A 4ª dimensão na cultura de massas: Flatland

Ilustração de Flatland: o narrador, um bidimensional quadrado, representando o unidimensional país das linhas, que visitou em sonhos

Stranger. Have you felt me enough by this time? Are you not introduced to me yet?

I. Most illustrious Sir, excuse my awkwardness, which arises not from ignorance of the usages of polite society, but from a little surprise and nervousness, consequent on this somewhat unexpected visit. And I beseech you to reveal my indiscretion to no one, and especially not to my Wife. But before your Lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly know whence his Visitor came?

Stranger. From Space, from Space, Sir: whence else?

I. Pardon me, my Lord, but is not your Lordship already in Space, your Lordship and his humble servant, even at this moment?

Stranger. Pooh! what do you know of Space? Define Space.

I. Space, my Lord, is height and breadth indefinitely prolonged. Stranger. Exactly: you see you do not even know what Space is. You think it is of Two Dimensions only; but I have come to announce to you a Third - height, breadth, and length.

I. Your Lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus denoting Two Dimensions by four names.

Stranger. But I mean not only three names, but Three Dimensions.

I. Would your Lordship indicate or explain to me in what direction is the Third Dimension, unknown to me?

Stranger. I came from it. It is up above and down below.

I. My Lord means seemingly that it is Northward and Southward.

Stranger. I mean nothing of the kind. I mean a direction in which you cannot look, because you have no eye in your side.

I. Pardon me, my Lord, a moment's inspection will convince your Lordship that I have a perfect luminary at the juncture of two of my sides.

Stranger. Yes: but in order to see into Space you ought to have an eye, not on your Perimeter, but on your side, that is, on what you would probably call your inside; but we in Spaceland should call it your side.

I. An eye in my inside! An eye in my stomach! Your Lordship Jests.

Stranger. I am in no jesting humour. I tell you that I come from Space, or, since you will not understand what Space means, from the Land of Three Dimensions whence I but lately looked down upon your Plane which you call Space forsooth. From that position of advantage I discerned all that you speak of as solid (by which you mean "enclosed on four sides"), your houses, your churches, your very chests and safes, yes even your insides and stomachs, all lying open and exposed to my view.

I. Such assertions are easily made, my Lord.

Stranger. But not easily proved, you mean. But I mean to prove mine. When I descended here, I saw your four Sons, the Pentagons, each in his apartment, and your two Grandsons the Hexagons; I saw your youngest Hexagon remain a while with you and then retire to his room, leaving you and your Wife alone. I saw your Isosceles servants, three in number, in the kitchen at supper, and the little Page in the scullery. Then I came here, and how do you think I came?

I. Through the roof, I suppose.

Stranger. Not so. Your roof, as you know very well, has been recently repaired, and has no aperture by which even a Woman could penetrate. I tell you I come from Space. Are you not convinced by what I have told you of your children and household?

Edwin A. Abbott (1838-1926), Flatland: A Romance of Many Dimensions, London, Seely & Co., 1884

Encontram-se muitas outras publicações "online" de Flatland. Destaco o fac-simile (em vários formatos) oferecido pelo "Internet Archive" e a tradução portuguesa, a descarregar ("download") a partir de um "site" de partilha de ficheiros (esnips).

Clicando no título desta entrada ("post"), tem-se acesso a um abrangente artigo, relacionando a 4ª dimensão com as artes, a ciência e a ficção científica. Quarta dimensão, movimentos espiritualistas e obras artísticas são sumarizados por Roann Barris em The Fourth Dimension and Theosophy: A Summary of Key Ideas (em pdf).

A utilização da tetradimensionalidade pelo Futurismo, em especial por Boccioni, posta em relação com a cultura filosófica (sobretudo Henri Bergson) e científica da época, é explorada em Mark Antliff, "The Fourth Dimension and Futurism: A Politicized Space", The Art Bulletin, December 2000.

As referências de Marcel Duchamp (1887-1968) à 4ª dimensão têm sido objecto de diversas reflexões. É possível encontrar muitas "online":

Jerrold Seigel, The Private Worlds of Marcel Duchamp. Desire, Liberation, and the Self in Modern Culture, Berkeley-Los Angeles-Oxford, University of California Press, 1997, sobretudo pp. 99-106

Josep Perelló, "Poincaré i Duchamp: Encontre a la Quarta Dimensió", Artnodes, Juliol de 2005 (em pdf)

Ronda Roland Shearer, Marcel Duchamp's Impossible Bed and Other "Not" Readymade Objects: A Possible Route of Influence From Art To Science / Part II

Roberto Giunti, "The Bachelor Stripped Bare by Cabri Geometre, Even", na revista Tout-Fait (2007), onde mais informação sobre o tema poderá ser encontrada (por exemplo, buscando "dimension").

Uma busca na internet facilmente multiplicará estas referências bibliográficas.

Para ver mexer o "Grand Verre" (actualizando o seu movimento virtual), visite-se Making Sense of Marcel Duchamp e clique-se sobre a obra, no ano de 1923. Jean Suquet, em "LE GRAND VERRE: Visite Guidée" (Paris, l'Échoppe, 1992, versão "online" na Tout-Fait), guia-nos pela sua leitura do "Grand Verre".

Sobre a 4ª dimensão em Malevich (1878-1935), outro dos seus mais constantes cultores, veja-se Kazimir Malevitch, Écrits, Paris, Ed. Lebovici, 1986, prefácio, selecção e tradução para francês de A. Nakov (existe no C.D. do Ar.Co com a cota 7 MAL 01).

Kazimir Malevich (1878-1935), Realismo Pictórico. Rapaz com Mochila - Massas de Cor na Quarta Dimensão, 1915, óleo sobre tela, 71.1 x 44.5 cm, MoMA, Nova Iorque