Wednesday, December 22, 2010

Shifrah and Puah

Were Shifrah and Puah the only two midwives at the time of Pharaoh's decree? If not, why are only they mentioned?

Let us assume the Jewish people grew from 70 to 600000 males over the course of about 200 years. To make this biologically possible, you have to assume roughly constant (and large, of course) family size throughout the period, which means exponential growth.

Let us assume the midwives' refusal happened midway through the 200 years - that is, 100 years before the end. It must have been at least 80 years before the end, since Moshe was born after the decree was instituted.

By the laws of exponential growth, at that time there were sqrt(70*600000)=6481 Jewish males, and a roughly equal number of females.

Let us assume that each woman alive at that time had 10 kids in her lifespan. That means 64810 births. Assuming a lifespan of 40 years (it was the ancient world), and 365 days per year, it follows that on average 64810/40/365=4.4 births occurred each day.

Would two midwives be able to handle 4.4 births a day? With that birthrate, I think I'd prefer to have maybe 5 to 10 midwives. But as physicists say, the answer has the correct "order of magnitude". We made several big assumptions in this calculation, and nevertheless, the results are not far from what we expected. Anyway, if there was a moderate shortage of midwives, no wonder births often occured before the midwives managed to arrive (Shemot 1:19).

In conclusion, it's within the realm of possibility that there were only two midwives at the time.


bachrach44 said...

You can add to this the fact that not all births were likely to have had midwives (it was after all, the ancient world).

Beisrunner said...

Very good point...