Erev Tov chevra,
Welcome to Rosh HaShana!
The first perek opens with some general thoughts about how years are marked. From there it moves on to the procedures through which testimony concerning the appearance of the new moon - which determines the declaration of Rosh Chodesh - was given.
(1) Mishnayot 1 and 2 remind us that fixing the beginning and end points of a year is a process that is both filled with endless possibilities and is also absolutely legally essential. While not a single one of the "rosh hashanas" that the Mishna defines is indicated in the Torah, it would be impossible to observe numerous Biblical commandments without the beginning and endpoints of a year being defined. The challenge the Mishna takes up is that of figuring which way of defining the beginning and end of a year is the most logical for the purposes of any given Mitzvah.
Also of interest of course, is the presumption (Mishna 2) that the year contains four points of judgment, also a presumption not found in the Torah. There is something to think about here in terms of how the rabbis are using the annual cycle of time time to construct at least this one aspect of our relationship with God. Of note, by the way, are the dissenting opinions cited in the Gemara: " R.Yossei says: A person is actually judged every day, as it is stated: “You visit him every morning” (Job 7:18) Rabbi Natan says: A person is judged every hour, as it is stated: “You try him every moment” (Job 7:18)
(2) Mishnayot 3 - 9 primarily discuss procedures around giving testimony regarding the new moon. Of particular interest is the way in which witnesses are not only permitted to, but are actually encouraged to violate Shabbat in order to deliver their testimony. Perhaps (?) it is less surprising that Shabbat was compromised in Temple times, as the witnesses' timely testimony was critical to the timely offering of the Rosh Chodesh Mussaf offering (end of Mishna 4 ), and Temple offerings routinely (every Shabbat!) overrode the restrictions of Shabbat. Somewhat more surprising is that the witnesses violated Shabbat for the sake of the farther-out communities knowing when to celebrate Yom Tov (beginning of Misnha 4), as the general rule of course is that Yom Tov yields to the restrictions of Shabbat (when the two coincide.) Clearly, the calculation here is not a technical Shabbat vs. Yom Tov one. It is rather about the uber-value of the calendar and its observances being a uniter of all Jews everywhere. Historically, one of the hallmarks of sectarian division is the establishment of competing calendars. Having everyone on the same calendrical page is a high religious value.
Just a final note: Rabban Gamliel's calculation in Mishna 7 comes up in discussions about whether doctors may drive back home after responding to a medical emergency on Shabbat. See for example https://medicalhalacha.org/2021/01/07/traveling-to-and-from-the-hospital-on-shabbos/
Our Mishna is not explicitly cited in this article, but the Halachik sentiment is.
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