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22 1 The Problems <strong>of</strong> Historical Chronology<br />

T . Such a function X(T ) is called by Fomenko the volume<br />

function for X. Of course, it is easy to define many other<br />

similar numerical functions that could be used as an “identificator”<br />

<strong>of</strong> the text X. For instance, the frequency the year T<br />

is mentioned in the subsequent chapters <strong>of</strong> X, the number <strong>of</strong><br />

all the names <strong>of</strong> historical persons listed in the text, or how<br />

many times these names were mentioned in the whole text. In<br />

his monograph [103], A.T. Fomenko used several such functions<br />

to analyze similarities and differences between various<br />

historical documents, for which carried appropriate statistical<br />

calculations and precise evaluations <strong>of</strong> probabilities. The<br />

main problem was to identify which <strong>of</strong> the considered documents<br />

referred to the same epoch or two different epochs.<br />

In the case <strong>of</strong> two volume functions, this could be done as<br />

follows: It is clear that for two different documents X and Y<br />

their volume functions X(T ) and Y (T ) can be completely different<br />

even if they refer to the same epoch. However, if X and<br />

Y describe the same sequence <strong>of</strong> events, then it is most probable<br />

that they will have the same distribution <strong>of</strong> local maxima.<br />

It is quite obvious, that important events in both documents<br />

would be presented in a more elaborated form. That means<br />

for those “important years” T the volume functions X(T )<br />

and Y (T ) would have local maxima. Consequiently, the both<br />

functions X(T ) and Y (T ) would have similar distribution <strong>of</strong><br />

their maxima or the “important years.” A question arises how<br />

to determine the probability that two volume functions with<br />

similar maxima distribution are referreing to the same sequence<br />

<strong>of</strong> events. A.T. Fomenko did the probability calculation<br />

and verify their accuracy on the chronicles related to the<br />

well documented epochs. On Figure 1.23 we show the distribution<br />

<strong>of</strong> local maxima for five different chronicles describing<br />

the same sequence <strong>of</strong> events. It is clear that, indeed, their<br />

maxima are located almost in the same positions.<br />

On the other hand, the coincidence <strong>of</strong> local maxima <strong>of</strong> two<br />

volume functions can be used to identify, with very high probability,<br />

that two hisorical texts describe the same epoch and<br />

the same sequence <strong>of</strong> events, even if they were mistakenly<br />

associated with different epochs. This method <strong>of</strong> matching<br />

dependent texts is called by A.T. Fomenko the principle <strong>of</strong><br />

maximal correlation. This principle was empirically checked<br />

using the reliable historical data <strong>of</strong> 16th – 19th centuries, and<br />

its correctness was confirmed. Therefore, the locations <strong>of</strong> the<br />

maxima constitute the numerical data that can be associated<br />

with the text X in order to characterize the epoch it is referring<br />

to.<br />

An example <strong>of</strong> a simple scalar function, which can be easily<br />

extracted from the historical database, is the functions<br />

<strong>of</strong> the time-span <strong>of</strong> the reign <strong>of</strong> subsequent rulers belonging<br />

to a certain specific dynasty. Such a dynasty function can be<br />

illustrated by its graph, which is shown on Figure 1.24. On<br />

the horizontal axis are placed the subsequent numbers <strong>of</strong> the<br />

consecutive rulers (or names <strong>of</strong> kings, emperors, etc.) and on<br />

the vertical axis is marked the length <strong>of</strong> the reign <strong>of</strong> the corresponding<br />

ruler. Fomenko calls such a sequence <strong>of</strong> rulers a<br />

numerical dynasty or simply a dynasty. The dynasty in the<br />

above example consists <strong>of</strong> 12 rulers. Again, it is clear that two<br />

Length <strong>of</strong> Reign (in years)<br />

25<br />

20<br />

15<br />

10<br />

5<br />

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Dynasty Function<br />

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1 2 3 4 5 6 7 8 9 10 11 12<br />

Consecutive Rulers<br />

Figure 1.24: Example <strong>of</strong> a dynasty function<br />

chronicles (even if they have some discrepancies and are written<br />

in different languages with different calendar conventions)<br />

describing the same portion <strong>of</strong> history, would produce similar<br />

dynasty functions. It is possible to determine the confidence<br />

interval corresponding to a very high probability, that allows<br />

us to identify such dependent dynasty functions, in which case<br />

we can determine that the similarities are not coincidental and<br />

in fact, they indicate that they represent the same sequence<br />

<strong>of</strong> historical events.<br />

The Roman coronation<br />

<strong>of</strong> the Holy Roman<br />

emperors in 10-13<br />

Centuries<br />

41<br />

38<br />

¢<br />

¢<br />

32<br />

¢<br />

24<br />

21 22<br />

1<br />

23<br />

¢<br />

21<br />

¢<br />

18<br />

¢<br />

¢<br />

13<br />

¢<br />

11<br />

9<br />

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8<br />

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3<br />

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2<br />

3<br />

4<br />

5<br />

6<br />

7<br />

8<br />

9<br />

10<br />

11<br />

12<br />

13<br />

¢<br />

2<br />

¢<br />

Biblical Israeli rulers<br />

from 922 BC<br />

Figure 1.26: Parallel between the Roman coronation <strong>of</strong> the<br />

Holy Roman emperors and the biblical Israeli rulers<br />

It may sounds strange that mathematical methods can be<br />

effectively used to investigate correctness <strong>of</strong> historical dating,<br />

but it is exactly what is the case here. The methods <strong>of</strong><br />

Fomenko, which are based on theoretical and empirical analy-<br />

¢<br />

¢<br />

¢<br />

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8<br />

12<br />

14<br />

12<br />

10<br />

¢<br />

¢<br />

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20<br />

¢<br />

22<br />

24<br />

¢<br />

¢<br />

30<br />

33<br />

¢<br />

¡<br />

41<br />

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