Sunday, March 18, 2007

Math while listening to the parsha

While I was listening to the Torah reading I did some quick math in my head twice

The first instance was when the Torah was going over the donations, I was wondering how much is a ככר(kikar, talent) of precious metal? So first I thought, well maybe

כד כָּל-הַזָּהָב, הֶעָשׂוּי לַמְּלָאכָה, בְּכֹל, מְלֶאכֶת הַקֹּדֶשׁ--וַיְהִי זְהַב הַתְּנוּפָה, תֵּשַׁע וְעֶשְׂרִים כִּכָּר, וּשְׁבַע מֵאוֹת וּשְׁלֹשִׁים שֶׁקֶל, בְּשֶׁקֶל הַקֹּדֶשׁ. 24 All the gold that was used for the work in all the work of the sanctuary, even the gold of the offering, was twenty and nine talents, and seven hundred and thirty shekels, after the shekel of the sanctuary.

So first I thought: maybe its 1000 shekel. its more than 730. But then:

כו בֶּקַע, לַגֻּלְגֹּלֶת, מַחֲצִית הַשֶּׁקֶל, בְּשֶׁקֶל הַקֹּדֶשׁ--לְכֹל הָעֹבֵר עַל-הַפְּקֻדִים, מִבֶּן עֶשְׂרִים שָׁנָה וָמַעְלָה, לְשֵׁשׁ-מֵאוֹת אֶלֶף וּשְׁלֹשֶׁת אֲלָפִים, וַחֲמֵשׁ מֵאוֹת וַחֲמִשִּׁים. 26 a beka a head, that is, half a shekel, after the shekel of the sanctuary, for every one that passed over to them that are numbered, from twenty years old and upward, for six hundred thousand and three thousand and five hundred and fifty men.
כז וַיְהִי, מְאַת כִּכַּר הַכֶּסֶף, לָצֶקֶת אֵת אַדְנֵי הַקֹּדֶשׁ, וְאֵת אַדְנֵי הַפָּרֹכֶת: מְאַת אֲדָנִים לִמְאַת הַכִּכָּר, כִּכָּר לָאָדֶן. 27 And the hundred talents of silver were for casting the sockets of the sanctuary, and the sockets of the veil: a hundred sockets for the hundred talents, a talent for a socket.
כח וְאֶת-הָאֶלֶף וּשְׁבַע הַמֵּאוֹת, וַחֲמִשָּׁה וְשִׁבְעִים, עָשָׂה וָוִים, לָעַמּוּדִים; וְצִפָּה רָאשֵׁיהֶם, וְחִשַּׁק אֹתָם. 28 And of the thousand seven hundred seventy and five shekels he made hooks for the pillars, and overlaid their capitals, and made fillets for them.
Which reminds me of the nice drasha how all the people of Israel were equal and of utmost importance when it came to the very foundation of the משכן(tabernacle). Well turns out, not quite, they really only needed 100 talents so 1775 shekel was used for other things, still a nice drasha so I am sure there is a way to work this out nicely.
Anyway the math
603,550 people (men over 20 of the nation of Israel) give 0.5 shekel which makes 301,775 shekel. Subtract 1775 for the left overs and you are left with 300,000 shekel being equal to 100 talents, meaning one talent was 3,000 shekel. Hmm before I calculated it during the reading I thought it would be 2,000 shekel, I wonder why I thought that?

Then later we have the Golden Altar for the sacrifices of animals, I always think of it as very big and impressive, tall and imposing. Well, it couldn't be that big, it would have to be carried whole.

א וַיַּעַשׂ אֶת-מִזְבַּח הָעֹלָה, עֲצֵי שִׁטִּים: חָמֵשׁ אַמּוֹת אָרְכּוֹ וְחָמֵשׁ-אַמּוֹת רָחְבּוֹ, רָבוּעַ, וְשָׁלֹשׁ אַמּוֹת, קֹמָתוֹ. 1 And he made the altar of burnt-offering of acacia-wood: five cubits was the length thereof, and five cubits the breadth thereof, four-square, and three cubits the height thereof.
An אמה(bredth) is normally 5 tefachim(handbreadth) but for the משכ ן(tabernacle) it is 6. A handbreadth is taken to be between 8-10cm. So it is between
3 x 6 x 8cm = 1.44 meters (4'8") and 3 x 6 x 10 cm= 1.8 meters (5'11")

I guess I already knew that, but I just usually thought of it as bigger in my mind. Well if you didn't know, now you do

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