Ptolemy with an armillary sphere model, circa 1476, attributed to Pedro Berruguete and Justus le Gand, public domain via Wikimedia Commons
Claudius Ptolemy, known in Arabic as Batlamyus,
, was one of the most influential scientists of his time who made significant contributions to several fields including mathematics, geography, astronomy, astrology, and literature. His name is a mixture of the Greek Egyptian “Ptolemy” and the Roman “Claudius.” The name Claudius indicates he lived under the Roman rule in Egypt, likely with the privileges and political rights of Roman citizenship. The name would have been taken by the first in the Ptolemy ancestry whom was granted citizenship, or perhaps by Claudius Ptolemy [1].
According to various sources, Claudius Ptolemy was born ca. 100 AD in Egypt [1]. He lived in or near Alexandria most of his life and died ca. 170 AD, also in Alexandria, Egypt [1, 2]. His recorded observations in Almagest, his astronomical treatise, can be traced back to the 11th Year of Hadrian’s rule (127 AD) and Pius’ reign (141 AD). Emperor Marcus Aurelius was in power from 161 – 180 AD, a period during which Claudius Ptolemy, as mentioned, passed away at an approximate age of 70 [2]. Very little is known of Ptolemy’s personal life including information pertaining to his ancestry or any significant relationships. Some scholars believe that Ptolemy was ethnically Greek [3], and some suggest he was a Hellenized Egyptian [4] and others, in Arabic sources, have referred to him as “the Upper Egyptian” [5]. The ninth-century Persian astronomer Abu Ma’shar Balkhi
, also listed Ptolemy as a member of Egypt’s royal lineage [6], although this has been disputed.
Ptolemy was the author of several scientific treatises, and his major works have fortunately survived. In general, he followed Aristotle philosophically; however, he regarded Aristotle’s division of science into theoretical, productive, and practical science with far greater reverence. He wrote in Greek and utilized Babylonian astronomical data. His work was translated to Arabic and then to Latin [7]. His three major contributions that influenced Byzantine, Islamic, and European science are Almagest, Geography, and Astrological Treatise.
Almagest is the astronomical treatise discussing planetary theory and was originally entitled the “Mathematical Treatise,” also known as the “Great Treatise.” It was in use from the second century up to the late Renaissance [8]. This is thought to be Ptolemy’s greatest contribution, providing, at the time, a satisfactory theoretical model to explain the rather complicated motions of the planets. Ptolemy wrote of his observations of solstices and equinoxes, and based on these observations, he determined the lengths of the seasons. He used geometric models to predict the positions of the sun, moon, and planets, using combinations of circular motion known as epicycles and then provided a model for the orbit of the sun, and the motion of the moon, as well as a theory of eclipses. Ptolemy then created a sophisticated mathematical model to fit observational data. His geocentric theory prevailed for nearly 1400 years until Copernicus offered a new one. In Geography, in eight books, Ptolemy attempted to map the known Greco-Roman world by giving latitude and longitude coordinates of the major locations. However, the maps drawn by Ptolemy were quite inaccurate because he was relying on data collected by questionable sources [9]. One of these maps was used by Christopher Columbus on his westward-bound trip to Asia, in which he discovered the Americas. In Astrological Treatise, Ptolemy attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. Ptolemy claimed that while the Almagest calculates the positions of the heavenly bodies, his astrology book was a companion work describing the effects of the heavenly bodies on people’s lives. This work is sometimes known as the Apotelesmatika but more commonly known as the Tetrabiblos or the “Four Books.”
4.1 Optics
Ptolemy’s Optica represents an advanced stage in Ptolemy’s intellectual development and consists of five books. The only surviving text of Ptolemy’s Optics is a badly mangled, twelfth-century Latin version of an Arabic translation in about twenty manuscripts, which was translated by Eugenius of Palermo (c. 1154) [10]. Lacking any trace of the original, it is very difficult to reconstruct the Optics’ early textual history with certainty. In Optics, Ptolemy writes about properties of light, the study of color, reflection (catoptrics), refraction (dioptrics), and mirrors of various shapes. The first chapter of the book deals with the subjects of light, the visual rays, and color, sections that unfortunately are lost. One of its most striking features is believed to be the establishment of theory by experiment, frequently supported by the construction of special apparatus. There is a debate, however, whether the subject matter was derived or original. Nonetheless, it is an impressive example of the development of a mathematical science using physical data.
Ptolemy’s work shaped part of the early history of optics [11] and influenced the more famous eleventh-century “Book of Optics” by Alhazen (Ibn al-Haytham). It contains the earliest surviving table of refraction from air to water and to glass. The refraction values (with the exception of the 60° angle of incidence) appear to have been obtained from an arithmetic progression [12]. Ibn al-Haytham devoted several studies to Ptolemy’s Optics and wrote a critique, “Doubts on Ptolemy,” including a point-by-point discussion of Ptolemy’s tenets. Ptolemy also differentiated seven colors in the rainbow, but his explanation of the phenomena was no different than that of Aristotle.
Optics is an important contribution to the early history of perception. Ptolemy’s view on vision was based on an extramission–intromission theory, whereby the rays (or flux) travel from the eye and form a cone. The extramission was in line with the earlier model proposed by Euclid (ca. 300 BC), and later also by Galen (130–200 AD), that shaped all geometrical optics [13]. The vertex of the vision cone would thus be within the eye, and the base would define the visual field. Ptolemy believed that the rays were sensitive and conveyed information back to the observer’s intellect about the distance and orientation of surfaces. His ideas about perception were similar to those of Aristotle. He believed that color is what is seen and that spatial characteristics of the scene, i.e., information pertaining to size, shape, position, and movement, were not specific for sight. The final stage of the visual process according to Ptolemy was the judgment phase when sensation becomes perception [12]. An important aspect of this model was the relationship between size and shape of the object according to the visual angle subtended at the eye combined with perceived distance and orientation. The relationship between the distance of objects and size was not well defined until this point and Ptolemy provided an early model that related perceptual size to distance and thus shape constancy, and this view was supported by the Stoics [14].
Ptolemy was probably the first to describe color mixing including the optical mixing in the eye. He used a wheel with colored sections to obtain an impression of the required time for a single observation. He also discussed the mixing of individually bright colors in a mosaic from a distance, whereby each is not individually interpreted or perceived and an optical mixture is viewed. Ptolemy offered explanations for several phenomena concerning illumination and color, size, shape, movement as well as binocular vision. His discoveries in the field of binocular vision and the explanation of the process were not far from the correct model [15]. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors. He attempted to explain the Moon illusion where the apparent size of the moon or the sun on the horizon is enlarged and attributed this to the difficulty of looking upwards; this is considered to be somewhat abstruse [16, 17].