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Title: Mathematics for history's sake : a new approach to Ptolemy's Geography
Author: Mintz, Daniel V.
ISNI:       0000 0004 2720 4134
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 2011
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Almost two thousand years ago, Claudius Ptolemy created a guide to drawing maps of the world, identifying the names and coordinates of over 8,000 settlements and geographical features. Using the coordinates of those cities and landmarks which have been identified with modern locations, a series of best-fit transformations has been applied to several of Ptolemy’s regional maps, those of Britain, Spain, and Italy. The transformations relate Ptolemy’s coordinates to their modern equivalents by rotation and skewed scaling. These reflect the types of error that appear in Ptolemy’s data, namely those of distance and orientation. The mathematical techniques involved in this process are all modern. However, these techniques have been altered in order to deal with the historical difficulties of Ptolemy’s maps. To think of Ptolemy’s data as similar to that collected from a modern random sampling of a population and to apply unbiased statistical methods to it would be erroneous. Ptolemy’s data is biased, and the nature of that bias is going to be informed by the history of the data. Using such methods as cluster analysis, Procrustes analysis, and multidimensional scaling, we aimed to assess numerically the accuracy of Ptolemy’s maps. We also investigated the nature of the errors in the data and whether or not these could be linked to historical developments in the areas mapped.
Supervisor: O'Connor, John J.; Gratwick, Adrian Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: History of mathematics ; Ptolemy ; Geography ; Historical maps ; G87.P93M5 ; Ptolemy, 2nd cent. Geographia ; Geography, Ancient--Maps ; Cartography--History ; Error analysis (Mathematics) ; Cluster analysis ; Multidimensional scaling