Bemidbar 3:39-43 (Bemidbar) - A baby boom

The first three chapters of the book of Bemidbar record various population data of the people. 1:46 and 2:32 record that as of the second month of the 2nd year of the people's stay in the desert there were 603,550 men age twenty years and up. 3:39 records that there were 22,000 Levites, and 3:43 records that there were 22,273 firstborn sons more than one month old.

One question that arises with these figures is how could there have been just 22,273 firstborn sons out of an adult male population of more than 600,000? If one assumes that that there were an equal number of adult females, and that the population of the people under twenty, both male and female, was equal to half the total adult population, then the population of the people one year after the Exodus was approximately 1.8 million people. If there were 22,273 first born males, then presumably there were also 22,273 firstborn females, which would mean that that there were approximately 45,000 families. The ratio of the total population to the number of families means that each family would have averaged 40 children, which is incredible.

While it is possible that G-d performed a miracle that enabled women to have such large families (see Rashi on Shemot 1:7), it is odd that by any list of children in a family in the Torah, there is a much smaller number of children. For example, Moshe had two siblings, and he had two children while Aharon had four sons. 3:17-20 records the families of the Levities, and there is no family listed with more than four sons. Similarly, Bemidbar 26:9 records that the family of Eliav had three sons. Bemidbar 27:1-3 records that Tzelofhad had five daughters and no sons. Accordingly, it is difficult to understand how there could have so few firstborn sons in 3:43. (One might claim that the firstborn sons died due to disease or due to the Egyptian decrees, but then there would be a corresponding increase in the number of non-firstborn sons who died, and the estimated family size would remain problematic.)

The Ramban (on 3:45) makes an interesting suggestion though he rejects his own suggestion. He writes that one cannot say that the firstborn sons were only those firstborn sons born after the Exodus, in the first year of the people's stay in the desert, since the population did not increase at such a rapid rate. This rejected suggestion is based on the very reasonable idea that the firstborn sons only acquired their special status as firstborn sons after the Exodus. Prior to the Exodus, there were firstborn sons, but there was no special status to being a firstborn son. However, after the tenth plague, when the firstborn sons were saved, then the firstborn sons had a special status (Shemot 13:15, see also Bemidbar 3:13; 8:17). Ramban's suggestion is that the special status was not applied retroactively to the firstborn sons who had already been born but only to the future firstborn sons. Ramban rejects this idea due to the technical problem that this rationale would sharply increase the growth rate of the Jewish population. If 22,000 firstborn sons were born just in the first year of the people's stay in the desert, then this implies that over forty years, the population was booming, but the male population at the end of the forty years in the desert, 601,730, Bemidbar 26:47, had decreased by 1,820 men.

Beller (1992) presents a mathematical model that builds on the Ramban's suggestion and gives a plausible outcome to explain the ratio of firstborn sons to the general population. However, the model, as by all models, is only as good as the assumptions that are the basis for the model, and some of the assumptions as to the growth rate and the length of years are difficult to accept. (For a discussion of the model, see Samet, 2002, Vol. 2, pp. 156-167.) Instead, we will suggest a different variation on the Ramban's suggestion.

In our commentary on Shemot 1:8-22, "Population dynamics," http://lobashamayim.blogspot.co.il/2009/01/shemot-18-22-population-dynamics.html, we suggested that Pharaoh did not intend to kill the entire male Jewish population, but that his goal was to control the male Jewish population in order to allow him to benefit from their work as slaves without having to fear that they would rebel. Thus, his decree to kill all the male children (Shemot 1:22) was a temporary recurring decree that was enacted whenever the male population passed some threshold level.

Overall Pharaoh's plan existed for at least eighty years since Moshe was 80 at the time of the Exodus, Shemot 7:7, but how long would the decree have been in effect each time? It would have to have been for a sufficient amount of time that the growth rate stopped, and this suggests that each set of parents was only allowed to have a limited amount of time to have male children. A possible system could have been that for ten years, all male children were killed, and then for five years the male children were allowed to live. In the "permitted" five years, a family could have had a few sons, but by the time another cycle of "permitted" years came around, the family might not have had more children. (One could lengthen the number of forbidden years or shorten the number of permitted years, but this would have no effect on the argument here.)

What was the reaction of the Jewish people to this decree? A rational response was to wait for the "permitted" years, in order not to have children during the forbidden years that would be killed. (This seems to be the initial response of Moshe's parents, see our discussion on Shemot 2:1, "Moshe’s parent’s marriage." Some parents might have succeeded in having children in the "forbidden" years, as by Moshe's parents, but these successes would have been rare.)

If our assumptions are correct, then the Jewish population at the time of the Exodus was not uniform, but consisted of discrete groups based on certain ages, with almost no population at all for most age groups. A possible example is an adult population consisting of four age groups, 20-24, 35-39, 50-54, and 65-69, with approximately 150,000 males in each age group. In addition, there would be another set of male children between the ages of 5-9, whose parents would be from the age group of 35-39. With such a system, the Exodus could have transpired in the middle of the "forbidden" years, meaning that the group of 20-24 year olds had no children prior to the Exodus. If this is true, then after the Exodus, when the restrictions on having children were abrogated, then the people compromising the age group 20-24 would have had children for the first time. Thus, almost all the children born in the first year after the Exodus were firstborn children. If there were 150,000 males in the age group 20-24, then the birth of 45,000 children (22,000 males) in the first year of the people's stay in the desert is very reasonable.

Thereafter the population would not have increased at a rate of 45,000 children a year since there were many age groups (for instance 10-19) with zero population. In some years of the people's stay in the desert there would have been large increases in the number of children, while in other years few children would have been born. If there were 20 years, of "high" population growth of 20,000 males, and 20 years of "low" population growth, then the adult male population would have been approximately 600,000 after forty years in the desert. Accordingly, the understating of Pharaoh's plan as being a temporary recurring decree not only provides a coherent explanation for chapter one in the book of Shemot but also explains the number of firstborn sons in the first year of the desert and the lack of population growth of the people in the desert.