For an explanation of the methodology of this series, see the introduction.

"You shall not plow with an ox and a donkey together." (Deut. 22:9)

Peshat (basic meaning):

Rashi: "You shall not plow with an ox and a donkey"
The same law applies to any two species in the world. [Similarly,] this law applies [also] to [merely] leading them together when they are bound to each other as a pair, for transporting any load.

...a righteous man should not enter into partnership with a wicked man.

Remez (hinted meaning):

Baal HaTurim: "You shall not plow with an ox and a donkey"
A non-kosher animal (donkey) with a kosher animal (ox). This alludes to the ethic that a righteous man should not enter into partnership with a wicked man.

Derash (interpretive meaning):

Tzeror HaMor: The Gentiles —especially the Romans — have been described as "donkeys" ever since Abraham, on the way of offering his son Isaac as an offering to G‑d, told his servants to remain at the bottom of the mountain together with the "donkey." (Gen. 22:5)

Ramban: Because it would lead to the further prohibition (in Levit. 19:19) of crossbreeding species, for the farmer will house the ox and donkey together and they will breed with each other.

Sod (esoteric, mystical meaning):

Zohar Kedoshim 86:
It is written, "but of the Tree of Knowledge of Good and Evil..." If Adam introduced death in this world for this matter, then how much more so is it for the one who exhibits an inappropriate act. An ox and donkey will prove this. On the side it is referred to as an ox; from that [Other] Side it is called donkey. Hence, the verse says, "You shall not plow with an ox and a donkey together." (Deut. 22:10) Do not mix them, because it causes the Other Side to assemble to cause evil in the world. He who parts them increases peace in the world. This is true here also for he who parts them in the said manner - as has been said, so that the crosswise (Shti va'Erev), the spun (tavuy) and the woven (nuz) do not come together, [thereby avoiding the prohibition of shatnez (ibid. 22:11)] - that person multiplies peace for himself and all the world.

Cain's sacrifice was flax, the sacrifice of Abel was wool. One sacrifice is not like the other. The secret of this matter is that Cain was a mixture, an inappropriate mix from the Other Side, not the species of Adam and Eve. And his sacrifice came from that side. Abel was of the same species as Adam and Eve. In the bowels of Eve were joined these two opposite aspects, and because they were joined together, no benefit came to the world, and they were lost.
Abel was of the same species as Adam and Eve.
Until this day, that aspect still exists. One who exhibits himself performing an act of joining this union awakens these sides together. He may get hurt and cause to hover over him an inappropriate spirit. Israel need to awaken upon them a saintly spirit in order to be holy, so that they will be in peace in this world and the World to Come.

BeRahamim LeHayyim:
We believe that some mixtures are dangerous: Nitro + Glycerin... Tylenol and Booze... Drinking and know what I mean. Those mixtures are problematic from a scientific perspective.

But once we start talking about mixing milk and meat, or Shatnez, the mixture of wool and linen, many start denying any problem, wishing it away as mere myth and old wives' tale.

Correction: the Torah is no old wives' tale!

One can see the humane reason in not making a donkey and an ox work together. The ox dribbles saliva in its food, which the donkey won't eat. Also the ox is much stronger, and will pull in a different manner, thus torturing the donkey.

The Zohar steps off however into the spiritual realities: both deal with negativity in some way. The ox is related to Esau, who was left of Isaac in a negative way.
The donkey is related to Ishmael, who was to the righ t of Abraham in a negative way.
The cures are found in Mashiach ben David...
The cures are found in Mashiach ben David, who will be a "poor man riding on a donkey", and Mashiach ben Yosef who will fulfill the verse [about Joseph], "his first born bullock, majesty is his".

Also, we are taught a reason why Cain and Abel could not dwell peacefully together as brothers: their offerings representing their characters were wool and flax, the mixture being unholy according to Levit. (19:19) and Deut. (22:10), the verse following the one quoted at the beginning.

We may not understand completely any ingrained nervousness we Jews may seem to have about Torah-forbidden mixtures, but that does not give us leave to wantonly abandon them. There are reasons way deeper beyond that given above, and the simple prohibition should give us great pause.

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