Claudius Ptolemy's Geography (c. AD 150) stretches the inhabited world across roughly 180 degrees of longitude, about 40% more than its true span, making this the most conspicuous error in ancient cartography. Shcheglov (Isis, 2016) refuted the single-factor explanation that blames Ptolemy's adoption of an underestimated Earth circumference and offered instead a qualitative multi-factor account: an underestimated circumference, systematically overreported travel distances, and losses introduced in the chain of unit conversions from surveyor reports through Marinus of Tyre to Ptolemy's coordinates. Converting that account into a quantitative, testable reconstruction remains open. This problem asks for the three missing measured inputs — the stade values actually used by Eratosthenes, Marinus, and Ptolemy; the statistical structure (by region, route type, and period) of the overestimation in transmitted distance figures; and the sequence of conversions and roundings in the transmission chain — integrated into a region-by-region numerical model that predicts local stretching factors (the factor by which east–west distances in each region are inflated relative to their true values) from these inputs and can be checked against the transmitted coordinates and independent philological, archaeological-metrological, and geodetic evidence.

Background

Ptolemy's Geography (Geographike Hyphegesis, c. AD 150) lists roughly 6,300 places of the oikoumene — the inhabited world known to the Greeks and Romans — with latitudes and longitudes, so that its coordinate tables amount to a virtual world map. Its most glaring defect is longitudinal: Ptolemy spans the oikoumene from the Fortunate Isles (the Atlantic islands, usually identified with the Canaries or Madeira, that serve as his prime meridian, i.e. his zero of longitude) to Sera, the capital of the Seres at the eastern limit of the inhabited world usually identified with Han-dynasty Chang'an in China, across about 180 degrees, whereas the true arc is roughly 130–140 degrees, so east–west distances on his map are inflated by a factor of about 1.4. A long tradition sought a single culprit: Ptolemy's adoption of Eratosthenes' too-small value for the circumference of the Earth. Eratosthenes (3rd century BC) had computed 252,000 stades; Ptolemy used 180,000 stades (500 stades per degree of a great circle). The stade (stadion, plural stadia) was the standard Greek unit of long distance, formally 600 feet, but its metrical value depended on which foot standard was in use: the 'common' stade of about 185 m attested by most sources, an 'Egyptian' stade near 157.5 m, and other candidates from roughly 148 m to 210 m. On the single-factor view, Ptolemy (or his predecessor Marinus of Tyre, whose work is lost and known only through Ptolemy's account of it) converted distances measured in stades of one standard into degrees using a circumference expressed in another, inflating longitudes accordingly. Shcheglov (2016) argued that this hypothesis does not stand up to scrutiny: the circumference shortfall can account for only about 17% of the east–west stretching, and presupposing a tradition of high-accuracy geodesy before Ptolemy is implausible. The remainder must come from other factors: systematically overestimated travel distances (ancient itinerary and periplus figures — periploi being the genre of coastal sailing directories — run high relative to modern measurements, a phenomenon documented for Pliny the Elder's figures), losses and roundings in the chain from land surveyors and ships' logs through Marinus to Ptolemy, and Ptolemy's own procedures. Prior quantitative work addressed pieces of this separately: statistical analyses of the coordinate tables show heavy rounding (coordinates given to whole, third, half, or twelfth degrees) and 'low resolution', and geodetic-statistical 'rectification' methods (Marx 2012) fit global transformations to identify groups of places with homogeneous systematic error, aiding identification of unknown places. But no analysis determines which stade values were used by which author, characterizes the overestimation bias statistically, or reconstructs the conversion chain — and no model predicts the local stretching factors of Ptolemy's map from measured inputs.

Problem Statement

Turn the qualitative multi-factor explanation of the longitudinal overextension of Ptolemy's map into a quantitative, testable reconstruction. Specifically, determine: (1) the numerical length(s) of the stade(s) actually employed by Eratosthenes, by Marinus of Tyre and other pre-Ptolemaic sources, and by Ptolemy in the Geography, with evidence tying particular values to particular authors, regions, or periods rather than a plausible range; (2) the statistical structure of the systematic overestimation in transmitted ancient distance figures — its distribution and its variation by region, route type (coastal periplus vs overland itinerary), and period; (3) the sequence of conversions and roundings by which measured distances were transformed in the chain from surveyor reports through Marinus to Ptolemy's coordinate tables, including which segments rest on Eratosthenes' degree framework; and (4) an integration of these into a region-by-region numerical model that predicts the local stretching factors of Ptolemy's map — the ratio of distances implied by Ptolemy's coordinates to the corresponding true distances in each region — from measured inputs, and is validated against the transmitted coordinates (across the manuscript recensions, i.e. the distinct manuscript traditions, chiefly the Byzantine Greek and Latin-derived families, that transmit partly conflicting coordinate variants) and against independent itinerary corpora, archaeological-metrological evidence, and modern geodesy. These four determinations are jointly required: the model of (4) integrates the measured inputs of (1)–(3), and completing a proper subset of them does not by itself resolve the problem. The reconstruction determines, for each part, its own quantitative result: (1) determinate stade values assigned to the named authors, regions, or periods by discriminating among the competing candidates; (2) the overestimation's distribution, specified parametrically or empirically, with its region, route-type, and period breakdown; (3) the conversion and rounding steps in order, with the unit ratio applied at each step; and (4) the model's quantitative fit against the transmitted coordinates and against the independent itinerary, archaeological-metrological, and geodetic evidence.

References

  1. Shcheglov, Dmitry A. (2016). 'The Accuracy of Ancient Cartography Reassessed: The Longitude Error in Ptolemy's Map.' Isis 107(4): 687–706. doi:10.1086/689763, https://doi.org/10.1086/689763 (source paper; full text paywalled)
  2. Shcheglov, Dmitry A. (2016). 'The Error in Longitude in Ptolemy's Geography Revisited.' The Cartographic Journal 53(1): 3–14. doi:10.1179/1743277414Y.0000000098, https://doi.org/10.1179/1743277414Y.0000000098 (companion precursor)
  3. Shcheglov, Dmitry A. (2017). 'Eratosthenes' Contribution to Ptolemy's Map of the World.' Imago Mundi 69(2): 159–175. doi:10.1080/03085694.2017.1312112, https://doi.org/10.1080/03085694.2017.1312112
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  13. Roller, Duane W. (2024). The Geographical Guide of Ptolemy of Alexandria: An Analysis. London and New York: Routledge. x + 231 pp., maps. ISBN 978-1-032-16441-0 (book; no DOI)
  14. Jones, Alexander (2025). '(D.W.) Roller The Geographical Guide of Ptolemy of Alexandria. An Analysis. Pp. x + 231, maps. London and New York: Routledge, 2024. ISBN: 978-1-032-16441-0.' The Classical Review 75(1): 110–112. doi:10.1017/S0009840X25000071, https://doi.org/10.1017/S0009840X25000071 (review of Roller 2024)