300 350 400 450

Fig. 5.11. Volume functions of the chronicle of the "ancient" Titus Livy and a modern textbook by Sergeyev. Part three.

300 350 400 450

Fig. 5.11. Volume functions of the chronicle of the "ancient" Titus Livy and a modern textbook by Sergeyev. Part three.

graph. When computing the coefficient p(X, Y) we have smoothed these graphs to emphasize only their main local maxima, not exceeding 15 in number. It turned out thatp(X, Y) = 2 X 10~12. The small value of the coefficient indicates dependence between the texts compared, which comes as no surprise in this particular case. As we have already noted, both texts describe the same historical time interval of the "ancient" Rome. The small value of the coefficient p(X, Y) proves the fact that if we consider the observed proximity of the splash points on both graphs as an random event, then its probability is extremely small. As we can see, the contemporary author V. S. Sergeyev reproduced the "ancient" original in his book quite accurately. He certainly supplemented it with his own considerations and commentaries, which, however, turn out to have no influence on the character of dependence between those texts.

Now, we shall use the book by V. S. Sergeyev as the "chronicle" X' once again, and as the "chronicle" Y', the same book, but with the order of the years in the text replaced by the opposite one - in other words, as if we have read the book by Sergeyev "back to front". In this case,p(X',Y') turns out to equal 1/3, a value substantially closer to 1 than the previous one and demonstrating the independence of compared texts - hardly surprising, since the operation of "inverting the chronicle" yields two a priori independent texts.

Example 2.

We shall regard the following a priori dependent historical texts as examples - the two Russian chronicles:

X - Nikiforovskaya letopis' (The Nikiforov Chronicle) [672],

Y- SuprasVskaya letopis' (The SuprasP Chronicle) [672].

Both chronicles cover the time interval of allegedly 850-1256 a.d.

Their volume graphs are presented at fig.5.12. Both volume graphs of "chapters" allegedly of 850-1255 a.d. have 31 peaks occurring virtually simultaneously, in the same years. The calculation yields p(X, Y) = 10~24, a fairly small value; therefore, dependence between those texts is confirmed. In Chroni, Appendix 5.1, we present precise numerical data for the volume functions of these chronicles.

Example 3.

We now shall consider two other Russian chronicles:

X - Kholmogorskaya letopis9 (The Kholmogory Chronicle) [672],

Y-Povesf vremennykh let (Story of Years of Time).

Both chronicles cover the time interval of allegedly 850-1000 a.d. Volume graphs of the chronicles reach their local maxima virtually simultaneously as well, which is again not by accident but in the order of things - otherwise, the sole chance out of 1015 would

a50 900

k 1U i kjbL

The SuprasV Chronicle

The Nikiforov Chronicle

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