As elsewhere, genealogy has its own laws and patterns that are very interesting and not at all boring.

We proceed to the study and so:

## I law. The activity of three generations falls for a hundred years

This chronological verification of the source material, murals is the first step in the study of the pedigree, followed by a concrete study of the history of the family. This means: if we have a painting according to which the ancestor of the family came to Dmitry Donskoy on Kulikovo Field, his sixth-generation descendant served in the clerk of Ivan the Terrible, and the activities of the persons placed in the paintings between the first and sixth generation are unknown, we must take a segment time between these events and divided by the number of generations (we have about 190 years divided by 6, about 31.5). If the result is the number 30 or very close to it (28-33), this text can be considered reliable. Of course, in order to verify the final reliability of the document, a special analysis of the genealogy must be made. For people working with early murals, where there is little specific information about persons, such a check becomes a prerequisite. This rule is valid for large quantities, when it is necessary to check the painting in 6-9 or more generations, when the interval between the dates known in the painting is 200-350 years.

A genealogical account is used in ethnographic and historical-cultural studies. When setting the time for the construction of a peasant house, the manufacture of an applied art object, owners can often only report that the item was purchased or the house was built by grandfather, great-grandfather, etc. Knowing the genealogy account allows you to set an approximate date.

## II law. In each next generation, the number of ancestors doubles, and the theoretical number of ancestors of each of us is 2^{n-1}

This progression of ancestral growth allows the use of the Eisinger-Stradonitz numbering when compiling tables of the ascending line of kinship.

A paradoxical situation arises with the genealogical account: in a person born in 1995, at the beginning of the 11th century. (1005) there were more ancestors than now lives on the whole globe (8589934592). This is explained by the fact that in reality each of us has much fewer real ancestors than theoretical ones. Hence the following law of genealogy.

## III law. The law of descending ancestors

This is because in the real table of ascending kinship the same person appears several times, which represents several theoretical ancestors at once. People, often not knowing this, marry distant relatives. Often, class restrictions contributed to this.

Otto Forst Battaglia gave a comparative table of the number of theoretical ancestors and real for historical persons, from which all ancestors are known. According to this table, in the XI generation, where the number of theoretical ancestors is 1024, the Spanish king Alfonso XIII has 111 of them (the least), the count of Henry of Paris (Henry VI) – 181, the largest number of ancestors in this generation – 588 – of the Belgian king Leopold III.

French researcher Sh.N. Marten introduces the concept of implex – the ratio (expressed as a percentage) of the real number of ancestors to the theoretical (for a given generation). For Alphonse XIII, the implex will be approximately 90%. Analyzing this law, Marten comes to the conclusion: “we are all relatives in the twentieth generation (maximum)”.

## IV law. Mathematical modeling of the life time of a surname (genus)

One of the main biological causes of male termination is the likelihood of the birth of some girls. For research, a program was created that simulated the dynamics of the development of the genus. In each generation, the program determines the number of men and women, using the fact that the sex of the child is due to a random process with a probability of 50%. This process is modeled by assigning a random number to each person in the generation using a random number generator, and depending on its parity or oddness, the gender of the person is determined. With the development of the genus, only male offspring is taken into account. If in one of the generations there are only women, then the gender on the male line is suppressed. The program was implemented in BASIC.

With the help of this program, the dynamics of the suppression of childbirth with a different fertility strategy was simulated. For clarity, it was assumed that each genus has a constant number of children. To obtain a probabilistic picture for each variant of the number of children, the dynamics of the development of a thousand births was calculated. From the analysis of the simulation results, conclusions are drawn about the laws of action of the investigated suppression mechanism:

- The maximum number of births is suppressed in the first generation.
- The number of suppressions decreases with increasing number of generations.
- All births with one child are suppressed for ten generations, with two children in the same interval, 75% of births are suppressed.
- Childbirths with three or more children are suppressed only in the first ten generations, and with an increase in the number of children, the number of generations in which suppression is possible decreases.
- The stability of the genus begins with three children (22% is suppressed) and increases with an increase in their number. Beginning with seven children (less than 0.9% is suppressed) and more, the likelihood of suppressing the genus is very small.

Good luck in finding.