Did Ptolemy Understand the Moon Illusion?

Abstract

Ptolemy is often wrongly credited with an explanation of the moon illusion based on the size-distance invariance principle. This paper elucidates the two Ptolemaic accounts: one in the Almagest, based on atmospheric refraction, and the other in the Optics, based on the difficulty of looking upwards. It is the latter passage which has been thought to refer to size-distance invariance, but it is more probable that it refers to the idea that the visual rays are diminished by the force of gravity (i.e. that the retinal image is reduced in size). Alhazen was probably the first author to explain the illusion by the size-distance invariance principle, and Roger Bacon the first to explain the enlarged apparent distance of the horizon by the presence of intervening objects. Della Porta was the first to credit Ptolemy with these explanations, and this mistake was repeated by many subsequent authors.