Mishnah Rosh Hashanah 1:1
There are four new years: The first of Nisan is the new year for kings and for festivals. The first of Elul is the new year for the tithe of beasts. Rabbi Elazar and Rabbi Shimon say: the first of Tishri. The first of Tishri is the new year for years, for shmita (sabbatical) and jubilee years, for planting and for [tithe of] vegetables. The first of Shevat is the new year for trees, according to the words of Bet Shammai. Bet Hillel says: on the fifteenth of that month.
(5) God called the light Day, and the darkness God called Night. And there was evening and there was morning, a first day.
(1) The LORD said to Moses and Aaron in the land of Egypt: (2) This month shall mark for you the beginning of the months; it shall be the first of the months of the year for you.
Seforno (16 Century Torah commentator in Italy) on Exodus 12:2:
from now on these months will be yours, to do with as you like. [you have My authority to organize your own calendar. Ed.] This is by way of contrast to the years when you were enslaved when you had no control over your time or timetable at all. While you were enslaved, your days, hours, minutes even, were always at the beck and call of your taskmasters.
Rabbi Joseph Soloveitchik, Halakhic Man
[In the matter of the calendar] the earthly court decrees, and the Holy One complies...man received the Torah from Sinai not as a simple recipient but as a creator of worlds, as a partner with the Almighty in the act of Creation.
(ב) בָּרִאשׁוֹנָה הָיוּ מַשִּׂיאִין מַשּׂוּאוֹת. מִשֶּׁקִּלְקְלוּ הַכּוּתִים, הִתְקִינוּ שֶׁיְּהוּ שְׁלוּחִין יוֹצְאִין:
(ג) כֵּיצַד הָיוּ מַשִּׂיאִין מַשּׂוּאוֹת, מְבִיאִין כְּלֻנְסָאוֹת שֶׁל אֶרֶז אֲרֻכִּין וְקָנִים וַעֲצֵי שֶׁמֶן וּנְעֹרֶת שֶׁל פִּשְׁתָּן וְכוֹרֵךְ בִּמְשִׁיחָה, וְעוֹלֶה לְרֹאשׁ הָהָר וּמַצִּית בָּהֶן אֶת הָאוּר, וּמוֹלִיךְ וּמֵבִיא וּמַעֲלֶה וּמוֹרִיד, עַד שֶׁהוּא רוֹאֶה אֶת חֲבֵרוֹ שֶׁהוּא עוֹשֶׂה כֵן בְּרֹאשׁ הָהָר הַשֵּׁנִי, וְכֵן בְּרֹאשׁ הָהָר הַשְּׁלִישִׁי:
(ד) וּמֵאַיִן הָיוּ מַשִּׂיאִין מַשּׂוּאוֹת, מֵהַר הַמִּשְׁחָה לְסַרְטְבָא, וּמִסַּרְטְבָא לִגְרוֹפִינָא, וּמִגְּרוֹפִינָא לְחַוְרָן, וּמֵחַוְרָן לְבֵית בִּלְתִּין, וּמִבֵּית בִּלְתִּין לֹא זָזוּ מִשָּׁם, אֶלָּא מוֹלִיךְ וּמֵבִיא וּמַעֲלֶה וּמוֹרִיד עַד שֶׁהָיָה רוֹאֶה כָל הַגּוֹלָה לְפָנָיו כִּמְדוּרַת הָאֵשׁ:
(2) Initially, after the court sanctified the new month they would light torches on the mountaintops, from one peak to another, to signal to the community in Babylonia that the month had been sanctified. After the Samaritans [Kutim] corrupted and ruined this method by lighting torches at the wrong times to confuse the Jews, the Sages instituted that messengers should go out to the Diaspora and inform them of the start of the month.
(3) ...And someone would then ascend to the top of the mountain and light the torch on fire with them, and wave it back and forth and up and down, until he would see his colleague doing likewise on the top of the second mountain. In this manner he would know that the next messenger had received the message and passed it on. And similarly, the second torchbearer would wait for a signal from the one on the top of the third mountain, and so on. In this manner the message would reach the Diaspora.
(4) ...The one who was appointed for this task would wave the torch back and forth and up and down, until he would see the entire Diaspora before him alight like one large bonfire, as they would light torches to continue transmitting the message from place to place all the way to the farthest reaches of the Diaspora.
