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Q&A: The Definition of Sekhakh

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This is an English translation (via GPT-5.4). Read the original Hebrew version.

The Definition of Sekhakh

Question

Rabbi Michi, hello.
The Talmud at the beginning of tractate Sukkah brings three reasons why the Sages disqualify a sukkah that is higher than 20 cubits.
One of the explanations is that in a sukkah over 20 cubits, the shade comes from the walls and not from the sekhakh. My question is: during the day there are times when the sun is above the sekhakh {when it is on the southern side}, and then most of the shade comes from the sekhakh and not from the walls, so in that case the height of the walls should not really matter, and seemingly it should be possible to validate a sukkah over 20 cubits. On the other hand, there are times when the walls of the sukkah are under 20 cubits but the sun is in the east. In that case, one could say that most of the shade comes from the walls and not from the sekhakh. So what is the formula for defining sekhakh whose shade exceeds its sunlight?
With blessings and appreciation.  

Answer

A few comments.
1. This obviously depends on one’s location on the globe.
2. Obviously, we should not require that at every moment this be the source of the shade. We are talking here about a general, average assessment.
3. It is quite clear that these are supporting reasons, not generating reasons—that is, the Jewish law was already known, and the reasons came only afterward to support it. The proof is that all these explanations somehow arrive at exactly the same limit of 20 cubits (as with the Hanukkah lamp and an alleyway).
4. If there is shade from both the walls and the sekhakh, that can still be fine. You can see this in the Talmud itself (“remove Ishtarot Karnayim”), and from Rav Huna’s practical difference in the name of Rav regarding a large sukkah. 
5. It seems that Jewish law uses these criteria to define the orientation of a sukkah, but there is no requirement that the shade actually come from the sekhakh rather than the walls. In other words, the shade is a sign, not the reason. That is implied somewhat by Rav Huna’s practical difference in the name of Rav regarding a large sukkah (more than 4 cubits), since in such a sukkah there is still wall-shade, but there is also sekhakh-shade, at least partially. Regarding the explanation of a temporary dwelling, the Talmud later says this explicitly (that it does not actually have to be temporary, and that this too is only a sign and not the reason).

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