## Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating: Volume I: The Development of the Statistical Tools Volume II: The Analysis of Ancient and Medieval RecordsToday the methods of applied statistics have penetrated very different fields of knowledge, including the investigation oftexts ofvarious origins. These "texts" may be considered as signal sequences of different kinds, long genetic codes, graphic representations (which may be coded and represented by a "text"), as well as actual narrative texts (for example, historical chronicles, originals, documents, etc. ). One ofthe most important problems arising here is to recognize dependent text, i. e. , texts which have a measure of "resemblance", arising from some kind of "common origin". For instance, in pattern-recognition problems, it is essential to identify from a large set of "patterns" a pattern that is "closest" to a given one; in studying long signal sequences, it is important to recognize "homogeneous subsequences" and the places of their junction. This includes, in particular, the well-known change-point prob lern, which is given considerable attention in mathematical statistics and the theory of stochastic processes. As applied to the study of narrative texts, the problern of recognizing depen dent and independent texts ( e . g. , chronicles) Ieads to the problern offinding texts having a common source, i. e. , the sameoriginal (such texts are naturally called dependent), or, on the contrary, having different sources (such texts are natu rally called independent). Clearly, such problems are exceedingly complicated, and therefore the appearance of new empirico-statistical recognition methods which, along with the classical approaches, may prove useful in concrete studies (e. g. , source determination) is welcome. |

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### Contents

Problems of Ancient and Medieval Chronology | 1 |

12 The Dark Ages and the Renaissance epochs | 2 |

13 How to substantiate ancient chronology | 3 |

new possibilities | 5 |

15 The duplication effect in ancient history and chronology | 7 |

16 The global chronological diagram and the modern textbook of ancient and medieval history | 8 |

17 The modern textbook a composition of four identical pieces | 10 |

18 Certain corollaries and interpretations | 11 |

References | 87 |

New Experimental and Statistical Methods for Dating Events of Ancient History and Their Applications to the Global Chronology of Ancient and Me... | 88 |

8 Problems of Historical Chronology | 89 |

82 Scaliger Petavius Christian chronographers and secular chronography | 90 |

83 Questioning the authenticity of Roman tradition Hypercriticism and T Mommsen | 93 |

84 Difficulties in the establishment of Egyptian chronology | 94 |

85 Competing chronological versions De Arcilla J Hardouin I Newton and R Baldauf | 96 |

86 Tacitus and Bracciolioni Cicero and Barzizza | 97 |

19 What is to be done with the moons elongation? | 12 |

References | 13 |

2 Computation of the Second Derivative of the Moons Elongation and Statistical Regularities in the Distribution of the Records of Ancient Eclipses | 15 |

22 Available observations of ancient solar and lunar eclipses | 17 |

23 A method of formal astronomical dating | 18 |

24 The effect of shifting the dates of eclipses forwards | 19 |

three eclipses of Thucydides | 20 |

the eclipse described by Livy | 22 |

the eclipse described by Livy and Plutarch | 23 |

the evangelical eclipse described in the New Testament in connection with the Crucifixion | 24 |

29 The oscillation of a new graph of D about one and the same value No nongravitational theories are necessary | 25 |

210 Three rigid astronomical shifts of ancient eclipses | 28 |

211 The complete picture of astronomical shifts | 31 |

3 Traditional Chronology of the Flares of Stars and the Dating of Ancient Horoscopes | 32 |

32 Astronomical dating of ancient Egyptian horoscopes | 34 |

33 Astronomical dating of the horoscope described in the Book of Revelation | 35 |

References | 37 |

New Statistical Methods for Dating | 39 |

42 Information characteristics ie informative functions of a historical text Volume function name function and reference function | 40 |

43 A theoretical model describing the distribution of local maxima for the volume function of a historical text Primary stock The information density... | 42 |

44 The correlation of local maxima for the volume graphs of dependent historical chronicles The survivingstock graph | 43 |

45 Mathematical formalization The numerical coefficient dXY which measures the distance between two historical texts X and Y | 44 |

46 Mathematical formulas for computing dXY Mathematical corrections of the maxima correlation principle | 47 |

47 Verification of the maxima correlation principle against concrete historical material | 49 |

48 A new method for dating historical events The method of restoring the graph of the primary and surviving information stock | 52 |

49 The discovery of dependent parallel historical epochs traditionally regarded as different | 53 |

410 The dynasty of rulers and the durations of their reigns as an important informative function | 54 |

411 Frequency distribution of the rules of kings who lived from AD 1400 to 1800 and from 3000 BC to AD 1800 | 55 |

412 The concept of statistically parallel historical texts and epochs | 57 |

414 A method of comparing the sets of informative functions for two historical epochs | 60 |

415 A computational experiment | 61 |

416 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 |

53 Dynasties of rulers The real dynasty and the numerical dynasty Dependent and independent dynasties The smalldistortion principle | 68 |

54 Basic errors leading to controversy among chroniclers as to the duration of kings rules | 69 |

55 The experimental frequency histogram for the duration of the rules of kings | 70 |

57 The smalldistortion principle and a computer experiment | 72 |

58 Pairs of dependent historical dynasties previously regarded as independent | 73 |

510 Dependent dynasties in the Bible and parallel with European history | 74 |

References | 75 |

6 A New EmpiricoStatistical Procedure for Text Ordering and Its Applications to the Problems of Dating | 76 |

63 The method of finding the chronologically correct order of chapters in a historical chronicle | 77 |

64 The frequencyduplicating principle and the method of duplicate recognition | 79 |

the Book of Revelation | 81 |

66 Duplicates of epochs in the modern textbook of ancient history | 83 |

87 Vitruvius and L Alberti | 98 |

88 The chaos of medieval datings E Bickerman Medieval anachronisms and medieval concepts of time | 99 |

89 The chronology of the biblical manuscripts L Teschendorf | 102 |

810 Vowels in ancient manuscripts | 103 |

811 Traditional biblical geography | 104 |

812 Problems of geographical localization of ancient events | 105 |

813 Modern analysis of biblical geography | 107 |

814 Ancient originals and medieval duplicates Anachronisms as a common feature in medieval chronicles | 110 |

815 Names and nicknames Handwritten books | 112 |

9 Astronomical and Mathematical Analysis of the Almagest | 113 |

92 On the statistical characteristics of the Almagest The structure of the star catalogue | 115 |

93 The accuracy of the Almagests star coordinates | 119 |

94 The problem of dating the Almagest from the individual stars proper motion | 120 |

95 Halleys discovery of the stars proper motion and the Almagest | 128 |

10 Archaeological Dating Methods | 131 |

102 Numismatics | 132 |

103 The dendrochronological method | 133 |

11 Astronomical Dating Ancient Eclipses and Horoscopes | 136 |

12 New Experimental and Statistical Methods of Dating Ancient Events | 140 |

123 Method of recognition and dating the dynasties of ancient rulers The smalldistortion principle | 143 |

124 The frequencydamping principle A method of ordering texts in time | 145 |

125 Applications to Roman and Greek history | 148 |

126 The frequencyduplication principle The duplicatediscovery method | 151 |

127 Statistical analysis of the complete list of all the names mentioned in the Bible | 152 |

128 Statistical analysis of the complete list of all parallel passages in the Bible | 155 |

129 Duplicates in the Bible | 157 |

1210 The enquetecode or formalized biography method | 159 |

1211 A method for the chronological ordering of ancient maps | 160 |

13 Construction of the Global Chronological Diagram and Certain Results of Applying the Dating Methods to Ancient History | 162 |

133 Dependent dynasties | 163 |

134 The agreement of different methods | 165 |

135 Three basic chronological shifts | 166 |

136 Biblical history and European history | 168 |

137 The beginning of authentic history in circa the 10th century AD | 173 |

138 The chronological version of Morozov and the authors conception | 174 |

139 The confusion between the two Romes | 175 |

1310 A universal mechanism which could lead to the chroniclers chronological errors | 177 |

1311 Scaliger Petavius and the Council of Trent Creation of traditional chronology | 178 |

14 The Dark Ages in Medieval History | 180 |

142 Medieval Greece and Athens | 187 |

143 The history of religions | 193 |

144 Indian history and chronology | 195 |

References | 196 |

203 | |

### Common terms and phrases

13th century Almagest analysis ancient and medieval ancient eclipses ancient events antiquity assumed astronomical astronomical solutions Athens Bible biblical Book of Judges Book of Kings Book of Samuel Byzantine Byzantine Empire calculated century A.D. chapters chronological shifts chronologically correct coefficient coincide computation dates of ancient dating method denoted dependent texts discovered documents duplicates enquete-code errors events described example fact famous Fomenko formal astronomical dating frequency-damping principle global chronological diagram global chronology Greece Greek Gregorovius historical epochs historical texts Holy Roman Empire horoscopes informative functions interval Italy Livy longitudes lunar eclipse manuscripts mathematical maxima medieval medieval history Middle Ages modern textbook Morozov Moscow names numerical dynasties obtained parameter Petavius priori problem Prof proper motion Ptolemy Ptolemy's regarded Rome rule duration rulers Russian Scaliger Second Book star catalogue texts describing textual traditional chronology traditional dating turns vector volume function volume graphs