Sukkah and Shemini Atzeres as outer and inner life

ח' ימי החג נותנים חיים לכל ימי השנה.

The eight days of the Chag (Sukkos, including Shemini Atzeres) give life to all the days of the year.

The festival of Sukkos, spanning eight days, is the wellspring of spiritual vitality for the entire coming year.

כי התפשטות החיות מר"ה הוא בחג וזה ניסוך המים.

For the spreading forth of the vitality from Rosh Hashanah occurs on the Chag, and this is [the meaning of] the nisuch hamayim (water libation).

The life-force granted at Rosh Hashanah flows out and is distributed on Sukkos. The pouring of water on the mizbeach symbolizes this outpouring of vitality.

וז' ימי סוכות הם חיי עולם הזה ולכך יש אחיזה גם לאומות וזהו ע' פרים.

And the seven days of Sukkos correspond to the life of this world, and therefore the nations too have a grasp [in them] — and this is [the meaning of] the seventy bulls.

The seven days of Sukkos relate to olam hazeh, the life of this world, in which the nations also have a share; hence the seventy bulls offered over the festival correspond to the seventy nations.

אבל שמיני עצרת הוא חיי עולם הבא.

But Shemini Atzeres is the life of olam haba (the World to Come).

The eighth day, Shemini Atzeres, stands apart, corresponding to the life of the World to Come.

והוא החיים המיוחד לישראל שהתורה עיקר חיינו.

And it is the life unique to Yisrael, for the Torah is the essence of our life.

Shemini Atzeres belongs exclusively to Bnei Yisrael, expressing that the Torah is our true life-source.

וזה עצרת כי התורה היא חיות הפנימיות רק שנתלבש במעשה בראשית.

And this is [the meaning of] "Atzeres" — for the Torah is the inner vitality, only that it became clothed within the works of creation (maaseh bereishis).

"Atzeres" connotes a gathering-in. The Torah is the innermost life-force, which is merely "garbed" within the physical world; on this day we gather back to that pure inner essence.

וחיי עוה"ז רק חיצוניות ולכך צריך הגנה וסוכה, שהיא העדות שהקב"ה מעיד עלינו כי עיקר חיינו התורה וחיי עוה"ב.

And the life of this world is only externality, and therefore it requires protection and a sukkah — which is the testimony that the Holy One testifies about us that the essence of our life is the Torah and the life of the World to Come.

Because olam hazeh is only the outer shell of life, it needs the protective shade of the sukkah. The sukkah serves as Hashem's testimony that, despite our involvement in this world, our true life is the Torah and olam haba.

וז"ש בזוה"ק שהיא צילא דמהמנותא כמש"ל.

And this is what is said in the holy Zohar, that it [the sukkah] is the "shade of emunah" (tzila di-mehemnusa), as explained above.

The Zohar calls the sukkah the "shade of faith" — its covering shelters and affirms our emunah that the Torah is the inner truth of our lives.

אבל שמ"ע שהוא ממש חיי עוה"ב כנ"ל לא צריך הגנה וצל הסוכה רק הוא בחי' סוכה ממש.

But Shemini Atzeres, which is literally the life of the World to Come, as above, does not require the protection and shade of the sukkah; rather, it is itself the aspect of "sukkah" in its very essence.

Since Shemini Atzeres is already the life of olam haba — pure inner light — it needs no protective covering. It has itself become the reality that the sukkah only points toward.

ואפשר זהו שארז"ל יתובי יתבינן אף שאין יושבין בסוכה נק' כך כנ"ל:

And perhaps this is what Chazal said: "We do sit [in the sukkah]" (Sukkah 47a) — that even though we do not [actually] sit in the sukkah [on Shemini Atzeres], it is still called thus, as above.

The Gemara's puzzling statement that "we do sit" on Shemini Atzeres, though we no longer dwell in the sukkah, can be understood this way: the day itself has become the inner reality of "sukkah," so one is in a sense still within it.

Summary: The eight days of Sukkos channel into the whole year the vitality granted at Rosh Hashanah (symbolized by the water libation). The seven days of Sukkos correspond to the life of olam hazeh — outer, physical life in which even the nations share (the seventy bulls) — and therefore require the protective "shade of emunah" of the sukkah, Hashem's testimony that our true life is the Torah. Shemini Atzeres, by contrast, is the life of olam haba, unique to Bnei Yisrael, the inner essence of Torah itself; needing no protective shade, it has become the reality of "sukkah" in its very essence — which is why Chazal can say that even then "we do sit."