Glossary

A posteriori: a type of reasoning, from observation to theory, from facts or particulars to general principles, from effects to causes; synonymous with inductive and empirical. See regular solids.

A priori: a type of reasoning, from theory or principles without prior observations. See regular solids.

Anomaly: a violation of expectation; a discovery for which an investigator's paradigm has not prepared him or her.

Anthropocentric universe: centered on human interests. The Copernican revolution saw a historical progression from belief in a small universe with humankind at its center to a larger, and eventually infinite, universe with Earth not in the center. The physical geometry of our universe was transformed from geocentric and homocentric to heliocentric, and eventually to a-centric. The psychological change was no less. We no longer command unique status as residents of the center of the universe, enjoying our privileged place. Nor are we likely the only rational beings in the universe.

Antiperistasis: Aristotle's convoluted explanation for how an arrow shot from a bow, or a stone thrown from a hand, continued in motion with continuing contact between the moved and the mover. Somehow, air pushed forward by the arrow or the stone moved around to the rear of the arrow or stone and then pushed it from behind. See impressed force.

Aphelion: the point in an orbit farthest from the Sun (apo, "away from"; helio, "the Sun"). See perihelion.

Apogee: the point in an orbit farthest from the Earth (gee, "Earth"). See perigee.

Apple: a fruit growing on trees, and supposedly instrumental in several major historical changes, beginning with Adam, Eve, a serpent, and an apple; moving on to a golden apple awarded by the prince of Troy to the most beautiful woman in the world, who then promised him another man's wife, thus setting off the Trojan War; and Isaac Newton's apple, which, in contrast to the first two, rendered great service to humankind.

Astrotheology: the eighteenth-century belief in the orderliness of the universe combined with a belief that determination of that order was an important theological, philosophical, and scientific endeavor.

Chain: Adam Smith, initially believing that philosophical systems were mere inventions of the imagination to connect together otherwise disjointed and discordant phenomena of nature, was persuaded by the example of Isaac Newton's science that there are real connecting principles or chains that bind nature. Circle: a closed curve everywhere the same distance from its center; acclaimed by ancient Greek mathematicians as the perfect geometrical figure. Supposedly, Plato set for astronomers the task of explaining the apparently irregular motions of the planets, the Sun, and the Moon as a combination of circular motions with constant speeds of rotation. See saving the phenomena. Comet: a celestial body with a dense head and a vaporous tail. It is visible only if, and when, its orbit takes it near the Sun. Aristotle had made a distinction between the corrupt and changing sublunary world (from the Earth up to the Moon) and the perfect, immutable heavens beyond. Tycho Brahe's observations of the comet of 1577 showed that it was above the Moon and moving through regions of the solar system previously believed filled with crystalline spheres carrying around the planets. Aristotle's world was shattered. See new star; crystalline sphere.

Commentaries: ancient and medieval discussions or presentations based on books by Aristotle. Commentaries were neither modern nor scientific in spirit. Everyone knew what the questions were and what the answers would be. The aim of an exercise was skillful presentation of known information, not discovery of new information. The medieval university curriculum was based partly on studying commentaries on Aristotle's works on logic and natural philosophy.

Condemnation of 1277: Necessary principles can result in truths necessary to philosophy but contradictory to dogmas of the Christian faith. In 1270 the bishop of Paris condemned several propositions derived from the teachings of Aristotle, including the eternity of the world and the necessary control of terrestrial events by celestial bodies. In 1277 the Pope directed the bishop to investigate intellectual controversies at the university. Within three weeks, over two hundred propositions were condemned. Excommunication was the penalty for holding even one of the damned errors. Some historians assert that the scientific revolution of the sixteenth and seventeenth centuries owes much to the Condemnation of 1277. Though intended to contain and control scientific inquiry, the condemnation may have helped free cosmology from Aristotelian prejudices and modes of argument. But if so, why did scholars wait hundreds of years before repudiating Aristotelian cosmology? Conic section: a curve produced from the intersection of a plane with a right circular cone: circle, ellipse, hyperbola, and parabola. Apollonius's book on conic sections, Conics, was recovered along with other ancient Greek classics in the early stages of the Renaissance. The circle and the ellipse are both conic sections, and for Kepler, neither geometrical figure may have seemed any more natural or more perfect than the other. And thus, maybe he could casually jettison circular orbits and some two thousand years of tradition. Crisis: in science, the period of great uncertainty when an anomaly is judged worthy of concerted scrutiny yet continues to resist increased attention, with repeated failures to make the anomaly conform, and thus leads to large-scale paradigm destruction and major shifts in the problems and techniques of normal science. External social, economic, and intellectual conditions may also help transform an anomaly into a crisis.

Crystalline sphere: in ancient Greek and medieval European cosmology, solid crystalline spheres provided a physical structure for the universe and carried the planets in their motions around the Earth. Then, Copernicus moved Earth out of the center of the universe, making the spheres obsolete, and Tycho Brahe shattered them with his observations of the comet of 1577. See comet. Cuneiform writing: wedge-shaped signs made by pressing a sharpened stylus or stick into soft clay tablets, often about the size of a hand. The tablets were then baked hard, preserving the contents, in some cases Babylonian astronomical knowledge.

Deduction: logical, often mathematical, derivation from theory of what phenomena may be expected. An inference of the sort that if the premises are true, the conclusion necessarily follows. See hypothetico-deductive method; induction.

Deferent: in ancient Greek geometrical astronomy, a large circle rotating at a constant speed around its center (coinciding with the Earth) and carrying around on its circumference the center of a smaller rotating circle, which in turn carried a planet on its circumference. See eccentric; epicycle. Earthshine: sunlight reflected from the Earth. Near new moon, the portion of the Moon shadowed from direct sunlight is slightly brightened by sunlight reflected from the Earth.

Eccentric: a deferent circle with its center offset from the Earth. See deferent. Eclipse: a partial or complete temporary blocking of light by an intervening body. A solar eclipse occurs when the Moon comes between the Earth and the Sun. A lunar eclipse occurs when the Earth is directly between the Moon and the Sun.

Ecliptic: the apparent path of the Sun among the stars; the intersection of the plane of the Earth's orbit around the Sun with the celestial sphere. See zodiac.

Ellipse: the closed curve generated by a point (the locus of the points) moving in such a way that the sum of the point's distances from two fixed points is a constant. Kepler showed (his first law) that the planets' orbits are not circles but ellipses. See Kepler sfirst law.

Enlightenment: t he eighteenth-century philosophical movement concerned with critical and rational examination of previously accepted ideas and institutions.

Ephemeris: a tabular statement of the places of a celestial body at regular intervals. Seemingly, ancient Babylonian astronomers were content with tables of predicted celestial positions. We have no evidence that they constructed geometrical models of the motions of celestial bodies, or that they expressed concern about the causes of the motions or any curiosity about the physical composition of the celestial bodies, at least not in their clay tablets found and studied so far.

Epicycle: in ancient Greek geometrical astronomy, a small circle rotating at a constant speed around its center and carrying around a planet on its circumference; the center of the epicycle is carried around on the circumference of a larger rotating circle, the deferent.

Equant point: a geometrical invention of the ancient astronomer Ptolemy necessary to save the phenomena. Uniform angular motion, previously defined as cutting off equal angles in equal times at the center of the circle, was now taken with respect to this new point not at the center of the circle. The equant point was a questionable modification of uniform circular motion, and Copernicus would condemn the equant point as an unacceptable violation of uniform circular motion. See saving the phenomena.

Equator: the great circle around the Earth's surface defined by a plane passing through the Earth's center and perpendicular to its axis of rotation. Equinox: either of the two points (the vernal, or spring, equinox, about March 21; and the autumnal, or fall, equinox, about September 22) on the celestial sphere where the plane of the Earth's orbit around the Sun and the plane of the Earth's equator intersect. At these times of the year the length of day and night are equal (12 hours) every place on the Earth. Ex post facto argument: made after the fact, or observation, on which it is based. Also a theory modified to bring it into agreement with new facts. Such theories carry less psychological conviction than do those predicting previously unknown phenomena, even if the strict logic of the two situations is equally compelling.

Foundational: leading to. Kepler's observations did not lead to Newton's derivation of the inverse square law of gravity. Rather, establishment of the concept of universal gravitation enshrined Kepler's three laws among the great achievements of science. Kepler's laws were important, however, in the acceptance of Newton's theory.

Full moon: the phase of the Moon when its entire disk is seen illuminated with light from the Sun. This occurs when the Moon is opposite the Earth from the Sun. See new moon.

Gravity: Isaac Newton explained the planetary motions and tides on the Earth by the inverse square power of a mysterious entity called gravity, but he was unable to explain the cause of this power. He argued for setting aside the question of what gravity is and to be content with a mathematical description of its effects: "And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea" (Principia III, General Scholium).

Great chain of being: in philosophical thought, it linked God to man to lifeless matter in a world in which every being was related to every other in a continuously graded, hierarchical order. Governmental order reflected the order of the cosmos, and thus social mobility and political change were crimes against nature. This began to change with Copernicus.

Handbook tradition: Greek science was distilled into handbooks, and through this medium it became known to Latin readers. Ptolemy's Almagest, however, was written after the incorporation of Greek science into handbooks.

Harmony: an aesthetically pleasing combination of parts. Believing that God established nothing without geometrical beauty, Kepler compared the intervals between planets with harmonic ratios in music. See symmetry. Humanism: a cultural and intellectual movement from roughly 1300 to 1600 centered on the recovery of ancient Greek knowledge. With humanism came a renewed interest in Plato. Neoplatonism, also called Neopythagoreanism, included belief in the possibility and importance of discovering simple arithmetical and geometrical regularities in nature, and a view of the Sun as the source of all vital principles and forces in the universe. Copernicus would rely on the recovery of Ptolemy's mathematical astronomy, for both its geometrical techniques and its philosophical human values. Eventually, critical thought was stimulated, and what had begun as a rebirth or recovery of old knowledge mutated into the creation of new knowledge.

Hypothetico-deductive method: First, a hypothesis is postulated; then, a prediction is deduced from the hypothesis; and finally, observations are made to determine if the phenomena deduced from the hypothesis exist. Note that hypotheses can be refuted but not proved.

Impetus: See impressed force; inertia; momentum.

Impressed force: an alternative to Aristotelian explanations of motion, which maintained contact between the mover and the moved (see antiperistasis). Some sort of incorporeal motive force could be imparted by a projector to a projectile. Planetary movements could be attributed to an impetus impressed by God at the creation. See impetus; inertia; momentum.

Induction: the reasoning process in which observations (phenomena) somehow are followed by the formation of theories (propositions). Science does not correspond to the inductive model in which all facts are collected and then inevitable theories are inevitably induced. This model fails because of an infinite number of possible observations. True inductive science would never advance beyond the infinite period of fact gathering to the stage of theory formulation. Modern science increasingly deviates from the inductive model. Theories increasingly are used to suggest observations of potential significance. In scientific discovery the catalytic role of intuition and hypothesis is essential in making sense of empirical results and in guiding further research. Note that unlike deduction, induction makes it possible for the premises to be true but the conclusion to be false. This is why it is possible logically to refute a theory but not to prove a theory. See deduction.

Inertia: the tendency of a body at rest to remain at rest, or if in motion to remain in motion. See impetus; impressed force; momentum. Inferior planet: a planet lying between the Sun and the Earth (Mercury and Venus). The inferior planets can never be seen on the opposite side of the Earth from the Sun. See opposition; superior planet.

Instrumentalism: in the instrumentalist view of the relationship between theory and observation, known empirical data are suspended and the study then becomes one of pure mathematics, not solving but still relevant to the scientific problem. All that remains are simple mathematical fictions and pure conceptions, with no question of their being true or in conformity with the nature of things or even probable. For so-called instrumentalists, it is enough that a scientific theory yields predictions corresponding to observations. Theories are simply calculating devices. See nominalism; realism. Kepler's first law: the planets move in elliptical orbits with the Sun at one focus; announced in Kepler's Astronomia nova (New Astronomy) of 1609, and discovered after his "second" law. That Tycho Brahe had set him to work on Mars's orbit Kepler later attributed to Divine Providence. Mars's orbit alone among the planetary orbits deviates so much from a circle that Tycho's observations would force Kepler from an eccentric circle to an oval. Then, Kepler found that the discrepancies between Tycho's observations and circular and oval orbits were equal and opposite, and that an elliptical orbit fit in between the circular and the oval. See ellipse.

Kepler's second law: or law of equal areas; also announced in Kepler's Astronomia nova (New Astronomy) of 1609, and discovered before his "first" law. The radius vector, the line from the Sun to the planet, sweeps out equal areas in equal times. If the areas of any two segments are equal, then the times for the planet to travel between the points on the orbit defining the two segments are also equal. Thus the distance of a planet from the Sun is inversely related to its orbital velocity: as the distance increases, the velocity decreases. That the planets move faster the nearer they are to the Sun had already been cited by Copernicus as a celestial harmony; Kepler now found further harmony in a quantitative formulation of the relationship. See harmony. Kepler's third law: or harmonic law; announced in Kepler's Harmonice mundi (Harmonies of the World) in 1619. Among many propositions in this book on cosmic harmonies detailing various planetary ratios was the statement that the ratio of the mean movements of two planets is the inverse ratio of the 3/2 powers of the spheres. Kepler's few readers could scarcely have guessed that this particular harmony would later be singled out for acclaim while all the other numerical relationships in the book would be discarded as nonsense, tossed into the garbage can of history. This third law is now usually stated as: the square of the period of time it takes a planet to complete an orbit of the Sun is proportional to the cube of its mean distance from the Sun. The law is also expressed as a ratio between two planets (A and B) going around the Sun (and also between two satellites going around a planet): the ratio of the periods squared is equal to the ratio of the distances cubed: (period A/period B)2 = (distance A/distance B)3. See harmony.

Logarithm: The logarithm L to the base 10 of the number X is defined by the equation X = 10L. Though it may not seem like a big deal to owners of electronic calculators, the introduction of logarithms early in the seventeenth century reduced the otherwise lengthy process of multiplication to simple addition and thus doubled Kepler's productivity and his working lifetime. Momentum: a force of motion, the product of a body's mass times its linear velocity. See impetus; impressed force; inertia.

Neoplatonism: accompanied humanism, between 1300 and 1600, and included a renewed interest in Plato and a new belief in the possibility and importance of discovering simple arithmetical and geometrical regularities in nature, as well as a new view of the Sun as the source of all vital principles and forces in the universe. The movement was also called Neopythagoreanism, after the ancient Greek mathematician Pythagoras.

New moon: the phase of the Moon when none of its disk is seen illuminated with light from the Sun. This occurs when the Moon is between the Earth and the Sun. See full moon.

New star: a nova or supernova, a star that explodes and increases hundreds of millions of times in brightness. The famous nova of 1572 struck a blow against the Aristotelian worldview, in which there could be no change in the heavenly spheres beyond the Moon. If nearby, the nova would appear to shift its position with respect to the background stars. But Tycho Brahe showed that its parallax, or angle of view, did not change from night to night. See comet. Nominalism: The nominalist thesis developed in the 1300s conceded the divine omnipotence of Christian doctrine but at the same time freed natural philosophy from religious authority. Science is a working hypothesis in agreement with observed phenomena. But we cannot insist on the truth of any particular working hypothesis. God could have made the world in some different manner but with the same set of observational consequences. Therefore scientific theories are tentative, not necessary, and can pose no challenge to religious authority. Nominalism has much in common with instrumentalism. Both philosophical concepts posit scientific theories as working hypotheses with no necessary links to reality. One might speculate that Catholic historians and philosophers of science in the twentieth century, justifiably impressed with fourteenth-century nominalism and also eager to praise the admirable achievements of that era by scholars working within and supported by the Catholic church, consequently were predisposed to formulate the concept of instrumentalism. Nominalism stripped of its religious context became instru-mentalism, and nominalists were favorably pictured as forerunners of modern, philosophically sophisticated instrumentalists. See instrumentalism. Normal science: the continuation of a research tradition, seeking facts shown by theory to be of interest. Nova: see new star.

Opposition: a celestial object in opposition is located on the opposite side of the Earth from the Sun. The inferior planets, Mercury and Venus, can never be at opposition, because of the geometry of the situation. Hence, in the Ptolemaic Earth-centered model, the speeds around the Earth of the Sun and an inferior planet (Mercury or Venus) must be nearly matched to keep the planet and the Sun in approximately the same angular direction as seen from the Earth. In the Copernican model, an inferior planet is always at a small angle from the Sun. Nothing further is required of the model builder to obtain this result; it is a natural, inherent, and inevitable consequence of the model. Paradigm: a universally recognized achievement temporarily providing model problems and solutions to a community of practitioners, telling scientists about the entities that nature contains and about the ways in which these entities behave.

Parallax: the difference in apparent direction of an object seen from different places. See stellar parallax. Perfect solids: See regular solids.

Perigee: the point in an orbit nearest the Earth (peri, "near"; gee, "Earth"). See apogee.

Perihelion: the point in an orbit nearest the Sun (helio, "the Sun"). See aphelion.

Platonic solids: see regular solids.

Positivism: with regard to science, a philosophy including beliefs that science is cumulative and consists of a logical structure of testable and thus objective statements about a real world independent of investigators' personal subjective beliefs and general culture.

Precursitis: an imaginary disease involving the unconscious assumption that ancient scientists were working on the same problems and using the same methods as modern scientists do today. Hence the search for ancient precursors of the observations and theories now acclaimed in textbooks and the myopic result: a chronology of cumulative, systematized positive knowledge. Pythagorean solids: See regular solids.

Quadrature: when the Moon is at 90 degrees from the line joining the Sun and the Earth.

Qualitative: not precise. See quantitative.

Quantitative: involving measurement and numbers. Throughout the eighteenth century, Newtonians piled quantitative success on quantitative success, mathematically explaining phenomena as the result of an inverse square force, while rival Cartesians failed to reconcile their vortex theory in any numerical detail with Kepler's mathematical laws of planetary motion. Realism: an insistence that scientific theories are descriptions of reality. Dogmatic realists insist on the truth of a theory. Critical realists concede a theory's conjectural character without necessarily becoming instrumentalists. A disappointed realist may appear to be a local instrumentalist with regard to a particular failed theory retaining instrumental value but is far from becoming a global instrumentalist. See instrumentalism.

Regular solids: geometrical solids, each with all its sides equal, all its angles equal, and all its faces identical. There are five regular (or perfect or Platonic or Pythagorean) solids; no more, no less. They are the tetrahedron (4 triangular sides), cube (6 square sides), octahedron (8 triangular sides), dodecahedron (12 pentagonal sides), and icosahedron (20 triangular sides). About the Earth's circle, Kepler circumscribed a dodecahedron; enclosed the dodecahedron with Mars's circle; circumscribed about Mars's circle a tetrahedron; enclosed the tetrahedron with Jupiter's circle; about Jupiter's circle circumscribed a cube; and enclosed the cube with Saturn's circle. Within the Earth's circle, Kepler inscribed an icosahedron; in the icosahe-dron, he inscribed Venus' circle; in this circle, he inscribed an octahedron; and inside the octahedron, he inscribed Mercury's circle. The coincidence could not be purely fortuitous, could it? He used six planets (all that were known then), five intervals between them, and five regular solids! Kepler proclaimed this discovery in his Mysterium cosmographicum (Cosmic Mystery) in 1596. Kepler's theory was perceived as a mystical a priori speculation. It had originated more in his imagination than in observation. His order of work was preposterous. The proper procedure decreed for astronomers (however much they believed a priori in uniform circular motion) was to derive the distances of the planets a posteriori from observations, not a priori from the geometry of regular solids.

Renaissance: the rebirth (re-nascence) of Greek classical culture that originated in Italy in the fourteenth century and spread to universities north of the Alps in the fifteenth and sixteenth centuries. The University of Cracow was one of the first northern European schools to teach Renaissance humanism, although astronomy was still taught there largely in terms of Aristotelian physics in Copernicus's time. At the University of Bologna, Copernicus studied with Domenico da Novara, an astronomy professor and one of the leaders in the revival of Platonic and Pythagorean thought and Greek geometrical astronomy. Ptolemy's Almagest had become available to scholars in the Latin-reading world late in the fifteenth century. Initially, Renaissance humanists looking to the past for knowledge from a higher civilization facilitated a rebirth of Greek philosophy and values. Inconsistencies within individual ancient works and between different authors, and discrepancies in the sciences between classical theory and contemporary observation were attributed to defects in transmission and translation. Eventually, however, what had begun as a rebirth or recovery of old knowledge mutated into the creation of new knowledge. Obviously, any ending date for the Renaissance is arbitrary; some choose 1632 and the trial of Galileo.

Revolution-making: as opposed to revolutionary. Thomas Kuhn argued that Copernicus's work was almost entirely within an ancient astronomical tradition and hence not revolutionary, but it contained a few novelties that would lead to a scientific revolution and hence was revolutionary. See revolutionary; scientific revolution.

Revolutionary: See revolution-making; scientific revolution. Saving the appearances: See saving the phenomena.

Saving the phenomena: in the context of ancient Greek geometrical astronomy, to devise a system of uniform circular motions that reproduced the observed phenomena, or appearances. The guiding themata or paradigm of

Greek planetary astronomy was attributed to Plato by the philosopher Simpli-cius of Athens in his commentary on Aristotle's book On the Heavens. Around 500 Simplicius wrote that Plato had set as a task for astronomers to explain the apparently irregular motions of the planets, the Sun, and the Moon as a combination of circular motions with constant speeds of rotation. Scholasticism: a fusion of Aristotelianism and Christian theology permeated thought in Western Europe between roughly 1200 and 1500, especially in universities.

Scientific revolution: an extraordinary episode during which scientific beliefs, values, and worldviews are abandoned, and ruling paradigms are replaced by incompatible or incommensurable new paradigms. The Ptolemaic and Copernican systems are an example of incompatible systems. While they predicted different results, such as the appearance of the phases of Venus, they were judged by the mutual standard of how well each saved the phenomena with systems of uniform circular motions. Descartes' vortex system and Newton's gravity were more incommensurable than incompatible. They had different goals and different measurements of success or failure. Descartes insisted on an explanation of the cause of gravity, while Newton abandoned that quest and argued instead that it was enough that gravity acted according to an inverse square force law and accounted for all the motions of the celestial bodies. Though Descartes' later followers eventually agreed that any successful vortex theory would have to account for Kepler's laws, Descartes himself had ignored Kepler's discoveries, if indeed he had known of them. Newton, on the other hand, asked that his theory be judged by its success in accounting for Kepler's laws. Descartes' and Newton's theories were not incompatible, with a mutual standard against which they could be judged, but incommensurable: not comparable on any mutually agreed upon basis. Some historians accept the replacement of one theory with a second, incompatible theory as a revolution. Others might withhold the word revolution for the replacement of one worldview with another worldview so incommensurable that rival proponents cannot agree on common procedures, goals, and measurements of success or failure.

Sexagesimal number system: based on the number 60. Our time system of 60 minutes in an hour and 60 seconds in a minute is an example. Ancient astronomical positions were reported as 28, 55, 57, 58, with each succeeding unit representing so many sixtieths of the preceding unit (i.e., 28 degrees, 55 minutes, 57 seconds, etc.).

Sidereal month: the period of revolution of the Moon with respect to the stars. See synodic month.

Solstice: the times of the year when the Sun is at its highest or lowest latitude as seen from the Earth. Summer solstice is about June 22, and winter solstice is about December 22.

Stellar parallax: the angle subtended by the radius of the Earth's orbit at its distance from a star; the angle that would be subtended by one astronomical unit (the mean distance of the Earth from the Sun) at the distance of the star from the Sun. Stellar parallax was predicted from Copernicus's heliocentric theory but was too small to detect because the stars are at great distances from the Earth. Not until the 1830s, with instruments vastly better than the best in Copernicus's time, was stellar parallax first measured. See parallax. Step function: Some Babylonian astronomers employed mathematical tables in which the solar velocity was represented as constant for several months, after which the Sun proceeded with a different constant speed for several more months before reverting to the initial velocity and remaining at that speed for several more months. Graphed, the motion would look like a series of steps up and down, and it is called a "step" function, although the Babylonians are not known to have used graphs. See also zigzag function.

Sunspots: dark spots appearing on the face of the Sun, associated with magnetic fields, and having a 22-year cycle from minimum to maximum activity and back to minimum activity.

Superior planet: a planet lying beyond the Earth outward from the Sun (Mars, Jupiter, etc.). See inferior planet.

Syllogism: a form of deductive reasoning. Aristotle established the use of syllogisms in logical presentations. He explained that a deduction is a discourse in which, certain things being stated, something other than what is stated follows of necessity. An example of a syllogism is the following: All organisms are mortal; All men are organisms; Therefore all men are mortal. Demonstrative syllogisms derive facts already known, not new facts. See deduction. Symmetry: a relationship between constituent parts, often involving a sense of beauty as a result of harmonious arrangement. Plato regarded heaven itself and the bodies it contained as framed by the heavenly architect with the utmost beauty of which such works were susceptible. Ptolemy contemplated many beautiful mathematical theories, which lifted him from the Earth and placed him side by side with Zeus. Copernicus found an admirable symmetry in the universe and a clear bond of harmony in the motion and magnitude of the spheres. Could there possibly be a genetic wiring of the human brain, shaping our requirements for an aesthetically satisfying understanding of nature? See harmony.

Synodic month: the period of revolution of the Moon with respect to the Sun.

See sidereal month.

Syzygy: when the Moon lies in a straight line with the Earth and the Sun, at opposition or conjunction.

Themata: underlying beliefs, values, and worldviews constraining or motivating scientists and guiding or polarizing scientific communities. Tusi couple: an innovative combination of uniform circular motions producing motion in a straight line; devised by the Islamic astronomer Nasir al-din al-Tusi in the thirteenth century. See saving the phenomena. Uniform circular motion: moving in a circle at a constant angular motion with respect to the center of the circle; Plato purportedly laid down the principle that the heavenly body's motions were circular, uniform, and constantly regular.

Vortices: huge whirlpools of cosmic matter. According to René Descartes, our solar system was one of many vortices, its planets all moving in the same direction in the same plane around a luminous central body. Planets' moons were swept along by the planets' vortices. All change in motion was the result of percussion of bodies; gravity was the result of celestial matter circulating about the Earth and pushing all terrestrial matter toward the Earth. Zigzag function: a decreasing, increasing, and again decreasing sequence of numbers in a Babylonian table of astronomical positions, so called after how it would appear on a graph. Note, however, that the Babylonians are not known to have used graphs. See step function.

Zodiac: a band around the celestial sphere in which the Sun, the Moon, and the planets appear to move. It includes the intersection of the plane of the Earth's orbit around the Sun with the celestial sphere. See ecliptic.

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