Flatland
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Flatland. A Romance of Many Dimensions is a novella published in 1884 by Edwin Abbott Abbott under the pseudonym A. Square. The writing is a satire on the structure of Victorian society and a mathematical essay on the fourth dimension .
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A. Square, the first-person narrator in Flatland , lives in a flat, i.e. two-dimensional world, whose inhabitants have the shape of simple geometric shapes and are subject to a strict caste system . Women are straight lines. Soldiers and workers are isosceles triangles . They belong to the lower class and have no social reputation because not all of their pages are of the same length and they are therefore considered defaced. Because of their acute angle, however, they are dangerous as they can easily cause fatal injuries to other figures. The middle class is formed by equilateral triangles such as merchants. Above it stand the scholars who are squares , like the narrator himself, or pentagons . All figures with six or more sides belong to the nobility, whereby their social position is higher, the more sides they have. The highest social position are held by the circles that make up the priestly caste. In Flatland it is natural law that every male descendant of an equilateral father has one more side than the father. So each generation goes up one level, with the exception of the descendants of isosceles triangles. The isosceles triangles always remain on the same level in the social hierarchy.
In the first part of the book, which is a satire on the structure of Victorian society, the square describes in detail the social characteristics of Flatland. In particular, the complicated methods are shown with which the residents recognize the shape of their counterpart and how to deal with them.
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In the second part, which is a mathematical essay about the existence of a fourth spatial dimension, A. Square visits the one-dimensional land of lines in a dream , a world whose inhabitants are only stretches of different lengths on a straight line , whereby their length determines their social position. He tries in vain to convince the king of lineage that there is another dimension. Another dream leads him into the zero-dimensional point land, where he sees nothing but a zero-dimensional point that only knows itself and praises itself in self-talk in the highest tones. Back in his two-dimensional world, the narrator sees a sphere , a guest from our three-dimensional world. Only after a long effort does the sphere succeed in convincing the square of the existence of the third dimension, and it takes it on a sightseeing flight over its two-dimensional home. The narrator, who has now fully realized dimensionality, then surpasses the sphere, his teacher, in that he even describes the conceivability of four- and higher-dimensional worlds, which annoys the sphere, which therefore pushes him back into his world. When the narrator finally wants to spread his knowledge of the higher dimensions among the residents of Flatland, he only meets with irritation and is ultimately incarcerated as a rebel.
interpretation
Abbott wanted to promote the geometric or stereometric thinking of his readers with his social satire and caricature the social order and prejudices of his time. The inhabitants of the open country have extremely rigid manners and consider women, who are lines with them, as intellectually poor, which can be interpreted as an exaggerated distortion of the conditions in Victorian England.
Today, in addition to its undiminished entertainment value, the book is mainly interesting because it gives the reader a vivid impression of other rooms . It is just as difficult for us to imagine the four- and multi-dimensional spaces of mathematics and physics as it is for the square to deal with the three-dimensional space that we take for granted.
Paul Watzlawick wrote the retelling Flachland and interpreted it as the relativity of reality.
reception
A short story inspired by Flatland was published by mathematician Charles Howard Hinton in 1907 during Abbott's lifetime under the title An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension . In 2001, the novel Flacherland by mathematics professor Ian Stewart was published , which transfers Abbott's work into the present with the help of current mathematical and physical knowledge. Stewart's novel retains its satirical character despite its obviously higher scientific content (topics such as Feynman diagrams , the superstring theory and quantum mechanics are built in), but transfers it to the unreality of today's physical worldview. Dionys Burger published a sequel to Flatlands with his novel New Year's Eve Conversations of a Hexagon , the main character of which is a grandson A. Squares.
The series The Big Bang Theory makes reference to Abbott's work (season 3, episode 12). In the series The Orville , the crew of the spaceship of the same name discovers a two-dimensional world that reminds Captain Mercer of Flatland (season 1, episode 11).
Translations into German
There are five German-language translations (see: German-language editions ). Werner Bieck does not offer the full text in his selection translation published in 1929. In his 1982 translation, Peter Buck used a freer translation style and - according to his foreword - defused the "misogynistic depictions" in his version. Joachim Kalka, Antje Kaehler and Daniel Tibi stay close to the original text in their translations and thus maintain the social criticism.
expenditure
- Edwin A. Abbott: Flatland: A romance of many dimensions. Seeley, London 1884.
- Edwin A. Abbott: Flatland: A romance of many dimensions. Seeley, London 2nd and rev. ed. 1884.
- Edwin A. Abbott: Flatland: A romance of many dimensions. Basil Blackwell, Oxford 3rd and rev. ed. 1926.
These three classic English-language editions were followed by a large number of modern editions. These include:
- Ian Stewart: The Annotated Flatland. Perseus Publishing, Cambridge 2002. ISBN 0-7382-0541-9 .
- Edwin A. Abbott: Flatland: A romance of many dimensions. Ed. by Rosemary Jann. Oxford University Press, Oxford 2006. ISBN 0-19-280598-3 .
German-language editions
- Edwin A. Abbott: Flat land. A story of the dimensions. Selected and translated into German by Werner Bieck. Teubner, Leipzig 1929.
- Edwin A. Abbott: Flat land. A multi-dimensional novel. Ed. U. trans. by Peter Buck. Franzbecker, Bad Salzdetfurth 1982. ISBN 3-88120-020-7 .
- Edwin A. Abbott: Flat land. A multi-dimensional novel. Trans. V. Joachim Kalka. Klett-Cotta, Stuttgart 1982; Götz, Laxenburg 1999. ISBN 3-9501011-0-1 .
- Edwin A. Abbott: Flatland. A fairy tale with many dimensions. Trans. V. Antje Kaehler. RaBaKa, Neuenkirchen 2009. ISBN 978-3-940185-15-0 .
- Edwin A. Abbott: Flatland. A fantastic story across many dimensions. Trans. V. Daniel Tibi. Verlag Traugott Bautz, Nordhausen 2012. ISBN 978-3-88309-767-1 .
See also
Web links
- Flatland with Flatland drawings
- Lesson on Abbot's lowland on lehrer-online.de
- Entry for Flatland in the MathEduc database
- Edward Rothstein: SHELF LIFE; Discovering Dimensions Beyond Imagining in the New York Times on April 21, 2001
Individual evidence
- ↑ Paul Watzlawick: How real is reality. (PDF 1.75 MB) Delusion - deception - understanding. (No longer available online.) Piper Verlag, Munich, 1976, pp. 274-279 , archived from the original on January 18, 2016 ; Retrieved January 19, 2016 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ^ Dionys Burger, New Year's Eve Talks of a Hexagon, Deubner-Verlag Cologne, Dutch original: Bolland, Een roman van Gekromde Ruimten en Uitdijend Heelal, 's-Gravenhage, 1957
