From Mythology to Science: the Development of Scientific
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COPYRIGHT NOTICE: for COURSE PACK and Other PERMISSIONS
COPYRIGHT NOTICE: Jean-Louis and Monique Tassoul: A Concise History of Solar and Stellar Physics is published by Princeton University Press and copyrighted, © 2004, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. For COURSE PACK and other PERMISSIONS, refer to entry on previous page. For more information, send e-mail to [email protected] Chapter One The Age of Myths and Speculations And God said, Let there be light, and there was light. —Genesis 1:3 For thousands of years men have looked up into the star-filled night sky and have wondered about the nature of the “fixed” stars as opposed to that of the five planets wandering among the constellations of the zodiac. The daily course of the sun, its brilliance and heat, and the passing of the seasons are among the central problems that have concerned every human society. Undoubtedly, the appearance of a comet or a shooting star, the passing phenomena of clouds and rain and lightning, the Milky Way, the changing phases of the moon and the eclipses—all of these must have caused quite a sense of wonder and been the source of endless discussions. Faced with this confusing multiplicity of brute facts, beyond their physical power to control, our ancestors sought to master these unrelated phenomena symbolically by picturing the universe in terms of objects familiar to them so as to make clear the unfamiliar and the unexplained. -
CURRICULUM VITA of ROBERT HAHN January 2015
CURRICULUM VITA OF ROBERT HAHN January 2015 I. PERSONAL A. Present University Department: Philosophy. II. EDUCATION Ph.D., Philosophy, Yale University, May 1976. M. Phil., Philosophy, Yale University, May 1976. M.A., Philosophy, Yale University, December 1975. B.A., Philosophy, Union College, Summa cum laude, June 1973. Summer Intensive Workshop in Ancient Greek, The University of California at Berkeley, 1973. Summer Intensive Workshop in Sanskrit, The University of Chicago, 1972. III. PROFESSIONAL EXPERIENCE 2002-present Professor of Philosophy, Southern Illinois University at Carbondale 1988-2001 Associate Professor of Philosophy, Southern Illinois University at Carbondale. 1982-1987 Assistant Professor of Philosophy, Southern Illinois University at Carbondale. 1981-1982 Assistant Professor of Philosophy, Denison University. 1978-1981 Assistant Professor of Philosophy and the History of Ideas, Brandeis University. 1979-1981 Assistant Professor, Harvard University, Extension. 1980 (Spring) Visiting Professor, The American College of Greece (Deree College), Athens, Greece. 1980 (Summer) Visiting Professor, The University of Maryland: European Division, Athens, Greece (The United States Air Force #7206 Air Base Group). 1977-1978 Assistant Professor of Philosophy, The University of Texas, Arlington. 1977 (Spring) Lecturer in Philosophy, Yale University. 1976 (Fall) Postdoctoral Research Fellow in Philosophy, The University of California at Berkeley. IV. TEACHING EXPERIENCE A. Teaching Interests and Specialties: History of Philosophy, History/Philosophy -
King Lfred's Version Off the Consolations of Boethius
King _lfred's Version off the Consolations of Boethius HENRY FROWDE, M A. PUBLISHER TO THE UNIVERSITY OF OF_0RD LONDON, EDINBURGH_ AND NEW YORK Kring e__lfred's Version o_/"the Consolations of Boethius _ _ Z)one into c_gfodern English, with an Introduction _ _ _ _ u_aa Litt.D._ Editor _o_.,I_ing .... i .dlfred_ OM Englis.h..ffgerAon2.' !ilo of the ' De Con.d.¢_onz,o,e 2 Oxford : _4t the Claro_don:,.....: PrestO0000 M D CCCC _eee_ Ioee_ J_el eeoee le e_ZNeFED AT THE_.e_EN_N PI_.._S _ee • • oeoo eee • oeee eo6_o eoee • ooeo e_ooo ..:.. ..'.: oe°_ ° leeeo eeoe ee •QQ . :.:.. oOeeo QOO_e 6eeQ aee...._ e • eee TO THE REV. PROFESSOR W. W. SKEAT LITT.D._ D.C.L._ LL.D.:_ PH.D. THIS _800K IS GRATEFULLY DEDICATED PREFACE THE preparationsfor adequately commemoratingthe forthcoming millenary of King Alfred's death have set going a fresh wave of popularinterest in that hero. Lectares have been given, committees formed, sub- scriptions paid and promised, and an excellent book of essays by eminent specialists has been written about Alfred considered under quite a number of aspects. That great King has himself told us that he was not indifferent to the opinion of those that should come after him, and he earnestly desired that that opinion should be a high one. We have by no means for- gotten him, it is true, but yet to verymany intelligent people he is, to use a paradox, a distinctly nebulous character of history. His most undying attributes in the memory of the people are not unconnected with singed cakes and romantic visits in disguise to the Danish viii Preface Danish camp. -
Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
Archimedes' Principle
General Physics Lab Handbook by D.D.Venable, A.P.Batra, T.Hubsch, D.Walton & M.Kamal Archimedes’ Principle 1. Theory We are aware that some objects oat on some uids, submerged to diering extents: ice cubes oat in water almost completely submerged, while corks oat almost completely on the surface. Even the objects that sink appear to weigh less when they are submerged in the uid than when they are not. These eects are due to the existence of an upward ‘buoyant force’ that will act on the submerged object. This force is caused by the pressure in the uid being increased with depth below the surface, so that the pressure near the bottom of the object is greater than the pressure near the top. The dierence of these pressures results in the eective ‘buoyant force’, which is described by the Archimedes’ principle. According to this principle, the buoyant force FB on an object completely or partially submerged in a uid is equal to the weight of the uid that the (submerged part of the) object displaces: FB = mf g = f Vg . (1) where f is the density of the uid, mf and V are respectively mass and the volume of the displaced uid (which is equal to the volume of the submerged part of the object) and g is the gravitational acceleration constant. 2. Experiment Object: Use Archimedes’ principle to measure the densities of a given solid and a provided liquid. Apparatus: Solid (metal) and liquid (oil) samples, beaker, thread, balance, weights, stand, micrometer, calipers, PASCO Science Workshop Interface, Force Sensors and a Macintosh Computer. -
Greeks Doing Algebra
Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks. -
Great Inventors of the Ancient World Preliminary Syllabus & Course Outline
CLA 46 Dr. Patrick Hunt Spring Quarter 2014 Stanford Continuing Studies http://www.patrickhunt.net Great Inventors Of the Ancient World Preliminary Syllabus & Course Outline A Note from the Instructor: Homo faber is a Latin description of humans as makers. Human technology has been a long process of adapting to circumstances with ingenuity, and while there has been gradual progress, sometimes technology takes a downturn when literacy and numeracy are lost over time or when humans forget how to maintain or make things work due to cataclysmic change. Reconstructing ancient technology is at times a reminder that progress is not always guaranteed, as when Classical civilization crumbled in the West, but the history of technology is a fascinating one. Global revolutions in technology occur in cycles, often when necessity pushes great minds to innovate or adapt existing tools, as happened when humans first started using stone tools and gradually improved them, often incrementally, over tens of thousands of years. In this third course examining the greats of the ancient world, we take a close look at inventions and their inventors (some of whom might be more legendary than actually known), such as vizier Imhotep of early dynastic Egypt, who is said to have built the first pyramid, and King Gudea of Lagash, who is credited with developing the Mesopotamian irrigation canals. Other somewhat better-known figures are Glaucus of Chios, a metallurgist sculptor who possibly invented welding; pioneering astronomer Aristarchus of Samos; engineering genius Archimedes of Siracusa; Hipparchus of Rhodes, who made celestial globes depicting the stars; Ctesibius of Alexandria, who invented hydraulic water organs; and Hero of Alexandria, who made steam engines. -
Champ Math Study Guide Indesign
Champions of Mathematics — Study Guide — Questions and Activities Page 1 Copyright © 2001 by Master Books, Inc. All rights reserved. This publication may be reproduced for educational purposes only. BY JOHN HUDSON TINER To get the most out of this book, the following is recommended: Each chapter has questions, discussion ideas, research topics, and suggestions for further reading to improve students’ reading, writing, and thinking skills. The study guide shows the relationship of events in Champions of Mathematics to other fields of learning. The book becomes a springboard for exploration in other fields. Students who enjoy literature, history, art, or other subjects will find interesting activities in their fields of interest. Parents will find that the questions and activities enhance their investments in the Champion books because children of different age levels can use them. The questions with answers are designed for younger readers. Questions are objective and depend solely on the text of the book itself. The questions are arranged in the same order as the content of each chapter. A student can enjoy the book and quickly check his or her understanding and comprehension by the challenge of answering the questions. The activities are designed to serve as supplemental material for older students. The activities require greater knowledge and research skills. An older student (or the same student three or four years later) can read the book and do the activities in depth. CHAPTER 1 QUESTIONS 1. A B C D — Pythagoras was born on an island in the (A. Aegean Sea B. Atlantic Ocean C. Caribbean Sea D. -
The Cambridge Companion to Greek Mythology (2007)
P1: JzG 9780521845205pre CUFX147/Woodard 978 0521845205 Printer: cupusbw July 28, 2007 1:25 The Cambridge Companion to GREEK MYTHOLOGY S The Cambridge Companion to Greek Mythology presents a comprehensive and integrated treatment of ancient Greek mythic tradition. Divided into three sections, the work consists of sixteen original articles authored by an ensemble of some of the world’s most distinguished scholars of classical mythology. Part I provides readers with an examination of the forms and uses of myth in Greek oral and written literature from the epic poetry of the eighth century BC to the mythographic catalogs of the early centuries AD. Part II looks at the relationship between myth, religion, art, and politics among the Greeks and at the Roman appropriation of Greek mythic tradition. The reception of Greek myth from the Middle Ages to modernity, in literature, feminist scholarship, and cinema, rounds out the work in Part III. The Cambridge Companion to Greek Mythology is a unique resource that will be of interest and value not only to undergraduate and graduate students and professional scholars, but also to anyone interested in the myths of the ancient Greeks and their impact on western tradition. Roger D. Woodard is the Andrew V.V.Raymond Professor of the Clas- sics and Professor of Linguistics at the University of Buffalo (The State University of New York).He has taught in the United States and Europe and is the author of a number of books on myth and ancient civiliza- tion, most recently Indo-European Sacred Space: Vedic and Roman Cult. Dr. -
Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy
Mathematical discourse in philosophical authors: Examples from Theon of Smyrna and Cleomedes on mathematical astronomy Nathan Sidoli Introduction Ancient philosophers and other intellectuals often mention the work of mathematicians, al- though the latter rarely return the favor.1 The most obvious reason for this stems from the im- personal nature of mathematical discourse, which tends to eschew any discussion of personal, or lived, experience. There seems to be more at stake than this, however, because when math- ematicians do mention names they almost always belong to the small group of people who are known to us as mathematicians, or who are known to us through their mathematical works.2 In order to be accepted as a member of the group of mathematicians, one must not only have mastered various technical concepts and methods, but must also have learned how to express oneself in a stylized form of Greek prose that has often struck the uninitiated as peculiar.3 Be- cause of the specialized nature of this type of intellectual activity, in order to gain real mastery it was probably necessary to have studied it from youth, or to have had the time to apply oneself uninterruptedly.4 Hence, the private nature of ancient education meant that there were many educated individuals who had not mastered, or perhaps even been much exposed to, aspects of ancient mathematical thought and practice that we would regard as rather elementary (Cribiore 2001; Sidoli 2015). Starting from at least the late Hellenistic period, and especially during the Imperial and Late- Ancient periods, some authors sought to address this situation in a variety of different ways— such as discussing technical topics in more elementary modes, rewriting mathematical argu- ments so as to be intelligible to a broader audience, or incorporating mathematical material di- rectly into philosophical curricula. -
What Did Shakespeare Know About Copernicanism?
DOI: 10.2478/v10319-012-0031-x WHAT DID SHAKESPEARE KNOW ABOUT COPERNICANISM? ALAN S. WEBER Weill Cornell Medical College–Qatar Abstract: This contribution examines Shakespeare’s knowledge of the cosmological theories of Nicolaus Copernicus (1473-1543) as well as recent claims that Shakespeare possessed specialized knowledge of technical astronomy. Keywords: Shakespeare, William; Copernicus, Nicolaus; renaissance astronomy 1. Introduction Although some of his near contemporaries lamented the coming of “The New Philosophy,” Shakespeare never made unambiguous or direct reference to the heliocentric theories of Nicolaus Copernicus (1473-1543) in his drama or poetry. Peter Usher, however, has recently argued in two books Hamlet’s Universe (2006) and Shakespeare and the Dawn of Modern Science (2010) that Hamlet is an elaborate allegory of Copernicanism, which in addition heralds pre-Galilean telescopic observations carried out by Thomas Digges. Although many of Usher’s arguments are excessively elaborate and speculative, he raises several interesting questions. Just why did Shakespeare, for example, choose the names of Rosenskrantz and Guildenstern for Hamlet’s petard-hoisted companions, two historical relatives of Tycho Brahe (the foremost astronomer during Shakespeare’s floruit)? What was Shakespeare’s relationship to the spread of Copernican cosmology in late Elizabethan England? Was he impacted by such Copernican-related currents of cosmological thought as the atomism of Thomas Harriot and Nicholas Hill, the Neoplatonism of Kepler, and -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books.