H

poor

votait)

poor

Fig. 5.20. The scribe accurately and scrupulously copies the "poor" zone of the remaining information fund of his time, and treats its richer zones with less reverence, selecting materials the way he sees fit.

Fig. 5.19. Significant and insignificant zeroes of the chronicle volume function.

poor

Fig. 5.20. The scribe accurately and scrupulously copies the "poor" zone of the remaining information fund of his time, and treats its richer zones with less reverence, selecting materials the way he sees fit.

We shall briefly formulate the model, the information respect principle, in the following way.

A chronicler's respect for surviving information is in inverse proportion to its volume.

The intuitive justification of this principle is clear. If some information has survived against a "zero-surrounded background", that is, when to the left and the right of it are the years of which the chronicler knows nothing, then the chronicler has to highly appreciate those scarce shreds of information miraculously spared by time. He copies them quite painstakingly, irrespective of his personal attitude towards their contents. Moreover, a chronicler in a poor zone of survived information fund has little space. He is limited in his freedom of action by a fairly small volume of surviving information. Therefore, the chronicler reproduces in good faith (by and large), the amplitudes of the volume function CM(t) for the information surviving in its poor zones.

The situation is different in what concerns the rich zones. A chronicler faces the necessity to select important things from the abundant choice of information. But the larger the volume of surviving information, the less does the chronicler appreciate individual pieces thereof, which often leads to distortions of volume graph amplitudes of the fund surviving in rich zones. Our statistical experiments have proved its veracity. The chronicler is free to be as subjective as he pleases: he can choose one kind of data and be intentionally "indifferent" to other.

2.5. The amplitude correlation principle of volume graphs in the poor zones of chronicles

We shall draw consequences from the information respect principle.

Let two chroniclers X and Y describe the same events on the same time interval (A, B). Each of them "copies" the volume graph of poor zones of the surviving information fund on the events of epoch (A, B) fairly well. Therefore, the volume graphs of chronicles X and Y will look alike within poor zones. Now we can formulate the model - the amplitude correlation principle in poor zones.

a) If chronicles X and Y are dependent, i. e., describe approximately the same events and trace back to a common original source, then their volume graphs vol X(t) and vol Y{t) should correlate quite well within their poor zones. In the meantime, within their rich zones there may be no amplitude correlation (upon superposition of graphs) at all.

b) If chronicles X and 7 are independent, their volume graphs within their poor zones should be also independent, that is, there should be no amplitude correlation (upon the superposition of graphs).

That is, in case of poor dependent chronicles not only do the peaks of comparable graphs correlate, but also their amplitudes.

2.6. Description of statistical model and formalization

We shall now consider the time period (A, B) and introduce the coordinate x varying from 0 to B-A thereon, where B - A is the length of the time period that we are interested in. It is clear that x = t - A. Let f(x) = vol X(x) be the volume function of the chronicle X. We shall mark as G(x) the function

G(x)=f(0)+f(l) + ...+f(x), or, the "integral" of the function/from 0 to x. We shall call this function the accumulated sum of the chronicle Xy and consider a normalized accumulated sum

F(x) = G(x) / vol X, where vol X is the total volume of the chronicle X. The normalized accumulated sum is presented as a

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