DIGITAL APPROACHES IN ELIMINATING THE HIGHER ORDER SYSTEMATIC EFFECTS IN PTOLEMYS GEOGRAPHIA LONGITUDE AND LATITUDE DIFFERENCES

A. Tsorlini, E. Livieratos

Aristotle University of Thessaloniki, Faculty of Surveying Engineering, Thessaloniki, Greece

atsorlin@topo.auth.gr

 

In his celebrated Geography, Claudius Ptolemy describes geographic sites (i.e. towns, mountain picks, river mouths, promontories and other) as points with given coordinates of spherical longitude and latitude type. These geographic coordinates are following the known Ptolemaic reference system of parallels and meridians, the origin of which are respectively close to actual Equator and close to the Canary Islands many degrees west of the todays origin at Greenwich. It is also known that though latitudes are rather well defined, considering the level of measuring accuracy at Ptolemys times, the longitudes suffer severe shortcomings which are due to the difficulties of measurement time, which corresponds to the longitude. The longitude values given by Ptolemy are also strongly dependent upon the distance from the Canaries eastwards. Previous research showed the order of magnitude of the longitude and latitude differences of Ptolemys values from the todays counterparts both in broader and local scale, but without diving into a systematic geodetic approach on the issue. The problem is challenging and deserves a revisiting because of the advances of digital computational and visualization technologies (informatics and infographics) which are massively available today allowing new approaches and techniques in studying this extraordinary document of our cartographic heritage as it is the Ptolemys Geographia. In the paper, part of a broader research carried out the last years by the Cartography Group of our Faculty we focus our interest on Ptolemys coordinates given in Geography for the area of actual Greece, listed mainly in Book III, Chapter XII about Europe and Table X, but also in some other associated Chapters and Tables about Greece. Storing digitally the coordinates for the area of interest (almost 600 pairs of coordinates), and snooping the data, which is a laborious process because it requires the cross-checking with the relevant coordinated given in a number of Ptolemys Geographia editions (in our case there are used five), the finally accepted list is formed which is compared with their todays values. The core of the study concerns a two-dimensional spatial analysis of the field of differences, testing various transformation functions in order to determine and eliminate the systematic error pattern inherent in Ptolemys coordinates. The result, using new reductive methods in the comparison analysis (e.g. the concepts of the unit sphere, of the common projective support) with all affined illustrations of the associated test, shows the pattern of coordinate differences free of systematic effects up to the 2nd order, testing also and some higher order effects in order to get a better understanding of the whole process. Finally a field of various classes of spatial deformations of isotropic and anisotropic character, are for the first time tested and visualized.