Ancient Geographical Thought
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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. -
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. -
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. -
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. -
THE PHILOSOPHY BOOK George Santayana (1863-1952)
Georg Hegel (1770-1831) ................................ 30 Arthur Schopenhauer (1788-1860) ................. 32 Ludwig Andreas Feuerbach (1804-1872) ...... 32 John Stuart Mill (1806-1873) .......................... 33 Soren Kierkegaard (1813-1855) ..................... 33 Karl Marx (1818-1883).................................... 34 Henry David Thoreau (1817-1862) ................ 35 Charles Sanders Peirce (1839-1914).............. 35 William James (1842-1910) ............................ 36 The Modern World 1900-1950 ............................. 36 Friedrich Nietzsche (1844-1900) .................... 37 Ahad Ha'am (1856-1927) ............................... 38 Ferdinand de Saussure (1857-1913) ............. 38 Edmund Husserl (1859–1938) ....................... 39 Henri Bergson (1859-1941) ............................ 39 Contents John Dewey (1859–1952) ............................... 39 Introduction....................................................... 1 THE PHILOSOPHY BOOK George Santayana (1863-1952) ..................... 40 The Ancient World 700 BCE-250 CE..................... 3 Miguel de Unamuno (1864-1936) ................... 40 Introduction Thales of Miletus (c.624-546 BCE)................... 3 William Du Bois (1868-1963) .......................... 41 Laozi (c.6th century BCE) ................................. 4 Philosophy is not just the preserve of brilliant Bertrand Russell (1872-1970) ........................ 41 Pythagoras (c.570-495 BCE) ............................ 4 but eccentric thinkers that it is popularly Max Scheler -
Anaximander's Ἄπειρον
1 Pulished in: Ancient Philosophy Volume 39, Issue 1, Spring 2019 Anaximander’s ἄπειρον: from the Life-world to the Cosmic Event Horizon Norman Sieroka Pages 1-22 https://doi.org/10.5840/ancientphil2019391 1 Current affiliation of author (July 2020): Theoretische Philosophie, Universität Bremen www.uni-bremen.de/theophil/sieroka Abstract Scholars have claimed repeatedly that Anaximander’s notion of the ἄπειρον marks the first metaphysical concept, or even the first theoretical entity, in Western thought. The present paper scrutinizes this claim. Characterizing natural phenomena as ἄπειρος— that is, as being inexhaustible or untraversable by standard human means—was common in daily practice, especially when referring to landmasses and seas but also when referring to vast numbers of countable objects. I will deny the assumption that Anaximander’s notion started off as being a theoretical answer to a specific philosophical question. That said, the aforementioned everyday notion of ἄπειρος could still lead to the development of theoretical concepts. Based on the observations Anaximander did with seasonal sundials, the inexhaustible landmasses and seas just mentioned became depicted on his world map by means of concentric circles. These circles then marked the bounds of experience and, by being fixed and finite, suggested the possibility of traversing beyond what is directly experienced. Evaluating claims from recent Anaximander scholarship, the paper ends with a brief comparison with concepts from modern physics which play an analogous role of demarcating the bounds of experience. Anaximander’s ἄπειρον: from the Life-world to the Cosmic Event Horizon Norman Sieroka Interest in Anaximander (c. 610-c. 547 BC) has increased in recent years. -
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. -
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar Ve Yorumlar
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar ve Yorumlar David Pierce October , Matematics Department Mimar Sinan Fine Arts University Istanbul http://mat.msgsu.edu.tr/~dpierce/ Preface Here are notes of what I have been able to find or figure out about Thales of Miletus. They may be useful for anybody interested in Thales. They are not an essay, though they may lead to one. I focus mainly on the ancient sources that we have, and on the mathematics of Thales. I began this work in preparation to give one of several - minute talks at the Thales Meeting (Thales Buluşması) at the ruins of Miletus, now Milet, September , . The talks were in Turkish; the audience were from the general popu- lation. I chose for my title “Thales as the originator of the concept of proof” (Kanıt kavramının öncüsü olarak Thales). An English draft is in an appendix. The Thales Meeting was arranged by the Tourism Research Society (Turizm Araştırmaları Derneği, TURAD) and the office of the mayor of Didim. Part of Aydın province, the district of Didim encompasses the ancient cities of Priene and Miletus, along with the temple of Didyma. The temple was linked to Miletus, and Herodotus refers to it under the name of the family of priests, the Branchidae. I first visited Priene, Didyma, and Miletus in , when teaching at the Nesin Mathematics Village in Şirince, Selçuk, İzmir. The district of Selçuk contains also the ruins of Eph- esus, home town of Heraclitus. In , I drafted my Miletus talk in the Math Village. Since then, I have edited and added to these notes. -
Meet the Philosophers of Ancient Greece
Meet the Philosophers of Ancient Greece Everything You Always Wanted to Know About Ancient Greek Philosophy but didn’t Know Who to Ask Edited by Patricia F. O’Grady MEET THE PHILOSOPHERS OF ANCIENT GREECE Dedicated to the memory of Panagiotis, a humble man, who found pleasure when reading about the philosophers of Ancient Greece Meet the Philosophers of Ancient Greece Everything you always wanted to know about Ancient Greek philosophy but didn’t know who to ask Edited by PATRICIA F. O’GRADY Flinders University of South Australia © Patricia F. O’Grady 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Patricia F. O’Grady has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identi.ed as the editor of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask 1. Philosophy, Ancient 2. Philosophers – Greece 3. Greece – Intellectual life – To 146 B.C. I. O’Grady, Patricia F. 180 Library of Congress Cataloging-in-Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask / Patricia F. -
1 Anaximander and the Origins of Greek Philosophy
1 Anaximander and the Origins of Greek Philosophy The Problem and the Three Tiers of Explanation ow shall we account for the origins of Greek philoso- phy? To answer the question requires, first of all, that we determine precisely what we are trying to explain. HThis, of course, proves to be a daunting task for it is in large measure a perennial problem for philosophers: What exactly is philosophy, and what did it mean to the ancient Greeks? We can profitably distinguish two kinds of questions in our inquiries: (A) What are the defining characteristics of Greek philosophy in terms of which we can distinguish it from earlier pre- philosophical thought? (B) What explains the rise of this particular type of thinking in Greece? 15 16 Anaximander Naturally, the answer we give to (A) will affect the way we and the approach (B). Reflecting upon the diverse scholarly literature Architects over the course of the last century, the disparate views and approaches suggest, not surprisingly, that there is considerable disagreement about precisely what “Greek philosophy” denotes and connotes.When the variety of opinions have been assem- bled, however, they may be roughly but usefully classified into two groups. On the one hand, we have what might be called first-tier accounts. These accounts answer (A) by identifying epistemological and ontological concerns in the systematic pro- grams of Plato and Aristotle as characteristic of philosophical thought. First-tier approaches offer historical narratives that tend to look backward in time, before the classical period, to determine who should and who should not be included in the story that leads up to them. -
Lecture 4. Pythagoras' Theorem and the Pythagoreans
Lecture 4. Pythagoras' Theorem and the Pythagoreans Figure 4.1 Pythagoras was born on the Island of Samos Pythagoras Pythagoras (born between 580 and 572 B.C., died about 497 B.C.) was born on the island of Samos, just off the coast of Asia Minor1. He was the earliest important philosopher who made important contributions in mathematics, astronomy, and the theory of music. Pythagoras is credited with introduction the words \philosophy," meaning love of wis- dom, and \mathematics" - the learned disciplines.2 Pythagoras is famous for establishing the theorem under his name: Pythagoras' theorem, which is well known to every educated per- son. Pythagoras' theorem was known to the Babylonians 1000 years earlier but Pythagoras may have been the first to prove it. Pythagoras did spend some time with Thales in Miletus. Probably by the suggestion of Thales, Pythagoras traveled to other places, including Egypt and Babylon, where he may have learned some mathematics. He eventually settled in Groton, a Greek settlement in southern Italy. In fact, he spent most of his life in the Greek colonies in Sicily and 1Asia Minor is a region of Western Asia, comprising most of the modern Republic of Turkey. 2Is God a mathematician ? Mario Livio, Simon & Schuster Paperbacks, New York-London-Toronto- Sydney, 2010, p. 15. 23 southern Italy. In Groton, he founded a religious, scientific, and philosophical organization. It was a formal school, in some sense a brotherhood, and in some sense a monastery. In that organization, membership was limited and very secretive; members learned from leaders and received education in religion. -
Geminus and the Isia
CORE Metadata, citation and similar papers at core.ac.uk Provided by DSpace at New York University GEMINUS AND THE ISIA ALEXANDER JONES T HE torical Greek interest, scientific including a lost writer treatise onGeminus the foundations wrote of several works of his- mathematics and an extant book on astronomy known as the Isagoge ("Introduction to the Phenomena"). The Isagoge is important to us as a witness to a stage of Greek astronomy that was both less advanced and less homogeneous in method than Ptolemy's. Approximate knowledge of when its author lived would be useful in several respects, for exam- ple in tracing the diffusion of elements originating in Babylonian lunar theory and in Hipparchus' work. Recent scholarship frequently cites Neugebauer's dating of Geminus to about A.D. 50, which has largely superseded the dating to the first half of the first century B.C. that used to be widely accepted.' Both dates derive, oddly enough, from analysis of the same passage in the Isagoge. The purpose of this note is to eluci- date the chronological issues, and to present documentary evidence that decisively establishes the earlier dating. The limits established by ancient citations are not very narrow. Isa- goge 4 mentions Hipparchus as an authority concerning constellations, and though Geminus does not say so, the lengths of the astronomical seasons listed in Isagoge I are the values that Hipparchus had used in deriving a model for the sun's motion. These passages cannot have been written before the 140s B.C. Moreover, Alexander of Aphrodisias (In Arist.