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מָאתַיִם עִזִּים צְרִיכוֹת עֶשְׂרִים תְּיָשִׁים, וְכֵן כֻּלָּם, הַזְּכָרִים כְּדֵי צֹרֶךְ הַנְּקֵבוֹת;
... לְפִי שֶׁהֵם פְּנוּיִים מִמְּלָאכָה דַּרְכָּם לְהַרְבּוֹת תַּשְׁמִישׁ וּלְעַבֵּר עֶשֶׂר נְקֵבוֹת, וּבְהֵמָה מִשֶּׁנִּתְעַבְּרָה אֵינָהּ מְקַבֶּלֶת זָכָר, וּפָרִים שֶׁעוֹסְקִין בִּמְלָאכָה, לֹא מָסַר לְזָכָר אֶלָּא אַרְבַּע נְקֵבוֹת, וְלַחֲמוֹר שֶׁהוֹלֵךְ בְּדֶרֶךְ רְחוֹקָה שְׁתֵּי נְקֵבוֹת לְזָכָר, וְלַגְּמַלִּים שֶׁהוֹלְכִים דֶּרֶךְ יוֹתֵר רְחוֹקָה נְקֵבָה אַחַת לְזָכָר:

Two hundred she-goats have need of twenty he-goats, and so too in the case of all the various species, the males were in number according to the need of the females. ... ten she-goats were given to each he-goat, and so [too] to each ram; [as] since they are free from work, their way is to be frequently involved in sexual relations and to impregnate ten females - and once an animal becomes pregnant, it does not accept a male. And [concerning] the bulls that engage in work, it only gave four females to the male; and to the donkey who goes on long journeys, [it gave] two females to the male, and to the camels that go on [even] longer journeys, [it gave] one female to the male. (Gen 32.15)

IMHO, if only one mating is needed to impregnate a female, one male is sufficient for any number of females, given enough time, but nobody mentions the עונה requirement for the animals (like once every x days). Also, I don't know of any empirical support that working animals (bulls) have lesser mating patterns than non-working (rams).

What is Rashi's logic here?

  • Didn't you answer your own question here? "one male is sufficient for any number of females, given enough time" - Some don't have the time, they work in the field\go on a journey. – Alaychem goes to Codidact Dec 15 '19 at 8:22
  • Even if animels have עונה, I don't think we must put considerations to this. – Alaychem goes to Codidact Dec 15 '19 at 8:25
  • Do you have a typo in the last word of your question? "Patterns", maybe? – Danny Schoemann Dec 15 '19 at 10:00
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The way this question framed, it is basically that Rashi says X, I think not X, so what is Rashi's logic. It may simply be that Rashi doesn't agree with your premise. (I am writing this not to be rude but because it seems like a common trend in the questions you pose, and this, by itself, might be the overarching answer.)

To the specifics. Firstly, Rashi begins by explicitly crediting Bereishit Rabba for the basic idea, although Rashi does expand upon it. Rashi fleshes out details and mentions animal work, parallel to human work. Bereishit Rabba states the following, and credits Rabbi Elazar with the idea:

וילן שם בלילה ההוא ויקח מן הבא בידו מנחה לעשו אחיו עזים מאתים ותישים עשרים אמר רבי אלעזר:

מכאן לעונה האמורה בתורה, הטיילים בכל יום, הפועלים שתים בשבת, הספנין אחת לששה חדשים.

עזים מאתים שהן צריכות תיישים עשרים.

רחלים מאתים שהן צריכות אילים עשרים.

גמלים מיניקות ובניהם שלושים ובנאיהם שלושים.

The idea is that the onah, required marital relations, differing for different human tradesmen, is here derived, or alluded to, in the Torah, from Yaakov's actions. How so, because we see that in Yaakov's gifts, he gave a different amount of males per female, because, from a practical - rather than halachic - perspective, this is the amount a breeder would match up, because of differing practical needs of the species.

This does not mean that there is a halachic requirement of onah by animals, as you are assuming. And I don't think Rashi or Rabbi Eleazar said otherwise.

You wrote:

IMHO, if only one mating is needed to impregnate a female, one male is sufficient for any number of females, given enough time

Yaakov was an extremely successful breeder, as we saw in the previous sidra regarding Lavan's sheep. Being a successful businessman, and multiplying your wealth, requires that you breed your animals in the most efficient manner possible, not to take one male animal to impregnate your sheep over several decades. In Vayeitzei, he worked with the striped rods not because of a sense of halachic obligation of onah for the poor female sheep, but to build wealth. So too here, the appropriate gift to Esav would be a sustainable one in which wealth could be built. That is pshat in Midrash Rabba and in Rashi, not what you are presuming and then asking about.

You further ask:

Also, I don't know of any empirical support that working animals (bulls) have lesser mating patterns than non-working (rams).

I don't know either, but this was presumably either the direct observation of Rabbi Eleazar or the assumption made based on a plain reading of the pesukim. Chazal often derive facts about nature from pesukim rather than citing scientific studies. They even have proofs from pesukim that the sun rises in the east and sets in the west, and of the direction from Eretz Yisrael to Bavel.

That you haven't seen empirical evidence to support this idea - well, firstly, have you seen empirical evidence that contradicts this idea? Without that empirical evidence, it isn't much of a question on Rashi. And even if such contrary empirical evidence exists, why would you assume that Rashi would be aware of said evidence, such that he would need to explain his logic? Perhaps he relied on the science stated by Chazal in Midrash Rabba, which he is surely entitled to do!

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  • I wish I could upvote this more than once. – N.T. Sep 11 at 19:12
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Note that the Rashi is separated by the pesukim.

Vayishlach 32:16

Thirty nursing camels with their young, forty cows and ten bulls, twenty she donkeys and ten he donkeys.

Rashi

Thirty nursing camels with their young: Heb. וּבְנֵיהֶם. And their young with them. According to the Midrash Aggadah, the word וּבְנֵיהֶם means בַּנָאֵיהֶם, their builders [those who impregnate them], a male corresponding to a female, but since it (the camel) is discreet in mating, Scripture did not publicize it (Gen. Rabbah 76:7).

According to other meforshim Vayishlach 31:16 this was the normal way of setting up a flock of the various animals so that the herds and flocks would be correctly handled. While one bull over a long period of time might be enough, this differentiation would allow Eisav to properly handle the animals.

Ibn Ezra explains that this showed that Yaakov was an expert herdsman on all of these animals. That is, he showed that he was sending a flock or herd of each animal with the appropriate mix of males and females.

עזים מאתים** – בצאן שם הנקבות עשר לזכר, ולפרים ארבע, ולעירים שנים, כי** ידע תולדותם, [שהיה רועה.]א

Two Hundred - With sheep there were 10 female for each male, for cows four, for donkeys two, because he knew how to breed them [that he was an expert herdsman].

The R'Y Bchor Shor says that the language used for camels does not differentiate between male and female. Thus, it says nursing camels to show the females and the young were the males.

גמלים מניקות – אין דרך העברי לתת חילוק בגמלים בין זכרים בין נקיבות ולומר גמלות ולא גמלה כמו בשאר בהמות,א כמו שאמר: ״עזים״ נקיבות, ״תיישים״ זכרים, וכן כולם. אבל בגמלים, אין העברי חולק. וכן בין הקטנים לגדולים, אלא שהקטן קורא בן גמל בתלמוד (בבלי חולין נ״ט.): וכנגדו ניכר בבן גמל. ולכך, גמלים מניקות – כלומר: נקיבות וראויות להניק.

ובניהם – כלומר: בחורים זכרים.

I have read other meforshim (this is from memory of some modern divrei Torah) that this actually refers to the fact that it was very difficult to breed camels in that part of the world. Thus, Yaakov sent nursing camels to show that he was such an expert that he could breed camels himself. This is similar to his sending the appropriate number of animals in each herd so that Eisav would be able to breed them properly.

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  • The question referred to Rashi. Talking about other meforshim is not really helpful. – N.T. Sep 11 at 12:04

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