Earlier today in a Borough Park Chabad Synagogue, Rabbi Yitzchak Reitport delivered an address which reached to the core of what the festival of Simchat Torah is all about.
Since Simchat Torah is about rejoicing and dancing with the Torah scrolls, he began with a question, "Why don't we celebrate this festival in late Spring on the anniversary of the day when God's revelation descended on Mount Sinai and He uttered the Ten Commandments?"
Rabbi Reitport continued by quoting well established Jewish tradition that after the Ten Commandments were uttered, Moses stayed up on the mountain another 40 days to receive the Tablets. He descended to the unfortunate incident of the golden calf and shattered the Tablets. Then he spent the next 40 days in prayer to reconcile God and the Jewish people. Next, he ascended for another 40 days to receive the second set of Tablets and descended with them on Yom Kippur (yes, that was our very first Yom Kippur).
Since Yom Kippur is a day of tremendous awe, lighthearted celebration is out of character. Our lighthearted celebration begins soon after Yom Kippur, with the festival of Succot, which culminates in Simchat Torah. So essentially, on Simchat Torah we celebrate the completion of the whole process of receiving the Ten Commandments.
There was a fundamental difference between the first and second set of Tablets. Had the golden calf not been built, reality would have been fundamentally different and we would have only needed the written Torah scroll for guidance, without the aid of an oral explanatory tradition. Hence, the first Tablets only came with the written part of our tradition.
The second Tablets came with both written Torah and an accompanying oral explanatory tradition. The nature of the oral explanatory tradition is that it requires a lot of mental effort; ponderous study, discussion and interpretation. Here the mind of flesh and soul meets the Divine Mind in sublime union.
Had we just had the first Tablets, we would have been missing out on the part of the Torah which lends itself to this special union with the Creator's Mind; as everything would have simply been clear procedure without any need to resort to ponderous efforts. So what we truly celebrate on Simchat Torah is that special union with the Divine Mind which only an oral explanatory tradition allows for.
Rabbi Reitport added that the sixth Lubavitcher Rebbe stated that the reason for why we recite the "Shecheyanu" blessing on Simchat Torah (a blessing normally reserved for new joyous events) is because of this special union with the Divine Mind which is renewed at this time of the year.