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The geometry of history. (English) Zbl 0986.00006
Summary: Symbols are not only one of the most ancient expressions of art, they are an integral part of modern life. They can be exceptionally diverse in their meaning. A simple cross can represent an entire theology, a way of life and the complex iconography that is involved within the bounds of the meaning of this symbol. Also logos of companies, political parties, or of a headache pills can inspire trust and confidence, or mistrust and deception. There are international symbols to inform us of the road conditions ahead, at airports or at railway stations to tell us where to put our luggage, the location of the lifts, and where to go to get tickets. We accept these symbols as an extension to our language.
Labyrinths are part of a universal symbolic language. Joseph Campbell claimed that it takes many thousands of years for a myth to change. However, it would appear that it takes twice as long for the essential structure of a symbol to change, if at all. Some labyrinths, complex and difficult geometry structures, have been used for many thousands of years completely unchanged in their structure. However, these structures became embedded into other cultures. While the format of the symbol can change the underlining structure remains untouched.
By examining the geometry of these formats that contain these structures it is possible to track connections in cultural transferences, philosophy, myths, religions and ritual. The purpose of this paper is to construct a topology that will assist in looking for these connection and transferences. In this way geometry can assist in revealing connections in the history of ideas behind the use of symbol.
MSC:
00A69 General applied mathematics
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