To comprehend the theme of Simchas Torah:לְהָבִין עִנְיַן שִׂמְחַת תּוֹרָה,
There is a well-known question:1 Why does the rejoicing (of Simchas Torah)וְיָדוּעַ הַדִּיּוּק בָּזֶה מַה שֶּׁאוֹפֶן הַשִּׂמְחָה (דְּשִׂמְחַת תּוֹרָה)
entail taking a Torah scroll while rolled and covered with its mantleהוּא שֶׁלּוֹקְחִים סֵפֶר תּוֹרָה כְּפִי שֶׁהִיא כְּרוּכָה וּמְכֻסָּה בְּמַפָּה
at which point, it is impossible to study it2
and dancing with it?וּמְרַקְּדִין עִמָּהּ.
Although the Torah is described with the verse,3 “It is your wisdom and your understanding,” the quintessence of intellectual development,דְּעִם הֱיוֹת שֶׁבַּתּוֹרָה כְּתִיב כִּי הִיא חָכְמַתְכֶם וּבִינַתְכֶם גו'
nevertheless, on Simchas Torah the manner in which this rejoicing is experienced is not through study and analytical thoughtמִכָּל מָקוֹם אוֹפֶן שִׂמְחָה זוֹ הוּא לֹא עַל יְדֵי לִמּוּד וְעִיּוּן
but through dancing.כִּי אִם עַל יְדֵי רִקּוּד דַּוְקָא.
Therefore, the rejoicing of Simchas Torah is experienced by all Jews,שֶׁלָּכֵן הַשִּׂמְחָה דְשִׂמְחַת תּוֹרָה הִיא אֵצֶל כָּל יִשְׂרָאֵל,
even the simplest of folk, who share no connection to matters of comprehension and understanding.גַּם אֵצֶל פְּשׁוּטִים בְּיוֹתֵר שֶׁאֵין שַׁיָּכִים לְהַשָּׂגָה וַהֲבָנָה
[Moreover, at the time of the rejoicing and dancing of the hakafos of Simchas Torah people who during the rest of the year evince no apparent connection to and identification with [matters] of Torah are also drawn in,[וִיתֵירָה מִזּוֹ, שֶׁבְּעֵת הַשִּׂמְחָה וְרִקּוּדִים דְּהַקָּפוֹת נִמְשָׁכִים (וֶוערְן צוּגֶעצוֹיגְן) גַּם כָּאֵלּוּ שֶׁבִּשְׁאָר יְמֵי הַשָּׁנָה אֵין נִכָּר הַקֶּשֶׁר וְהַהִתְאַחְדּוּת שֶׁלָּהֶם עִם [עִנְיְנֵי] הַתּוֹרָה,
as can be seen in actual fact.]כְּמוֹ שֶׁרוֹאִים בְּמוּחָשׁ].
This concept (that the rejoicing of Simchas Torah relates to every Jew)וְעִנְיָן זֶה (שֶׁהַשִּׂמְחָה דְשִׂמְחַת תּוֹרָה הִיא בְּכָל אֶחָד מִיִּשְׂרָאֵל)
is also expressed by their dancing with a Torah scroll – no one dances with a volume of Mishnayos or Gemara –מִתְבַּטֵּא גַּם בָּזֶה שֶׁמְּרַקְּדִין עִם סֵפֶר תּוֹרָה –
i.e., specifically the Written Law,תּוֹרָה שֶׁבִּכְתָב דַּוְקָא,
concerning which it is said that even one who does not understand what he is saying must nevertheless recite the blessings over Torah study before studying the Written Law.4 In contrast: “With regard to the Oral Law, if one does not understand its meaning, [his recitation of the words] is not considered study at all.”שֶׁאֲפִילוּ זֶה שֶׁלֹּא יָדַע מַאי קָאָמַר מְבָרֵךְ בִּרְכַּת הַתּוֹרָה כְּשֶׁקּוֹרֵא בַּתּוֹרָה שֶׁבִּכְתָב.
All Jews thus share a connection to the Written Law. On the other hand, there are those who on a conscious level do not relate to the Oral Law. This leads to a deeper point: When a connection is dependent on one’s understanding, it is the person’s mind that is involved, not his fundamental “I,” who he really is. A connection that is not dependent on understanding, by contrast, is capable of touching his essential being.
Since the requirement to recite the blessings over Torah study is mandated by the Torah, which is the Torah of truth,וּמִכֵּיוָן שֶׁזֶּה מַה שֶּׁמְּבָרֵךְ בִּרְכַּת הַתּוֹרָה הוּא עַל פִּי צִוּוּי תּוֹרַת אֱמֶת,
it goes without saying that this reflects the true reality,הֲרֵי פָּשׁוּט שֶׁכֵּן הִיא הַמְּצִיאוּת,
that even a person who does not understand what he is saying when studying the Torah draws down G‑d’s infinite light –שֶׁגַּם זֶה שֶׁלֹּא יָדַע מַאי קָאָמַר מַמְשִׁיךְ אוֹר אֵין סוֹף
and indeed, His very Essence and Being (the Giver of the Torah) –וְעַד עַצְמוּת וּמַהוּת (נוֹתֵן הַתּוֹרָה)
into the Torah he studies.בְּהַתּוֹרָה שֶׁלּוֹמֵד.
The expression used is kore baTorah, “he reads the Torah.” The Hebrew word kore also means “call.” Reading the Torah is calling to G‑d – indeed, calling Him forth – and drawing down His essential light into the Torah.
There is another well-known question:5גַּם יָדוּעַ הַדִּיּוּק
Why is Simchas Torah celebrated on Shemini Atzeresלָמָּה עוֹשִׂין שִׂמְחַת תּוֹרָה בִּשְׁמִינִי עֲצֶרֶת
(and in the Diaspora, on the second day of Shemini Atzeres)?(וּבְחוּץ לָאָרֶץ בְּיוֹם-טוֹב שֵׁנִי דִּשְׁמִינִי עֲצֶרֶת),
It would seem that we should celebrate with the Torah on Shavuos, the festival of the Giving of the Torah.דְּלִכְאוֹרָה הָיָה צָרִיךְ לִהְיוֹת בְּחַג הַשָּׁבֻעוֹת זְמַן מַתַּן תּוֹרָתֵנוּ.

Summary

Many of the maamarim concerning Simchas Torah often focus on two concepts:
a) that the rejoicing of Simchas Torah entails celebrating with a Torah scroll while rolled up and covered with its mantle, and
b) the reason that Simchas Torah is celebrated on Shemini Atzeres and not on Shavuos, the festival of the Giving of the Torah.
To explain the first concept: The Torah is described as “your wisdom and your understanding.” Nevertheless, the manner in which this rejoicing is experienced is neither through study nor analytical thought, but specifically through dancing. Therefore, the rejoicing of Simchas Torah is experienced by all Jews, even those who are not at all able to comprehend and understand the Torah, and even those whose connection to the Torah is not apparent throughout the rest of the year.
For this reason, Simchas Torah is celebrated by dancing with a Torah scroll, i.e., the Written Law, for a Jew’s connection to the Written Law is not dependent on his understanding or knowledge.