Wednesday, March 05, 2008

Parsha Points to Ponder #3 - Pekudei: Do the numbers add up?

Bust out your abacus, my friend 'cuz this week we get hit with a load of numbers early on. I thought it might be more worthwhile, instead of giving a math quiz, to speak about how we can understand these figures (can we?).

As all the Hulk Hogan-style Parsha-Maniacs know, all of Israel was to give a half-shekel donation to the building of the Mishkan, which provides us with a number...

בֶּקַע, לַגֻּלְגֹּלֶת, מַחֲצִית הַשֶּׁקֶל, בְּשֶׁקֶל הַקֹּדֶשׁ--לְכֹל הָעֹבֵר עַל-הַפְּקֻדִים, מִבֶּן עֶשְׂרִים שָׁנָה וָמַעְלָה, לְשֵׁשׁ-מֵאוֹת אֶלֶף וּשְׁלֹשֶׁת אֲלָפִים, וַחֲמֵשׁ מֵאוֹת וַחֲמִשִּׁים [Exodus 38:26]

TA-DA! 603,550 men aged 20 and up.If we assume an equal number of women that would equal 1,207,100 people aged 20 and up. So far this is all probably rehash for many of you, but...
There are other places where counts are given, as you may have guessed by now, that is the Book of Numbers (AKA Sefer Bamidbar). There we find this figure of 603,550 given again, but there is a count of a different kind given as well. The count of the first-born.

וַיְהִי כָל-בְּכוֹר זָכָר בְּמִסְפַּר שֵׁמֹת, מִבֶּן-חֹדֶשׁ וָמַעְלָה--לִפְקֻדֵיהֶם: שְׁנַיִם וְעֶשְׂרִים אֶלֶף, שְׁלֹשָׁה וְשִׁבְעִים וּמָאתָיִם [Numbers 3:43]

The number of first-born MALES is given as 22,273. Why is this noteworthy? If we (reasonably) assume that a first-born child has a 50% likelihood of being male, then there should be twice as many mothers because even with polygamous practices the first-born status for purposes of redemption went according to the mother as we have seen earlier.

קַדֶּשׁ-לִי כָל-בְּכוֹר פֶּטֶר כָּל-רֶחֶם, בִּבְנֵי יִשְׂרָאֵל--בָּאָדָם, וּבַבְּהֵמָה: לִי, הוּא [Exodus 13:2]

וְכָל-פֶּטֶר חֲמֹר תִּפְדֶּה בְשֶׂה, וְאִם-לֹא תִפְדֶּה וַעֲרַפְתּוֹ; וְכֹל בְּכוֹר אָדָם בְּבָנֶיךָ, תִּפְדֶּה [Exodus 13:13]

This gives us 44,546 mothers; now if we assume that there were approximately the same number of women as men (a reasonable assumption made even more so, since we know there were active attempts to curb the male population in Egypt; see Exodus 1:15-22) this would indicate that only 1 out of 14 women age 20 and up, approximately, were mothers!!! If that were the case it would seem to indicate a scenario where individual couples were siring something like 27 children. Even if that WERE the case, how could some be so fruitful while a seeming majority not at all??? Or was there really just a 96% probability that first-born Israelites would be female???