Galileo and Einstein Text for Physics 109, Fall 2009 Michael Fowler, UVa Physics 8/21/2009 2 TABLE OF CONTENTS 1 INTRODUCTION: WHAT IS THIS COURSE ABOUT? ......................................................... 12 1.1 Some Basic Ideas .......................................................................................................................... 12 1.2 Babylonians and Greeks ................................................................................................................ 12 1.3 Greek Classics Come to Baghdad................................................................................................... 12 1.4 Monasteries and Universities ....................................................................................................... 13 1.5 Galileo .......................................................................................................................................... 13 1.6 Newton ......................................................................................................................................... 13 1.7 From Newton to Einstein .............................................................................................................. 13 1.8 What about Other Civilizations? ................................................................................................... 14 1.9 Plan of the Course ......................................................................................................................... 14 2 COUNTING IN BABYLON ............................................................................................................ 16 2.1 The Earliest Written Language ...................................................................................................... 16 2.2 Weights and Measures: 60s everywhere! ..................................................................................... 16 2.3 Number Systems: Ours, the Roman and the Babylonian ............................................................... 17 2.4 Fractions ....................................................................................................................................... 19 2.5 Ancient Math Tables ..................................................................................................................... 19 2.6 How Practical are Babylonian Weights and Measures? ................................................................. 20 2.7 Pythagoras’ Theorem a Thousand Years before Pythagoras.......................................................... 20 2.8 Babylonian Pythagorean Triplets .................................................................................................. 21 3 EARLY GREEK SCIENCE: THALES TO PLATO ...................................................................... 22 3.1 The Milesians ................................................................................................................................ 22 3.2 Early Geometry ............................................................................................................................. 23 3 3.3 Early Geometry According to Proclus ............................................................................................ 24 3.4 The Pythagoreans: a Cult with a Theorem, and an Irrational Discovery ........................................ 26 3.5 The Square on the Hypotenuse ..................................................................................................... 26 3.6 Rational and Irrational Numbers ................................................................................................... 27 3.7 What’s so Important about Irrational Numbers? .......................................................................... 30 3.8 Change and Constancy in the Physical World ................................................................................ 30 3.9 Hippocrates and his Followers ...................................................................................................... 31 3.10 Plato ......................................................................................................................................... 32 3.11 References ............................................................................................................................... 33 4 MOTION IN THE HEAVENS: STARS, SUN, MOON, PLANETS ........................................... 34 4.1 Introduction .................................................................................................................................. 34 4.2 Looking at the Stars ...................................................................................................................... 34 4.3 Motion of the Sun ......................................................................................................................... 34 4.4 Motion of the Moon against the Starry Vault ............................................................................... 37 4.5 Motion of the Planets ................................................................................................................... 38 5 ARISTOTLE .................................................................................................................................... 40 5.1 Beginnings of Science and Philosophy in Athens ........................................................................... 40 5.2 Plato’s Idea of a Good Education .................................................................................................. 40 5.3 Aristotle and Alexander ................................................................................................................ 40 5.4 Aristotle Founds the Lyceum ......................................................................................................... 41 5.5 Aristotle’s Science ......................................................................................................................... 42 5.6 Aristotle’s Method ........................................................................................................................ 42 5.7 “Causes” ....................................................................................................................................... 43 5.8 Biology .......................................................................................................................................... 44 4 5.9 Elements ....................................................................................................................................... 44 5.10 Dynamics: Motion, And Why Things Move ............................................................................... 45 5.11 Natural Motion and Violent Motion ......................................................................................... 45 5.12 Aristotle’s Laws of Motion ....................................................................................................... 46 5.13 Planetary Dynamics .................................................................................................................. 47 5.14 Aristotle’s Achievements .......................................................................................................... 47 6 MEASURING THE SOLAR SYSTEM .......................................................................................... 48 6.1 How Big is the Earth? .................................................................................................................... 48 6.2 How High is the Moon? ................................................................................................................. 49 6.3 How Far Away is the Sun? ............................................................................................................. 51 7 GREEK SCIENCE AFTER ARISTOTLE ..................................................................................... 53 7.1 Strato ............................................................................................................................................ 53 7.2 Aristarchus .................................................................................................................................... 53 7.3 Euclid ............................................................................................................................................ 54 7.4 Plato, Aristotle and Christianity .................................................................................................... 54 7.5 Archimedes ................................................................................................................................... 55 7.6 Archimedes’ Principle ................................................................................................................... 55 7.7 Archimedes and Leverage ............................................................................................................. 57 7.8 Apollonius ..................................................................................................................................... 59 7.9 Hypatia ......................................................................................................................................... 59 8 BASIC IDEAS IN GREEK MATHEMATICS .............................................................................. 60 8.1 Closing in on the Square Root of 2 ................................................................................................ 60 8.2