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The Mystery of The Moon IllusionExploring Size Perception$

Helen Ross and Cornelis Plug

Print publication date: 2002

Print ISBN-13: 9780198508625

Published to Oxford Scholarship Online: April 2010

DOI: 10.1093/acprof:oso/9780198508625.001.0001

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(p.199) Appendix: Summary of scientific developments relating to the moon illusion

(p.199) Appendix: Summary of scientific developments relating to the moon illusion

The Mystery of The Moon Illusion
Oxford University Press

Prehistoric period

3000–2000 BC Late Neolithic people built stone circles, such as Stonehenge in England, which acted as calendars and show systematic interest in the movements of the sun and moon.

Classical period (700 BC–AD 200)

The scientific tradition

600–300 BC

A scientific world view developed in Greece: for the first time philosophers attempted to give a natural, rather than a supernatural, explanation of the world. The climax of this Golden Age was marked by the works of Aristotle (350 BC).

300 BC–AD 200

In spite of the development of natural philosophy, science and magic were for many centuries not seen as separate provinces of knowledge. This is evident in, for example, Pliny’s 37-volume Natural history (AD 77).

AD 0–200

Greek scientific knowledge reaches China.

The solar system

700 BC

Arithmetical methods to describe the irregular motions of the sun, moon, and planets were developed by the Babylonians for astrological purposes. The systems of time and angle measurement used by them (based on much older Babylonian systems of measurement) have remained basically the same to the present day.

550 BC

Anaximander pictured the heavens as a sphere rotating around the earth on a fixed axis.

(p.200) 500 BC

Pythagoras taught that the earth was spherical, that the morning and evening star were the same planet, that the moon’s orbit was not in the plane of the earth’s equator, and that the sun, moon, and planets all travel in their own separate paths. He proposed separate celestial spheres to carry them – a notion that survived to the sixteenth century.

450 BC

Anaxagoras explained the phases of the moon and eclipses.

350 BC

Heracleides suggested that the apparent daily rotation of the heavens could be explained by the rotation of the earth on its axis, and that Mercury and Venus revolve around the sun. These views were not generally accepted until the time of Copernicus in the fifteenth century.

270 BC

Aristarchus suggested that all the planets revolve around the sun, but his theory, like that of Heracleides, found no favour. He also attempted the first scientific estimate of the relative distances to the moon and sun.

240 BC

Eratosthenes made the first scientific (and reasonably accurate) estimate of the size of the earth.

130 BC

Hipparchus developed a model of planetary motion in terms of deferents and epicycles; compiled the first star catalogue, containing the positions and brightnesses of 1000 stars; and made the first reasonably accurate measurement of the moon’s parallax (and therefore its distance from the earth). He knew that the moon’s distance was not the same at all points in its orbit.

AD 140

Ptolemy’s Almagest was published: it remained the standard work in astronomy to the fifteenth century. Ptolemy rejected the rotation of the earth and the theory that some or all the planets move around the sun. As a result these theories were not generally accepted for the next 14 and 15 centuries respectively.

Optics, physiology and vision

450 BC

Alcmaeon discovered the optic nerve, and concluded that the brain is the central organ in sensation and perception. Empedocles’ theory of vision: visual rays emitted by the eye fall on the object and return to the eye to cause a visual image. This theory remained important throughout classical times.

(p.201) 430–330 BC

The Hippocratic medical corpus was written by various authors, establishing empirical medicine and medical ethics.

320 BC

Euclid’s book on optics claimed that perceived size is equivalent to visual angle.

300 BC

Hirophilus dissected the brain and nervous system, distinguishing between sensory and motor nerves.

100 BC

The refraction of light was recognized.

AD 140–170

Ptolemy studied the refraction of light (in water), and discussed many perceptual effects including the scaling of image size for perceived distance.


Cleomedes argued that perceived size is equivalent to linear size scaled for distance.


The Greek physician Galen studied the brain and nervous system through dissections. His description of the anatomy of the eye was accepted for several centuries, until improved upon by Arab scholars.

Arabic science (750–1200)


Origin of Arabic science.


During the reign of Caliph al-Mamun many classical Greek works were translated into Arabic in Baghdad, including Ptolemy’s Almagest (by the Jew Sahl al-Tabari) and the works of Plato and Aristotle. Hunayn ibn Ishaq translated the medical texts of Galen and the Hippocratic corpus.

c. 830

Al-Kwarizmi compiled his book on algebra, in which Hindu numerals, including zero (now usually referred to as ‘carabic numbers’) were introduced to the Arab world.


Arabic science surpassed that of any other culture. The climax of Arabic learning was reached during the first half of the eleventh century.

(p.202) 1040

Ibn al-Haytham, perhaps the greatest physicist of medieval times, investigated the rainbow, estimated the height of the earth’s atmosphere and improved understanding of the anatomy of the eye. Like the ancients, he regarded the lens as the sensitive organ of vision. He rejected the visual ray theory in favour of the idea that vision occurs when light scattered from objects enters the eye. He also discussed many perceptual effects, including the scaling of image size for perceived distance.

Science in medieval Europe (900–1500)

The scientific tradition


Gerbert of Aurillac (later Pope Sylvester II) introduces Hindu-Arabic numerals (except for 0) to the diocesan school of Reims, but with little effect. Subsequent translations into Latin of al-Kwarizmi’s book on algebra (e.g. by Robert of Chester, c. 1100) and books on arithmetic with the new numbers (e.g. by Leonardo Fibonacci of Pisa, 1202) led to their gradual adoption in Europe over the next few centuries, making arithmetic much easier and stimulating progress in mathematics.


Many important classical and Arabic works were translated from Arabic into Latin for the first time, especially in Toledo, by Gerard of Cremona (1114–87) and others: these works included Ptolemy’s Almagest and works of Aristotle, Galen, and the Hippocratic corpus. During this and the next century there was much interaction between the declining Arabic science, Jewish scholarship, and emerging Christian science. This led to the supremacy of Latin as the scientific language for three centuries, and the scientific supremacy of western Europe.


Rise of the universities in Europe, continuing in the next century.


Direct translation of classical works from Greek into Latin commenced, while translation from Arabic declined.


Printing with moveable type was introduced in Europe. It soon spread throughout Europe and resulted in increased literacy and improved scientific communication. (Printing with moveable type of ceramic and wood was invented in China about 1050, by Pi Sheng. Due to the large number of Chinese characters it was not very successful.)

(p.203) 1420–1520

Voyages of exploration, especially by the Portuguese, led to a rapid expansion of geographical and related knowledge.

Medieval optics


A period of heightened interest in‘optics’, which at that time included the study of the eye, illusions, perspective, binocular vision, shadows, colours, refraction, the camera obscura, the rainbow, and height of the atmosphere. This interest resulted mainly from Ibn al-Haytham’s work of the eleventh century. Some of the leading writers were Dietrich of Freiberg, John of Paris, Kamal al-Din, Roger Bacon, John Pecham, Witelo, and Levi ben Gerson. The latter studied the small variations in the angular diameters of the moon and sun with a camera obscura. Spectacles were mentioned from 1289.

Science in modern times (1500–2000)

The scientific tradition


A new approach to the study of nature (and man) developed in Europe. It was characterized by a mechanistic view of nature and the human body, inspired mainly by the mechanics of Galileo and the philosophy of Descartes. The latter was especially influential in separating answerable from unanswerable questions. This allowed the working of the senses to be investigated with some success, as it led to the realization that perception involves aspects of physics, anatomy, physiology, and psychology.

Francis Bacon’s support of empirical science and inductive logic helped to advance the scientific approach. (He did not accept the Copernican theory.)

Scientific institutions began to flourish: the Royal Society of London was founded in 1663, and the Academia del Cimento in Italy some years earlier. The Royal Greenwich Observatory was founded in 1675.

The language of science gradually changed from Latin to various European languages: Newton’s Principia mathematica was one of the last major works written in Latin.


English, French, German, Italian, and other national languages were used by scientists. This caused communication problems that were almost unheard of in the preceding centuries. During the twentieth century English gradually became the dominant language in science.

The solar system


Copernicus’s On the revolution of the heavenly spheres contained the hypothesis that the sun, rather than the earth, was the centre of the solar system. Although the idea was not (p.204) new (see Aristarchus above), Copernicus presented the theory in full mathematical detail. It neatly explained the limited motions of Mercury and Venus and the retrograde motions of the outer planets. The theory was not generally accepted at the time, mainly due to the counterintuitive implication that the earth moves around the sun at great speed. It was not taught to students during the sixteenth century. Copernicus retained the complex system of circular motions and epicycles of the ancients.


A vast series of very accurate planetary observations were made by the Danish astronomer Tycho Brahe. He also inferred from parallax observations that the comet of 1577 was further than the moon (and therefore not an atmospheric phenomenon as Aristotle had thought). Furthermore, the comet’s orbit was found to be elongated rather than circular, showing that the planetary spheres have no material existence.


Galileo established the science of mechanics. His work removed the main objection to the Copernican theory, namely that the earth’s rapid motion would strip it bare.


Galileo first used a spyglass for astronomical observations. His discovery of the satellites of Jupiter and the phases of Venus contributed to the gradual acceptance of the Copernican system between 1610 and 1640. He also discovered craters on the moon, many stars not visible to the unaided eye, sunspots, and the round appearance of the planets. He explained the dimly visible new moon in terms of earthshine.


Kepler discovered his three laws of planetary motion, confirming the sun as the centre of the solar system. He also did away with celestial spheres and the complex system of circles and epicycles. The importance of his work was not immediately appreciated. The English astronomer Jeremiah Horrocks was the first fully to accept Kepler’s laws: in 1640 he applied them to the moon’s motion around the earth.


The measurement of atmospheric pressure was initiated by Evangelista Torricelli.


The first lunar atlas was drawn up by Johannes Hevelius, in which the‘seas’ and mountain ranges were named.


Giovanni Riccioli named the craters of the moon after famous astronomers, a practice universally adopted since then.

(p.205) 1656–1658

Christiaan Huyghens developed the first accurate pendulum clock, introducing accurate time measurement into astronomy. He also invented a micrometer for the accurate measurement of small angles with the telescope.


The circumference of the earth was measured accurately for the first time, by the French astronomer Jean Picard.


Distances in the solar system were first established with reasonable accuracy by Giovanni Cassini, from his measurements of the parallax of Mars.


The velocity of light was estimated for the first time by Olaus Roemer, from occultations of Jupiter’s satellites.


Sir Isaac Newton’s Principia mathematica revolutionized theoretical astronomy by introducing the theory of universal gravitation and advanced mathematical methods. This work explained Kepler’s laws of planetary motion and other phenomena, and predicted many new ones. It was immediately recognized as a momentous achievement.


The planet Uranus, the first new planet to be discovered since antiquity, was identified by William Herschel.


The first scientific observations of the atmosphere at different heights were made from a balloon by Jean Biot and Joseph Gay-Lussac.


The 11-year sunspot cycle was discovered by the German astronomer Heinrich Schwabe.


The planet Neptune was discovered on the basis of perturbations of the orbit of Uranus. The required calculations were made independently by Urbain Leverrier of France and John Adams of England. The discovery provided yet another dramatic demonstration of the power of Newton’s work.


The first photographs of the moon were taken by William Bond and Warren de la Rue. A solar eclipse was photographed by the Italian astronomer Pietro Secchi, who also obtained a full set of lunar photographs between 1851 and 1859.

(p.206) Although the rotation of the earth had been generally accepted since the sixteenth century, the first direct evidence was provided by Jean Foucault’s pendulum experiment in 1851.


Spectral analysis was first applied to the sun’s light by the Swedish physicist Anders Ångström, and to starlight by Pietro Secchi.


Space vehicles were utilized to study the solar system, resulting in rapid growth and public awareness of astronomical knowledge.


The first manned moon landing.

Optics and vision


The Italian mathematician Maurolico first explained how the lens of the eye focuses light on the retina, the causes of long- and shortsightedness, and the benefits of concave and convex spectacle lenses. However, his work was published posthumously, after that of Kepler.


The physician Felix Plater recognized the retina as the receptor of visual images.


Johann Kepler asserted, on the basis of his geometric optical analysis of the eye, that the cornea and lens form a real inverted image on the retina.


The Dutchman Snell discovered the sine law of optical refraction. It was first published by Descartes in 1638.


William Harvey described the circulation of the blood. During the next few decades his work helped to end Greek medicine and to found physiology.


René Descartes described accommodation and convergence, and proposed that the latter underlies distance perception.


Mariotte discovered the blind spot.

(p.207) 1709

Bishop George Berkeley distinguished between the angular and perceived size of objects, and explained both size and distance perception in terms of learned cues. These included bodily cues, and visual cues such as aerial perspective. He disowned size-distance invariance.


Pierre Bouguer developed a quantitative optical theory of visibility through the atmosphere. His essay of 1729 contained the main ideas and a more complete theory appeared posthumously in 1760. (The theory is often attributed to Lambert, 1774.)


The astronomer N. Maskelyne calculated the chromatic aberration of the eye and first described night myopia.


Electrophysiology was founded by the German physiologist Emil Du Bois-Reymond, who first detected the small electric currents produced in nerves and muscles.


Substantial developments in sensory physiology and physiological optics were reported by Hermann von Helmholtz.


Psychophysical methods for determining sensory thresholds were developed by Gustav T. Fechner.


Wilhelm Wundt founded the first laboratory devoted entirely to psychological research, including studies of visual perception.


M. Wertheimer founded Gestalt psychology, a school that had a lasting influence on the study of perception.


The term ‘size constancy’ came into use among Gestalt psychologists.


J. J. Gibson introduced the ecological approach to visual perception, describing perception as entirely stimulus-driven.


The presentation of the visual field on the primary visual cortex, and the specialized visual sensitivities of neurons within it, were described by D. H. Hubel and T. N. Wiesel.

(p.208) 1980–1990

Following studies in visual neuroscience by S. Zeki and others, a broad consensus was reached on three organizing principles of visual analysis: first, analysis is modular, in the sense that different features of a visual image are analysed separately; second, analysis is broadly hierarchical, in the sense that it proceeds in stages; and, third, a considerable degree of parallel processing may occur within stages.