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Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating Volume I , Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating Volume I: The Development of the Statistical Tools by A.T. FOMENKO Department of Geometry and Topology Faculty ofMathematics, Moscow University, Moscow, Russia KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 0-7923-2604-0 (Volume I) ISBN 0-7923-2606-7 (Set of 2 Volumes) Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W, Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. Translated by O. Efimov Ailwork on the cover by the author Printed on acid-free paper All Rights Reserved © 1994 Kluwer Academic Publishers No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the Netherlands Contents Foreword xi Preface xiii Chapter 1. Problems of Ancient and Medieval Chronology 1 §1. The Global Chronological Diagram of Ancient and Medieval History 1 1.1. The moon’s elongation and R. Newton’s conjecture 1 1.2. The Dark Ages and the Renaissance epochs 2 1.3. How to substantiate ancient chronology 3 1.4. Statistical dating methods: new possibilities 5 1.5. The duplication effect in ancient history and chronology 7 1.6. The global chronological diagram and the “modern textbook” of ancient and medieval history 8 1.7. The “modern textbook”, a composition of four identical pieces 10 1.8. Certain corollaries and interpretations 11 1.9. What is to be done with the moon’s elongation? 12 References 13 §2. Computation of the Second Derivative of the Moon’s Elongation and Statistical Regularities in the Distribution of the Records of Ancient Eclipses 15 2.1. Parameter D" and R. Newton’s paper “Astronomical evidence concerning non-gravitational forces in the Earth-Moon system” 15 2.2. Available observations of ancient solar and lunar eclipses 17 2.3. A method of formal astronomical dating 18 2.4. The effect of shifting the dates of eclipses forwards 19 2.5. An example: three eclipses of Thucydides 20 2.6. An example: the eclipse described by Livy 22 2.7. An example: the eclipse described by Livy and Plutarch 23 2.8. An example: the evangelical eclipse described in the New Testament in connection with the Crucifixion 24 2.9. The oscillation of a new graph of D ft about one and the same value. No nongravitational theories are necessary 25 v VI Contents 2.10. Three rigid “astronomical shifts” of ancient eclipses 28 2.11. The complete picture of astronomical shifts 31 2.12. The coincidence of the astronomical shifts with the three basic chronological shifts in the global chronological diagram 31 §3. Traditional Chronology of the Flares of Stars and the Dating of Ancient Horoscopes 32 3.1. Ancient and medieval flares of stars. The star of Bethlehem 32 3.2. Astronomical dating of ancient Egyptian horoscopes 34 3.3. Astronomical dating of the horoscope described in the Book of Revelation 35 References 37 Chapter 2. New Statistical Methods for Dating 39 §4. Certain Statistical Regularities of Information Density Distribution in Texts with A Scale 39 4.1. Text with a scale. The general notion 39 4.2. Information characteristics (i.e., informative functions) of a historical text. Volume function, name function, and reference function 40 4.3. A theoretical model describing the distribution of local maxima for the volume function of a historical text. Primary stock. The information density conservation law 42 4.4. The correlation of local maxima for the volume graphs of dependent historical chronicles. The surviving-stock graph 43 4.5. Mathematical formalization. The numerical coefficient d(X, Y), which measures the “distance” between two historical texts X and Y 44 4.6. Mathematical formulas for computing d(X, Y). Mathematical corrections of the maxima correlation principle 47 4.7. Verification of the maxima correlation principle against concrete historical material 49 4.8. A new method for dating historical events. The method of restoring the graph of the primary and surviving information stock 52 4.9. The discovery of dependent (parallel) historical epochs traditionally regarded as different 53 4.10. The dynasty of rulers and the durations of their reigns as an important informative function 54 4.11. Frequency distribution of the rules of kings who lived from a.d. 1400 to 1800 and from 3000 B.c. to a.d. 1800 55 4.12. The concept of statistically parallel historical texts and epochs 57 4.13. The “written biography” or enquete-code of a historical character 57 Contents vii 4.14. A method of comparing the sets of informative functions for two historical epochs 60 4.15. A computational experiment 61 4.16. The remarkable decomposition of the global chronological diagram into the sum of four practically indistinguishable chronicles 62 References 66 §5. A Method of Duplicate Recognition and Some Applications to the Chronology of Ancient Dynasties 67 5.1. The process of measuring random variables 67 5.2. The distance between two random vectors 67 5.3. Dynasties of rulers. The real dynasty and the numerical dynasty. Dependent and independent dynasties. The small- distortion principle 68 5.4. Basic errors leading to controversy among chroniclers as to the duration of kings’ rules 69 5.5. The experimental frequency histogram for the duration of the rules of kings 70 5.6. Virtual dynasties and a mathematical model for errors made by the chronicler in measuring the rule duration 70 5.7. The small-distortion principle and a computer experiment 72 5.8. Pairs of dependent historical dynasties previously regarded as independent 73 5.9. The distribution of dependent dynasties in the “modern textbook” of ancient history 73 5.10. Dependent dynasties in the Bible and parallel with European history 74 References 75 §6. A New Empirico-Statistical Procedure for Text Ordering and Its Applications to the Problems of Dating 76 6.1. The chapter generation 76 6.2. The frequency-damping principle 76 6.3. The method of finding the chronologically correct order of chapters in a historical chronicle 77 6.4. The frequency-duplicating principle and the method of duplicate recognition 79 6.5. The distribution of old and new duplicates in the Old and New Testament. A striking example: the Book of Revelation 81 6.6. Duplicates of epochs in the “modern textbook” of ancient history 83 References 87 viii Contents Chapter 3. New Experimental and Statistical Methods for Dating Events of Ancient History, and Their Applications to the Global Chronology of Ancient and Medieval History 88 §7. Introduction. N.A. Morozov and Modern Results 88 §8. Problems of Historical Chronology 89 8.1. Roman chronology as the “spinal column” of European chronology 89 8.2. Scaliger, Petavius, Christian chronographers and secular chronography 90 8.3. Questioning the authenticity of Roman tradition. Hypercriticism and T. Mommsen 93 8.4. Difficulties in the establishment of Egyptian chronology 94 8.5. Competing chronological versions. De Arcilla, J. Hardouin, I. Newton and R. Baldauf 96 8.6. Tacitus and Bracciolioni. Cicero and Barzizza 97 8.7. Vitruvius and L. Alberti 98 8.8. “The chaos of medieval datings” (E. Bickerman). Medieval anachronisms and medieval concepts of time 99 8.9. The chronology of the biblical manuscripts. L. Tischendorf 102 8.10. Vowels in ancient manuscripts 103 8.11. Traditional biblical geography 104 8.12. Problems of geographical localization of ancient events 105 8.13. Modern analysis of biblical geography 107 8.14. Ancient originals and medieval duplicates. Anachronisms as a common feature in medieval chronicles 110 8.15. Names and nicknames. Handwritten books 112 §9. Astronomical and Mathematical Analysis of the Almagest 113 9.1. Morozov’s analysis of the first medieval editions of the Almagest 113 9.2. On the statistical characteristics of the Almagest. The structure of the star catalogue 115 9.3. The accuracy of the Almagest’s star coordinates 119 9.4. The problem of dating the Almagest from the individual stars’ proper motion 120 9.5. Halley’s discovery of the stars’ proper motion and the Almagest 128 §10. Archaeological Dating Methods 131 10.1. Classical excavation methods 131 10.2. Numismatics 132 10.3. The dendrochronological method 133 10.4. The radiocarbon method 133 §11. Astronomical Dating. Ancient Eclipses and Horoscopes 136 §12. New Experimental and Statistical Methods of Dating Ancient Events 140 Contents IX 12.1. Introduction 12.2. Volume graphs for historical chronicles. The maximum correlation principle. Computational experiments and typical examples 12.3. Method of recognition and dating the dynasties of ancient rulers. The small-distortion principle 12.4. The frequency-damping principle. A method of ordering texts in time 12.5. Applications to Roman and Greek history 12.6. The frequency-duplication principle. The duplicate- discovery method 12.7. Statistical analysis of the complete list of all the names mentioned in the Bible 12.8. Statistical analysis of the complete list of all parallel passages in the Bible 12.9. Duplicates in the Bible 12.10. The enquete-code or formalized “biography” method 12.11.
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