Shattering Geocentric, Anthrocentric Worldviews Since 1543. SASS 2009
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In the Wake of the Compendia Science, Technology, and Medicine in Ancient Cultures
In the Wake of the Compendia Science, Technology, and Medicine in Ancient Cultures Edited by Markus Asper Philip van der Eijk Markham J. Geller Heinrich von Staden Liba Taub Volume 3 In the Wake of the Compendia Infrastructural Contexts and the Licensing of Empiricism in Ancient and Medieval Mesopotamia Edited by J. Cale Johnson DE GRUYTER ISBN 978-1-5015-1076-2 e-ISBN (PDF) 978-1-5015-0250-7 e-ISBN (EPUB) 978-1-5015-0252-1 ISSN 2194-976X Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2015 Walter de Gruyter Inc., Boston/Berlin Typesetting: Meta Systems Publishing & Printservices GmbH, Wustermark Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ♾ Printed on acid-free paper Printed in Germany www.degruyter.com Notes on Contributors Florentina Badalanova Geller is Professor at the Topoi Excellence Cluster at the Freie Universität Berlin. She previously taught at the University of Sofia and University College London, and is currently on secondment from the Royal Anthropological Institute (London). She has published numerous papers and is also the author of ‘The Bible in the Making’ in Imagining Creation (2008), Qurʾān in Vernacular: Folk Islam in the Balkans (2008), and 2 (Slavonic Apocalypse of) Enoch: Text and Context (2010). Siam Bhayro was appointed Senior Lecturer in Early Jewish Studies in the Department of Theology and Religion, University of Exeter, in 2012, having previously been Lecturer in Early Jewish Studies since 2007. -
Babylonian Astral Science in the Hellenistic World: Reception and Transmission
CAS® e SERIES Nummer 4 / 2010 Francesca Rochberg (Berkeley) Babylonian Astral Science in the Hellenistic World: Reception and Transmission Herausgegeben von Ludwig-Maximilians-Universität München Center for Advanced Studies®, Seestr. 13, 80802 München www.cas.lmu.de/publikationen/eseries Nummer 4 / 2010 Babylonian Astral Science in the Hellenistic World: Reception and Transmission Francesca Rochberg (Berkeley) In his astrological work the Tetrabiblos, the astronomer such as in Strabo’s Geography, as well as in an astrono- Ptolemy describes the effects of geography on ethnic mical text from Oxyrhynchus in the second century of character, claiming, for example, that due to their specific our era roughly contemporary with Ptolemy [P.Oxy. geographical location „The ...Chaldeans and Orchinians 4139:8; see Jones 1999, I 97-99 and II 22-23]. This have familiarity with Leo and the sun, so that they are astronomical papyrus fragment refers to the Orchenoi, simpler, kindly, addicted to astrology.” [Tetr. 2.3] or Urukeans, in direct connection with a lunar parameter Ptolemy was correct in putting the Chaldeans and identifiable as a Babylonian period for lunar anomaly Orchinians together geographically, as the Chaldeans, or preserved on cuneiform tablets from Uruk. The Kaldayu, were once West Semitic tribal groups located Babylonian, or Chaldean, literati, including those from in the parts of southern and western Babylonia known Uruk were rightly famed for astronomy and astrology, as Kaldu, and the Orchinians, or Urukayu, were the „addicted,” as Ptolemy put it, and eventually, in Greco- inhabitants of the southern Babylonian city of Uruk. He Roman works, the term Chaldean came to be interchan- was also correct in that he was transmitting a tradition geable with „astrologer.” from the Babylonians themselves, which, according to a Hellenistic Greek writers seeking to claim an authorita- Hellenistic tablet from Uruk [VAT 7847 obv. -
Models for Earth and Maps
Earth Models and Maps James R. Clynch, Naval Postgraduate School, 2002 I. Earth Models Maps are just a model of the world, or a small part of it. This is true if the model is a globe of the entire world, a paper chart of a harbor or a digital database of streets in San Francisco. A model of the earth is needed to convert measurements made on the curved earth to maps or databases. Each model has advantages and disadvantages. Each is usually in error at some level of accuracy. Some of these error are due to the nature of the model, not the measurements used to make the model. Three are three common models of the earth, the spherical (or globe) model, the ellipsoidal model, and the real earth model. The spherical model is the form encountered in elementary discussions. It is quite good for some approximations. The world is approximately a sphere. The sphere is the shape that minimizes the potential energy of the gravitational attraction of all the little mass elements for each other. The direction of gravity is toward the center of the earth. This is how we define down. It is the direction that a string takes when a weight is at one end - that is a plumb bob. A spirit level will define the horizontal which is perpendicular to up-down. The ellipsoidal model is a better representation of the earth because the earth rotates. This generates other forces on the mass elements and distorts the shape. The minimum energy form is now an ellipse rotated about the polar axis. -
Anaximander and the Problem of the Earth's Immobility
Binghamton University The Open Repository @ Binghamton (The ORB) The Society for Ancient Greek Philosophy Newsletter 12-28-1953 Anaximander and the Problem of the Earth's Immobility John Robinson Windham College Follow this and additional works at: https://orb.binghamton.edu/sagp Recommended Citation Robinson, John, "Anaximander and the Problem of the Earth's Immobility" (1953). The Society for Ancient Greek Philosophy Newsletter. 263. https://orb.binghamton.edu/sagp/263 This Article is brought to you for free and open access by The Open Repository @ Binghamton (The ORB). It has been accepted for inclusion in The Society for Ancient Greek Philosophy Newsletter by an authorized administrator of The Open Repository @ Binghamton (The ORB). For more information, please contact [email protected]. JOHN ROBINSON Windham College Anaximander and the Problem of the Earth’s Immobility* N the course of his review of the reasons given by his predecessors for the earth’s immobility, Aristotle states that “some” attribute it I neither to the action of the whirl nor to the air beneath’s hindering its falling : These are the causes with which most thinkers busy themselves. But there are some who say, like Anaximander among the ancients, that it stays where it is because of its “indifference” (όμοιότητα). For what is stationed at the center, and is equably related to the extremes, has no reason to go one way rather than another—either up or down or sideways. And since it is impossible for it to move simultaneously in opposite directions, it necessarily stays where it is.1 The ascription of this curious view to Anaximander appears to have occasioned little uneasiness among modern commentators. -
Nicolaus Copernicus: the Loss of Centrality
I Nicolaus Copernicus: The Loss of Centrality The mathematician who studies the motions of the stars is surely like a blind man who, with only a staff to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. [Rheticus, Narratio Prima (1540), 163] 1 Ptolemy and Copernicus The German playwright Bertold Brecht wrote his play Life of Galileo in exile in 1938–9. It was first performed in Zurich in 1943. In Brecht’s play two worldviews collide. There is the geocentric worldview, which holds that the Earth is at the center of a closed universe. Among its many proponents were Aristotle (384–322 BC), Ptolemy (AD 85–165), and Martin Luther (1483–1546). Opposed to geocentrism is the heliocentric worldview. Heliocentrism teaches that the sun occupies the center of an open universe. Among its many proponents were Copernicus (1473–1543), Kepler (1571–1630), Galileo (1564–1642), and Newton (1643–1727). In Act One the Italian mathematician and physicist Galileo Galilei shows his assistant Andrea a model of the Ptolemaic system. In the middle sits the Earth, sur- rounded by eight rings. The rings represent the crystal spheres, which carry the planets and the fixed stars. Galileo scowls at this model. “Yes, walls and spheres and immobility,” he complains. “For two thousand years people have believed that the sun and all the stars of heaven rotate around mankind.” And everybody believed that “they were sitting motionless inside this crystal sphere.” The Earth was motionless, everything else rotated around it. “But now we are breaking out of it,” Galileo assures his assistant. -
The Planetary Increase of Brightness During Retrograde Motion: an Explanandum Constructed Ad Explanantem
Studies in History and Philosophy of Science 54 (2015) 90e101 Contents lists available at ScienceDirect Studies in History and Philosophy of Science journal homepage: www.elsevier.com/locate/shpsa The planetary increase of brightness during retrograde motion: An explanandum constructed ad explanantem Christián Carlos Carman National University of Quilmes/CONICET, Roque Sáenz Peña 352, B1876BXD Bernal, Buenos Aires, Argentina article info abstract Article history: In Ancient Greek two models were proposed for explaining the planetary motion: the homocentric Received 5 May 2015 spheres of Eudoxus and the Epicycle and Deferent System. At least in a qualitative way, both models Received in revised form could explain the retrograde motion, the most challenging phenomenon to be explained using circular 17 September 2015 motions. Nevertheless, there is another explanandum: during retrograde motion the planets increase their brightness. It is natural to interpret a change of brightness, i.e., of apparent size, as a change in Keywords: distance. Now, while according to the Eudoxian model the planet is always equidistant from the earth, Epicycle; according to the epicycle and deferent system, the planet changes its distance from the earth, Deferent; fi Homocentric spheres; approaching to it during retrograde motion, just as observed. So, it is usually af rmed that the main ’ Brightness change reason for the rejection of Eudoxus homocentric spheres in favor of the epicycle and deferent system was that the first cannot explain the manifest planetary increase of brightness during retrograde motion, while the second can. In this paper I will show that this historical hypothesis is not as firmly founded as it is usually believed to be. -
You Can Only Use a Planar Surface So Far, Before the Equidistance Assumption Creates Large Errors
You can only use a planar surface so far, before the equidistance assumption creates large errors Distance error from Kiester to Warroad is greater than two football fields in length So we assume a spherical Earth P. Wormer, wikimedia commons Longitudes are great circles, latitudes are small circles (except the Equator, which is a GC) Spherical Geometry Longitude Spherical Geometry Note: The Greek letter l (lambda) is almost always used to specify longitude while f, a, w and c, and other symbols are used to specify latitude Great and Small Circles Great circles splits the Small circles splits the earth into equal halves earth into unequal halves wikipedia geography.name All lines of equal longitude are great circles Equator is the only line of equal latitude that’s a great circle Surface distance measurements should all be along a great circle Caliper Corporation Note that great circle distances appear curved on projected or flat maps Smithsonian In GIS Fundamentals book, Chapter 2 Latitude - angle to a parallel circle, a small circle parallel to the Equatorial great circle Spherical Geometry Three measures: Latitude, Longitude, and Earth Radius + height above/ below the sphere (hp) How do we measure latitude/longitude? Well, now, GNSS, but originally, astronomic measurements: latitude by north star or solar noon angles, at equinox Longitude Measurement Method 1: The Earth rotates 360 degrees in a day, or 15 degrees per hour. If we know the time difference between 2 points, and the longitude of the first point (Greenwich), we can determine the longitude at our current location. Method 2: Create a table of moon-star distances for each day/time of the year at a reference location (Greenwich observatory) Measure the same moon-star distance somewhere else at a standard or known time. -
“Point at Infinity Hape of the World
“Point at Infinity hape of the World Last week, we began a series of posts dedicated to thinking about immortality. If we want to even pretend to think precisely about immortality, we will have to consider some fundamental questions. What does it mean to be immortal? What does it mean to live forever? Are these the same thing? And since immortality is inextricably tied up in one’s relationship with time, we must think about the nature of time itself. Is there a difference between external time and personal time? What is the shape of time? Is time linear? Circular? Finite? Infinite? Of course, we exist not just across time but across space as well, so the same questions become relevant when asked about space. What is the shape of space? Is it finite? Infinite? It is not hard to see how this question would have a significant bearing on our thinking about immortality. In a finite universe (or, more precisely, a universe in which only finitely many different configurations of maer are possible), an immortal being would encounter the same situations over and over again, would think the same thoughts over and over again, would have the same conversations over and over again. Would such a life be desirable? (It is not clear that this repetition would be avoidable even in an infinite universe, but more on that later.) Today, we are going to take a lile historical detour to look at the shape of the universe, a trip that will take us from Ptolemy to Dante to Einstein, a trip that will uncover a remarkable confluence of poetry and physics. -
Paths Between Points on Earth: Great Circles, Geodesics, and Useful Projections
Paths Between Points on Earth: Great Circles, Geodesics, and Useful Projections I. Historical and Common Navigation Methods There are an infinite number of paths between two points on the earth. For navigation purposes there are only a few historically common choices. 1. Sailing a latitude. Prior to a good method of finding longitude at sea, you sailed north or south until you cane to the latitude of your destination then you sailed due east or west until you reached your goal. Of course if you choose the wrong direction, you can get in big trouble. (This happened in 1707 to a British fleet that sunk when it hit rocks. This started the major British program for a longitude method useful at sea.) In this method the route follows the legs of a right triangle on the sphere. Just as in right triangles on the plane, the hypotenuse is always shorter than the sum of the other two sides. This method is very inefficient, but it was all that worked for open ocean sailing before 1770. 2. Rhumb Line A rhumb line is a line of constant bearing or azimuth. This is not the shortest distance on a long trip, but it is very easy to follow. You just have to know the correct azimuth to use to get between two sites, such as New York and London. You can get this from a straight line on a Mercator projection. This is the reason the Mercator projection was invented. On other projections straight lines are not rhumb lines. 3. Great Circle On a spherical earth, a great circle is the shortest distance between two locations. -
The Arithmetic of the Spheres
The Arithmetic of the Spheres Je↵ Lagarias, University of Michigan Ann Arbor, MI, USA MAA Mathfest (Washington, D. C.) August 6, 2015 Topics Covered Part 1. The Harmony of the Spheres • Part 2. Lester Ford and Ford Circles • Part 3. The Farey Tree and Minkowski ?-Function • Part 4. Farey Fractions • Part 5. Products of Farey Fractions • 1 Part I. The Harmony of the Spheres Pythagoras (c. 570–c. 495 BCE) To Pythagoras and followers is attributed: pitch of note of • vibrating string related to length and tension of string producing the tone. Small integer ratios give pleasing harmonics. Pythagoras or his mentor Thales had the idea to explain • phenomena by mathematical relationships. “All is number.” A fly in the ointment: Irrational numbers, for example p2. • 2 Harmony of the Spheres-2 Q. “Why did the Gods create us?” • A. “To study the heavens.”. Celestial Sphere: The universe is spherical: Celestial • spheres. There are concentric spheres of objects in the sky; some move, some do not. Harmony of the Spheres. Each planet emits its own unique • (musical) tone based on the period of its orbital revolution. Also: These tones, imperceptible to our hearing, a↵ect the quality of life on earth. 3 Democritus (c. 460–c. 370 BCE) Democritus was a pre-Socratic philosopher, some say a disciple of Leucippus. Born in Abdera, Thrace. Everything consists of moving atoms. These are geometrically• indivisible and indestructible. Between lies empty space: the void. • Evidence for the void: Irreversible decay of things over a long time,• things get mixed up. (But other processes purify things!) “By convention hot, by convention cold, but in reality atoms and• void, and also in reality we know nothing, since the truth is at bottom.” Summary: everything is a dynamical system! • 4 Democritus-2 The earth is round (spherical). -
The Shape of the Earth
The Shape of the Earth Produced for the Cosmology and Cultures Project of the OBU Planetarium by Kerry Magruder August, 2005 2 Credits Written & Produced by: Kerry Magruder Nicole Oresme: Kerry Magruder Students: Rachel Magruder, Hannah Magruder, Kevin Kemp, Chris Kemp, Kara Kemp Idiot Professor: Phil Kemp Andrew Dickson White: Phil Kemp Cicero, Aquinas: J Harvey NASA writer: Sylvia Patterson Jeffrey Burton Russell: Candace Magruder Images courtesy: History of Science Collections, University of Oklahoma Libraries Digital photography and processing by: Hannah Magruder Soundtrack composed and produced by: Eric Barfield Special thanks to... Jeffrey Burton Russell, Mike Keas, JoAnn Palmeri, Hannah Magruder, Rachel Magruder, Susanna Magruder, Candace Magruder Produced with a grant from the American Council of Learned Societies 3 1. Contents 1. Contents________________________________________________3 2. Introduction_____________________________________________ 4 A. Summary____________________________________________ 4 B. Synopsis____________________________________________ 5 C. Instructor Notes_______________________________________6 3. Before the Show_________________________________________ 7 A. Video: A Private Universe______________________________ 7 B. Pre-Test_____________________________________________ 8 4. Production Script_________________________________________9 A. Production Notes______________________________________9 B. Theater Preparation___________________________________10 C. Script______________________________________________ -
307 Lesson 21: Eratosthenes' Measurement of the Earth the Most
307 Lesson 21: Eratosthenes’ Measurement of the Earth The most important parallel of latitude is the equator; it is the only parallel of latitude that is a great circle. However, in the previous lesson we learned about four other parallels of latitude which are of great importance because of the relative geometry of the Earth and the Sun. These are the Tropics of Cancer and Capricorn and the Arctic and Antarctic Circles. We briefly review the basic facts about these four parallels. At each moment on the day of the summer solstice, there is a single point on the surface of the Earth that is closet to the Sun. As the Earth rotates through the day of the summer solstice, this closest point to the Sun moves around the surface of the Earth and traces a parallel of latitude called the Tropic of Cancer. Another description of the Tropic of Cancer is that it is the set of all points on the Earth’s surface where the Sun is directly overhead at solar noon on the day of the summer solstice. The latitude coordinate of the Tropic of Cancer equals the measure of the angle that the Earth’s axis makes with the perpendicular to the ecliptic plane: approximately 23.5º N. On the day of the summer solstice, as the Earth rotates about its axis, the terminator (the division between daytime and nighttime) moves, and its northernmost point traces out a parallel of latitude called the Arctic Circle. Similarly, as the Earth rotates, the southernmost point of the terminator traces out a parallel of latitude called the Antarctic Circle.