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

"And he took cream and milk and the calf that he had prepared, and he placed [them] before them, and he was standing over them under the tree, and they ate" (Gen. 18:9)

Peshat (basic meaning):

Rashi: "and they ate". They appeared to be eating. From here we learn that a person should not deviate from custom.

Remez (hinted meaning):

Baal HaTurim: they ate" and then "they said to him". This is a hint to the Sages' words that one should not speak in the middle of a meal, lest the food descend into the trachea rather than the esophagus. (See Taanit 5b)

Terrestrial food has valuable spiritual elements

Derash (interpretive meaning):

Ohr HaChayim: Terrestrial food has valuable spiritual elements as we know from Proverbs (13:25) "a tzaddik eats to satisfy his soul." Abraham said to the angels that the reason they appeared like humans was so that they could eat his food, that the spiritual content of the food also assumed the forms of the physical world. The angels said that Abraham was correct, and so he should do as he said, to let them enjoy the spiritual content of the food.
Targum Yonatan: He set them before them, according to the way and conduct of the creatures of the world; and he served before them, and they sat under the tree; and it seemed to him as if they ate.
Maggid Mesharim: "A calf, soft and good" was intended to repair the aspect of din/judgment hinted at in "the young calf", and to lighten the severity of din.
He took "cream and milk" to hint at chesed/kindness to sweeten din/judgment.
"Under the tree" was to unite it with the Tree of Life which is tiferet.
Lubavitcher Rebbe: The Torah states that the angels ate the food which Abraham served to them, but Rashi above says "they appeared to be eating." If so, then Abraham did not do a mitzvah by feeding his guests since they were angels who did not need to eat and Abraham left the presence of the Shechina unnecessarily, how can we learn that "welcoming guests is greater than welcoming the Shechina" (Shabbat 127a) where no real guests were there, but rather angels?
But, as the Rebbe notes, in general with gemilut chasadim/acts of loving kindness, we focus on the result of the mitzvah such as the benefit to the guests in the food and drink received. However, with Hachnasat Orchim/hospitality, we rather focus not on the benefits received but rather on the good will demonstrated by the host, which Abraham showed in the highest degree possible. (Likutei Sichot 25:70)

Sod (esoteric, mystical meaning):

Do celestial angels eat?

Zohar 102: and they ate. " but do celestial angels eat? For the sake of Abraham's honor, so it seemed. Rabbi Elazar said: They did actually eat, because they are the "fire that consumes fire," and it is not as though. So they ate everything Abraham offered them, because from the perspective of Abraham [who represents chesed, it was perceptible that] they ate on a supernal level.

BeRahamim LeHayyim: "He took cream and milk and the calf...."
Hey, wait right here! I learned in Ba'al Teshuva 101 that there is a problem mixing milk and meat. Cream and Milk and then Calf? Did not Abraham observe all of the commandments before the Torah was given? What is going on here?

The Course Manual for Introduction to Kashrut says: Milk then meat, never meat then milk. Remember the Shavuot festival and the dairy frenzy, particularly with the complicated morning meal when we eat dairy first, then wait, then eat the meat to satisfy the mitzvah of eating meat during the Holidays. Guess what? Perhaps that is what Abraham was doing. The Torah tells us that he asked Sarah to make cakes, which some interpret as Matzot. If they are making Matzot, then this is Holiday time, and we must eat meat.

Tiferet is...the middle harmonizing bar

What is the reason for our uptightness about mixing? It is the Torah that tells us to not do so, three times in fact, if you didn't get it in the first two. Three always relates to tiferet, the synthesis of thesis and antithesis, the middle harmonizing bar. Jacob who redeemed Abraham/chesed from the right, and Isaac/gevura who came from on the left. Titen Emet LeJacob--"Give truth to Jacob." That's the truth mentioned above. Jacob stands as the vehicle for G‑d's attribute of tiferet/Harmony, related to the letter vav of G‑d's 4-letter Name of yud and hei and vav and hei.Vav's gemataria is 6, so is it surprising that between the red gevura of meat and the white chesed of milk we need a 6 hour = vav = tiferet period of time between eating?! (And for those traditions that require only 3 hours, well all 3's are tiferet, right?)

Note, though, we can go from white milk chesed directly to red meat gevura without such a break, as long as we take precautions like rinsing our mouth, changing the bread we used for dairy to fresh bread for meat, etc., although there are many communities that mandate an hour's wait as well. [See your laws of Shavuot morning meal for more]. Perhaps that is because we are following the "normal" progression of going from chesed/kindness to gevura/strictness by having meat after milk. When we do the reverse, namely from meat to milk, we need a "resistor", the letter vav which is shaped like a resistor, for the tiferet Harmonizer, and the 6 hours intermezzo.

Guess what we just did? Alchemy. That is right. We are being spiritually attuned to using physical substances to create a certain vibration here on the earth-plane. And that most likely was what our forefather Abraham was doing when he first brought cream and milk, and then the calf. No veal parmesan here. Guaranteed.

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