"Seeking the Truth about Chronology Today"

**Authorial Invariant:**

The “quantitative characteristics of texts” (“unconscious parameter”) that an author has little to no control over. Fomenko identified 9 parameters for the possible discovery of the authorial invariant:

1 – “The length of sentences, or the average amount of words in a sentence calculated for every sample.”

2 – “The length of words, or the average amount of syllables in a word calculated for every sample.”

3 – “General frequency of function word usage (prepositions, conjunctives and particles), or the percentage of function words contained in every sample.”

4 – “Noun usage frequency, or the percentage of nouns for every sample.”

5 – “Verb usage frequency, or the percentage of verbs for every sample.”

6 – “Adjective usage frequency (percentage).”

7 – “Usage frequency of the preposition “in” (percentage, Russian equivalent).”

8 – “Usage frequency of the particle “not” (percentage, Russian equivalent).”

9 – “The amount of function words in a sentence (the average quantity of conjunctions, prepositions and particles contained in every sentence).”^{[4, p.438]}

Parameter 3 (function word usage frequency) is the only non-dubious parameter and is the authorial invariant.^{[4, pp.442-443]} The larger the difference between compared values, the more reason there is to believe the texts were authored by two different people. Similar values alone don’t automatically mean that the texts were written by the same author.^{[4, p.445]}

“Let us point out that such conclusions can only be made after large-scale computational experimentation. Only upon having received empiric proof that this or the other parameter really stabilizes within the framework of œuvres written by a single author one can consider the parameter in question an invariant.”^{[4, p.443]}

Page [4]: 438, 442-443, 445.

**Enquête-Code (Written Biography):**

Fomenko laid out 34 points of investigation that can be used to create a biography for an historical figure. These can each be marked as EC1 to EC34. Check my article on it here.

Page [1]: 57-59.

**The F-model:**

A corollary of local maximas between volume graphs vol *X(t)* and vol *Y(t)*. A corollary to the basic hypothesis of 4.3.1. ^{[1, p.51]}

The hypothesis – “Though, with time, the amplitude of the volume graph for the surviving textual stock decreases gradually (since ancient texts get lost and destroyed), more remains from those years c_{i} whose events were described by contemporaries in a considerable number of texts.” ^{[1, p.43]}

“Namely, the years of local maxima r_{i}(X) should be close to those denoted by r_{i}(Y) for any two historical texts X and Y describing one historical epoch (A, B) in the history of the same region *Γ*.

In other words, the volume graphs *vol* X(t) and *vol* Y(t) must attain local maxima, i.e., form peaks, approximately at the same points (years) in the time interval (A, B).” ^{[1, p.43]}

Page [1]: 43, 51.

**Generation Chapter:**

“In short, we call a fragment of a text describing the events of one generation “a generation chapter”.”

Page [1]: 146.

**The K-model:**

A statistical hypothesis… A corollary to the basic hypothesis of 4.3.1. ^{[1, p.51]}

The hypothesis – “Though, with time, the amplitude of the volume graph for the surviving textual stock decreases gradually (since ancient texts get lost and destroyed), more remains from those years c_{i} whose events were described by contemporaries in a considerable number of texts.” ^{[1, p.43]}

Page [1]: 43, 50, 51.

**Laws of Information Density Conservation:**

“The laws of information density conservation permit us to introduce a formal procedure to date the events described in texts with lost or unknown dating.”

Page [1]: 39, 52.

**Law of Information Density Conservation:**

???

Page [1]: 42.

**Local maxima:**

The point where “The height of the function at “a” is greater than (or equal to) the height anywhere else in that interval.” [source]

Page [1]: 42.

**The Map-Code:**

Explained on page 11.

Page [2]: 11.

**Method for Comparing the Sets of Informative Functions for Two Historical Epochs:**

Explained on pages 60 and 61 in [1].

Page [1]: 60-61.

**Method for Dating Historical Events Described in Chronographic Texts:**

Explained on pages 9 and 10.

Page [2]: 9-10.

**Method for Discovery of Dependent Historical Texts:**

???

Page [2]: S2.

**Method for Duplicate-Discovery**/**Duplicate Discovery Method:**

Explained on pages 151 and 152 in [1].

Page [1]: 151-152.

**Method for Duplicate Recognition:**

“In the experiment which I performed, the discovery of such double peaks of the frequency graph (which corresponds to the duplicates) occurred as follows. Let *a _{ij}* be an element of the matrix

Then, by marking all those elements

Page [1]: 79, 81.

**Method for Finding the Chronologically Correct Order of Chapters in a Historical Chronicle/Method of Chapter Ordering:**

“We now describe the method of finding the chronologically correct order of chapters in a historical text *X* (or in a whole set of texts). Number all the chapters of the text X in a certain order, e.g., in which they occur in the text itself. We then determine the graph of *K*(*T*_{0}*, T*) described above for each separate chapter *X*(*T _{0}*). The number of these graphs will equal that of the chapters in the text

“This method of chapter ordering permits us to date ancient events.”

Page [1]: 77, 79.

**Method for Ordering Texts in Time:**

“The present method permits us, for example, to discover a chronologically correct order for individual textual chapters and duplicates on the basis of the collection of proper names mentioned.” ^{[1, p.145]}

“The method also permits us to date events.” ^{[1, p.150]}

Page [1]: 145, 150.

**Method for Restoring the Graph of the Primary and Surviving Information Stock:**

“Construct the informative functions* ƒi*(*t*, *Y*) and consider the set of all absolutely dated texts *X*. We also construct their informative functions *ƒi*(*t*, *X*) and assume that we can choose *X* with some *ƒi*(*t*, *X*), or at once their whole set, close in the sense of smallness of the coefficient d to an informative function *ƒi*(*t*, *Y*). In other words, *d*(* ƒi(X)*,

Page [1]: 52.

**Method for Text Ordering and Duplicate Recognition:**

“The method of text ordering and duplicate recognition is also applicable to the list of reciprocal citations in any closed collection of historical and other texts.” ^{[1, p.81]}

Page [1]: 81.

**Methods for Ordering and Dating Old Geographic Maps and Descriptions:**

???

Page [2]: S4.

**Numerical Dynasty:**

The “sequence of numbers represented as an integral vector *a* in the space *R*^{n}“. The sequence of numbers is obtained from a real dynasty. Two chroniclers writing about the same real dynasty could, due to differences in chronicling, produce two differing numerical dynasties (based on the original real dynasty).

Page [1]: 68.

**Primary information stock:**

The total amount of textual information.

Page [1]: 42.

**Principle of Amplitude Correlation/ Amplitude Correlation Principle:**

A – “If texts X and Y are dependent, then their volume graphs vol X(t) and vol Y(t) must correlate strongly within their poor zones. On the other hand, there may be little or no amplitude correlation within their rich zones when the graphs are superimposed.”

B – “If texts X and Y are independent, then their volume graphs must be independent within their poor zones.”

Page [5]: 192, 198.

**Principle of Maximum Correlation/Principle of Correlation of Maxima/Maxima Correlation Principle/Maximum Correlation Principle:**

A – “If two texts X and Y are dependent, then their volume functions exhibit “splashes” that are essentially simultaneous, i.e. the local maxima of vol X(t) and vol Y(t) correlate.”

B – “If two texts X and Y are independent then the local maxima of their volume function do not correlate.”

“The volume graphs for the chapters of two dependent texts X and Y which describe the same period (A, B) and the state Γ must attain local maxima, or form peaks, simultaneously, i.e. years described in X and Y in detail should be close or coincide. Conversely, if two texts X and Y are known as undoubtedly independent and describe either different periods (A, B) and (C, D) of the same length or different states, then their volume graphs reach local maxima at different points if we let (A, B) and (C, D) coincide.” ^{[1, p.141]}

“The graphs of undoubtedly dependent texts form peaks almost simultaneously, and the peaks are not correlated on graphs of undoubtedly independent texts”.

Page [1]: 47, 141, 142-143.

Page [5]: 188.

Page [3]: 668.

**Principle of Frequency Damping/Frequency Damping Principle:**

“In numbering the chapters chronologically correctly (i.e., chapters describing the same events), with duplicates being absent among them, each graph of *K(T _{0}, T)* vanishes to the right of the point T

“In the correct enumeration of chapter generations, the author of the text, while proceeding from the description of one generation to another, also describes other historical figures, namely, he does not speak at all of the personages of the generations (since they have not yet been born) belonging to those prior to a generation numbered T

“In the chronologically correct enumeration of chapter generations, each graph of K(T

Page [1]: 76-77, 146-147.

**Principle of Frequency Decay/Frequency Decay Principle:**

???

Page [5]: 189.

**Principle of Frequency-Duplicating/Frequency-Duplicating Principle:**

“Thus, if the chapters of the text, which in general are numbered chronologically correctly, contain two whose frequency graphs have the form approximately in Fig. 17, then they are probably duplicates and should be identified.” ^{[1, p.80]}

Page [1]: 79, 80.

**Principle of Map-Improvement:**

“A sequence of maps is ordered chronologically correctly if and only if each graph of *L*(*T*_{0}, *T*) is of the form shown in Fig.39, i.e., vanishes to the left of *T*_{0}, attains an absolute maximum at T_{0}, and falls monotonically to the right.” ^{[2, pp.12-13]}

Page [2]: 12-13.

**Principle of Monotone Information Loss/Monotone Information Loss Principle:**

“The farther we move in time from the epoch [A, B] of interest, the fewer documents from this epoch usually remain and the less we can learn about it.”

Page [5]: 188.

**Principle of “Regard-for-Information”/ “Regard-for-Information” Principle:**

“The regard for information varies inversely with its volumes.” Chroniclers are forced to give full attention to poor texts than rich texts, as there is less to draw from a poor text than a rich one.

Page [5]: 192.

**Principle of Small Distortion/Small Distortion Principle:**

“If two numerical dynasties are sufficiently close (in the sense of the measure λ), then they indeed represent the same real dynasty of kings, i.e., they are merely two different versions of its description.

Such numerical dynasties will be called dependent. On the contrary, if two numerical dynasties represent two real dynasties of kings, known a priori as different, then the numerical dynasties are much different from one another (in the sense of the measure λ). Such numerical dynasties will be called independent.”

Page [1]: 68, 69.

**Real Dynasty:**

Let *n* represent “consecutive authentic rulers”, and the “true rule durations” of those rulers be “*p*1, *p*2, …, *p*n”.

Page [1]: 68

**Statistical hypothesis (theoretical model):**

“is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.” [source]

Page [1]: 50, 68.

**Stream Deviation Coefficient (SDC):**

The coefficient λ.

Page [1]: 60.

**Surviving information stock:**

The remaining amount of textual information left over from the primary information stock.

Page [1]: 43.

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**References:**

[1] – http://chronologia.org/en/kw1.pdf (1994). Accessed 26 July 2020.

[2] – http://chronologia.org/en/kw2.pdf. Accessed 26 July 2020.

[3] – Statistical estimation of chronological nearness of historical texts (1986). Accessed 26 July 2020.

[4] – http://chronologia.org/en/seven/2NA3-EN.pdf. Accessed 27 July 2020.

[5] – http://chronologia.org/en/volume_functions_of_historical_texts.pdf (1990). Accessed 27 July 2020.

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