When the new moon first appears in the sky, that night (and the next
day) is *Rosh Chodesh* - the first day of the new month. If the new moon
appears on the thirtieth night (i.e. the night before the thirtieth day)
then the old month is twenty-nine days long. If the new moon appears on
the thirty-first night then the old month is thirty days long.

The *Chachamim* had remarkably accurate mathematical models to predict
precisely when the new moon was due to appear each month. The
*Chachamim* from the tribe of *Issaschar* were particularly renowned for
being experts in astronomy^{15}. However, the *Beit Din* decided what
day was *Rosh Chodesh* based on witnesses who actually saw the new moon
and came to to testify. Why then did the *Chachamim* need their
mathematical models?

There are at least 3 reasons.

Firstly, in our time we do not have a *Beit Din* that is qualified to
receive the testimony of witnesses. Therefore, we are forced to rely on
a fixed calendar that is calculated based on those mathematical models.
In fact, today we are still using the calendar that was calculated by
*Hillel* II about 1600 years ago.

Secondly, the *Beit Din* would test the witnesses by asking them various
questions^{16}. Through using the mathematical models the *Beit Din*
could calculate at what time the new moon would appear, where it would
be located in the sky and which way the crescent would be facing. By
asking each witness some basic questions about the moon’s appearance and
location the *Beit Din* could establish the veracity of the witness.

Thirdly, as the *Rambam* explains^{17}, the mathematical models were
used to ensure that the calendar remained in sync with the actual phase
of the moon. This is explained as follows. The phase of the moon is
slightly more than twenty-nine and a half days long. A calendar month
can only be twenty-nine or thirty days long. Slightly more than half of
all months should have thirty days and slightly less than half should
have twenty-nine days (thus averaging out to slightly more than
twenty-nine and a half days per month i.e. the length of the phase of
the moon).

If valid witnesses saw the new moon on the thirtieth night and they
testified in time, the *Beit Din* would declare that day to be *Rosh
Chodesh* and the old month would be a short month of twenty-nine days.
If witnesses did not turn up in a particular month, then that month
would automatically be a long month of thirty days. If witnesses did not
turn up for a number of consecutive months (eg if the moon was not
visible due to cloud coverage) then each of those months would by
default be thirty days long and after a short while the calendar would
no longer be synchronised with the phase of the moon. After a number of
months a new moon might eventually be sighted on the twenty-fifth or
twenty-sixth night of the month.

In order to avoid this outcome and to keep the calendar in sync with the
moon, the *Beit Din* would sometimes designate short months of
twenty-nine days even if witnesses did not turn up. This was done if the
new moon was not sighted for a number of months in a row. These short
months were inserted based on calculations using the mathematical models
to ensure that if the new moon was sighted on the next month it would
appear on the thirtieth or thirty-first night, but not earlier.

Given the accuracy of the mathematical models, it seems that the
question that we posed at the beginning of this article could be asked
the other way around. That is, instead of asking why the *Beit Din*
needed the mathematical models, a better question might be - why was the
*Beit Din* required to rely on witnesses who took the trouble of
travelling to to testify? The journey could be dangerous^{18} and
witnesses were even given permission to desecrate *Shabbat* in order to
testify. Why couldn’t the *Beit Din* simply rely on their mathematical
models to determine when *Rosh Chodesh* should be?

As was noted in the previous article*,* sanctifying the new moon allows
the Jewish people to have a part in determining what day *Yom Tov* will
be. We are literally partners with *Hashem* in bringing *kedushah* to
the world. When the witnesses embarked on the journey to to testify they
were actively participating in this partnership. Perhaps the lesson that
we can learn is the importance of actions. *Hashem* wants us to be
actively involved in carrying out His work in this world.

^{15} See *Rashi* to *Bereshit* 49:15

^{16} See *Mishnah* 6 of *Perek* 2

^{17} *Hilchot Kiddush HaChodesh* 18:5-9

^{18} As we see in *Mishnah* 9 of *Perek* 1

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