1: 1 scale map

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The 1: 1 scale map is a hypothetical map created on a 1: 1 scale , i.e. without any form of generalization . It represents a paradox in cartographic modeling and has been described in several short stories and essays, including by Jorge Luis Borges , Lewis Carroll , Umberto Eco and Michael Ende .

background

A map on a scale of 1: 1,000,000 can show an area of ​​1 million square kilometers in one square meter (approx. The area of Egypt ), a map on a scale of 1: 1000 shows information about one square kilometer on the same area and is therefore more accurate. On a scale of 1: 1, the map area is just as large as the area of ​​the earth's surface shown .

In the history of cartography , maps were also used as objects of prestige . The more precise the map, the better informed the user was. This led to the idea that a ruler interested in information would need a replica of his empire as precisely as possible - possibly on a 1: 1 scale.

Literary reception of the idea

The description of the map on a scale of 1: 1 appears for the first time in 1893 in the novel Sylvie and Bruno Concluded by Lewis Carroll , in which a stranger by the name of "My Lord" reports that a map on a scale of 1: 1 was produced in his country on imperial orders be. It was never used much because the farmers protested against the unfolding. That is why you are now using the country itself as your own map, and this is almost as practical (“we now use the country itself, as its own map, and I assure you it does nearly as well”).

Jorge Luis Borges took up the idea in the short story Del rigor en la ciencia (Eng .: Of the rigor of science ). There he describes an empire with such perfect maps that the map of a single province took up the space of a city and the map of the empire that of a province. When these maps were no longer sufficient, a map was created "which was exactly the size of the empire and coincided with it in every point". Later generations neglected the maintenance of the map, so that only ruins remained. Borges published this story as a purported quote from a fictional author from 1658 to create the illusion of historical authenticity .

The philosopher Umberto Eco also processed the thought game in his work Diario minimo from 1963 . In a humorous but scientific style, in the essay Die Karte des Reiches on a scale of 1: 1, he first defines the requirements for this map (territorial co-extensive and not laid out in foreign territory ; unrestricted or simplified accuracy of reproduction; usability as a semiotic instrument, consequently mobile ; neither packaging nor atlas , but map). From these basic conditions, Eco postulates different practical implementations of a map on a scale of 1: 1 and derives their insoluble representation paradoxes. His 13-page essay closes with three corollaries :

  • "A map on a scale of 1: 1 only gives an imprecise representation of the territory."
  • "The realm becomes unrepresentable the moment you create your map."
  • "Every map on a 1: 1 scale seals the end of the empire as such and would therefore be a map of a territory that is no longer an empire."

In Momo from 1973 Michael Ende used the motif and had the figure Gigi tourist guide invent the story of the tyrant Marxentius Communus, who ordered “a globe to be made that should be as big as the old earth and on which everything [...] would have to be depicted very faithfully [...] ”. The creation of the model consumes all the resources in the world, so that the new mapping ultimately turns out to be identical to the reality to be mapped previously , but which no longer exists.

Scientific reception of the idea

The impracticability of a map on a scale of 1: 1 is obvious, but the literary mind game also served cartographic textbooks as a starting point for looking at maps and scales. It is pointed out that maps are a graphic model of the earth obtained through measurements and that it is impossible to capture and store all details of reality down to the micro level. Problems of the map 1: 1 are, besides the paradoxes listed by Eco:

  • It misses the real purpose of a map, namely as an aid to convey spatial information to the observer in an abstract way, but is an end in itself.
  • Metrological effort, data volume and production costs increase enormously, but the earth's surface can only be described as precisely as the measurement process allows, so generalization always takes place.

Furthermore, parallels can be drawn to any scientific modeling , compare Bonini's paradox .

literature

  1. ↑ a b Alexander CT Geppert, Uffa Jensen, Jörn Weinhold: local calls . Space and Communication in the 20th Century, 2005.
  2. ^ Lewis Carroll: Sylvie and Bruno Concluded . 1893.
  3. ^ Jorge Luis Borges, 1960: El Hacedor . in: Obras Completas . Emecé Editores, Buenos Aires, 1974; dt. Jorge Luis Borges: Borges and me . in: Collected Works . Volume 6, Carl Hanser Verlag, Munich 1982
  4. ^ Umberto Eco, 1963: Diario minimo . (Plato in the striptease bar. Parodies and Travesties, 1990).
  5. ↑ Michael Ende, 1973: Momo . Thienemann, Stuttgart 1973.
  6. ↑ Michael Frank Goodchild, James Proctor: Scale in a Digital Geographic World . in: Geographical and Environmental Modeling . Vol. 1, 1997.
  7. ↑ Guenther Hake, Dietmar Grünreich, Liqiu Meng: Cartography , Berlin 2002, p 168