The chagim of Tishei culminate with Shemini Atseres. Chazal enacted that we also celebrate Simchas Torah on this day by completing the annual cycle of reading the Torah. The commentaries ask why Chazal chose to coincide the completion of the Torah with Shemini Atseres in particular, as opposed to the other chagim. In order to explain this, it is first necessary to understand the essence of Shemini Atseres.
Chazal bring an analogy to explain the difference between Sukkos and Shemini Atseres. They compare Sukkos to a large feast, in which all the King's servants are invited. After the feast ends, the King invites his closest friend to join him for a small meal one last time. Similarly, on Sukkos we offer up 70 paros to Hashem on behalf of the 70 nations, whereas on Shemini Atseres we only bring one, on behalf of the Jewish nation to demonstrate our unique relationship with Hashem.. In giving these instructions, Hashem tells the Jewish people, "it is difficult for Me that you are separating from me, stay one more day." Shemini Atseres is that extra day dedicated purely to the relationship between Hashem and the Jewish people. Rav Chaim Friedlander zt"l asks a very strong question on this Chazal: The reason that Hashem makes this extra day of Shemini Atseres is because it is difficult for Him to separate from the Jewish people. How does this allay the pain of separation, all it achieves is to prolong the festivities for one more day, and then the separation will take place. Indeed this the extra day will likely make the ultimate parting even more painful.
In order to explain this, the Sifsei Chaim outlines the difference between Sukkos and Shemini Atseres. He brings the Sefer HaChinuch who tells us that Sukkos is a time of natural joy because it is when we gather in the produce and bring it into our homes. Hashem wants us to direct that joy to spirituality by providing us with numerous mitzvos, such as holding the arba minim (four species), and dwelling in a Sukkah. By engaging in physical actions dedicated to Hashem, we are supposed to direct our natural physical joy to connection to Him. However, on Shemini Atseres there is no mitzvo of arba minim or sukkah, because there is no need for all these 'tools' for bringing us close to Hashem, the connection is intrinsic. After the holy days of Rosh Hashana and Yom Kippur, and then the 7 days of Sukkos, a person is supposed to have brought himself so close to Hashem that there is no necessity for external tools in developing that connection. Accordingly, there is no need for extra mitzvos on Shemini Atseres. This helps understand how the extra day of Shemini Atseres allays the pain of Hashem's separation from the Jewish people. The Sifsei Chaim explains that the extra day without any external tools teaches us that there is in fact no separation at all. By spending that extra day alone with the Jewish people, Hashem shows us that we don't need the mitzvos of arba minim and sukkah on a permanent basis in order to have a relationship with Him, He is constantly involved in our lives and desires that we come close to Him.
There is one 'tool' that we do need to maintain that connection with Him - that of the Torah. Without the Torah it is impossible to build a relationship with Hashem. This is because the Torah is Hashem's means of communicating with us. Without the Torah, one can have no understanding of what Hashem wants from us, or how He views the world. We can now understand why Chazal saw fit to celebrate the completion of the Torah on Shemini Atseres. Shemini Atseres is the day that teaches us that there is never any separation from Hashem. We can permanently be connected to Him, but only through the means of the Torah. Accordingly, we express our joy at the Torah on this day, to remind us that by continuing to study it, we can maintain our closeness to Him through the long winter days.
We now understand the relevance of Torah to Shemini Atseres. However, one may ask why there is such an emphasis on expressing our joy through dancing with the Torah. Would it not make more sense to spend the entire day engrossed in the actual study of Torah? It seems that the emphasis on expressing our joy at the Torah teaches us a fundamental lesson about our relationship to Torah. It is of course, essential that a person learn Torah as much as possible, however it is also essential that he develop a sense of joy through his learning Torah. There would seem to be a lacking for a person who spends all his time learning Torah and never appreciating the actual Torah that he is learning. There are a number of reasons for this: One is that if a person doesn't truly enjoy his learning as a spiritually uplifting experience, then there is always the risk that other, more temporal pleasures may draw him away from his learning. It is well-known that young men who truly love learning Torah, are far less likely to be lured by the temptations of the secular world. A second reason for the importance of feeling joy at learning Torah is that a person's learning will be far more effective when he enjoys it.
A third, key reason for feeling the joy of learning Torah is demonstrated by the following story involving two Gedolim, Rav Chaim Ozer Grodzensky zt"l and Rav Elazar Shach zt"l. Rav Shach tragically lost his eldest daughter to illness when she was only 14 year of age. Soon after her death, Rav Shach went to visit Rav Chaim Ozer. Rav Chaim Ozer quoted to him a passuk from Tehillim, "Were your Torah not my delight, I would have perished in my affliction." Rav Chaim Ozer then told Rav Shach, "without Torah, there would be no meaning to my life." From that time on, Rav Chaim Ozer would repeat that verse every time he saw Rav Shach.
Many years later, Rav Shach offered an explanation of what Rav Chaim Ozer had said: He gave an analogy of two prisoners both sitting in jail in a state of utter humiliation, their heads shaved, wearing prison uniforms. However, despite their identical appearance, their is a difference between them. One smiles and says a friendly word to someone now and then, whereas the other is always grim and silent. The difference between the two prisoners is that one knows that his present situation is temporary, soon he'll be released and allowed to go home. The other has been sentenced to life imprisonment and so there is nothing for him to look forward to. In a similar way, two people can endure tragic situations and react in very different ways. One who has no Torah has nothing to hold on to, nothing to comfort him. Accordingly, he may well be unable to recover from such a blow. Rav Shach pointed out that this was, in fact the case with many people who were not connected to Torah and suffered tragedies. In contrast, one who has love of Torah, can cling to the realization that he can continue to learn and grow closer to Hashem through the Torah. This attachment to Torah, Rav Chaim Ozer was telling Rav Shach, can keep a person sane whilst enduring terrible pain. Thus, the joy of learning Torah enables a person has the vital benefit that it enables a person to withstand great suffering.
We have seen how Shemini Atseres is a day of great connection to Hashem, and that the Torah is the means to achieving this connection. It is essential that we bring this lesson with us into the long winter. One possible way of developing one's love of Torah is discovering which areas of Torah and styles of learning most appeal to him. Three Gedolim were once asked what was the correct way of learning. They all answered that there is no single 'correct' way', rather a person must find what his heart desires and learn in that way. This is because a person will not be able to thrive if he derives no enjoyment from his style of learning. It is instructive, with the advice of one's Rav, to find areas of Torah that he relates to.
Simchas Torah is a time of great joy at the gift of Torah. May we take this joy and apply it throughout the year.