional pronunciation of the Latin and promoted

a Philology class, which reached the level of the best Colleges. In

1889 he retired and devoted his life to cultural pursuits. A

biographer writes "He burnt with intellectual energy" . He considered E. A. Abbott

culture a sort of religion. He wrote more than fourty books, dealing with the most different

subjects. From education, to science, to philology, to theology. All his works are

characterized by an ironical and liberal way of analysing the world. He died in 1926.

FLATLAND: THE STORY OF A BIDIMENSIONAL WORLD

' Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons,

Hexagons, and other figures, instead of remaining fixed in their places, move freely about,

on or in the surface, but without the power of rising above or sinking below it, very much

like shadows -- only hard with luminous edges -- and you will then have a pretty correct

notion of my country and countrymen.'

This is the simple and original idea at the basis of the book. The main character, which is

also the narrator, is an argute square, called simply A. Square, who describes his world

and his fantastic experience of discovering the third dimension. The book is distinctly

divided in to two very different parts. The first one

deals with the precise and funny description of

the features of Flatland, its inhabitants, and the

institutions, which regulate their lives. In the

second part a Sphere introduces A. Square to

Spaceland and to other worlds. This bipartition

isn't just a narrative device, but it reflects a

precise intention of the author, which builds the

story on two different sides, corresponding to two different aims, he wants to reach. These aims are explicitated in the dedication of the book.

The book, as the Square says, is dedicated to the inhabitants of  Space, in the

hope that they would aspire higher and higher to the secrets of five, six, even seven

dimensions, thereby contributing "To the enlargement of the imagination and the

possible development of that most rare and excellent gift of modesty among the superior

races of solid humanity". Imagination is the quality which allows, with the contribute of

mathematic knowledge, to reach the truth. But the result isn't only an increasement of knowledge, it is also SOCIAL. The discovery of other dimensions shows that our world isn't the only one, existing. We believe that we are the centre of the Universe, while we are just as the poor squares, triangles and other figures, confined in our dimension. We have to learn modesty, while increasing knowledge.

FLATLAND AS A SATIRE OF VICTORIAN SOCIETY

The most remarkable thing about this novel is the incredibly precise description of an invented world. Life on a plane may seem quite impossible: figures can only slip on it and all they can see on their horizon is a line. Abbott ideates some genial devices and rules, which can regulate and make all aspects of this sort of life possible, with a precision which recalls the assiomatic and deductive approach of Mathematics. The inhabitants of Flatland are polygons, whose social class depends on the number of their sides. The Triangles, who have only three sides, are the bottom of social

ladder, while the Priests are multi-sided polygons and they approximate circles, which are

considered the perfect figures. The population can evolve thanks to the fact that a male child should have one more side than his father.

The situation is different for irregular figures and women.

Only regular polygons have rights in this society, while irregular ones are subjected to a severe

regulation. In particular Isoscel Triangles can't

evolve and are confined to their social class.

They are very dangerous, since their angle is

very sharpened, but they are generally

unintelligent too. But the condition of women is even worse. They are so thin triangles, that they approximate lines, A little Hexagon frightened by a "Quite-Circle" the result is that in some positions they are seen as points.

But the most interesting thing is that they are considered inferior to male figures, because they develop in their personality Emotion more than Ration.

"About three hundreds years ago, it was decreed by the Chief  Circle that, since women are deficient in Reason but abundant in Emotion, they ought no longer to be treated as rational, nor receive any mental education."

Each figure in Flatland appears as a line, if seen by another plane figure. They can recognize people by touching each other, or by the superior " Art of Sight Recognition". The more evolved

figures in fact can determine the depth of an object thanks to the presence of fog, which

is very common in Flatland. Even though they can see nothing more than lines, they can

infer angles and other geometrical concepts with great precision. But Abbott sketches

these figures and their society with so great abundance of particulars, that it's really

impossible to summarize it. The incredible fact is that it's very similar to ours. Many

readers of Flatland have considered the book a sort of satire of Victorian society, as it was

during Abbot's life, and a satire of societies in general, as they are also now. The greatest

of problems of Flatland is the condition of life for women. We must say that Abbott was a

supporter of equality of educational opportunity, in particular for women. For the truth at

that time women could get an education, but it was very difficult for them to be accepted

into Universities and Abbott's daughter had experienced it. Abbott recognized also the

existence of two different cultures. Men represent the rational and scientific one, while

women the emotional one. Even though the narrator (which is a male figure) apparently

approves his society and agrees with the point of view of the majority, we understand that

the position of the author is different. And it's expressed by the words of the Sphere, who

introduces a doubt, the possibility of a different point of view: "It is not for me to classify

human faculties according to merit. Yet many of the best and wisest in Spaceland think

more of the affections than of the understanding, more of your despised Straight Lines

than of your belauded Circles." An other interesting satirical element is the position of

Irregular figures. In Victorian Society omologation was the basis of civil life. Irregularities,

unusual behaviours, were always connected with criminal tendencies and deviant

personalities. Abbott exaggerates the situation: irregulars are eliminated in Flatland society

ore used as objects in schools to be studied by regular pupils. Then they are left to starve

to death. The satirical intent is even too evident in this page. In the end he deals with the

problem of freedom of thought and expression. In fact the Square is imprisoned because

he had revealed the existence of an other world, which may have the consequence of

troubling their static society. Which solution does Abbot propose? An incrementation of

modesty in people, who are no more than points or figures in the immensity of space.

A SQUARE: A SECOND PROMETHEUS IN THE DISCOVERY OF SPACE

'Either this is madness or it is Hell.' 'It is neither,' calmly replied the voice of the Sphere,

'it is Knowledge; it is Three Dimensions"

The adventurous part of the book begins with the appearance of a strange visitor in the

A. Square's house, on the first day of the Third Millenium. The night before A. Square had

had a singular dream. He had dreamt about a one dimensional

world, Lineland, where beings are segments on

the same straight line. Their horizon is only a point and they

communicate by using sounds. A. Square tries to reveal to the Monarch of this world the existence of the second dimension, but he discovers that it's impossible to make him realize that his line isn't the entire world.                           "He was persuaded that the Straight

Line which he called his Kingdom, and in which he passed his A. Square staring to Lineland

existence, constituted the whole of the world, and indeed the whole of Space. Not being

able either to move or to see, save in his Straight Line, he had no conception of anything

out of it."

The day after A. Square receives the visit of a strange figure: a perfect Circle, who can

change his measures and even disappear from the world! After a moment of terror,

Sphere tries to explain that he comes from the tridimensional space, Spaceland. At the

turn of each millenium he visits Flatland to introduce a new apostle to the idea of the third

dimension, which becomes a sort of religion. The dialogue between the two is very funny:

A.Square has the same reactions that the Monarch of Lineland had had in the dream. His

world is the only possible, there can't be a superior one! Sphere tries to persuade the

square in many ways, especially with geometrical reasons, but in the end he has to

demonstrate the truth by facts. He "picks up" the square and he leads him to Spaceland.

From the space they can look at Flatland,

seeing all the inhabitants of Flatland and

their "interior". Square is persuaded and

finds himself in great excitement. Then,

there would be also the fourth, the fifth,

and so on, dimensions, they could discover

new worlds, just imaging them. The

reaction of the Sphere is strange, but not

completely unexpected for the readers: the

Sphere can't believe in the existence of a

fourth dimension, he thinks that his world is

the highest and nothing superior can exist.

Each being thinks himself to be the perfection of the existence, while

there is always something more. Offended by this idea the Sphere returns A.Square to

Flatland in disgrace. There he tries to explain the third dimension to the other figures but

he isn't believed, he is persecuted and imprisoned. He says that he feels like a new

Prometheus. His existence is now condamned to unhappyness. Knowledge means necessarily also unhappyness. The message of the author is a deep and hearty eulogy of

knowledge: the only way to gain freedom is to reach Knowledge, by using both Ration and

Imagination, and to spread it.

"Learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is

better than to be blindly and impotently happy".

There's only a question left. Did really Abbott believe in the existence of other dimensions?

Considering the period of his life, probably not. Well, he didn't believe in the real existence

of Pointland, Lineland, Flatland, and so one. But he firmly believed in the existence of an

other world: Thoughtland. At the end of the book A.Square feels that also his world is just

a dream. It is not important. The important thing is to develop the faculty of Imagination

and build new possible worlds with the help of reason, even though they are the baseless

fabric of a dream.