In this case, where the witnesses withhold testimony about what they saw and the New Moon is pushed off to the next day, it looks like a lie, as the moon might have been seen by others as well, and people will wonder why the New Moon was not sanctified the previous day. In that case, where the witnesses testify about something that they did not see and the New Moon is a day early, it does not look like a lie, as everybody knows that it is possible that only a few people saw the new moon.

§ Shmuel said: I am able to fix the calendar for the entire Diaspora without witnesses. Shmuel was an expert on the movement of the celestial bodies and on the principles governing leap years and additional days added to months.

Abba, the father of Rabbi Simlai, said to Shmuel: Does the Master know the meaning of this statement, as it is taught in a baraita dealing with the secret of addition, which discusses calendric calculations: Differentiate between when the molad occurred before midday and when the molad occurred after midday? He said to him: No, I do not know what this means. He said to him: Since the Master does not know this, there are probably other matters that the Master does not know, and therefore you must not establish a calendar, relying upon calculations that were made based on faulty or insufficient knowledge.

As for the meaning of this obscure baraita, when Rabbi Zeira went up from Babylonia to Eretz Yisrael, he sent back a letter to his colleagues in Babylonia: In order for a day to be sanctified as the New Moon, it is necessary that both the night and the day be of the new month. That is to say, the molad must occur before the beginning of the night.

And this is what Abba, the father of Rabbi Simlai, said: The baraita means as follows: They calculate the molad; if the molad occurred before midday, so that there are at least six more hours left of the day, it is known that the moon will be visible close to sunset. If, however, the molad did not occur before midday, so that there are fewer than six hours left of the day, it is known that the moon will not be visible close to sunset.

The Gemara asks: What is the practical difference that this statement makes? In any case, the court is dependent upon the testimony of witnesses. Rav Ashi said: This information is used to refute the witnesses, as if the witnesses claim that they saw the new moon at a time when it was not visible according to the calculations, they are clearly false witnesses.

Rabbi Zeira said that Rav Naḥman said: For twenty-four hours the moon is covered, i.e., not visible. This occurs between the last sighting of the old moon and the first sighting of the new moon. For us, in Babylonia, it is not visible for six hours of the old moon and eighteen hours of the new; for them, in Eretz Yisrael, it is not visible for six hours of the new moon and eighteen hours of the old.

The Gemara asks: What is the practical difference that this statement makes? Rav Ashi said: It is used to refute the witnesses, as if they testify that they saw two moons, the old and the new, within a single twenty-four hour period, they are certainly false witnesses.

§ The Master said above: In order for a day to be sanctified as the New Moon, it is necessary that both the night and the day be of the new moon. The Gemara asks: From where do we derive this? Rabbi Yoḥanan said: The verse states: “From evening to evening shall you celebrate your Shabbat” (Leviticus 23:32). This teaches that the day follows the night for all the calculations pertaining to the Festivals and New Moons.

Reish Lakish said: It is derived from the verse that states: “In the first month, on the fourteenth day of the month at the evening, you shall eat unleavened bread, until the twenty-first day of the month at the evening” (Exodus 12:18). This teaches that the Festival terminates at the end of the day, and a new day begins in the evening.

The Gemara asks: What is the practical difference between these two derivations? Abaye said: There is no practical difference between them. The interpretation of the meaning of the verse is the difference between them.

Rava said: There is a practical difference between them with regard to the hours before midnight. According to Rabbi Yoḥanan, who derives the halakha from the verse: “From evening to evening,” the previous day ends at nightfall. Therefore, if the new moon was seen only at the beginning of the night of the thirtieth, the thirtieth is not sanctified as the New Moon. However, according to Reish Lakish, who derives the halakha from the verse with regard to Passover: “Until the twenty-first day of the month at the evening,” the moon may be sanctified if it was seen before midnight. Eating unleavened bread on Passover is an obligation only on the first night until midnight. After that time, it is optional. The verse states: “You shall eat unleavened bread, until the twenty-first day of the month at the evening,” implying that it is not obligatory but optional to eat unleavened bread. Since the optional time of eating unleavened bread begins at midnight, after the conclusion of the obligatory time, the conclusion of that time is also at midnight on the twenty-first day. This implies that there is a concept of a day beginning at midnight. Accordingly, if the new moon was seen at the beginning of the night of the thirtieth, the thirtieth can still be sanctified as the New Moon.

§ With regard to the extra Festival day that is observed in the Diaspora, Rabbi Zeira said that Rav Naḥman said: Any time that an extra Festival day is observed out of uncertainty with regard to the calendar, we cast it forward, i.e., it is observed on the following day and not on the preceding day. That is to say, owing to the uncertainty we observe Sukkot in the Diaspora on the fifteenth and the sixteenth of Tishrei, but not on the fourteenth.

The Gemara asks: But why not observe it also on the fourteenth, as perhaps both the month of Av and the month of Elul were made short? In that case, the day that is considered the fourteenth of Tishrei in the Diaspora would actually be the fifteenth of Tishrei, and therefore it should also be observed as Sukkot.