Could the world have repopulated from 3 or 4 woman as is implied in the most literal way of reading the Noah’s ark story?

I got a confession to make: I started the calculations below with the assumption: “Genesis should in some places be read figuratively. Now what objective way can I proof that to other Christians? I know! I’ll show them how it is mathematically impossible for the earth to repopulate quickly enough after Noah!” Oops. When I finished the sums, the result did nothing to prove my stated objective. Here are my calculations:

Why these calculations will be inadequate:

a) Many believers hold that the flood in Genesis could be correctly understood as a local, instead of global flood. As such, it may not have been needed to repopulate the world from the few women on the ark.

b) The geneaologies of Genesis mentions very long life spans, and men who apparently still fathered children for a long part of those centuries. It don’t mention women’s ages in those geneaologies. It is very likely to assume, though, that if men in those times literally stayed reproductive for centuries, that women could have done the same. That means that each of them could have concieved many more children than in the calculations below.

c) Some Bible scholars also believe that the Hebrew word for “son” could also mean “grandson,” “great-grandson,” etc. In that case, the earth had even more generations to repopulate before the Tower of Babel or before Abraham encountered other nations.

However, here are calculations using my modern assumptions on how long woman can stay fertile, and assuming the fewest number of generations: These two assumptions are as strict as can be. If I assumed longer fertility times (argument b), or more generations (argument c), I would have made the job of proving the Genesis account a lot easier.

(It may seem strange to assume that a woman can have, on average, 3 or 3,5 daughters in a lifetime – thus 6 or 7 children. But in the times before birth control it was not rare for woman to have much larger families than that. One of my grandmothers married at 28, the other at age 30 – yet they each gave birth 6 times.)

The numbers below only represent the girls and women of the new generation. You could assume that there are still older woman too, and about as many men and boys as woman and girls.

SCENARIO 1: Each woman has, on average, 3 daughters who reach adulthood, and gets her girls on average at age 25

From the ark comes 3 woman of child-bearing age =3

25 years later: 3×3 young woman/ girls of next generation.

50 years later: 3x3x3

100 years later: 3 to the power of 5

200 years later: 3 to the power of 9 =19 683

350 years later: 3 to the power of 15 =14 348 907
500 years later: 3 to the power of 21= 10 460 353 203 (More young woman and girls than there are people in the world now.)

SCENARIO 2: Each woman has, on average, 3,5 daughters who reach adulthood, and get her girls on average at age 25 (Rounded off to whole numbers.)

From the ark comes 3 woman of child-bearing age =3

25 years later: 3×3,5 young woman/ girls of next generation =10 or 11

50 years later: 3×3,5×3,5 = 37

100 yr.: 3x(3,5 to the power of 4) =450

200 yr.: 3x(3,5 to the power of 8 ) =67 556

350 yr.: 3x(3,5 to the power of 14) =124 186 354

450 yr.: 3x(3,5 to the power of 18) =18 635 714 698
(More than double as many young woman and girls than there are people in the world now.)

The bible first mentions contact with other nations again, after the flood, at a time when Abram was older than 75 years. (Before that, it mentions nations in 2 ways: Mostly in the sense of “So-and-so was the forefather of this nation.” Secondly in the story “the tower of Babel,” an explanation why the one group split up into nations.)

Since the exact ages of Abraham’s forefathers are mentioned when they became fathers, it could be calculated that more than 367 years have expired from the ark until the date Abraham gets into contact with other nations. By either of my scenarios, there could have been more enough people on earth for different nations to exist.

The descendants of Noah could well have splattered into several large nations by the time Abram encounters other nations.

Conclusion: It is mathematically possible to believe that the earth could have repopulated from a 3 woman in a few centuries. It may not be necessary to assume that it happened (other options are mentioned in the “Why these calculations will be inadequate” paragraph), but it is possible.