Many lists in davening come in sixes and sevens. A lot of my comments were based on seeing “6” as representing the six workdays, and “7” as the holy within this world, such as Shabbos. Or as the Maharal discusses, logically even before that six refers the six directions (up, down, right, left, forward, back), the surfaces of things and thus the mundane aspects of this world, and seven is the hidden internal of the object.

This explains the week. And Shemittah. Both are ways of finding the spiritual within this world.

As just one example we visited already, in Sim Shalom, we ask for 6 kinds of external peace — שָׁלוֹם, טוֹבָה, וּבְרָכָה, חֵן וָחֶסֶד וְרַחֲמִים. And the justification we give for asking this? “For You have already given us a תּוֹרַת חַיִּים, וְאַהֲבַת חֶסֶד, וּצְדָקָה וּבְרָכָה וְרַחֲמִים וְחַיִּים וְשָׁלוֹם — seven forms of internal peace: a Torah of Life, a Love of Chessed, Justice, Blessing, Compassion, Life and Peace. It is the bearers of internal harmony who can seek to express it externally.

But the miraculous isn’t really the normality of this world, or even the holiness inherent in it. Miracles of the sort of Yetzi’as Mitzrayim, crossing the Red Sea, the Revelation at Sinai, the Ananei haKavod, a traveling well, mon, all go well beyond this world’s order.

This creates a problem explaining the length of Pesach being only seven days. I invite answers.

But Sukkos + Shemini Atzeres, which combine as Zeman Simchaseinu, do fit. Sukkos itself is universalist. The sum of 70 cows brought in the Mussaf offering on 7 days of Sukkos are seen by Chazal as corresponding to the 70 nations of the world first created at Migdal Bavel. Similarly Zekhariah 7:16-19 (in the Haftara for the first day of Sukkos) says that every nation that rose up against Yerushalayim will come there to pray on Sukkos.

Then Hashem asks for one day, the eighth day, for just Him and the Jewish People. An Atzeres, a pause before return to normal life after a month of holidays.

Eight goes beyond this world, even the holiness of this world. It bridges to the world to come.* The role of the Jewish People as a Mamlekhas Kohanim, a Kingdom of Priests, is to help humanity reach this new plane, the “שָׁמַ֥יִם חֲדָשִׁ֖ים וָאָ֣רֶץ חֲדָשָׁ֑ה – new heavens and new earth” promised by Yeshaiah (65:17).

Similarly, this would explain the Beris Milah being on the eighth day (when safe to do so).

And, finally getting to the promised Tefillah Meaning, it explains the number of verbs in Yaaleh VeYavo:

יַעֲלֶה וְיָבֹא וְיַגִּיעַ וְיֵרָאֶה וְיֵרָצֶה וְיִשָּׁמַע וְיִפָּקֵד וְיִזָּכֵר…

May our memory and our recognition and…
(1) rise, (2) come, (3) reach, (4) appear, (5) be favored, (6) heard, (7) regarded and (8) remembered before You…

A prayer about miracles, about breaking this world’s natural order to set in motion a step toward the World to Come’s order breaks are norms of sixes and sevens. It talks of Hashem bringing us upward to the eighth.

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* Perhaps that’s why the letter as it appears in the Torah, Tefillin and Mezuzah is traditionally two zayins bridge together. Each 7 is a world, and the 8th letter bridges from one to the next. Although that hint isn’t in Ari-influenced scripts, which use a vav for the right leg, and only the left is a zayin.