What is the nature of the numeral "ashtei-asar" (11)?

Question

What is the nature of the numeral ashtei-asar (meaning 11) as in (BeMidbar 29:20, Parashat Pinchas):

וּבַיּוֹם הַשְּׁלִישִׁי פָּרִים עַשְׁתֵּי-עָשָׂר

• What is the basic word? Is this using semichus, as in ashtaim of asar? If so, what does that mean? (I was thinking of some sort of contraction with shtayim, but that would be feminine.)
• Why does the the Torah sometimes use ashtei-asar and other times achad-asar as in (Bereshit 37:9, Parashat Vayeshev)?

וְהִנֵּה הַשֶּׁמֶשׁ וְהַיָּרֵחַ וְאַחַד עָשָׂר כּוֹכָבִים, מִשְׁתַּחֲוִים לִי

• Does the basic word (i.e. עשתי) appear anywhere without the word asar (עשר) or esreh (עשרה)?

Answer 1

Ibn Ezra was not aware of the evidence from the Akkadian language, and therefore suggests what he suggests from a mixture of partial textual evidence and sevara.

As I discuss in this parshablog post (linked in another answer), it is from Akkadian ishteneshret, meaning eleven. And this from the Akkadian ishten + eshret, where ishten means 'one' (and there are examples of Akkadian usage of this) and eshret means ten. Ishten does not appear by itself in Tanach.

Had Ibn Ezra and Radak been aware of this, they would have said the same and retracted their explanations.

Answer 2

Radak cites an explanation that it's a contraction of על שתי, the number that is "on top of" two, i.e. one. However, he rejects this interpretation (as does Ibn Ezra, cited in msh210's answer). I have long wondered about the reason for the unique construction of this phrase.

A few minutes of searching got me to this document, which addresses the issue at length (pg. 7). Unfotunately I do not have the time to peruse it now, maybe someone else can summarize it here?

Answer 3

Regarding question 3 - The word Ashtei only appears with either עָשָׂר or עֶשְׂרֵה in Tanach.

Ashtei Asar or Ashtei Esrei appears 19 times in Tanach, Achad Asar appears 4 times in Tanach, Achas Esrei appears 10 times in Nach.

(Sanhedrin 29) By adding the Ayin in front of the Shtei it becomes 11 - this shows us that Kol Hamosif Goraya.

אמר חזקיה מניין שכל המוסיף גורע שנאמר (בראשית ג) אמר אלהים לא תאכלו ממנו ולא תגעו בו רב משרשיא אמר מהכא (שמות כה) אמתים וחצי ארכו רב אשי אמר (שמות כו) עשתי עשרה יריעות

Answer 4

Many thanks to a commenter at parshablog for pointing me to the ibn Ezra to Bamidbar 7:72, who writes (loose translation my own):

I've already written in Moznayim why this numeral is different: eshte is like eshtonosav, "the offspring of his thoughts", as if ten had sired: it's a big secret. Rabbi Yona, the Spaniard, explains it as al shte asar, the number it precedes, but he erred doubly: first, because twelve is al eleven (as we see from miben esrim shana vama'la), whereas he said the opposite, and, second, if it were al twelve, it should say ashne asar rather than ashte asar, as the latter is feminine. Rather, it's one word.

Answer 5

Going along the ibn Ezra's reasoning, eshtonotav means plots and schemes.

My understanding is that humans are usually pretty good at seeing groups of things and knowing how many, up to about ten. Beyond ten, we need to use more abstract reasoning. Note that Hebrew's ordinal numbers stop at ten:

shishi, shvii, shimini, t'shii, asiri, ha-achad asar, ha-shneim asar, ha-shlosha asar, ...

sixth, seventh, eighth, ninth, tenth, the-eleven, the-twelve, the-thirteen ...

Rabbi Emanuel Gettinger has suggested that the Torah says a mamzer may not marry into the Jewish mainstream, "not second generation, not third, not tenth" -- why stop at ten? Because it's the biggest ordinal number Hebrew has.

So putting this all together, ashtei asar may mean abstract away from ten.