## FOREWORD OF A.N.SHIRYAEV

(With the present foreword of an outstanding specialist in the theory of probabilities and mathematical statistics opened the very first chronological book of A.T.Fomenko "Methods of statistical analysis of narrative texts and applications to chronology", issued in the publishing house of the MSU in 1990).

Today the methods of applied statistics enter the most different fields of knowledge, including the tasks of study of the texts of different nature. And under the "text" sequences of signals of one or another type, long codes, appearing in genetics, graphical pictures (which could be coded and imagined as "text"), and also real narrative texts (for example, historical chronicles, primary sources, documents etc.) are meant.

One of important, appearing here, tasks is in the identification of dependent texts, that is "similar" texts, having in some sense common nature, common origin. For example, in the task of identification of the images it is important to discover among the whole of "images" such, which is maximally "close" to the beforehand given: in the task of the study of long sequences of signals it is important to be able to discover "homogeneous sequences" and places of their joining. Here, in particular, is related a problem about discord, to solution of which much attention is paid in mathematical statistics, statistics of casual processes.

Applicably to the problems of study of narrative texts the problem of identification of dependent and independent texts (for example, chronicles) sounds as a problem of search of texts, dating back, for example, to one common primary source, original (it is natural to call such texts dependent), or, instead, dating back to considerably different primary sources (it is natural to call such texts independent). It is clear that the problems of such type are extremely difficult and that's why it is worth welcoming the appearance of new empirical-statistical methods of identification, which, in the aggregate with classical approaches could be useful in specific studies (for example, historiographical).

The present book of professor of net mathematics A.T.Fomenko is oriented, mainly, at the development of such new methods applicably to the problem of identification of dependent and independent narrative texts and for their dating (relatively to the texts with beforehand known authentic dating).

The author of the book proposes a new approach to the task of identification of dependent and independent narrative (historical) texts based on some new empirical-statistical models (regularities), discovered by him as a result of wide statistical experiments with different quantitative characteristics of definite texts, chronicles, primary sources etc. Check of these models (statistical suppositions) on a definite material of chronicles confirmed the efficiency of models and let to propose new methods of dating of texts (to clarify, the described in these texts events).

Proposed by A.T.Fomenko approach is not standard and requires a known attention and hard work from the reader in order to familiarize with new and probably unusual logical constructions. At the same time the main ideas of the author are accepted rather naturally from the point of modern mathematical statistics and easily fit the system of thinking of the specialists in applied statistics.

The received by author scientific results are interesting and, probably, today it is worth speaking about the appearance of new (and rather unexpected) scientific direction in applied statistics, the development of which is definitely interesting. All these results are based on a huge amount of work, done by the author together with a team of his colleagues-scientists, who are mainly specialists-professionals in mathematical statistics and applications.

As the book is devoted to the problems, which lie at the interface of several scientific disciplines, then inevitably appear the problems of contact between the specialists of different specialties. Many notions and terms, customary for one community of scientists, need special translation into the language of scientists of another specialty or orientation. The readers of the present book, both representatives of natural sciences and humanities, should remember about it. Well, such "communication difficulties" are typical and are successfully overcome within any mixed team of scientists, working under the solution of applied scientific problem. Hopefully, many future readers of the book will compose such team, which would successfully continue the studies, started in the book, written by a well-known professional-mathematician.

Along with the development of new empirical-statistical methods of dating of events, the book contains also applications to the problem of modern scientific proof of the chronology of events of the past. Here it is necessary to separate clearly the main statistical result, received in the book (that is a layered structure of the global "chronological map" and its dissociation to the "total" of four layers), and its different interpretations and readings. Suppositions and interpretations of the results are already out of the frames of precise mathematical knowledge, and because of this, as the author notes, it is worth extremely carefully state the conclusions, related to possible building of new "statistical chronology of the Ancient times". The author many times insists on the necessity of critical analysis and separation of clearly established facts from suppositions and interpretations of these facts.

The proposed by A.T.Fomenko concept is new, partly unexpected and deserves the most focused attention.

The book is written on a high scientific level, it represents a unique occurrence in international scientific literature in the field of application of methods of mathematical statistics, and it will not leave indifferent any reader. It also gives the reader a possibility to get acquainted with an attractive personality of its author – mathematician and history researcher...

It is desirable, that the reader, after acquaintance with the first pages of the book, with a relentless interest will read it till the end and, at least, will learn about an interesting scientific problem, and probably will join further studies in this new and challenging scientific field.

A.N.SHIRYAEV

President of the International Community of mathematical statistics and theory of probabilities n.a. Bernoulli (in 1989-1991),

(A.N.Shiryaev, correspondent member of the Russian Academy of Sciences (RAS), professor, doctor of physical-mathematical sciences, head of the department of the theory of probabilities of the mechanical-mathematical faculty of the MSU, head of the department of the theory of probabilities and mathematical statistics of the institute of mathematics n.a. V.A.Steklov of the Russian Academy of Sciences).