History Online - Chronology

The whole set of empirico-statistical methods we developed was applied to the GCD statistical material (see the first 'fibre'). All possible pairs of time intervals (epochs) along with the basic texts describing them were considered, and the texts were statistically examined and compared. The 'proximity coefficients' or textual 'dependence coefficients' were subsequently calculated. If the dependence coefficient for two texts X and Y was the same (in order) as for two a priori, positively dependent texts from the 13th to the 20th century, then X and Y along with the associated time intervals were called 'statistically dependent'. This was represented in the GCD by denoting the corresponding time segments by the same symbols, for example, by the same letter T. The symbols were chosen arbitrarily. However, if the proximity coefficient was the same (in order) as for two a priori independent texts from the 13th to the 20th century, then X and Y were termed 'statistically independent' and hence represented by noncoincident symbols like the letters H and C. We would like to make it clear that by investigating experimentally reliably dated texts describing the 13th to the 20th century, it was discovered that the proximity coefficients distinguish between a priori dependent and independent texts. For example, one of these coefficients, p(X, Y), did not exceed 10~8 for two texts known previously as dependent and was not less than 10~3 for two surely independent texts, which shows the difference of about 4-5 orders. Now, comparing two arbitrary texts X and V, we can say whether the value of the coefficient is in the zone for dependent or independent texts. It can also be in the zone of 'neutral' texts. It goes without saying that the indicated bounds for the values of the coefficient have been found experimentally. Further discovery of dependent and independent texts is then carried out within the framework of the experimental material (which is, though, sufficiently large).

For vast computational experiments, the GCD revealed pairs of statistically dependent texts and the corresponding epochs. The results of applying different methods turned out (and this is very important) to be remarkably consistent; namely, if a pair of texts (and periods) were statistically dependent from the standpoint of one method, then they were also dependent from the point of view of other methods applicable, in principle, to the tests in question. This consistency seems to be important. Our methods discovered no unexpected, formerly unknown duplicates of documents belonging to the period from the 13th to the 20th century. However, for documents preceding the 13th, and especially the 10th century, the same methods led to the quite unexpected discovery of many new statistical duplicates regarded as independent in all respects, and referring to different epochs.

The global chronological diagram showing all statistical duplicates is the second principal empirico- statistical result obtained by the author.

The third basic result is the decomposition of the GCD into the sum of four chronicles practically identical to each other, but shifted by considerable time intervals. To give a rough idea, the third statistical result can be formulated in the following way: The modern 'textbook' of traditional ancient and medieval chronology and history is the sum, from the statistical point of view, of the four replicas of one shorter 'chronicle'.

The principal part of the book concentrates on these three empirico-statisti-cal results. The subsequent 'fibres' are mostly of hypothetical and interpreta-tional character. Roughly speaking, they are required so that we may answer the question: What do the obtained empirico-statistical results mean?

It can be called interpretational. Here, we offer different hypotheses which can explain the regularities discovered and the reasons for the duplicate appearance. We do not regard this material as final. The 'shorter' textbook I suggested certainly does not claim completeness and can only be regarded as a possible version. Interpretations of the obtained statistical results can be of different nature and will require much work by many specialists in various fields.