Quarta dimensione

La Quarta Dimensione

FLATLAND

Edwin Abbott Abbott

Edwin Abbott Abbott was born on 20 December 1838, in London, he was the eldest son of Edwin

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Abbot and Jane Abbot.

His parents were first cousins, which explains how Edwin could have

“Abbot Abbot” as both as surname and middle name. He was

educated at the City School of London and in 1857 Abbot entered St.

John's College in Cambridge, taking excellent notes in mathematics

classics and theology. In 1863 he became an Anglican priest and he

got married to Mary Elizabeth Rangeley who gave him a son and a

daughter. When he was twenty-six, in1864, he was appointed

headmaster of the City School of London and after this he wrote

some of Philology books like “Shakespear Grammar” (1870) and

“How To Write Clearly” (1872), he wrote also theological writing, they were published

anonymously.”Philochristus” (1878) and “Onesimus” (1882) are the most renowned among his

books. In 1884 Abbott published his masterpiece “Flatland: A Romance of Many Dimensions”

writing anonymously as “A Square” (the curiosity of the same middle name and surname lets us

think about a mathematical analogy Abbott Abbott can signify Abbott Squared and maybe A

Square). Edwin used the fictional two-dimensional world of Flatland to offer pointed observations

on the social hierarchy of Victorian culture. However, the novella's more enduring contribution is its

examination of dimension. th

Abbott died of influenza at his home on October 12 1926 in Hampestad, near London. He was

buried a couple of days later with great honors. 6 La Quarta Dimensione

Flatland: The Plot

The first part of the story is set in a two-dimensional world referred to as Flatland. The narrator,

simply calling himself A. Square, guides the reader through some of the implications of his life in

two dimensions. The society is strongly hierarchical, dividing his citizens into classes according to

the number of sides they own. The Square has a dream about a visit to a one-dimensional world

(Lineland), and attempts to convince the realm's ignorant monarch of a second dimension, but he

finds that it is essentially impossible to make him see outside of his eternally straight line.

The narrator is then visited by a three-dimensional sphere, which he cannot comprehend until he

sees Spaceland for himself. This sphere, visits Flatland at the turn of each millennium to introduce

a new apostle to the idea of a third dimension hoping to succeed in educating the population of

Flatland about the existence of Spaceland. Being in Spaceland and therefore outside Flatland, the

sphere and the square are able to observe the leaders of Flatland secretly acknowledging the

existence of the sphere and prescribing the silencing of anyone found preaching the existence of

Spaceland and the third dimension. After this proclamation is made, many witnesses are

massacred or imprisoned (depending on the caste they belong to).

After the Square's mind is opened to the idea of new dimensions, he tries to convince the Sphere

of the theoretical possibility of the existence of a fourth (and then fifth, and sixth ...) spatial

dimension. Offended by this presumption and incapable of comprehending other dimensions, the

Sphere sends his impudent student back to Flatland.

The Square has another dream, in which the Sphere visits him again, this time to introduce him to

Pointland. The point (sole inhabitant, monarch, and universe in one) perceives any attempt at

communicating with him as simply being a thought originating in his own mind.

The Square recognizes the connection between the ignorance of the monarchs of Pointland and

Lineland with his own (and the Sphere's) previous ignorance of the existence of other dimensions.

Once returned to Flatland, the Square finds it difficult to convince anyone of Spaceland's

existence, especially after official decrees are announced - anyone preaching the lies of three

dimensions will be imprisoned or even executed. 7 La Quarta Dimensione

Social satire in Flatland

<<Besotted Being! You think yourself the perfection of existence,while you are in reality the most imperfect and

imbecile.>> (Edwin Abbott Abbott, Flatland,Section14)

The first half of this little masterpiece is reserved to a long dissertation explaining some of the

social habits in Flatland. Abbott uses a subtle irony in giving information in order to underline and

criticize several aspects of the Victorian society.

<<Since women are deficient in Reason but abundant in Emotions, they ought no longer to be treated as rational, nor

receive any mental education.>>[…] <<They are wholly devoid of brain-power and have neither reflection,

judgment nor forethought, and hardly any memory.>>(Edwin Abbott Abbot,Flatland,Section12)

The first subject that has to be addressed is the treatment of women. According to Abbott’s social

reformist spirit, learning opportunities should have been equal, although Victorian society was

likely to put women on a second level. As a matter of fact, they have been permitted to attend

classes at university only since late XIX century. Many of the young women who gained entrance

to a superior teaching, like Abbott’s daughter, had received most of their education at home. In

Flatland, females are presented as totally incapable of understanding basic teachings. Moreover,

they are just straight line segments, in a world in which cerebral skills are linked to the number of

sides a figure has. Women also embody abstract concepts such as loyalty and love, so difficult to

describe in a scientific language and therefore pointless in a utilitarian world – for instance

Flatland or England. Men in Flatland consider important only what is rational and quantifiable, but

women have other qualities such as genuine feelings. For that reason, men invented two

separated languages, one to talk among them about the “important” things of life and science, the

other to chat with women, who are considered simple-minded if not stupid.

8 La Quarta Dimensione

<<I for my part have never known an Irregular who was not also what Nature evidently intended him to be – a

hypocrite, a misanthropist and, up to the limits of power, a perpetrator of all manners of mischief.>>

(Edwin Abbott Abbott,Flatland,Section 13)

Another aspect of the satire in Abbott’s work is the treatment of those who did not fit in. In the

rigid Victorian society there was little tolerance for irregularity. As a matter of fact, it was often

associated with criminal tendency. The same happens in Flatland: there are some figures that are

not geometrically regular and are therefore discriminated. Isosceles triangles with a very acute

angle are kept in chains and shown during lessons as objects to be studied by Flatland’s pupils. The

narrator spends some words in explaining how schools spare a lot of money in letting them

starving. And if a man from a higher class was born with a small irregularity, there are two options:

either a surgical operation or the internment in an asylum for the rest of his life.

<<As to the doctrine of the Circles, it may briefly be summed up in a single maxim, Attend to your

Configuration.>>[…] <<The duty of fathers is to subordinate their own interest to those of posterity.>>

(Edwin Abbott Abbott,Flatland,Section 12)

Furthermore, Abbott criticizes Victorian culture because the social hierarchy was too rigid and

climbing to a higher class was almost impossible. In Flatland, Edwin takes this aspect to the limit:

the profession and the social status of a person totally depends on the number of sides he has.

A physical peculiarity defines the whole life (this referring also to the slavery of the black people).

Even though it is true that the son would have an extra side and so on – thus elevating the nobility

throughout generations – a square dies a square. The entire existence of anybody would be spend

to ensure his children a better future and protect them. As a matter of fact, according to the

Victorian morality, childhood was a golden age and had to be sanctified; the older must respect

the younger, which is to say the opposite of what any past etiquette had ever stated before.

It is evident that Edwin Abbott Abbott strongly disagreed with the Victorian compromises. He

preferred the kind of education that allowed people to rise on the basis of merit rather than of the

social class into which they were born. The prevailing system is the target of his satire in Flatland.

9 La Quarta Dimensione

A prerogative to the Fourth Dimension

One of the most important features of Flatland is the prerogative of a superior dimension.

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We can find it in the 19 part when the Square was taken by the Sphere from his flat and he starts

asking about the existence of a fourth dimension.

[Square]<<But my Lord has shown me the intestines of all my countrymen in the Land of Two Dimensions by taking

me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into

the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three

Dimensions, and see the inside of every three-dimensioned house, the secrets of the solid earth, the treasures of the

mines of Spaceland, and the intestines of every solid living creature, even the noble and adorable Spheres.

[Sphere] <<But where is this land of Four Dimensions?>>

[Square]<<I know not: but doubtless my Teacher knows.>>

[Sphere] << Not I. There is no such land. The very idea of it is utterly inconceivable>>

(Edwin Abbott Abbot,Flatland,Section 18)

The interesting thing in this passage is that the Square supposes the existence of a fourth dimension,

when he has the knowledge of the third but the Sphere negates it. So the student exceeds the master

thanks to his “open mind” in contrast with the “closed mind” typical of the Victorian period. Thanks

to his way of thinking Abbott was the first who introduced the spacial concept of the fourth

dimension, his reflections were very important and led to the conception of new revolutionary ideas

in the physical and scientific world. 10 La Quarta Dimensione

LA QUARTA DIMENSIONE FISICA

Einstein e la Relatività Ristretta : lo spazio-tempo

Era il 1905. Un ragazzo di ventisei anni, impiegato all'ufficio Brevetti di Berna, nel tempo libero si

dedicava a studi di fisica moderna. E' stato l'atto di nascita della relatività ristretta e il suo ideatore,

Albert Einstein, sarebbe sempre stato ricordato come uno dei più grandi scienziati di tutti i tempi.

La relatività ristretta (o speciale) ha come base la fisica Newtoniana e Galileiana, ma la rivoluziona

in molte sue parti. Tuttavia essa prende in considerazione solo i sistemi di riferimento inerziali,

sistemi che o sono fermi oppure si muovono di moto rettilineo uniforme gli uni rispetto agli altri.

I principi a base di questa teoria sono due: il principio di relatività di Galileo, che afferma che

nessun osservatore chiuso all'interno del proprio sistema di riferimento può dire se esso sia in moto

o fermo e il principio di velocità limite, che invece afferma che la velocità della luce nel vuoto è di

circa 300'000 km/s (che per comodità è indicata con c) e nessun oggetto o nessun segnale può

muoversi a velocità più grande di questa.

Einstein aveva osservato che a velocità relativistiche le trasformazioni di Galileo non sono più

valide, dal momento che la velocità della luce rimane invariata sia che noi ci avviciniamo a una

sorgente luminosa sia se ce ne allontaniamo.

Per avere un riscontro pratico possiamo pensare a quando vediamo una macchina che marcia a

100km/h superarci in autostrada, mentre noi marciamo a 90km/h. Essa sembrerà allontanarsi con

una velocità di 10km/h come enunciato dalle trasformazioni di galileo.

Queste trasformazioni tuttavia descrivono il movimento di un corpo che

si muove a velocità lontano da quelle della luce,come quelle che siamo

abituati s a vedere nella nostra immediata esperienza quotidiana.

Se invece pensiamo a un automobile che ci viene incontro a una velocità di 150km/h e nel