Application of variation modeling to reconstruct the size of the medieval rural population (using the example of the Pskov land in the middle of the 16th century)

As part of an interdisciplinary approach, historians are increasingly using the ideas and methods of the mathematical sciences in their research. This, for example, arises in reconstruction problems from the field of historical geography, when the initial data is insufficient for traditional analysis. The subject of this study is to model the system of spatial distribution of the medieval population and demonstrate its results using a specific example. To take into account the condition of territory heterogeneity during modeling, the author develops a variational approach proposed by S.M. Huseyn-Zade. Using the methods of the calculus of variations and Pareto optimality within the framework of this approach makes it possible to identify and numerically describe the relationships between the optimal parameters of the system. To solve this problem of reconstruction, a model of a two-level hierarchy of placement of centers was previously proposed. Its approbation on the material of the scribal description of the Shelonskaya Pyatina of the Novgorod land at the end of the 15th century showed a high degree of correlation between real and theoretical data. The first surviving scribal description of the Pskov lands dates back to the second half of the 80s XVI century. It records a huge mass of abandoned lands as a result of the Livonian War. To assess the scale of this crisis, we first need data on the size of the rural population in the previous period of time. Unfortunately, the scribal description of the mid-16th century, which is closest to it in time, has not survived. However, the above-mentioned first surviving scribal description contains retrospective information about an earlier time, which makes it possible to apply the modeling results to solve the desired reconstruction problem, which is novel.

mathematical modeling, scribe 's book, center placement system, population density function, pogosts, hierarchy of centers, Pareto equilibrium, calculus of variations, functional, linear regression