A.T.Fomenko
EMPIRICO-STATISTICAL ANALYSIS OF NARRATIVE MATERIAL
AND ITS APPLICATIONS TO HISTORICAL DATING

Volume 1
The Development of the Statistical Tools

Kluwer Academic Publishers. 1994. The Netherlands.
ISBN 0-7923-2604-0
ISBN 0-7923-2606-7 (Set oftwo volumes)
Translated by O.Efimov

Volume 1: The Development of the Statistical Tools (*pdf)

Volume 2: The Analysis of Ancient and Medieval Records.

CONTENTS

Foreword (by Albert N. Shiryaev)

Preface.

Chapter 1. PROBLEMS OF ANCIENT AND MEDIEVAL CHRONOLOGY.

1. The Global Chronological Diagram of ancient and medieval history.

1.1. Moon's elongation and R. Newton's conjecture.

1.2. The Dark Ages and Renaissance epochs.

1.3. How to substantiate ancient chronology.

1.4. Statistical methods: new possibilities.

1.5. Duplication effect in ancient history and chronology.

1.6. Global Chronological Diagram and "Modem Textbook" of anciem and medieval histow..

1.7. The "Modem Textbook" is composed from four identical pieces.

1.8. Certain corollaries and interpretations.

1.9. What's to be done with Moon's elongation?

2. Computation of second derivative of Moon's elongation and statistical regularities in distribution of certain astronomical data.

2.1. Parameter D and R. NEWTON's paper "Astronomical evidence concerning non-gravitational forces in the Earth-Moon system".

2.2. Available observations of ancient solar and lunar eclipses.

2.3. Method of formal astronomical dating.

2.4. Effect of shifting the eclipse dates upwards.

2.5. Example" three famous eclipses of Thucydides.

2.6. Example" eclipse described by Livy.

2.7. Example: eclipse described by Livy and Plutarch.

2.8. Example: evangelic eclipse described in the New Testament and connected with the Crucifixion.

2.9. New graph of D" oscillates about one and the same value. No non-gravitational theories are necessary.

2.10. Three rigid "astronomical shifts" of ancient eclipses.

2.11. Complete picture of astronomical shifting.

2.12. Coincidence of the astronomical shifts with the three basic chronological shifts on the Global Chronological Diagram.

3. Traditional chronology of the flares of stars and the dating of ancient horoscopes.

3.1. Ancient and medieval flares of stars. Famous Bethlehem star.

3.2. Astronomical dating of ancient Egyptian horoscopes. 3 :,3. Astronomical dating of the horoscope described in the Book of Revelation.

Chapter 2. NEW STATISTICAL METHODS FOR DATING.

4. Certain statistical regularities of information density distribution in texts with scale.

4.1. Text with scale. General notion.

4.2. Information characteristics ( informative functions) of a historical text. Volume function, name function, reference function.

4.3. Theoretical model describing the distribution of local maxima for the volume function of a historical text. Primary stock. Information density conservation law.

4.4. Correlation of local maxima for the volume graphs of dependent historical chronicles. Surviving stock graph.

4.5. Mathematical formalization. Numerical coefficient d(X,Y) which measures "the distance" between two historical texts X and Y.

4.6. Mathematical formulas for computing d(X,Y). Mathematical corrections of maxima correlation principle. Empirico-Sta tistica l Methods for Analysis 97

4.7. Verification of maxima correlation principle against a concrete historical material.

4.8. New method for dating historical evems.

4.9. Discovery of dependem (parallel) historical epochs traditionally regarded as different.

4.10. Dynasty of rulers and durations of kings' rule as important informative function.

4.11. Frequency distribution of those kings' rules who lived in 1,400 1,800 A.D. and in 3,000 B.C. 1,800 A.D.

4.12. Concept of statistical parallel historical texts and epochs.

4.13. "Written biography" or enqu^ete-sode of a historical character.

4.14. Method of comparing the sets of informative functions for two historical epochs.

4.15. Computational experiment.

4.16. Remarkable decomposition of the Global Chronological Diagram into the sum of four practically indistinguishable chronicles.

5. Method of duplicate recognition and some applications to chronology of ancient dynasties.

5.1. Process of measuring random variables.

5.2. Distance between two random vectors.

5.3. Dynasty of rulers. Authentic dynasty and numerical dynasty. Dependent and independent numerical dynasties. Small distortion principle.

5.4. Basic errors leading to controversy among chroniclers as to the duration of kings' rule.

5.5. Experimental frequency histogram for kings' rule duration.

5.6. Virtual dynasties and mathematical model for an errors of the chronicler made in measuring of the rule duration.

5.7. Small distortion principle and computer experiment.

5.8. Pairs of dependent historical dynasties earlier regarded as independent.

5.9. Distribution of dependent dynasties in the "Modem Textbook of Ancient History".

5.10. Dependent dynasties in the Bible and parallel with the European history.

6. New empifico-statistical procedure for historical text ordering and its application to problem of dating.

6.1. Chapter-generation.

6.2. Frequency damping principle.

6.3. Method of finding the chronologically correct order of chapters in a historical chronicle.

6.4. Frequency duplicating principle and method of duplicate recognition.

6.5. Distribution of old and new duplicates in the Old and New Testament. Striking example: the Revelation of John. 6.6. Epochs-duplicates in the "Modem Textbook of Ancient History".

Chapter 3. NEW EXPER/MENTAL AND STATISTICAL METHODS FOR DATING ANCIENT HISTORY EVENTS AND APPLICATION TO GLOBAL ANCIENT WORLD AND MEDIEVAL CHRONOLOGY.

7. Introduction. N.A. Morozov and modem results.

7.1. Introduction. N.A. MOROZOV and modem results.

8. Problems &historical chronology.

8.1. Roman chronology as the "spinal column" ofEuropean chronology.

8.2. J. Scaliger, D. Petavius, Christian chronographers and secular chronography.

8.3. Questioning the authemicity ofRoman tradition. Hypercriticism and T. Mommsen.

8.4. Difficulties accompanied the establishment ofEgyptian chronology.

8.5. Competing chronological versions. De Arcilla, J. Hardouin, I. Newton and R. Baldauf.

8.6. Tacitus and Bracciolioni. Cicero and Barzizza.

8.7. Vitruvius and L. Alberti.

8.8. "Chaos of medieval dating" (E. Bickerman). Medieval anachronisms and medieval ideas of time.

8.9. Chronology of the biblical manuscripts. L. Tischendorf.

8.10. Vowels of ancient manuscripts.

8.11. Traditional biblical geography.

8.12. Problems of geographical localization of ancient events.

8.13. Modem analysis of biblical geography.

8.14. Ancient originals and medieval duplicates. Anachronisms as a common feature in the medieval chronicles.

8.15. Names and nicknames. Hand-written books.

9. Astronomical and mathematical analysis of the Almagest.

9.1. Morozov's analysis of the first medieval editions of the Almagest.

9.2. On the statistical characteristics of the Almagest. Star catalogue structure.

9.3. Accuracy of the Almagest star coordinates.

9.4. Problem of dating the Almagest from the individual stars' proper motion.

9.5. Halley's discovery of stars' proper motion and the Almagest.

10. Archaeological dating methods.

10.1. Classical excavation methods.

10.2. Numismatics.

10.3. Dendrochronology method.

10.4. Radiocarbon method.

11. Astronomical dating. Ancient eclipses and horoscopes.

12. New experimental and statistical methods of dating ancient events.

12.1. Introduction.

12.2. Volume graphs for historical chronicles. Maximum correlation principle. Computational experiment and typical examples.

12.3. Method of recognition and dating ancient rulers' dynasties. Small distortion principle.

12.4. Frequency damping principle. The method of ordering historical texts in time.

12.5. Applications to the Roman and Greek history.

12.6. Frequency duplication principle. 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 enqu^ete-code or formalized "biography" method.

12.11. A method for the chronological ordering of ancient maps.

13. Construction of the Global Chronological Diagram and certain results of dating methods application to ancient history.

13.1. Ancient and medieval history "textbook".

13.2. Duplicates.

13.3. Dependent dynasties.

13.4. Agreement of different methods.

13.5. Three basic chronological shifts.

13.6. Biblical history and European history. a. Volume graphs for the Old Testament and "European textbook" from 850 B.C. to 1400 A.D. b. The overlap of some biblical and European events. Babylonian captivity and Avignon exile.

13.7. The beginning of"authentic" history in the 10th century A.D.

13.8. The chronological version of Morozov and the author's conception. 13.9. The confusion between the two Romes, viz., in Italy and the Bosphorus (New Rome).

13.10. A universal mechanism which could lead to the chroniclers' chronological errors.

13.1 I. J. SCALIGER, D. PETAVIUS and the famous Council of Trent. Creation of traditional chronology.

14. The "dark ages" in medieval history.

14. I. Medieval Italy and Rome.

14.2. Medieval Greece and Athens.

14.3. History of religions.

14.4. Indian history and chronology

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