RAV KOOK ON Bo Part 3: Two New Years - Nisan and Tishrei

The first mitzvah given to the Jewish people was to establish their own calendar. The Jewish calendar, based on the lunar cycle, starts with the month of Nisan in the spring, when the Israelites left Egypt. “This month will be for you the head month, the first of the months of the year.” (Ex. 12:2) There is, however, another start of the Jewish year — Rosh Hashanah, on the first of Tishrei in the fall. So when is the true New Year, Tishrei or Nisan? Also: why is the Jewish calendar based on the cycles of the moon, while the non-Jewish Gregorian calendar is based on the 365-day cycle of the sun?