A Mishnah that we studied a couple of days ago on page 53a described how the Cohen Gadol (High Priest) would sprinkle the blood of his sacrifice in Temple on Yom Kippur.
נִכְנַס לַמָּקוֹם שֶׁנִּכְנַס, וְעָמַד בַּמָּקוֹם שֶׁעָמַד, וְהִזָּה מִמֶּנּוּ אַחַת לְמַעְלָה וְשֶׁבַע לְמַטָּה
He entered into the place that he had previously entered, the Holy of Holies, and stood at the place where he had previously stood to offer the incense, between the staves. And he sprinkled from the blood, one time upward and seven times downward.
And then he would count to avoid any error:
וְכָךְ הָיָה מוֹנֶה: אַחַת, אַחַת וְאַחַת, אַחַת וּשְׁתַּיִם, אַחַת וְשָׁלֹשׁ, אַחַת וְאַרְבַּע, אַחַת וְחָמֵשׁ, אַחַת וְשֵׁשׁ, אַחַת וָשֶׁבַע. יָצָא וְהִנִּיחוֹ עַל כַּן הַזָּהָב שֶׁבַּהֵיכָל.
And this is how he would count as he sprinkled, to avoid error: One; one and one; one and two; one and three; one and four; one and five; one and six; one and seven. The High Priest then emerged from there and placed the bowl with the remaining blood on the golden pedestal in the Sanctuary.
Today’s page of Talmud comments on this interesting way of keeping track of the sprinklings:
יומא נה, א
תָּנוּ רַבָּנַן: אַחַת, אַחַת וְאַחַת, אַחַת וּשְׁתַּיִם, אַחַת וְשָׁלֹשׁ, אַחַת וְאַרְבַּע, אַחַת וְחָמֵשׁ, אַחַת וָשֵׁשׁ, אַחַת וָשֶׁבַע, דִּבְרֵי רַבִּי מֵאִיר. רַבִּי יְהוּדָה אוֹמֵר: אַחַת, אַחַת וְאַחַת, שְׁתַּיִם וְאַחַת, שָׁלֹשׁ וְאַחַת, אַרְבַּע וְאַחַת, חָמֵשׁ וְאַחַת, שֵׁשׁ וְאַחַת, שֶׁבַע וְאַחַת.
וְלָא פְּלִיגִי: מָר כִּי אַתְרֵיהּ וּמָר כִּי אַתְרֵיהּ
The Sages taught in a baraita that when sprinkling, the High Priest counted: One; one and one; one and two; one and three; one and four; one and five; one and six; one and seven. This is the statement of Rabbi Meir. Rabbi Yehuda says that he counted: One; one and one; two and one; three and one; four and one; five and one; six and one; seven and one.
The Gemara comments: They do not disagree about the matter itself that the High Priest sprinkles once upward and seven times downward. Rather, this Sage rules in accordance with the norm in his place, and this Sage rules in accordance with the norm in his place. In one place they counted the smaller number first, while in the other place they would count the larger number first.
WHo excels at math?
In a 1994 study of forty second-generation Chinese-American and 40 Caucasian-American preschoolers and kindergartners, the Chinese-American children outperformed Caucasian-American children on measures of mathematics, spatial relations, visual discrimination, numeral formation, and name writing. A 2011 study that explored cultural differences in young children’s early math competency prior to their school showed that Taiwanese children performed better than U.S., Peruvian, and Dutch children. More Taiwanese four-year-olds were able to count up to at least 21 when compared with children from the other three countries. There are more studies like these, but you get the idea. But why should some cultures be especially good at math? The answer, it appears, is in the language.
The Best language to learn math…is not english
From here.
It turns out that the way numbers are counted in different languages may make arithmetic easier - or harder. In a fascinating article in The Wall Street Journal, Sue Shellenbarger noted that Chinese, Japanese, Korean and Turkish use simpler number words and express math concepts more clearly than English. And this makes it easier for small children to learn counting and arithmetic. “The trouble starts at "11” she wrote:
English has a unique word for the number, while Chinese (as well as Japanese and Korean, among other languages) have words that can be translated as "ten-one"—spoken with the "ten" first. That makes it easier to understand the place value—the value of the position of each digit in a number—as well as making it clear that the number system is based on units of 10.
English number names over 10 don't as clearly label place value, and number words for the teens, such as 17, reverse the order of the ones and "teens," making it easy for children to confuse, say, 17 with 71, the research shows. When doing multi-digit addition and subtraction, children working with English number names have a harder time understanding that two-digit numbers are made up of tens and ones, making it more difficult to avoid errors.
These may seem like small issues, but the additional mental steps needed to solve problems cause more errors and drain working memory capacity…
This suggestion was supported by a more recent study that showed that among Chinese children language abilities were able to significantly predict both informal and formal math skills.
| Language | 17 | 27 |
|---|---|---|
| English | 'seventeen' | 'twenty-seven' |
| Chinese | 'ten-seven' | 'two-ten-seven' |
| Japanese | 'ten-seven' | 'two-ten-seven' |
| Turkish | 'ten-seven' | 'two-ten-seven' |
| Hebrew | 'seven-ten' | 'twenty-seven' |
Today’s discussion in the Talmud notes that there were different ways of counting the one “upward sprinkling” and the seven “downward” ones. Of course neither effected the way that numbers higher than eleven are counted in Hebrew, but it is a reminder that the order in which we count things plays a very significant role in how we might see the world. And how good we are at getting our sums right.
