Discovery of the image at the back of the eye

Kepler and Paralipomenes

Most people know that the astronomer Johannes Kepler[1] (1571-1630) is famous for his discovery of the elliptical orbits of the planets and of the three laws that govern their motion. These discoveries had considerable impact on the practice of astronomy because, by replacing the earlier, cumbersome, and inaccurate methods, Kepler's ellipses significantly simplified the astronomical calculations necessary for determining longitude in navigation. Casting horoscopes, which was also an important part of astronomers' science in the Renaissance, taken seriously by even the most rigorous scientists of the time, was also greatly simplified by Kepler's work. Thus, owing to their practical usefulness, Kepler's discoveries greatly contributed to consolidate the Galilean revolution[2]: Kepler's theory was based on Copernicus' revolutionary heliocentric theory, according to which the earth revolves around the sun rather than the other way around, as Aristotle and Ptolemy had thought,

But it is less well known that, in addition to being the purveyor of the Galilean revolution, Kepler was also the author of a truly revolutionary work on light and vision: Ad Vitellionem paralipomenes, quibus astronomiae pars optica traditur (1604) ("Extensions to the work of Witelo, representing the optical part of astronomy"). For some reason this book of monumental importance, at the watershed between medieval and modern science, remains relatively unknown. Yet its content constitutes the basis of the modern science of optics.

The impetus for Paralipomenes had come from a measurement problem that Kepler had encountered in his astronomical observations with the camera obscura. As suggested by the word camera, which means 'vault' in latin, the camera obscura was originally a real room of normal size, completely dark except for a single small opening for light: for example a missing tile in the attic of a church. As had been known since Aristotle, it was possible with this camera obscura,  to project an image of the sun or the moon on the floor. In the middle ages, before the discovery of the telescope, astronomers used the camera obscura to observe bright heavenly bodies and their eclipses[3]: Artists also made use of the camera obscura: Leonardo da Vinci made a number of notes concerning it[4], and from the Renaissance onwards, painters like Canaletto Bellotto and Vermeer used it to help make accurate reproductions of scenes.  As late as the beginning of the twentieth century the camera obscura could be seen at tourist spots in the form of a cabin with a hole in the roof and a mirror set above it: An image of the surrounding panorama would be projected on a white table inside the cabin[5] Experimental Interlude 3 is devoted to some observations with the camera obscura.

Thus, the use of the camera obscura for observing astronomical events was well-known in Kepler's time. But a troubling fact had been noticed: the angular size of the image of the sun or moon was slightly larger when observed with a camera obscura than when observed with the naked eye[6]. Why was this? Rigging together a concrete demonstration of the paths of the rays of light passing through a many-cornered aperture using bits of thread stretched out from a point, Kepler realised that the solution to the enigma lay in the size of the aperture. In a way analogous to the figure above, Kepler showed that when the aperture is not extremely small, the image projected is formed of multiple replicas of the aperture's shape, and so is slightly blurred, and thus larger. After this first analysis, Kepler realised that all measurements made in astronomy suffered from errors due to the instruments being used, and in particular, to errors induced by the size of the pupil of the eye itself. In order to advance astronomy, it was necessary to understand better the functioning of the eye. In Paralipomenes, Kepler succeded in doing this, and, for the first time in history, put forward the correct principles of image formation on the retina at the back of the eyeball. He also prepared the way for his analysis of the functioning of concave and convex lenses and of the construction of telescopes and microscopes, to be published a few years later in Dioptrica, (1611).

The key concept in Kepler's theory is the concept of an 'image' (he calls it a pictura or 'painting'[7]) that can be created when light passes across a curved surface like the cornea at the front of the eye. Until Kepler's time, scientists studying light had been troubled by the problem that if light is emitted in different directions from each point of an object, then when the light impinges on the eye, the rays from the different points and the different objects will be totally mixed up and not retain their correct positions. Kepler solved this problem by showing how the rays can be regrouped together, focussed, by the cornea and crystalline lens so that to every point in the object there corresponds again a distinct point in the image. It is difficult for us to appreciate how revolutionary this concept of image formation was: our present-day culture is so imbibed with images that it is hard to conceive how painters and scientists in the middle ages and Renaissance could have got along without them...

The novelty of the notion of 'image' is the more surprising when one considers that in Kepler's time lenses had actually been in common use for more than 300 years[8]: florentine artisans had discovered around 1280 that discs of glass could be used to facilitate reading and improve vision[9]. In fact a whole industry of artisans existed in Kepler's time to manufacture spectacles and pince-nez to correct presbyopia (and later, myopia). But no scientist had understood how these glasses worked, and the notion of 'image' seems not to have existed. In fact there may actually have been a sort of taboo against the study of the visual phenomena associated with lenses[10]: Plato had said 'non potest fieri scienscia per visum solo' (science cannot be done through vision alone -- he thought that vision was very unreliable compared to touch). The study of the evanescent, often illusory phenomena of vision was not a dignified scientific pursuit. In fact the word 'lens', coming from the word for the 'lentil' vegetable, shows clearly the vulgar origin of lenses. Thus, there had been virtually no scientific study of the action of lenses despite their widespread use. The exception was della Porta (but it has been claimed he was not really a man of science[11]), who, in addition to mentioning lenses as his "secret" for improving the camera obscura, had written about the action of transparent spheres and lenses in De refractione optices parte libri novem (1593). However his treatment was confused and gave no new insights: certainly della Porta had not understood the formation of images[12]. Francesco Maurolico had suggested that lenses could make light converge or diverge but he had also not understood the principles of image formation.

Kepler's explanation of the focussing action of the eye was thus a real revolution. Paralipomenes strikes us today by its perfectly clear style and modern language compared to other works of the time. Of course the reason we find Kepler so easy to read is that his ideas are precisely those which we have inherited, and which we use today to understand light and vision. But whereas Kepler's text is clear to us, his contemporaries considered it illegible. A subsequent work (Dioptrica, 1611) was better received. Without going into the theory of the nature of light and vision, it explained, among other things, the operation of the telescope that Galileo had just introduced, and it proposed how to construct improved versions of that instrument.

As concerns the eye, Kepler's proposition was correct. He suggested that the cornea and the crystalline humor together act as a lens and focus an image on the retina, on the inside back surface of the eyeball. Only a few years after he made this suggestion, the jesuit anatomist Scheiner[13], and then Descartes and others, cut windows at the back of animals' eyes and confirmed experimentally the existence of the image postulated by Kepler.

The trouble was: the image was upside down...



[1]Kepler studied Copernicus and Ptolomy under the astronomer Michael Maestlin at Tbingen. Interrupting Lutheran theological studies there he became mathematician in Graz, where, producing annual calendars and prognostications he had time to study astronomy. In 1600 he became Tycho Brahe's assistant at the court of Rudolf II in Prague and succeeded him as imperial mathematician in 1601 (cf Lindberg, p. 186). 

[2]But, as shown in A. Koestler's fascinating book 'The Sleepwalkers', we must not commit the error of thinking that Kepler was a genius with a modern, empirical approach to science. On the contrary, much of his theorizing was steeped in medieval concepts and involved mystical and religious arguments.

[3] Roger Bacon and John Pecham mentioned the camera obscura for observing eclipses (1279), and ??? used it to observe the planet Mercury pass across the disk of the sun (Fabrizio used it to observe sunspots...). Roger Bacon (c. 1214 - c. 1292). was a Franciscan monk who worked in Oxford and Paris, where he was sent by his superiors to be watched over, because of his rebellious nature (according to Lindberg, p. 108). He was dedicated to the aim of incorporating all human knowledge into one teachable system, wherein the study of optics was for him particularly important. His optics (Perspectiva; De multiplicatione speciarum; and sections of other works) constituted a synthesis of all preceding theories, but depended most heavily on Al Hazen. Use of the camera obscura in observing eclipses is mentioned in De multiplicatione speciarum, according to Enc. Univ. p. 657. The Franciscan monk John Pecham (c.1235-1292) studied in Oxford, Paris, Viterbo and Rome, and became archbishop of Canterbury in 1279. Like Witelo, he was a younger contemporary of Roger Bacon, and through his Tractatus de perspectiva and Perspectiva communis contributed in furthering Al Hazen's views on optics (cf. Lindberg, p. 116ff

[4]In Codex atlanticus 135 b, 138 a, 179 b and manuscript D 78,  acc to Enc Univ. p. 657.

[5]According to Enc. Britt p. XXX

[6]Tycho Brahe had noticed this, as had Kepler while observing the solar eclipse of July 10th, 1600. Lindberg (p. 186) cites Straker (1970; "Kepler's Optics") as giving an authoritative analysis of the events that led to Kepler's discoveries. .

[7]In different places in Paralipomena he also calls it idolum, imago or species. Cf Lindberg p.202  and his note 99.

[8]Lenses have actually been found at many ancient archeol sites throughout Europe and the Middle East, as in Nimrud in Assyria, in Crete, at Pompei, in Turkey, at Mainz and sites in France (according to Polyak, 1957, p. 13; and Thorpe & XXX), suggesting that they were used as magnifying glasses or burning lenses early as 3000 BC. Minute possibly secret inscriptions on babylonian seals, and on coins and artwork throughout antiquity suggest that artisans probably used such magnifying lenses. It may be that the use of minute inscriptions, readable only to rare possessors of lenses, was used to protect against forgery. Polyak (1957; pp 28 ff. gives an admirable history of the invention of eyeglasses

[9]V. Ronchi (XXX) suggests that the discovery might have been made by artisans in the glass works of Murano near Venice or in the valley of the Arno. Discs of glass were used as decorations in windows. Alternatively, slices cut from spheres of glass might have been used. .

[10]This idea, and the other suggestions made in this paragraph are due to V. Ronchi (XXX). They make a good story, but the truth may be more subtle.

[11]Ronchi's (XXX)  claim is that there was a conspiration against the serious study of lenses among scientists, and only an amateur or popular scientist like Della Porta will have had the courage to ignore it.

[12]cf. Lindberg, p. 183 ff.

[13]It was also Scheiner who had too hastily concluded that .... and so entered into a feud with Galileo, probably contributing to the ... cf Men of Science...XXX