History Online - Chronology

An independent experimental investigation of the GCD was then also carried out on the basis of the dependent dynasty recognition method, for which lists of all the rulers from 4000 B.C. to A.D. 1800 for the indicated regions have been made. The method described in Section 3 was applied to this collection (each of the dynasties consisting of 15 kings). The experiment has unexpectedly led to the discovery of the special pairs of dynasties M and H earlier regarded as independent (in all respects), but for which the proximity coefficient A(M, H) is of the same order as for a priori dependent dynasties, i.e., it oscillates from 10"12 to 10-8.

Let us give several examples. By a dynasty, we understand a sequence of actual rulers of a country without regard to their titles and relations. Due to the existence of co-rulers, difficulties in arranging dynasties in a row sometimes arise; the simplest principle of their ordering, i.e., with respect to the midpoints of the periods of their rules, has therefore been adopted. We call a sequence of rules in the history of a state a dynastic stream, and its subsequences obtained by rejecting some particular co-rulers dynastic jets. It was required of a jet that it should be monotone (i.e., the midpoints of the periods of the rules making up a jet should be monotonically increasing) and complete (i.e., gap-free and covering the whole period embraced by the stream, with overlapping being permitted). Understandably, these requirements may not always be satisfied in real situations. For example, a chronicler's story may omit the year between two rules, and so forth. Therefore, we should admit insignificant gaps (no more than one year long) and the three types of errors described and modelled in ). 7" There is another reason for which a precise formal picture can be distorted:
It is sometimes difficult to establish with certainty the start of a rule (e.g., to count from the moment of actually starting the rule or formally ascending the throne), whereas there are usually no difficulties about its end: In most cases, it is the ruler's death. For example, sources supply different dates for the enthronement of Frederick II, namely, 1196, 1212,1215 and 1220, thus making it necessary to "double" the king or to consider him even in a larger number of versions, all included in the general dynastic stream. Meanwhile, it was required V^that no jet should contain two different variants for the same ruler. We-now give examples of dependent-dynasties.