We say in the Hagadah

אמר רבי אלעזר בן עזריה: הרי אני כבן שבעים שנה ולא זכיתי שתאמר יציאת מצרים בלילות, עד שדרשה בן זומא “למען תזכור את יום צאתך מארץ מצרים כל ימי חייך”: ימי חייך – הימים, כל ימי חייך – הלילות. וחכמים אומרים: ימי חייך – העולם הזה, כל ימי חייך – להביא לימות המשיח.

Rabbi Elazar ben Azariah said: Here I am like 70 years old, and I didn’t merit [having a proof] that the Exodus from Egypt must be spoken about at night. Until Ben Zomah expounded “So that you shall remember the day you went out of the Land of Egypt all the days of your life’. ‘The days of your life’ — would mean daytime, ‘All the days of your life’ — [adds] the nights.”
But the sages say: “The days of your life” — this world, “All the days of your life” — includes the messianic era.”

The topic under dispute is the nature of saying the last paragraph of Shema. According to Ben Zoma and R’ Elazar ben Azariah (REbA), the pasuq “… asher hotzeisi eskhem meiEretz Mitzrayim — Who took you out of the Land of Eqypt…” as a fulfillment of the biblical obligation to discuss the Exodus at night. According to the Chakhamim, the obligation is rabbinic.

I recently encountered a Yerushalmi that has a different dispute between REbA and the majority of the  Chakhamim that I think dovetails with this one. But, as the subject line says, it’s not on a topic appropriate for the seder table.

If after relations semen emits from the woman’s body (as is true for a man), the woman is temei’ah. In the days of the beis hamiqdash, when there are mitzvos that depend on her being tehorah, she would have to go to the miqvah. However, in order for this law to apply, the semen still has to be fresh (viable?), and therefore must be within three days of intimacy. This is deduced from the instructions given to the Jews at Mount Sinai: “וַיֹּאמֶר אֶל-הָעָם, הֱיוּ נְכֹנִים, לִשְׁלֹשֶׁת יָמִים;  אַל-תִּגְּשׁוּ אֶל-אִשָּׁה — [Moshe] said to the people, ‘Be prepared for the third day, do not [sexually] approach a woman.'” (Shemos 19:15) Thus implying that three days is sufficient to guarantee that no woman would be temei’ah (at least, not more so than tevul yom).

There is a four-way machloqes in the Yerushalmi (Shabbos 9:3, Vilna 59b) about how to define those three days; the result of two open questions:

1. When Moshe Rabbeinu said “third day”, is this because one needs three entire days, or is overlapping with part of the day sufficient?
2. What do we mean by “days”? Three daylight units of time, with the two nights between them, or 3 24-hour cycles? In other words, is the time specified 5 onos, i.e. 12-hour units, or 6?

There are tannaim with each combination of answers:

• Rabbi Yishmael says that the time must cover at least parts of 5 12-hour units. So, if they had relations just before sundown, that counts as the first onah, then the next two days are another 4 onos, and if she emits semen a few moments later it is during the 6th onah, and she is tehorah. Altogether the minimum amount of time is just over 2 days. However, if they had relations just after sunset, then the first onah is pretty much the entire night, and the emission might be toward the end of the 6th onah, meaning a total of just under 3 days.
• Rabbi Aqivah also holds that the relevant unit is the onah, not the day, but holds one needs 5 complete onos. Therefore, time limit is always 5 x 12 = 60 hours after they had relations. Regardless of the time of day of the relations or the emission.
• Rabbi Elazar ben Azariah holds that we need parts (not whole durations) of three 24-hour days (not 5 onos). Therefore, if they had relations shortly before nightfall that’s day one, then if a day passes beyond the next nightfall, that’s already part of the third day, and she would be tehorah. This is the most lenient opinion — the minimum is only just over 24 hours. The longest possible time would be just under 2 days.
• Last, the sages are quoted as holding that one needs three complete days, meaning 3 x 24 = or 72 hours.

Note that both R’ Elazar ben Azariah and the Chakhamim consider the day and the night to be a single unit. When we speak of yom, by default we mean 24 hours.

How do they differ? REbA holds that something happening even on the edge of that day is enough to characterize the day. The Chakhamim hold that it must last the entire duration of the day.

Perhaps we can say the following:

According to Rabbi Yishmael and Rabbi Aqiva, the question of whether or not there is a Torahitic obligation to discuss the Exodus at night wouldn’t even arise. The verse telling us to speak of the Exodus says “yom“, which by default is the daylight onah.

However, between R’ Elazar ben Azariah and the Sages,  the point of dispute is whether something happening for a moment during the day is sufficient to characterize the day, or if the thing must last the entire day. According to REbA, then, there are two ways of understanding this obligation. Either as an utterance, an obligation that happens to occur daily, or as an obligation to make each day about remembering the Exodus.  If the latter, he would say that one utterance a day is sufficient, since an event during the day is part of the entire day’s character. Therefore, he is excited to learn from Ben Zoma that the obligation is twice daily. A mitzvah that is twice daily is simply a mitzvah whose schedule is twice daily, and not about characterizing the day as a whole.

The Chakhamim, however, say the mitzvah is to characterize the entire day. The mitzvah is thus once daily.