Fig. 5.12. Volume graphs for dependent chronicles: the Suprasl'skaya and the Nikiforskaya. The graph peaks are almost simultaneous.

iMiil

Fig. 5.13. The graphs of three dependent chronicles: the SuprasVskaya letopis\ the Nikiforovskaya letopis\ and the "richer" Povesf vremennykh let. Calculations show a distinct dependence of the respective peak points.

Povesf vremennykh let (Story of Years of Time)

iMiil m

Povesf vremennykh let (Story of Years of Time)

Fig. 5.13. The graphs of three dependent chronicles: the SuprasVskaya letopis\ the Nikiforovskaya letopis\ and the "richer" Povesf vremennykh let. Calculations show a distinct dependence of the respective peak points.

have been realized. Here, p(X, Y) = 10"15. These two chronicles are dependent in the stated time interval. Fig. 5.13 simultaneously presents three volume graphs - for SuprasVskaya letopis\ Nikiforovskaya letopis\ and Povesf vremennykh let, the latter chronicle being "richer", therefore its graph has more local maxima, and its dependence is not so obvious. Nevertheless, an explicit dependence between those three graphs is as well revealed after smoothing. We shall describe comparison between "rich" and "poor" chronicles in the next chapters. The distribution of volumes of the mentioned chronicles is given in Chroni, Appendix 5.1.

Example 4.

X - The History of the City of Rome in the Middle Ages, a fundamental monograph by F. Gregorovius, a German historian, Vols. 1-5 ([196]). This book was written in the XIX century on the basis of a great number of mediaeval secular and ecclesiastic documents.

Y - Liber Pontificalis (T. Mommsen, Gestorum Pontificum Romanorum, 1898). This "Book of Pontiffs", the list and biography of the mediaeval Roman Popes, was restored by Theodor Mommsen, a German historian of the XIX century, from mediaeval Roman texts. Here, p(X, Y) = 10"10, which demonstrates an obvious dependence between these two texts. To assume such proximity is accidental, the sole chance out of 10 billion would have been realized.

And so on. The several dozen examples of historical texts we processed, -a priori dependent as well as a priori independent, - confirmed our theoretical model. Thus, we managed to reveal regularities that allow us to statistically characterize dependent historical texts, or those covering the same time interval and the same "flow of events" in the history of the same region or the same state. In the meantime, experiments have demonstrated the following: if two historical texts X and Y are, on the contrary, independent, that is, describe obviously different historical epochs, or different regions, or essentially different "flows of events", then the peaks on volume graphs vol X(t) and vol Y(t) occur in substantially different years. In the latter case, a typical value of coefficient p(X, Y), the local maxima varying from 10 to 15, fluctuates from 1 to 1/100. Here is a typical example.

We now return to the "ancient" history of Rome. In the capacity of compared texts X and Y, we have taken two other fragments from the book Essays on the History of Ancient RomebyV. S. Sergeyev ([767]). The first fragment covers the alleged years 520-380 b.c., the second one - the alleged years 380-240 b.c. These periods are considered independent. The computation of the coefficient p(X, Y) yields 1/5, a striking value, different from typical values - 10~12 - 10"6 - for a priori dependent texts with a similar value of local maxima by several orders of magnitude. Thus, these two texts, "two halves" of the book by V. S. Sergeyev, are truly independent.

Above, we have used a numerical characteristic of volume for the "chapter". However, as our research has demonstrated, a similar statistical regularity becomes apparent for fairly large historical texts when other numerical characteristics are used - for instance, the number of names in each "chapter", the number of references to other chronicles, etc.

In our computational experiment we compared:

a) ancient texts with ancient texts;

b) ancient texts with contemporary texts;

c) contemporary texts with contemporary texts.

As we have already mentioned, other numerical characteristics of texts were analyzed along with volume graphs of "chapters". For instance, graphs for number of names mentioned, numbers of a specific years mentions in the text, the frequency of references to some other fixed text, and so on ([904], [908], [1137] and [884]). The same maxima correlation principle turns out to be true for all of these characteristics - namely, the peaks on graphs for dependent texts occur virtually simultaneously, and as for independent texts, their peaks do not correlate at all.

We shall formulate one more consequence of our basic model, the statistical hypothesis.

If two historical texts are a priori dependent, that is, if they describe the same "flow of events" on the same time interval in the history of the same state, then the peaks on corresponding graphs for any pair of numerical characteristics stated above occur approximately in the same years. In other words, if a year is recorded by both chronicles in more detail than the adjoining ones, then the number of mentions of this year, as well as the number of names of characters mentioned in that year, and so on, will increase (locally) in both chronicles. The situation for a priori independent texts is directly opposite - no correlation between the stated numerical characteristics is due.

The "secondary maxima correlation principle" proved to be correct when tested on specific, a priori dependent, historical texts ([884], pp.110-111).

Since our theoretical model is supported by the results of experiments, we can now propose a new method of dating the ancient events, - not a universal one, though, - and describe the main idea thereof.

The Dvina Book of Chronicles

The Dvina Book of Chronicles

Let Y be a historical text covering an unknown "flow of events", its absolute dates being lost. Let years t be counted in the text from some event of a local importance, for instance, the foundation of a town, the coronation of a king, whose absolute dates remain unknown to us. We shall calculate the volume graph of "chapters" for text Y and compare it with the volume graphs of other texts, for which we know the absolute dating of events described. If text X is revealed among those texts, and its number p(X, Y) is small -i. e., has the same order of magnitude as pairs of dependent texts (for instance, does not exceed 10"8 for the corresponding number of local maxima) - then a conclusion can be made, with a sufficient probability, of coincidence or the proximity of the "flows of events" described in those texts. Moreover, the smaller the number p(X, Y), the bigger this chance.

Furthermore, both compared texts may appear completely different - for instance, two versions of the same chronicle written in different countries, by different chroniclers, in different languages.

This method of dating was experimentally tested on mediaeval texts with a priori known dates, and the newly acquired dating coincided with those. Now, let us give a few typical examples.

In the capacity of the text Y, we have chosen a Russian chronicle, the so-called short edition of the Dvinskoy Letopisets (The Dvina Book of Chronicles), describing the events in the time interval of 320 years ([672]). We shall try and date the events recorded in this chronicle using said method. Looking through all chronicles published in The Complete Russian Chronicles, we shall soon discover text X, for which the peaks on volume graph volX(t) occur virtually in the same years that those on graph vol Y{t) of the chronicle Y, fig. 5.14.

While comparing the graphs, we made sure to have preliminarily superposed time intervals (A, B) and (C, D) one over another. The result of calculation is p(X, Y) = 2 X 10"25. Therefore, these two chronicles most probably describe approximately the same "flows of events". Thus, we manage to date the events recorded in text Yin a fairly formal way, on the basis of the sole comparison of statistical characteristics of texts. The chronicle X turns out to be a lengthy edition of the Dvinskoy Letopisets ([672]). This chronicle is considered to describe the "flow of events" of 1390-1707 A.D.

As a result, the dating of the text Ywe obtained co-

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