Is

'Me Academic chronicle

Fig. 5.15. Graphs of dependent chronicles - the SuprasVskaya and the Akademicheskaya on the interval of 1336-1374 A.D. The peaks of the volume graphs occur identically all the time, with just one exception. The locations of local maxima of the graph are marked with thick black dots underneath the graphs - in case of the Supraslskaya Chronicle, these two chains of dots are nearby each other. One sees that the peak points only fail to coincide once. The two chronicles are thus clearly of a dependent nature.

Fig. 5.15. Graphs of dependent chronicles - the SuprasVskaya and the Akademicheskaya on the interval of 1336-1374 A.D. The peaks of the volume graphs occur identically all the time, with just one exception. The locations of local maxima of the graph are marked with thick black dots underneath the graphs - in case of the Supraslskaya Chronicle, these two chains of dots are nearby each other. One sees that the peak points only fail to coincide once. The two chronicles are thus clearly of a dependent nature.

incides with its standard dating, which proves the efficiency of our method.

Example 7.

We shall take the Russian Akademicheskaya leto-pis' (Academic Chronicle) ([672]) as "text Ywith unknown dating". Following the example described above, we soon discover text X, namely, a part of the SuprasVskaya letopis9 ([672]) thought to have described years 1336-1374 a.d. The peaks on the volume graph vol X(t) turns out to occur virtually in the same years as those on the volume graph vol Y(t), fig. 5.15.

Calculation yields the result p(X, Y) = 10"14. Such a small value of the coefficient clearly indicates the dependence of these two texts. Since chronicle X is dated, we can date the chronicle Y, too. The obtained dating of text Y coincides with its dating as known before.

Our research was based on several dozens of similar texts of the XVI-XIX century, and in all cases the acquired dating of the "unknown text Y" coincided with its usual dating.

In fact, we have learnt nothing new from the examples stated above, because the dating of the short edition of the Dvinskoy Letopisets, for instance, has been known in advance, and we had no reasons to doubt its correctness, since it belongs to the XIV-XVIII century, that is, the epoch when the chronology is more or less dependable. Nevertheless, soon we shall see our method to yield very interesting results regarding chronicles attributed to earlier epochs, that is, those preceding the XIV century a.d.

The maxima correlation principle has been stated above in its rough form, without an attempt to go deep into statistical detail, because we were only after being understood by our readers as fast as possible. Meanwhile, a strict mathematical presentation of the method and its clarifications demand a substantially more detailed study. We would refer our readers wishing to delve into the described method to scientific publications [884] and [892].

The coefficient p(X, Y) can conditionally be called PACY - the Probability of Accidental Coincidence of Years described in detail by chronicles X and Y.

A further development and adjustment of the idea is presented in the works by V. V. Fedorov and A. T. Fomenko ( [868] ), as well as A. T. Fomenko, V. V. Ka-lashnikov and S. T. Rachev ( [357] ). It was further re vealed that the maxima correlation principle manifests itself most explicitly when comparing historical texts of approximately the same volume and "density of description". Moreover, in some cases not only the local maxima points for a priori dependent texts, but also their volume functions, or amplitudes, turned out to correlate! The correlation of volume function amplitudes is especially visible when comparing "fairly poor" texts, or the chronicles with large lacunae - considerable time intervals not reflected in the chronicle. The process of writing "fairly poor" chronicles turns out to be subject to a fairly interesting principle - "respect for information", or "preservation of rarities", a regularity discovered by A. T. Fo-menko and S. T. Rachev ([723] and [ 1140]). For preliminary research in this direction and the formulation of the principle of respect for information, see works [723] and [ 1140], as well as below in the paragraph written by A. T. Fomenko and S. T. Rachev.

The maxima correlation principle was successfully applied to the analysis of certain Russian chronicles of the period of "strife" at the end of the XVI century -beginning of the XVII century a.d. See related works by A. T. Fomenko and L. E. Morozova ([902] and [548]). N. S. Kellin took a major part in this research as well. See below the part written by A. T. Fomenko, N. S. Kellin, and L. E. Morozova.

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