1) PEOPLE OF TRUSTWORTHINESS
QUESTION: Rav Katina teaches that even during the time of the fall of Yerushalayim and the destruction of the Beis ha'Mikdash, "men of trustworthiness did not cease [to exist]." The Gemara challenges this from a teaching of Rava, who says that the Beis ha'Mikdash was destroyed because there ceased to exist men of trustworthiness.
The Gemara concludes that with regard to business activities, there were no trustworthy people left in Yerushalayim. In Torah matters, though, there were still trustworthy people who could be believed when they said that they did not know Torah.
What is so noteworthy about the fact that people were proud to be honest and say that they did not know Torah?
ANSWER: HA'GAON RAV SHLOMO FISHER (author of SEFER BEIS YISHAI) explains the Gemara as follows (as heard from him in person). The SEFER HA'AKEIDAH and ABARBANEL explain that Hash-m gave the Jewish people a special blessing that "men of trustworthiness in Torah would not cease to exist." The essence of this blessing is Hash-m's promise that the Torah will never be forgotten (Devarim 31:21). In order for the Torah not to be forgotten, Hash-m blessed the people that when the elders do not know the Torah, they will admit it; this blessing prevents the forging and misconstruing of the Torah.
Rav Fisher adds that this approach may explain the choice of Tehilim 12 as the Psalm of the day for Shemini Atzeres (Simchas Torah). This Psalm does not seem to be related in any way to Shemini Atzeres or Simchas Torah. The Psalm reads, "Save us Hash-m, because... no one can be trusted anymore, everyone speaks falsely... the words of Hash-m are pure words, like finely refined silver. You, Hash-m, will protect them, You will preserve them from this generation forever."
RAV SAMSON REFAEL HIRSCH writes that there is a fine correlation between Pesach\Shavuos and Sukos\Shemini Atzeres. The first pair, Pesach and Shavuos, represents the "birth" of the nation and the Torah. The second pair, Sukos and Shemini Atzeres, represents the continuity of the nation and the Torah.
Accordingly, Tehilim 12 indeed is most appropriate for Shemini Atzeres. The subject of Tehilim 12 is the special blessing that men of trustworthiness in Torah will never cease. As explained above, this blessing safeguards the continuity of the Torah. Since Shemini Atzeres celebrates the continuity of the nation and the Torah, it is most appropriate to discuss on that day Hash-m's blessing that the Torah will be preserved through all of the generations: "No one can be trusted anymore, everyone speaks falsely... [but] the words of Hash-m (i.e. the Torah) are pure... You, Hash-m, will protect them, You will preserve them from this generation forever."

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2) AGADAH: WHAT NOT TO SAY WHEN ONE VISITS THE PARDES
QUESTION: Rebbi Akiva warned those who planned to enter the Pardes that when they see the "clear marble stones" they should not say, "Water! Water!" because "the speaker of falsehood shall not stand before My eyes" (Tehilim 101:7).
Although calling a marble stone "water" indeed is a falsehood, why is such a statement of falsehood so terrible? Why did Rebbi Akiva need to warn them specifically about this?
ANSWER: The Izhbitzer Rebbe, in MEI HA'SHILO'ACH (volume 1, Parshas Emor) and BEIS YAKOV (Ki Sisa 17), explains that Rebbi Akiva warned them not to say "Mayim" ("water") twice, lest they make a tragic error. Rebbi Akiva realized that those who visit the Pardes might misconstrue what they see and think that there is a division in authority over the upper and lower realms, represented by the "Mayim Elyonim" and "Mayim Tachtonim" (upper waters and lower waters). Saying "Mayim" twice implies that the upper and lower waters are separate and distinct from each other, which in turn implies that Hash-m is not directly involved with everything that happens in the realm of the Mayim Tachtonim. In reality, however, all realms -- upper and lower -- are connected and are under the sole authority of Hash-m.
When the Gemara says that Acher's tragic flaw was that "he cut the Neti'os (plantlings)," it means that he denied Hash-m's power and control over the lower worlds, the Tachtonim. (The Ge'onim, cited in OTZAR HA'GE'ONIM, write that his sin was the attribution of authority to two deities, one of good and one of bad.) Ben Zoma did not "cut off the Neti'os" as Acher did, but he nevertheless remained confused and uncertain about the extent of Hash-m's dominion. That is why Rebbi Yehoshua, when he heard Ben Zoma's comment that there is a three-Etzba separation between the upper waters and lower waters, said that Ben Zoma is "still on the outside," meaning that he still did not come to the realization that there is no more than a "hairsbreadth" ("k'Malei Nima") of space between the upper and lower waters.
Perhaps the "hairsbreadth" alludes to the Yetzer ha'Ra which is likened to a hair (Sukah 52a). That hairsbreadth, the Yetzer ha'Ra, is the only force which prevents the people from fully recognizing the connection and inseparability between the upper realm and the lower realm.
This approach may also conform with RASHI's explanation. According to Rashi, Rebbi Akiva warned them that when they see a floor of clear marble, they should not say, "It is water! How can I walk there?" That is, they should not mistakenly think that there is a moat around Hash-m's palace, so to speak, as though He is cut off from the rest of the world.
RABEINU CHANANEL explains that "clear marble stones" comprise the wall of the palace of the Shechinah. A person should not think that the material which surrounds the palace is made of water and serves to separate between the outside and inside of the palace. Rather, one should know that it is clear marble which serves only to give honor to Hash-m and not to separate the inside from the outside. The fact that the stone is clear and transparent shows that Hash-m is connected to everything in this world even when He is in His palace, so to speak, and He sees everything through the transparent walls of His palace.

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