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Historical Epistemology of Space pp 33–41Cite as

Social Control of Space and Metrization

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Abstract

A new form of spatial knowledge develops in early civilizations, in which the allocation and management of land necessitates an administrative control of space and leads to the formation of new means of knowledge representation. The chapter discusses the transformation of human societies from bands and tribes to city-states and empires, which brought about new forms of the social control of space, involving techniques of surveying, writing, and drawing, which became the precondition for the development of geometry and thereby shaped the further development of spatial thinking. The example of Mesopotamia is presented, where practices of area determination are documented on clay tablets from the late fourth millennium BCE on. In the following millennia the system of representations developed in the context of administrative and educational institutions. It is argued that this resulted in a metrization of cognitive models of space, albeit confined, at the time, to a small group of experts.

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Notes

  1. 1.

    Koch and Schiefenhövel (2009), Koch (1984, 49–54). See also Thiering and Schiefenhövel (forthcoming).

  2. 2.

    Wulf Schiefenhövel, personal communication. See also Michel (1983). Other instances of the mythical control of space may be identified in the spatial practices and the spatial thinking reported for the Bororo of the Brazilian central plateau—see the account of the socio-spatial structure of the village Kejara given by Lévi-Strauss (1955, 244–277) —and for the Temne in northern Sierra Leone (Little John 1963).

  3. 3.

    These professions are documented in administrative sources of ancient Mesopotamian cities; they are, e.g., explicitly mentioned in texts from the city of Šuruppag (modern Fara) dating from around 2540 BCE, see Robson (2008, 31). In the proto-literate period, many of these functions were fulfilled by the temple-managers, see Høyrup (1994, 55).

  4. 4.

    Damerow and Lefèvre (1996, 396–397). See also Renn and Valleriani (2014, in particular 13–18).

  5. 5.

    We here follow the middle chronology, for which the third dynasty of Ur roughly coincides with the 21st century BCE and Hammurabi’s reign dates from 1792 to 1750 BCE.

  6. 6.

    See, e.g., Lyons (1927).

  7. 7.

    The earliest evidence for the use of measuring ropes in Egypt is probably the Egypt numeral ‘100’, which has the shape of a coil of rope and is attested in the Second Dynasty (ca. 2890 – ca. 2686 BC) (see Clagett 1992–1999, 752), but probably dates from an earlier time. I am grateful to Jens Høyrup for pointing this out to me.

  8. 8.

    Consider, in particular, the Jiu zhang suan shu ( Nine Chapters on Arithmetical Techniques) , containing, among other things, problems on the calculation of field areas and probably dating to the first century CE. (Guo 1993, 79–213. For editions in European languages, see Vogel 1968; Shen et al. 1999; Chemla and Guo 2004.)

  9. 9.

    On Aztec , Inca , and Maya city planning see, for instance, the respective entries in Selin (1997). On the difficulty to reconstruct the mathematical knowledge involved, see Ascher (1986), Vinette (1986), and other contributions in Closs (1986).

  10. 10.

    Surveying and the determination of field sizes in ancient Mesopotamia and the emergence of Babylonian geometry are discussed in more detail by Damerow (forthcoming); see further Damerow (2001), Høyrup (2002), and Robson (2008).

  11. 11.

    Damerow (2001, 247).

  12. 12.

    See the entry for éš [rope] in the electronic Pennsylvania Sumerian Dictionary at http://psd.museum.upenn.edu/epsd/nepsd-frame.html. Accessed February 7, 2012.

  13. 13.

    See Damerow (2012, 170). For a discussion of the concept of glottographic writing , see Hyman (2006).

  14. 14.

    This way of determining areas remained in use through millennia; it is documented much later in Egypt (Neugebauer 1934, 123), and was also used by the Roman agrimensores (Folkerts 1992, 324). The method may have been used independently by Aztec surveyors; for a reconstruction and discussion of Aztec methods of determining area, see Williams and del Carmen Jorge y Jorge (2008).

  15. 15.

    See Gandz (1929), who distinguishes a geometry of lines and a geometry of angles .

  16. 16.

    For a discussion of possible roles of these texts in the surveyors’ tradition, see Damerow (2001, 271). A brief outline of the development of Sumerian and Babylonian mathematical practices in their institutional contexts is presented by Høyrup (1994, 4–9).

  17. 17.

    Robson (2008, 75–83).

  18. 18.

    Schooltexts from 2700 BCE onwards document the need to learn the relation between unit areas and combinations of unit lengths; see the discussion by Damerow (forthcoming, Sect. 3.3).

  19. 19.

    Owing to the lack of a cipher zero and of a separation between whole units and fractions, the use of the positional system implied the difficulty of keeping track of the order of magnitude for reconversion into the traditional units.

  20. 20.

    See the discussion of tablet YBC 4675 by Damerow (2001, 280–286).

  21. 21.

    Volumes were usually measured in area units, assuming them to be of a conventionally fixed thickness equal to a unit measure of length. If necessary, the thickness was ‘raised’, i.e., the area was multiplied to obtain a volume of different thickness (Høyrup 2002, 22, 36). The results were sometimes converted to measures of capacity; see Friberg (2007, 196–198).

  22. 22.

    See Damerow (2012).

  23. 23.

    Gandz (1929, 453).

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  1. Max Planck Institute for the History of Science, Berlin, Germany

    Matthias Schemmel

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Schemmel, M. (2016). Social Control of Space and Metrization. In: Historical Epistemology of Space. SpringerBriefs in History of Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-25241-4_4

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