Shmini Atzeres & Simchas Torah
In the musaf prayer of Shmini Atzeres we begin saying He causes the wind to blow and the rain to descend. This can be connected to the coming of Moshiach:
The phrase, He causes the wind (ruach) to blow, uses the same word as the verse, The spirit (ruach) of G‑d hovered on the surface of the waters, and our sages say, This is the spirit of King Moshiach.
He causes the rain to descend means that the coming of Moshiach actually occurs, in physicality (gashmiyus related to geshem). Not only the spirit of Moshiach, but a soul in a body, i.e., Moshiach in the simple, literal sense in this physical world.
Moreover, geshem has the numerical value of 343, and this is connected to the prophecy that in the Messianic future, the light of the sun will be seven-fold as the light of the seven days. Rashi paraphrases this as seven sevens as the light of the seven days, i.e., 49 sevens, equaling 343.
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On Simchas Torah, all the gates are opened the portals of light, portals of blessing, portals of success. And all are taken by means of Torah.
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