History Online - Chronology

Let us describe a method of comparing the sets of informative functions v and v' for two epochs. The comparison has been carried out in terms of coordinates, i.e., the functions /, and /,' of the same kind are compared to each other. For /i, /2> o o o, the coefficients of the above [f-type were calculated. The comparison of the dynastic enquete-codes, i.e., the EC-dynasties and EC'-dynasties, is more complicated owing to a finer structure of these informative functions. Without going into details, we only discuss the comparison principle.

We start with the comparison of rule durations. Let Ti,... ,Tn and T[,... , T^ be two sequences of dynastic rule durations in the epochs (A, B) and (C,D), respectively. We will measure the 'distance' between them using the coefficient A introduced in §5; see below. The coefficient A can be called 'stream deviation coefficient' (SDC).

Thus, we compared the items of the enquete-codes EC-3 and EC'-3 of two rulers R and R'. The comparison of the remaining items will be done as follows. Let EC-1, ..., EC-34 be the enquete-code EC for the ruler R, and EC'-l, ..., EC'-34 the enquete-code EC' for R'. We introduce the numerical coefficients E\,... , £34 measuring the proximity (or remoteness) of the items EC-1 and EC'-l, ..., EC-34 and EC'-34. We have omitted here the times EC-3 and EC'-3, since they are compared already by means of the SDC. To compare the items EC-J and EC'-.;', we introduce the coefficients E-j. Then the following three situations are possible.

(1) The biographical data compared are similar. For example, the items EC-5 and EC'-5 state that both rulers died a natural death, in which case we put £'-5 = +1.
(2) The biographical data compared are not explicitly coincident. For example, EC-5 states that a ruler died a natural death, and EC'-5 that he died as the result of a conspiracy. We then put £-5 = -1.
(3) The biographical data compared are neutral in the sense that they are consistent, but not identically coincident. For example, EC-5 states that a ruler 'died', whereas EC'-5 states that a ruler 'was killed'. We then put £-5 = 0.
We now introduce the resultant coefficient E = E-1 + E-2 + £-4 + o o o + £'-33. The coefficient £-3 is absent because the rule durations are compared by means of the SDC. Thus, the coefficient £ measures the proximity of the enquete-codes of the two rulers R and R'. Now, given two sequences of rulers {Ri} and {R',}, we obtain a sequence of coefficients £, comparing them. Finally, we introduce the average coefficient £av. = ^ SF=i ^' measuring the proximity of the complete enquete-codes of the dynasties of {-R,} and {R'i}- Collecting this information, we might be able to estimate the remoteness or proximity of the enquete-codes of two dynasties and their corresponding epochs by means of the coefficients £av. and the SDC.

A computational experiment

From 1978 to 1979, I performed a computational experiment, comparing several hundred pairs of epochs (A,B) and (C,D), i.e., sets of their informative functions v = {/i, /2, o o o, EC of dynasties of rulers}. The time limits for the experiment were 3000 B.C. and A.D. 1800, with the events localized in Europe, the Mediterranean region, Egypt, and the Near East.

In particular, the experiment showed that, in comparing the enquete-codes of some personages, we often had to put the coefficient E-j equal to zero, which occurred because the information compared there was consistent and, at the same time, unconfirmed. The role of+1 and -1 was therefore heightened. We discovered further that, in the overwhelming majority of concrete enquete-codes, the coefficient £-34 has to be made equal to zero, again because of the consistency of information compared. Recall that item EC-34 of an enquete-code is the personage's 'bibliographical remainder'. For a reliable comparison of the items EC-34 and EC'-34 in two biographies, we must be certain that we really possess sufficiently complete 'written biographies' of the personages compared. However, to guarantee the completeness of the rulers' enquete-codes (all the more, of whole dynasties) is usually a complicated matter, due to which we have resorted to the following formal method.

For each historical epoch, we have chosen a (possibly) uniform and sufficiently large historical text describing the events. We took either a fundamental monograph of the type of Gregorovius' work or a fundamental primary source of Livy's type. Then item EC-34 of the enquete-code was identified with the 'bibliographical remainder' for a historical character given in the historical work. For simplicity, the volume of item EC-34 was usually calculated as a percentage of the volume of the entire 'biography' of the personage. Meanwhile, as a rule, we did not analyze the components of item EC-34.

We illustrate this with an example. The epoch of regal Rome from 753 to 510 B.C. described by Livy turns out to be sufficiently close to that of the Roman Empire in A.D. 300-552, with the SDC being less than the lower bound for most of the SDC values for independent dynasties. Further, it turns out for these epochs that E^, = +19, and that the volume of item EC-34 equals 29%. In other words, about 29% of the 'biographies' of historical characters in these epochs were 'thrown overboard' from the discussed parallels, it being important that this entire 'biographical remainder' is zero for the coefficient of EC-34, which means that the information not involved in the parallel is noncontradictory within the framework of the comparison.

It is useful to compare this result, which probably indicates the dependence of the epochs, with the numerical parameters found for an arbitrarily chosen pair of independent epochs. As an example of independent historical epochs, we take the following dynasties, i (1) The dynasty of the Russian grand dukes from Igor (912-944) to Demetrius I (1275-1293).
(2) The dynasty of the Byzantine emperors from Theodosius II (408-450) to Theophilus (829-842) . Calculations show that the SDC is 'very large';
further E^i. = -8.7. In this case, the volume of the 'remainder' EC-34 is equal to 40%. This pair of dynasties is independent from the standpoint of the coefficients we introduced.
A great difference is obvious between this and the example of the two dependent Roman Empires (see above).
We shall now describe the results of the global computational experiment of comparing different epochs.