History Online - Isaac Newton

To overcome the above difficulties, we should try to consider the subject from a different angle and create a certain independent dating method which is not based on subjective estimation. This done, we can start analyzing the whole of chronology. In my opinion, an approach involving the statistical analysis of various numerical characteristics associated with ancient texts is most suitable for this purpose. The interested reader can learn about concrete methods and some of their applications to the analysis of global chronology from the short bibliography at the end of the section. Here, we shall confine ourselves to a short account of the essentials and give several examples.

We make the immediate reservation that the methods suggested by the author do not pretend to be universal. Moreover, the results obtained by each individual method cannot be regarded as impeccably trustworthy. A sound criterion of their validity is the consistency of the dating obtained by different methods (today, there are seven of them). The general scheme is as follows. First, a statistical hypothesis is formulated for modelling some process (e.g., loss of information with time). Then numerical coefficients are introduced which permit us to quantitatively measure the deviations of experimental curves from those predicted theoretically. Further, the model is checked against a priori true historical material, and if it is confirmed, then the method can be used for the dating of events.

For simplicity, we give an example. Let a period in the history of a region P from a year M to a year N be described in a text X (chronicle or annals) broken into separate chapters X(T), each of which is devoted to the events of a year T. We calculate the volume of all the chapters (number of pages or lines) and represent the obtained data as a volume graph, plotting the years, T, on the horizontal, and the volumes of the chapters on the vertical axis. A similar graph for another text, Y, describing the same events, in general will have different form; most probably, the interests or tendencies of the chronologist will have bearing on it. But how essential are these differences? Is there anything common between the volume graphs? Indeed, there is. But, before stating the details, some words about the information-loss pattern.

The essential characteristic of any graph is its peaks, or extremal points. In our volume graph, they correspond to the years in which the curve attains local maxima. Such peaks indicate the years described by the chronicle in the time interval under investigation with the finest points of detail. Denote by C(T) the volume of all texts created by contemporary writers and describing a year T. We call it the 'primary stock'. The precise form of its graph is not known to us, since texts get partly lost in the course of time.

We now formulate the information-loss model, namely, there will be more texts for those years to which more texts were originally devoted. It goes without saying that to verify the model in this form is difficult, because the graph of the primary stock remains unknown. But one of the corollaries can be verified. Later authors, X and Y, while describing the same period (and not being its contemporaries), will be forced to employ approximately the same set of ancient texts available. Therefore, they will be able to describe best those years from which more texts remain.

Eventually, the model conjecture is formulated as follows: The graphs of the volumes of chapters for two dependent texts X and Y (i.e., describing the same period of history and the same region) must have simultaneous peaks; in other words, the years described in detail in X and Y should coincide or be close. On the other hand, if two texts X and Y are independent (either describing essentially different periods of history of the same length, or for different regions), then the graphs of the volume for X and Y attain local maxima at different points .

After the mathematical formalization, an experiment was carried out in which the model (maximum correlation principle) was verified for several hundreds of pairs of dependent and independent historical sources. The principle was confirmed, which made it possible to offer a method for dating texts and also for discovering interdependency among them. For example, to date events described in a chronicle, we have to try to choose an a priori dated text such that the volume graphs attain maxima practically simultaneously. If, however, the dating of two comparable texts is unknown, but the peaks in the graphs coincide, then we can assume with a high degree of probability that the texts are dependent, i.e., the events described are close or coincide.

Now, just a few words about some other methods of dating. They are based on the statistical analysis of such parameters as the frequency of mentioning the names of historical characters and that of various astronomical phenomena, the period of the rule of kings in various dynasties, formalized biographical data of historical figures, and so on. All these methods have been verified for undoubtedly true material of the 13th to the 20th century, and their validity has been confirmed.

The methods briefly described above are applicable not only to the dating of texts. They also permit us to find various literary borrowings, repetitions, literary cliches, citations, and parallels in the texts being compared. For example, if in comparing two dynasties of kings a certain dependence is discovered (i.e., if the corresponding graphs of the rule duration are extremely close), then this can be interpreted in different ways. One interpretation consists of our probably having discovered an intentional imitation by the annalist of a certain authoritative source. However, another version is also probable, namely, that we are dealing with duplicates which were never recognized to be identical and are narrating the same events, and which were related to different historical epochs.

Sometimes these methods help discover the proximity of chronicles, i.e., their having originated from the same source. In particular, they make it possible to indicate the duplication effects discussed at the beginning of the section in connection with the Renaissance epochs. As it turns out, there are essentially more such historical epochs than is usually thought. To avoid a terminological muddle, we will speak in the following simply of duplicates.

It is now time to formulate our problem: to find possibly all duplicates in ancient and medieval history, and if we succeed, to construct on their basis a hypothetical chronology without repetitions and Renaissance periods which are sometimes hard to explain.