Perception, 2014, volume 43, pages 1283 – 1285
doi:10.1068/p4312ed
Guest editorial
Johannes Kepler: the sky as a retinal image Why are there seven days in the week? A day is the time it takes for one rotation of the Earth on its axis. A month is the time of the moon’s orbit around the Earth, and a year is the time of the Earth’s orbit around the sun. But what is a week, and why is it seven days long? The answer is not based on the Bible; nor is a week one quarter of a month. (Spoiler alert: the answer is given in the next paragraph, so stop reading here if you want to think about it. For a hint: think about the names of the days, especially in the romance languages.) As ancient people watched the sky at night, they observed that the stars move across the sky during the night much as the sun moves across the sky during the day. During this movement, the stars maintain a constant spatial relationship to one another. Except for seven bodies: the sun, the moon, and the five planets visible to the naked eye! The seven days of the week are named for these seven bodies. Indeed, the word planet, in Latin, means wanderer. Were it not for these seven wanderers, the early cosmology could have been much simpler: a giant star-studded opaque sphere rotating silently around the Earth. For his geocentric scheme Ptolemy required, in addition to this outer opaque sphere, seven transparent spheres, one for each of the heavenly wanderers, with each sphere corresponding to one of the days of the week. The scientific revolution began with questions about the sky. This is not surprising given that the sky—or rather the movement of heavenly bodies across it—is both obvious and mysterious. Though the sky appeared as a two-dimensional curved surface, it was thought to represent a three-dimensional space. The Greeks were familiar with the problem. According to Simplicius (quoted in Kraut, 1992), Plato had challenged his students to explain the twodimensional pattern of movements observed in the sky “by hypothesizing what uniform and ordered motions is it possible to save the appearances relating to planetary motions.” Fifteen hundred years elapsed before Ptolemy’s scheme began to unravel. Copernicus, after prodding by Rheticus, published his heliocentric model. Tycho Brahe, given funds and his own island by the Danish king, built an amazing observatory and, over almost a decade, accumulated a huge dataset of pretelescopic measurements of the nightly position of the stars in the sky. Brahe’s measurements confirmed one of the most difficult appearances to save: the retrograde motion of Mars. If you track the wandering position of Mars across the sky night after night, you find a steady eastward movement relative to the fixed stars. But about once every two years Mars begins to slow down and start moving westward for a short time before resuming its eastward path. To save this appearance, Ptolemy had added epicycles to his model: small spheres attached to the large ones. The problem of retrograde motion was resolved by heliocentrism; in their race around the sun, the Earth, being on the inside track, periodically overtakes Mars. Brahe kept his dataset close to his vest, but on his death his assistant Johannes Kepler inherited the data. Kepler crunched the numbers and derived his three laws of planetary motion: (1) planets move in elliptical, not circular, orbits; (2) though a planet does not move at a constant speed, a line connecting the planet to the sun sweeps out equal areas in equal amounts of time; and (3) the length of a planet’s orbit is proportional to its distance from the sun. Newton (1676/1992) said “If I have seen further it is by standing on the shoulders of giants.” One of those giants was Kepler. His law of elliptical orbits implied Newton’s inverse-square law of gravitation.
1284
Guest editorial
Kepler must be regarded as a giant of vision science as well because he basically discovered the retinal image. Alhazen had understood the requirement for a one-to-one relationship between points in the eye and points on the object, but he believed that the representation was formed in the lens. He rejected the idea that the image was farther back in the eye because then it would be upside down. It was Kepler who nailed it: “Therefore vision occurs through a picture of the visible things on the white, concave surface of the retina.” That discovery launched the scientific study of vision. If some thinkers thought that Kepler had solved the problem of vision, it wasn’t long before the profound discrepancies between the properties of the retinal image and the properties of visual experience began to be recognised. This discrepancy is like the one that Kepler confronted between appearances in the sky and the underlying motion in three-space. It may seem remarkable that Kepler made seminal contributions to astronomy and vision science, two fields so seemingly far removed from one another. Moreover, apart from the difference in subject matter, astronomy came early while vision science came late. And yet there is an uncanny parallel between the sky and the retina. In both cases we find a puzzling and complicated pattern on a seemingly two-dimensional curved surface that becomes very simple when construed as the two-dimensional projection of a three-dimensional scene. Whether or not Kepler saw a specific analogy between the sky and the retina, he certainly knew that both were subject to the laws of projective geometry. His interest in vision came through his work in astronomy. In his book Astronomiae Pars Optica [The optical part of astronomy] (1604) he described the inverse square law of light intensity and the principles of the pinhole camera. The pinhole camera had already played a role in early astronomy, sponsored ironically by the Catholic church. Everyone knows how the church had tried to suppress Galileo and the heliocentric theory. Less well known is how the church fostered astronomy and the scientific revolution by turning cathedrals into giant scientific instruments. The interest of the church in astronomy came from a calendar problem. Initially Christmas had been placed at the winter solstice. Easter had been placed at the vernal equinox. The church used the Egyptian calendar, according to which the length of the year was said to be 365 and one quarter days long. This is very accurate. It is only eleven minutes too long. That might not seem like much, but after 1500 years Christmas and Easter were coming ten days too late. Embarrassed by the calendar problem, the church asked Johannes Mueller (1436–76) to solve the problem. He tried but failed. Copernicus was asked to solve it. He replied that he didn’t think he was up to the task. As part of this effort, the church converted several European cathedrals into solar observatories. A hole several inches in diameter was cut in the roof, causing a bright disk of light to appear on the cathedral floor, the image of the sun. The whole building was turned into a large camera obscura. During the course of the day the disk-image would travel across the floor. A long brass bar embedded in the marble floor was located so that the disk crossed it at exactly 12 o’clock noon. The point at which the disk crossed the bar migrated from one end of the bar to the other during the yearly cycle, as the sun grew higher and lower in the sky. Though inspired by an applied problem, the solar observatories led to basic scientific advances. For example, sunspots were discovered using the cathedral of San Petronio in Bologna. A central theme of the scientific revolution was replacing spirits with mechanisms. William Harvey showed that the heart and blood were better explained by pumps, tubes, and circulation rather than vital spirits. Redi, Spallanzani, and Pasteur debunked spontaneous generation. Kepler and Newton laid bare the clockwork of a universe that no longer required spirits to operate it. Despite all this, Harvey continued to believe that the blood contains a vital spirit.
Guest editorial
1285
Newton continued to believe that a divine spirit periodically calibrates the clockwork. And Kepler continued to search for the spiritual music of the heavens. But each of them paved the way for the more thoroughly materialistic accounts of the younger generation. Kepler created our field by discovering the picture in the eye. Alhazen had resisted locating the image in the back of the eye because there the image would be inverted. Indeed, Kepler struggled to solve the inversion problem. We know now that Kepler’s worry about the inverted image was unnecessary. The retinal image is not a picture—because there is no eye that looks at it. Kepler’s worry implied yet another spirit—that little person inside your head that looks at the picture. But Kepler can be forgiven. He gave us the proximal stimulus, and it is up to us to explain how visual experience is produced without the help of ghosts in the machine. Alan Gilchrist
Department of Psychology, Rutgers University, Newark, NJ 07102, USA; e‑mail: [email protected] References Kepler, J. (1604). Astronomiae pars optica [The optical part of astronomy]. Letter from Isaac Newton to Robert Hooke, 5 February 1676, as transcribed in Jean-Pierre Maury (1992). Newton: Understanding the cosmos—new horizons. London: Thames & Hudson. Simplicius. Commentary on Aristotle’s “On the Heavens” 488.7–24, quoted in Mueller’s chapter 5 “Mathematical method and philosophical truth” (p. 174), in R. Kraut (Ed.). (1992). The Cambridge companion to Plato. Cambridge: Cambridge University Press. Editorial note: We welcome comments on our editorials; these may be published in a later issue subject to editorial review. Please send comments to Gillian Porter at [email protected]
doi:10.1068/p4312ed
Guest editorial
Johannes Kepler: the sky as a retinal image Why are there seven days in the week? A day is the time it takes for one rotation of the Earth on its axis. A month is the time of the moon’s orbit around the Earth, and a year is the time of the Earth’s orbit around the sun. But what is a week, and why is it seven days long? The answer is not based on the Bible; nor is a week one quarter of a month. (Spoiler alert: the answer is given in the next paragraph, so stop reading here if you want to think about it. For a hint: think about the names of the days, especially in the romance languages.) As ancient people watched the sky at night, they observed that the stars move across the sky during the night much as the sun moves across the sky during the day. During this movement, the stars maintain a constant spatial relationship to one another. Except for seven bodies: the sun, the moon, and the five planets visible to the naked eye! The seven days of the week are named for these seven bodies. Indeed, the word planet, in Latin, means wanderer. Were it not for these seven wanderers, the early cosmology could have been much simpler: a giant star-studded opaque sphere rotating silently around the Earth. For his geocentric scheme Ptolemy required, in addition to this outer opaque sphere, seven transparent spheres, one for each of the heavenly wanderers, with each sphere corresponding to one of the days of the week. The scientific revolution began with questions about the sky. This is not surprising given that the sky—or rather the movement of heavenly bodies across it—is both obvious and mysterious. Though the sky appeared as a two-dimensional curved surface, it was thought to represent a three-dimensional space. The Greeks were familiar with the problem. According to Simplicius (quoted in Kraut, 1992), Plato had challenged his students to explain the twodimensional pattern of movements observed in the sky “by hypothesizing what uniform and ordered motions is it possible to save the appearances relating to planetary motions.” Fifteen hundred years elapsed before Ptolemy’s scheme began to unravel. Copernicus, after prodding by Rheticus, published his heliocentric model. Tycho Brahe, given funds and his own island by the Danish king, built an amazing observatory and, over almost a decade, accumulated a huge dataset of pretelescopic measurements of the nightly position of the stars in the sky. Brahe’s measurements confirmed one of the most difficult appearances to save: the retrograde motion of Mars. If you track the wandering position of Mars across the sky night after night, you find a steady eastward movement relative to the fixed stars. But about once every two years Mars begins to slow down and start moving westward for a short time before resuming its eastward path. To save this appearance, Ptolemy had added epicycles to his model: small spheres attached to the large ones. The problem of retrograde motion was resolved by heliocentrism; in their race around the sun, the Earth, being on the inside track, periodically overtakes Mars. Brahe kept his dataset close to his vest, but on his death his assistant Johannes Kepler inherited the data. Kepler crunched the numbers and derived his three laws of planetary motion: (1) planets move in elliptical, not circular, orbits; (2) though a planet does not move at a constant speed, a line connecting the planet to the sun sweeps out equal areas in equal amounts of time; and (3) the length of a planet’s orbit is proportional to its distance from the sun. Newton (1676/1992) said “If I have seen further it is by standing on the shoulders of giants.” One of those giants was Kepler. His law of elliptical orbits implied Newton’s inverse-square law of gravitation.
1284
Guest editorial
Kepler must be regarded as a giant of vision science as well because he basically discovered the retinal image. Alhazen had understood the requirement for a one-to-one relationship between points in the eye and points on the object, but he believed that the representation was formed in the lens. He rejected the idea that the image was farther back in the eye because then it would be upside down. It was Kepler who nailed it: “Therefore vision occurs through a picture of the visible things on the white, concave surface of the retina.” That discovery launched the scientific study of vision. If some thinkers thought that Kepler had solved the problem of vision, it wasn’t long before the profound discrepancies between the properties of the retinal image and the properties of visual experience began to be recognised. This discrepancy is like the one that Kepler confronted between appearances in the sky and the underlying motion in three-space. It may seem remarkable that Kepler made seminal contributions to astronomy and vision science, two fields so seemingly far removed from one another. Moreover, apart from the difference in subject matter, astronomy came early while vision science came late. And yet there is an uncanny parallel between the sky and the retina. In both cases we find a puzzling and complicated pattern on a seemingly two-dimensional curved surface that becomes very simple when construed as the two-dimensional projection of a three-dimensional scene. Whether or not Kepler saw a specific analogy between the sky and the retina, he certainly knew that both were subject to the laws of projective geometry. His interest in vision came through his work in astronomy. In his book Astronomiae Pars Optica [The optical part of astronomy] (1604) he described the inverse square law of light intensity and the principles of the pinhole camera. The pinhole camera had already played a role in early astronomy, sponsored ironically by the Catholic church. Everyone knows how the church had tried to suppress Galileo and the heliocentric theory. Less well known is how the church fostered astronomy and the scientific revolution by turning cathedrals into giant scientific instruments. The interest of the church in astronomy came from a calendar problem. Initially Christmas had been placed at the winter solstice. Easter had been placed at the vernal equinox. The church used the Egyptian calendar, according to which the length of the year was said to be 365 and one quarter days long. This is very accurate. It is only eleven minutes too long. That might not seem like much, but after 1500 years Christmas and Easter were coming ten days too late. Embarrassed by the calendar problem, the church asked Johannes Mueller (1436–76) to solve the problem. He tried but failed. Copernicus was asked to solve it. He replied that he didn’t think he was up to the task. As part of this effort, the church converted several European cathedrals into solar observatories. A hole several inches in diameter was cut in the roof, causing a bright disk of light to appear on the cathedral floor, the image of the sun. The whole building was turned into a large camera obscura. During the course of the day the disk-image would travel across the floor. A long brass bar embedded in the marble floor was located so that the disk crossed it at exactly 12 o’clock noon. The point at which the disk crossed the bar migrated from one end of the bar to the other during the yearly cycle, as the sun grew higher and lower in the sky. Though inspired by an applied problem, the solar observatories led to basic scientific advances. For example, sunspots were discovered using the cathedral of San Petronio in Bologna. A central theme of the scientific revolution was replacing spirits with mechanisms. William Harvey showed that the heart and blood were better explained by pumps, tubes, and circulation rather than vital spirits. Redi, Spallanzani, and Pasteur debunked spontaneous generation. Kepler and Newton laid bare the clockwork of a universe that no longer required spirits to operate it. Despite all this, Harvey continued to believe that the blood contains a vital spirit.
Guest editorial
1285
Newton continued to believe that a divine spirit periodically calibrates the clockwork. And Kepler continued to search for the spiritual music of the heavens. But each of them paved the way for the more thoroughly materialistic accounts of the younger generation. Kepler created our field by discovering the picture in the eye. Alhazen had resisted locating the image in the back of the eye because there the image would be inverted. Indeed, Kepler struggled to solve the inversion problem. We know now that Kepler’s worry about the inverted image was unnecessary. The retinal image is not a picture—because there is no eye that looks at it. Kepler’s worry implied yet another spirit—that little person inside your head that looks at the picture. But Kepler can be forgiven. He gave us the proximal stimulus, and it is up to us to explain how visual experience is produced without the help of ghosts in the machine. Alan Gilchrist
Department of Psychology, Rutgers University, Newark, NJ 07102, USA; e‑mail: [email protected] References Kepler, J. (1604). Astronomiae pars optica [The optical part of astronomy]. Letter from Isaac Newton to Robert Hooke, 5 February 1676, as transcribed in Jean-Pierre Maury (1992). Newton: Understanding the cosmos—new horizons. London: Thames & Hudson. Simplicius. Commentary on Aristotle’s “On the Heavens” 488.7–24, quoted in Mueller’s chapter 5 “Mathematical method and philosophical truth” (p. 174), in R. Kraut (Ed.). (1992). The Cambridge companion to Plato. Cambridge: Cambridge University Press. Editorial note: We welcome comments on our editorials; these may be published in a later issue subject to editorial review. Please send comments to Gillian Porter at [email protected]
