Get Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating by Fomenko A.T.
Kluwer Academic Publishers | 1994 | 0792326040 9780792326045 0792326067 | 230 pages | PDF/djvu | 22 MB
Volume concentrates mainly on the development of the mathematical statistical tools and their application to astronomical data, including the Almagest and simulated data. This book presents new empirico-statistical methods for the discovery of dependences between texts, on which we base our dating methods. As one of various possible applications, the datings (or dates) of certain events described in ancient and medieval texts are analyzed. Substantial material dealing with historical data and chronology is also included.
The present book by A.T. Fomenko, professor of pure mathematics, is mainly aimed at developing such new methods to be applied to recognizing dependent and independent narrative texts and dating them (with respect to texts with known reliable dates).
The author proposes a new approach to the problem of recognizing dependent and independent narrative (historical) texts based on the several new empirico-statistical models (regularities) which he has discovered during his extensive statistical emperiments involving various quantitative characteristics of concrete texts, chronicles, originals, and so forth. Verification of these models (statistical hypotheses) on concrete chronicles confirmed the efficacy of the models and made it possible to put forward new methos for dating texts (more precisely, for dating events described in the texts).
Contents
Foreword
Preface
Chapter 1. Problems of Ancient and Medieval Chronology
1. The Global Chronological Diagram of Ancient and Medieval
History
1.1. The moons elongation and R. Newtons conjecture
1.2. The Dark Ages and the Renaissance epochs
1.3. How to substantiate ancient chronology
1.4. Statistical dating methods: new possibilities
1.5. The duplication effect in ancient history and chronology
1.6. The global chronological diagram and the modern textbook of ancient and medieval history
1.7. The modern textbook, a composition of four identical pieces
1.8. Certain corollaries and interpretations
1.9. What is to be done with the moons elongation?
References
2. Computation of the Second Derivative of the Moons Elongation and Statistical Regularities in the Distribution of the Records of Ancient Eclipses
2.1. Parameter D and R. Newtons paper Astronomical evidence concerning non-gravitational forces in the Earth-Moon system
2.2. Available observations of ancient solar and lunar eclipses
2.3. A method of formal astronomical dating
2.4. The effect of shifting the dates of eclipses forwards
2.5. An example: three eclipses of Thucydides
2.6. An example: the eclipse described by Livy
2.7. An example: the eclipse described by Livy and Plutarch
2.8. An example: the evangelical eclipse described in the New Testament in connection with the Crucifixion
2.9. The oscillation of a new graph of D about one and the same value. No non gravitational theories are necessary
2.10. Three rigid astronomical shifts of ancient eclipses
2.11. The complete picture of astronomical shifts
2.12. The coincidence of the astronomical shifts with the three basic chronological shifts in 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. The star of Bethlehem
3.2. Astronomical dating of ancient Egyptian horoscopes
3.3. Astronomical dating of the horoscope described in the
Book of Revelation
References
Chapter 2. New Statistical Methods for Dating
4. Certain Statistical Regularities of Information Density Distribution in Texts with A Scale
4.1. Text with a scale. The general notion
4.2. Information characteristics (i.e., informative functions) of a historical text. Volume function, name function, and reference function
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
4.4. The correlation of local maxima for the volume graphs of dependent historical chronicles. The surviving-stock graph
4.5. Mathematical formalization. The 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 the maxima correlation principle
4.7. Verification of the maxima correlation principle against concrete historical material
4.8. A new method for dating historical events. The method of restoring the graph of the primary and surviving information stock
4.9. The discovery of dependent (parallel) historical epochs traditionally regarded as different
4.10. The dynasty of rulers and the durations of their reigns as an important informative function
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
4.12. The concept of statistically parallel historical texts and epochs
4.13. The written biography or enquete-code of a historical character
4.14. A method of comparing the sets of informative functions for two historical epochs
4.15. A computational experiment
4.16. The remarkable decomposition of the global chronological diagram into the sum of four practically indistinguishable chronicles
References
5. A Method of Duplicate Recognition and Some Applications to the Chronology of Ancient Dynasties
5.1. The process of measuring random variables
5.2. The distance between two random vectors
5.3. Dynasties of rulers. The real dynasty and the numerical dynasty. Dependent and independent dynasties. The small-distortion principle
5.4. Basic errors leading to controversy among chroniclers as to the duration of kings rules
5.5. The experimental frequency histogram for the duration of the rules of kings
5.6. Virtual dynasties and a mathematical model for errors made by the chronicler in measuring the rule duration
5.7. The small-distortion principle and a computer experiment
5.8. Pairs of dependent historical dynasties previously regarded as independent
5.9. The distribution of dependent dynasties in the modern textbook of ancient history
5.10. Dependent dynasties in the Bible and parallel with European history
References
6. A New Empirico-Statistical Procedure for Text Ordering and Its Applications to the Problems of Dating
6.1. The chapter generation
6.2. The frequency-damping principle
6.3. The method of finding the chronologically correct order of chapters in a historical chronicle
6.4. The frequency-duplicating principle and the method of duplicate recognition
6.5. The distribution of old and new duplicates in the Old and New Testament. A striking example: the Book of Revelation
6.6. Duplicates of epochs in the modern textbook of ancient history
References
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
7. Introduction. N.A. Morozov and Modern Results
8. Problems of Historical Chronology
8.1. Roman chronology as the spinal column of European chronology
8.2. Scaliger, Petavius, Christian chronographers and secular chronography
8.3. Questioning the authenticity of Roman tradition. Hypercriticism and T. Mommsen
8.4. Difficulties in the establishment of Egyptian 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. The chaos of medieval datings (E. Bickerman). Medieval anachronisms and medieval concepts of time
8.9. The chronology of the biblical manuscripts. L. Tischendorf
8.10. Vowels in ancient manuscripts
8.11. Traditional biblical geography
8.12. Problems of geographical localization of ancient events
8.13. Modern analysis of biblical geography
8.14. Ancient originals and medieval duplicates. Anachronisms as a common feature in medieval chronicles
8.15. Names and nicknames. Handwritten books
9. Astronomical and Mathematical Analysis of the Almagest
9.1. Morozovs analysis of the first medieval editions of the Almagest
9.2. On the statistical characteristics of the Almagest. The structure of the star catalogue
9.3. The accuracy of the Almagests star coordinates
9.4. The problem of dating the Almagest from the individual stars proper motion
9.5. Haileys discovery of the stars proper motion and the Almagest
10. Archaeological Dating Methods
10.1. Classical excavation methods
10.2. Numismatics
10.3. The dendrochronological method
10.4. The 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. 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. A method for the chronological ordering of ancient maps
13. Construction of the Global Chronological Diagram and Certain Results of Applying the Dating Methods to Ancient History
13.1. The textbook of ancient and medieval history
13.2. Duplicates
13.3. Dependent dynasties
13.4. The agreement of different methods
13.5. Three basic chronological shifts
13.6. Biblical history and European history
13.7. The beginning of authentic history in circa the 10th century A.D.
13.8. The chronological version of Morozov and the authors conception
13.9. The confusion between the two Romes
13.10. A universal mechanism which could lead to the chroniclers chronological errors
13.11. Scaliger, Petavius, and the Council of Trent. Creation of traditional chronology
14. The Dark Ages in Medieval History
14.1. Medieval Italy and Rome
14.2. Medieval Greece and Athens
14.3. The history of religions
14.4. Indian history and chronology
References
Index
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