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During that time. Identifying ngereven one astronomical dis- prints, bloodstains, bers, the marks on a bullet, footprints, covery of primary importance various marks on the body and all kinds of even microscopic was made. Theoretical traces, require more than just an impression that two patastronomy barley made some terns are similar. To determine with high condence a match progress and in some sense between two patterns is a serious mathematical problem recases suered retrogression.

Morozov identied inferior to the Ptolemys several similarities between the so-called dynasty functions. As we have seen, in the Western European ments, it is necessary to analyze them statistically exactly in astronomy nothing substantial took place during the ve the same way as it is done regarding the physical evidence centuries after the death of Ptolemy.

After that there was in a criminal investigation. The method suggested by A. Finally, he concludes that Regarding the historical chronicles, but in other areas of sciences, for examEurope, the gloomy period following the collapse of the ple in studying biological codes. Roman Empire apparently in the 6th. For example, it is possible to extract all kinds of nuIn our opinion these disruptions, periods od silence, merical information from these documents.

Suppose we are dark ages etc. We can create a sequence of integers representing the number of words used in incorrect Scaliger version of chronology. It is possible to determine the condence interval corresponding to a very high probability, that allows us to identify such dependent dynasty functions, in which case we can determine that the similarities are not coincidental and in fact, they indicate that they represent the same sequence of historical events.

It may sounds strange that mathematical methods can be eectively used to investigate correctness of historical dating, but it is exactly what is the case here. The methods of Fomenko, which are based on theoretical and empirical analy-. An example of a simple scalar function, which can be easily extracted from the historical database, is the functions of the time-span of the reign of subsequent rulers belonging to a certain specic dynasty. Such a dynasty function can be illustrated by its graph, which is shown on Figure 1.

On the horizontal axis are placed the subsequent numbers of the consecutive rulers or names of kings, emperors, etc. Fomenko calls such a sequence of rulers a numerical dynasty or simply a dynasty. The dynasty in the above example consists of 12 rulers. Again, it is clear that two. On the other hand, the coincidence of local maxima of two volume functions can be used to identify, with very high probability, that two hisorical texts describe the same epoch and the same sequence of events, even if they were mistakenly associated with dierent epochs.

This method of matching dependent texts is called by A. Fomenko the principle of maximal correlation. This principle was empirically checked using the reliable historical data of 16th 19th centuries, and its correctness was conrmed.

Therefore, the locations of the maxima constitute the numerical data that can be associated with the text X in order to characterize the epoch it is referring to. Such a function X T is called by Fomenko the volume function for X. Of course, it is easy to dene many other similar numerical functions that could be used as an identicator of the text X. For instance, the frequency the year T is mentioned in the subsequent chapters of X, the number of all the names of historical persons listed in the text, or how many times these names were mentioned in the whole text.

In his monograph [], A.

Fomenko used several such functions to analyze similarities and dierences between various historical documents, for which carried appropriate statistical calculations and precise evaluations of probabilities. The main problem was to identify which of the considered documents referred to the same epoch or two dierent epochs. In the case of two volume functions, this could be done as follows: It is clear that for two dierent documents X and Y their volume functions X T and Y T can be completely different even if they refer to the same epoch. However, if X and Y describe the same sequence of events, then it is most probable that they will have the same distribution of local maxima.

It is quite obvious, that important events in both documents would be presented in a more elaborated form. Consequiently, the both functions X T and Y T would have similar distribution of their maxima or the important years. A question arises how to determine the probability that two volume functions with similar maxima distribution are referreing to the same sequence of events. Fomenko did the probability calculation and verify their accuracy on the chronicles related to the well documented epochs.

It is clear that, indeed, their maxima are located almost in the same positions. These methods were extensively tested on the data referring to well documented epochs. It was proved that if two dynasty functions for 15 rulers or volume functions were not related, the measure of distinctiveness between numerical functions associated with these dynasties was between 1 and However, in the case of related events from the same epoch, the measure of distinctiveness was never larger than Jet A: the Holy Roman Empire in the th cc.

Jet B: the Roman Empire in the th cc.

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Two graphs combined. In order to give to similarity a more precise meaning, Fomenkos introduced a routine for distinguishing functions referring to dierent dynasties and dened a certain measure of distinctiveness between them or rather a probability measure for distinctiveness. In simple words, he found a way to measure a distance between the above numerical functions like for example dynasty functions as we measure a distance between two dierent locations.

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Mathematicians say that in such a case that they are dealing with a metric space. The geometry of a metric spaces is denitely dierent from the geometry we learn in school, but the usual properties related to the measurement of distances are still valid there. Now we can apply the idea, that if a distance, lets say, between two towns A and B is less than few hundreds meters, then we are justied to think that in fact A and B represent practically the same town. Similarly, if a distance between two dynasty functions is suciently small we may think that indeed they. Rigid year shift.

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It is dicult to imagine that two dierent dynasties could have identical or almost identical dynasty functions. The probability of such a coincidence is extremely small already for dynasties composed of 10 rulers. Nevertheless, the number of such coincidences, for even longer dynasties of 15 rulers, turns out to be unexpectedly large. Morozov, who noticed the coincidence between the ancient Rome and the ancient Jewish state, discovered the rst examples of surprisingly identical pairs of dynasty graphs.

A formal method to study such similarities was introduced by A. Jet A: the Second Roman Empire in the 1st c. D, and the Third Roman Empire in the 3rd-6th cc. Approximately year shift. Jet B: the Hapsburgs Empire in the th cc. There is another surprise, besides coincidence of the dynasty functions, the other numerical functions conrm with very high probability that these dynasties are indeed the same.

It brings us to a suspicion that in fact we are dealing with repetitions in the conventional version of the history.

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Fomenko discovered dozens of strong coincidences, sometimes between three and more dynasties. But, there are no more such coincidences in the history of the better-documented epochs, for example starting from the 16th century. Using empirico-statistical analysis A. Fomenko and his collaborators discovered dozens of historical repetitions which most probably were mistakenly organized as unrelated sequences of historical events.

Extremely high probability for these identications exclude any possibility for an accidental coincidence. Let us illustrate several such historical duplicates based on selected from the book [].

We begin with an example showing similarities between two dynasties, one the dynasty of the Holy Roman-German Empire 10th 13th. Jet A: the Carolingians in the th cc. Charles Empire and the Third Roman Empire in the th cc. Jet B: the biblical Kingdom of Judah in them th cc. The year rigid shift. The work of Fomenko and his collaborators proves that the statistical analysis can be successfully applied to analyze the numerical data contained in historical documents.

Nosovsky also developed several other There are many more examples of similar dynasty pairs statistical criteria for distinguishing or recognizing identical in the conventional chronology.

For instance, the parallel be- sequences of historical events. We should mention for examtween the rst period of the Roman episcopate in ple the method of detecting chronological shifts based on the A. All cles into its source fragments see []. The parallel between the Roman coronations of the Holy Roman emperors and the biblical Israeli rulers shown in Figure 1. Another historical duplicate, or parallel is illustrated on Figure 1. In the example on Figure 1.