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Ari Sacher
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‘Demographic Problem’ Parashat Bemidbar 5783

If you do the math, and factor in ancient infant mortality rates, the only reasonable explanation for the Israelites' exploding population is God
The census of the Israelites in the wilderness. (via Facebook)
The census of the Israelites in the wilderness. (via Facebook)

It would not be a mistake to say that the primary motif of the Portion of Bemidbar is “counting.” No fewer than three censuses are taken. First, all of the males, other than the Tribe of Levi, above the age of 20 are counted. Then all of the males in the Tribe of Levi older than one month are tallied. The last census taken is of the first-born males in all tribes other than the Tribe of Levi who are older than one month. Eventually, the holiness that was destined for the first-born is transferred to the Levites.

The Portion of Bemidbar is exceptionally laconic: numbers are followed by numbers, which are followed by more numbers. What could possibly be of interest? Counterintuitively, quite a bit. In an earlier essay[1], we noted a statistical anomaly that the populations of every single Tribe of Israel is divisible by the number 10 and all but one of them is divisible by 100. In another essay[2], we discussed the abnormally fast growth of family of Kehat, the son of Levi. In this essay, we encounter a demographic problem that has been staring me in the face for the past 59 years but I never slowed down enough to notice it.

The total number of Israelite males above the age of 20 is given as [Bemidbar 1:46] 603,550. Let us assume that the number of males between one month and 20 years of age is equal to at least half the number of males above the age of 20. Using this assumption, the total number of males greater than one month of age is somewhere around 1,000,000. The total number of first-born males over the age of one month is [Bemidbar 3:43] 22,273. Noting that each family must have a first born, the number of families must also have been equal to 22,273. Now, by dividing the total number of males by the total number of families, it can be shown that the size of the average family is sons. Adding women to the equation does not help us out: while the number of first-born is doubled, so is the total number of people, leaving the quotient unchanged. Does the Torah really expect us to believe that Jewish women were having 45 babies?

My wife, Dr. Tova Sacher, answers this question in the affirmative, suggesting that this could be a result of the miraculous growth experienced by the Jewish people in Egypt, as described by our sages. The Jewish nation that arrived in Egypt grew extraordinarily quickly [Shemot 1:7]: “The Children of Israel were fertile and prolific (va’yishretzu); they multiplied and increased very greatly so that the land was filled with them” Rashi[3] brings the Midrash Tanchuma that points out that the word “va’yishretzu” has the same root as “swarm,” suggesting that Jewish women gave birth like reptiles, having six children at one time. A woman would need to become pregnant only seven or eight times in order to bear 45 children.

The Ramban[4] takes another path, first proposing that the 22,273 first-born were born in the one year between the exodus and the date at which the census was taken[5], while the 600,000 were born in Egypt. The Ramban then rejects his own hypothesis out of hand, asserting that 22,273 first-born could not possibly have been born in only slightly more than one year. He concludes that the all of the first-born were born in Egypt, returning us to our demographic problem. Rabbi Elchanan Samet, who teaches in Yeshivat Har Etzion and Yeshivat Birkat Moshe in Maaleh Adumim, provides an in-depth analysis[6] of the explanation of the Ramban, and even brings a proof for the Ramban’s rejected hypothesis. Nevertheless, he does not explain how so many first-born males could be born in only 12 months.

A compelling explanation for our demographic problem was advanced by my son, Elyasaf. Elyasaf identifies a gaping hole in our logic. We have correctly assumed that each family must have one first-born child. We have incorrectly assumed that each family must have a first-born child who was still alive at the time of the census. We in the 21st century have become accustomed to an extremely low child mortality rate. Modern technology has eradicated most of the diseases that ravaged children in the past. Today’s child mortality rate in the United States for children under the age of 5 is slightly more than 5 per 1,000 births. This number is almost half of what it was (9.4) only 30 years ago. Turning back the clock even further to 1800, the child mortality rate in the United States was 462.9 deaths per 1,000 births. This means that for every thousand babies born in 1800, over 46% did not make it to their fifth birthday.

The child mortality rate in ancient Egypt is estimated to be about the same. An additional factor contributing to Jewish child mortality in Egypt was the mistreatment of the Jewish slaves by their Egyptian masters. This led to an increased mortality rate of mothers, which led to a corresponding increase in the mortality rate of their children, who were left to fend for themselves. Pharaoh’s instruction that [Shemot 1:22] “Every boy that is born you shall throw into the Nile” was another contributor to the high child mortality rate. Elyasaf’s explanation goes a long way in alleviating our demographic problem: While there might have been 22,273 surviving first-born children, there was a much greater number of families whose first-born children were dead and buried, leading to a much smaller average number of children per family. I must admit that my son’s answer was a great source of nachas (pride).

But the story does not end here. After proudly presenting my son’s explanation to a friend, he asked whether my son had studied at Yeshivat Birkat Moshe. When I answered in the affirmative, he smiled broadly. He told me that his two sons had also studied there and that they had also been bothered by our demographic problem. They consulted with their headmaster (rosh yeshiva), Rabbi Nahum Eliezer Rabinovitch, who gave them the exact same solution proposed by my son. Rabbi Rabinovitch added yet another layer, noting that women in ancient Egypt were married at a very early age. Their bodies were often too underdeveloped to carry their first child to term, resulting in an even higher child mortality rate for their first-born children. The fact that my son independently proposed the same solution proposed by his rosh yeshiva multiplied the nachas factor sevenfold.

The extremely high child mortality rate among Jewish slaves in Egypt begs a new question: Jacob went down to Egypt with a contingent of 70 people. At the exodus, 210 years later, this number had bloomed to more than 600,000 men over the age of 20. If we include women and children, it is safe to assume that the Jewish nation that left Egypt numbered about 2 million souls. Assuming that the child mortality rate was significantly higher than 50%, this means that with a 2023 North American child mortality rate, the Jewish people would have numbered more than 4 million. To go from 70 to 4 million — a factor of almost 60,000 — in only 210 years is unheard of. Compare this with the US, the population of which increased from 1800 to 2010 by less than a factor of 60. This returns us to the answer proposed earlier by my wife — that the explosive Jewish growth in Egypt could only have been the result of Divine Intervention. In the words of the Talmud [Eiruvin 13b]: “These and these are the words of the living G-d (Elu v’elu divrei E-lokim Chaim).”

Talk about family pride…

Ari Sacher, Moreshet, 5783

Please daven for a Refu’a Shelema for Yehuda ben Tzivia, Sheindel Devorah bat Rina, Geisha bat Sara, Hila bat Miriam, and Rina bat Hassida.

[1] Bemidbar 5761

[2] Vaera 5783

[3] Rabbi Shlomo Yitzchaki, known by his acronym “Rashi”, was the most eminent of the medieval commentators. He lived in northern France in the eleventh century.

[4] Rabbi Moshe ben Nachman, known by his acronym “Ramban”, lived in Spain and Israel in the thirteenth century.

[5] The exodus took place on the 15th of Nissan and the census was taken 12½ months later on the 1st of Iyyar.

[6] See https://etzion.org.il/en/tanakh/torah/sefer-bamidbar/parashat-naso/naso-census-leviim-and-number-firstborn

About the Author
Ari Sacher is a Rocket Scientist, and has worked in the design and development of missiles for over thirty years. He has briefed hundreds of US Congressmen on Israeli Missile Defense, including three briefings on Capitol Hill at the invitation of House Majority Leader. Ari is a highly requested speaker, enabling even the layman to understand the "rocket science". Ari has also been a scholar in residence in numerous synagogues in the USA, Canada, UK, South Africa, and Australia. He is a riveting speaker, using his experience in the defense industry to explain the Torah in a way that is simultaneously enlightening and entertaining. Ari came on aliya from the USA in 1982. He studied at Yeshivat Kerem B’Yavneh, and then spent seven years studying at the Technion. Since 2000 he has published a weekly parasha shiur that is read around the world. Ari lives in Moreshet in the Western Galil along with his wife and eight children.
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