Succah 12 - 18
Three is a … "Group"
How many does it take to form a group? Regarding the blood of the korban Pesach which Jews slaughtered on the threshold of their Exodus from Egypt, the Torah commanded: "Take a group of eizov (a kind of vegetable), dip it into the blood in the vessel, and apply it to the doorposts." (Shemos 12:20)
Eizov is also prescribed by the Torah (Bamidbar 19:18) for sprinkling the purifying waters upon people and objects spiritually contaminated by contact with the dead. In that context, the Torah does not use the word "group." Nevertheless, our Sages derive from the Torah that there, too, a group is required. (Sifri Parshas Chukas)
What is the definition of a group? This question has relevance to the laws of succah as well, since there is a rabbinic decree disqualifying a bunch of schach sticks tied together (for fear that someone may bring home such a bunch of wet, freshly cut sticks from the field, place them atop his succah to dry, and only later decide to leave them for the purpose of schach. Such a succah is invalid, as the schach must at the outset be placed for the purpose of shade.)
In regard to all of these areas, Rabbi Chisda states that three constitute a "group." This leads Tosefos to ask how we reconcile this definition of "group" with the one we find in Mesechta Avos (3:6). The mishna there tells us that when five people study Torah, the Divine Presence is with them. The source for this is the passage (Amos 9:6) "His grouping was the foundation of the earth." This seems to indicate that the minimum "group" is five. How, asks Tosefos, can Rabbi Chisda define a group as consisting of three?
Tosefos' resolution is that although in all other matters three is enough to form a group, the mishna in Avos understood that the "group" in the verse about Hashem's creation of the earth must refer to five. Why? Because in another verse (Yeshayahu 48:13) Hashem says, "My hands founded the earth." We must therefore conclude that the terms "group" and "hand" used in this context help define each other. A "hand" contains five fingers, and that number therefore constitutes a "group."
Tiferes Yisrael sees in the number five a hint to the fifth letter of the Hebrew alphabet, the letter hei, with which Hashem created the earth (Menachos 29b); the combination of five people learning the Torah for which the world was created brings that world into closer contact with its Creator.
The Slanted Wall
The "slanted wall" is one of those special laws of a succah which Moshe received at Sinai but which are not recorded in the Torah. Earlier in this mesechta (4a) we were introduced to this concept, but it is here that it appears in a mishna and this is its classical expression:
The roof of a one-room house has collapsed in the middle, leaving only a section adjoining the walls. The owner now wishes to convert this house into a succah by placing schach on the empty section of the roof. The only obstacle is that this schach will not reach the wall (or walls) necessary for making it a succah. The remnant of roof separating them is not kosher schach because it was initially put there for a house and not for a succah. If this remnant is less than four amos (cubits), we apply the principle of "dofen akumah" (slanted wall) to render the succah kosher. This principle allows us to view the roof remnant as being an extension of the wall, and therefore no non-kosher schach separates the wall from the kosher schach.
This principle requires greater clarification, however, in light of the first part of the mishna. There we are told about someone who places schach in a regular succah but leaves an airspace between that schach and the wall, or walls. The mishna tells us that if that airspace is less than three tefachim (handbreadths), then the succah is kosher. This too is based on one of those unwritten laws received by Moshe at Sinai. This principle is called "lavud," and it allows us to view as nonexistent any airspace which is less than three tefachim.
We now see a sharp distinction between removing the obstacle of non-kosher schach as a separation between kosher schach and wall, in which we allow up to four amos, and removing the obstacle of airspace, in which we allow only an eighth of that amount (six tefachim = one amah). Why do we not apply the principle of dofen akumah for up to four amos of airspace as well, by viewing the wall as having slanted laterally to reach the schach?
Rabbeinu Asher (Rosh) explains that dofen akumah does not allow us to view a wall as slanting to meet schach, for then indeed it would apply to airspace as well. Rather, it allows us only to view the remnant of the roof as a part of the wall which we imagine as slanted. Airspace, however, can never be considered as part of a wall, and therefore only "lavud," with its shorter dimensions, is applicable.