Ptolemy : biography
Maps based on scientific principles had been made since the time of Eratosthenes (3rd century BC), but Ptolemy improved projections. It is known that a world map based on the Geographia was on display in Augustodunum, Gaul in late Roman times. In the 15th century, Ptolemy’s Geographia began to be printed with engraved maps; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 (Campbell, 1987). An edition printed at Ulm in 1482, including woodcut maps, was the first one printed north of the Alps. The maps look distorted when compared to modern maps, because Ptolemy’s data were inaccurate. One reason is that Ptolemy estimated the size of the Earth as too small: while Eratosthenes found 700 stadia for a great circle degree on the globe, Ptolemy uses 500 stadia in the Geographia. It is highly probable that these were the same stadion, since Ptolemy switched from the former scale to the latter between the Syntaxis and the Geographia, and severely readjusted longitude degrees accordingly. If they both used the Attic stadion of about 185 meters, then the older estimate is 1/6 too large, and Ptolemy’s value is 1/6 too small, a difference explained due to ancient scientists’ use of simple methods for measuring the earth, which were corrupted either high or low by a factor of 5/6, due to the air’s bending of horizontal light rays by 1/6 of the Earth’s curvature. See also Ancient Greek units of measurement and History of geodesy.
Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree (2 degrees for Byzantium, 4 degrees for Carthage), though capable ancient astronomers knew their latitudes to more like a minute. (Ptolemy’s own latitude was in error by 14′.) He agreed (Geographia 1.4) that longitude was best determined by simultaneous observation of lunar eclipses, yet he was so out of touch with the scientists of his day that he knew of no such data more recent than 500 years before (Arbela eclipse). When switching from 700 stadia per degree to 500, he (or Marinos) expanded longitude differences between cities accordingly (a point first realized by P.Gosselin in 1790), resulting in serious over-stretching of the Earth’s east-west scale in degrees, though not distance. Achieving highly precise longitude remained a problem in geography until the invention of the marine chronometer at the end of the 18th century. It must be added that his original topographic list cannot be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony to the persistent popularity of this influential work in the history of cartography.
Optics
His Optics is a work that survives only in a poor Arabic translation and in about twenty manuscripts of a Latin version of the Arabic, which was translated by Eugene of Palermo (c. 1154). In it Ptolemy writes about properties of light, including reflection, refraction, and colour. The work is a significant part of the early history of optics and influenced the more famous 11th century Optics by Alhazen (Ibn al-Haytham). The work is also important for the early history of perception. Ptolemy combined the mathematical, philosophical and physiological traditions. He held an extramission-intromission theory of vision: the rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer’s intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy, a view supported by the Stoics.H. W. Ross and C. Plug, "The History of Size Constancy and Size Illusions", in V. Walsh & J. Kulikowski (eds.) Perceptual Constancy: Why Things Look as They Do. Cambridge: Cambridge University Press, 1998, pp. 499-528. Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement and binocular vision. He also divided illusions into those caused by physical or optical factors and those caused by judgemental factors. He offered an obscure explanation of the sun or moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards.H. E. Ross and G. M. Ross, "Did Ptolemy Understand the Moon Illusion?", Perception 5 (1976): 377-395.A. I. Sabra, "Psychology Versus Mathematics: Ptolemy and Alhazen on the Moon Illusion", in E. Grant & J. E. Murdoch (eds.) Mathematics and Its Application to Science and Natural Philosophy in the Middle Ages. Cambridge: Cambridge University Press, 1987, pp.217-247.
