Beshallah 5778

D'var Torah | Exodus

The Torah reports (Exodus 12:37) that six hundred thousand adult males left Egypt after 430 years of slavery. However, the Torah enumerates only four generations covering that same period of time, namely, Jacob to Levi, Levi to Kohat, Kohat to Amram, and Amram to Moses. Reconciling these tow facts led RaShI, for example, to conclude that only 210 of the 430 years are to be counted from the time of Jacob’s arrival in Egypt until the Exodus (Commentary on Exodus 12:40). The larger problem, however, is how a family of only seventy individual males could grow to a population so large in such a relatively short period of time. RaShI attempts to answer this question as well.


Based on an early Midrash (Tanhuma, Shemot 5), RaShI (on Exodus 1:7) suggests that each Israelite female gave birth to sextuplets! Without resorting to such a statistically dubious explanation, Professor David Faiman, a physicist at Ben Gurion University, applies the mathematics of exponential growth to solve the problem.


The simplest way of expressing mathematically how an undisturbed and unconstrained biological population increases is in terms of its “doubling time,” that is to say, the period of time over which a given population will double in numbers. In the case at hand, the initial population of seventy, over the course of 210 years and reaching a final figure of 600,000, would have to double every sixteen years. Hence, after sixteen years the population would be 140; after 32 years, 280; after 48 years, 560, and so on. For this to happen, and allowing for a high mortality rate, the females would need to give birth to a mere two males in each sixteen-year period.


Confirming this solution are the population statistics of the Druse village of Hurfeish in Israel’s Galilee. The Druse prohibit intermarriage and do not allow conversion so that the only growth in population is by internal growth. In 1948 the village population stood at approximately 700 to 800. By 1988, the population had grown to about 4000. These statistics yield the mathematical conclusion that the doubling time is between 15 to 17 years – almost the identical results derived from the Scriptural account. This supports the idea that the figures given in the Book of Exodus are realistic. While there may be reasons to question the veracity of the Biblical text, the seemingly extraordinary population growth of the Israelites is not one of them.








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