Foreword by A. Shiryaev (1990)

to the first edition of A. T. Fomenko’s Methods of statistical analysis of narrative texts and their applications to chronology, 1990. Based on research materials of 1973-1988


The methods of applied statistics affect a wide range of scientific paradigms today, including the research of a great variety of texts. We use the word “text” to refer to sequences of diverse signals here, such as the lengthy codes one finds in genetics, graphical representations of this kind or the other that can be encoded and represented in a textual form, as well as actual narrative texts, such as historical chronicles, original sources, documents etc.

One of the key objectives we encounter here is learning to identify dependent texts, by which we mean texts possessing some degree of affinity between them – similarities in their nature or history, for instance. We may regard the recognition problem as an example, where one is confronted with the task of finding the visual representation that bears the greatest resemblance to the given prototype. The subject of long signal sequence research emphasizes the ability to find uniform subsequences and their joining points. All of the above bears equal relevance to solving the classical change-point problem, for instance, which is of vital importance to mathematical statistics and the statistics of stochastic processes.

In application to narrative text studies and their needs, the problem of differentiating between dependent and independent texts (such as chronicles) can be formulated as that of tracing out the texts that hail back to a common original source (the ones that can logically be referred to as “dependent”), or those of non-correlating origins (the ones we can logically refer to as “independent”). It is well understood that problems of this kind are exceptionally complex, and thus new empirico-statistical identification methods deserve full recognition for their ability to complement classical approaches to actual research (in source studies, for instance).

The present book by A. T. Fomenko, Professor of Pure Mathematics, is primarily oriented at the development of said methods as applied to identifying and dating dependent and independent texts (in relation to the texts that possess veritable datings a priori).

The author of the book suggests a new approach to the recognition of dependent and independent narrative (historical) texts based on a number of models he had constructed and trends discovered with the aid of empirico-statistical methods and as a result of extensive statistical experimentation with varying quantitative characteristics of actual texts such as chronicles, original sources etc. The verification of these models (statistical hypotheses) by subsistent chronicle material confirmed their efficacy and allowed us to suggest new methods of dating texts, or, rather, the events they describe.

The approach suggested by A. T. Fomenko is rather unorthodox and requires the reader to possess a certain degree of attentiveness and diligence in order to become accustomed with his innovative logical constructions which may be perceived as uncanny; however, one has to note that the author’s principal ideas are perfectly rational from the point of view of contemporary mathematical statistics and fit into the cognitive paradigm of experts in applied statistics with the utmost ease.

The scientific results obtained by the author are most remarkable indeed, and what we witness today can already be referred to as the rather sudden evolvement of a whole new scientific division in applied statistics that is definitely of interest to us. All of the results in question were educed from a tremendous body of work performed by the author with the assistance of his fellow academicians, most of them specializing in mathematical statistics and its applications.

Seeing as how the book relates to problems that concern several scientific disciplines, one is confronted with the necessity of finding points of contact between experts working in different areas. A wide number of terms and definitions common for scholars of one discipline may need to be explicitly translated for scientists of a different specialization and orientation. This is to be borne in mind by the representatives of both natural sciences and humanities among the readers of this book. However, said miscommunications are common and are easily overcome by any mixed collective of scientists collaborating on solving a particular problem. One may hope that the potential readers may prove this very collective that will carry on with the research commenced by an eminent professional mathematician.

In addition to the development of new empirico-statistical methods as applied to dating events, the present book contains a number of applications to the problem of validating the chronology of historical events. One has to differ clearly here between the primary statistical result achieved by the book, namely, defining the layer structure of the global chronological map and its representation as a “sum” of four layers, and the plethora of available interpretations. Interpreting the results and building hypotheses is well beyond the scope of precise mathematical knowledge, so the author urges us to be extremely careful with the conclusions relating to a potential revision of the “static chronology of ancient history”. The author repeatedly insists on the necessity of critical analysis and separating verified facts from their interpretations and various hypotheses.

The concept offered by A. T. Fomenko is novel and somewhat startling, and by all means deserves a meticulous study.

The book is written in conformance to the most demanding scientific standards and is an unprecedented phenomenon in the area of international scientific literature on applied mathematical statistics, so no reader shall be left indifferent. It also offers us a glimpse of the rather charming personality of its author, a mathematician and a history scholar.

One hopes that the reader studies the book in its entirety with undiminished attention after the perusal of the first couple of pages and, at the very least, becomes familiar with a fascinating scientific problem, or maybe even joins the research in this new and promising field of science.


A. N. Shiryaev,
President of the International Bernoulli Society for Mathematical Statistics and Probability Theory in 1989-1991.


A. N. Shiryaev, Corresponding Member of the Russian Academy of Sciences, Doctor of Physics and Mathematics, Head of the Probability Theory Studies Department of the Moscow State University Department of Mathematics and Mechanics, Head of the Probability Theory and Mathematical Statistics Department of the V. A. Steklov Mathematics Institute of the Russian Academy of Sciences.

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