Saturday, September 16, 2006

Daf Yomi - Sukkah 14/15 - Masters in Physics Required

The Rambam in Hilchos Sukkah (5:16) rules that if one's sukkah consists of precisely the same amount of S'chach which is valid and s'chach that is invalid, the sukkah is disqualified even if there is not any place that has three tefachim of invalid s'chach. The Rambam offers a reason for this by stating that we view the invalid s'chach as if it would be completely opened.

The Magid Mishna asks that the Rambam is seemingly in contradiction with his ruling in Hilchos Shabbos (16:16) regarding a wall that exactly half of the wall is solid and the other half is opened, it is regarded as a wall. This is because the Rambam rules in accordance with Rabbi Papa who maintains that a fifty percent wall is sufficient. This principle is known as 'porutz keomed' - if the porutz, the opening is precisely the same measurement as the omed, the standing (wall), it is considered a wall. Why does the Rambam rule by the s'chach that it is invalid?

The Magid Mishna answers based on a Gemora 22b which rules that if a sukkah consists of precisely fifty percent s'chach which is valid and the other half is left empty, the sukkah is disqualified. The reason given is because there will be more sunlight on the ground than shade. The Gemora explains that sunlight that shines through a hole on top which is the size of a small coin will spread to the size of a larger coin on the ground. Therefore, explains the Magid Mishna, the Rambam is viewing the invalid s'chach as if it would be completely opened and the valid s'chach is not producing even half the shade, therefore the sukkah is disqualified.

The mefarshim ask on the analogy of the Magid Mishna. The Ran explicitly states that the two cases are not comparable. When the entire sukkah is covered with s'chach, there is shade on the ground and consequently the sukkah should be valid for the kosher s'chach is producing fifty percent of the shade?

The Steipler explains the Magid Mishna with a mathematical demonstration. If a sukkah would have two hundred tefachim and there would be only one hundred tefachim of valid s'chach, it would produce ninety-nine tefachim of shade. The same would be obviously true if the sukkah was covered with one hundred tefachim of invalid s'chach. In our situation that the entire sukkah is covered with s'chach, however half of it is s'chach which is invalid, the remaining two tefachim that now has shade must be coming from a combination of the valid s'chach and the invalid s'chach. This would be considered as if there would be a mixture of valid s'chach with invalid s'chach, which the Rambam rules is invalid. Therefore, the Rambam is forced to disqualify this sukkah even though he maintains that a fifty percent covering is sufficient, here there is not enough shade being produced by the fifty percent valid s'chach.

It would seem to me that one can ask on the Steipler's logic. He assumes that one hundred tefachim s'chach produces ninety-nine tefachim of shade even in a case when there is no open areas and therefore he explains the remaining two tefachim (ninety-nine from the valid s'chach and ninety-nine from the invalid s'chach) as being produced from a mixture of the two s'chachs. Can't we say that one hundred tefachim of s'chach produces one hundred tefachim of shade except when there is one hundred tefachim of open area and there the sunlight overrides the shade and therefore in our case there is fifty percent shade coming from the valid s'chach and hence the sukkah should be valid?


kishnevi said...

One hundred tefachim of covering will produce one hundred tefachim of shade only when the sun is directly overhead (that is, at local physical noon); at any other time of the day, it will produce shade whose area would be mathematically computed. I don't have the formulas handy, but the basis would be a pyramid A, whose apex is the sun, whose base is the section of ground covered by the shade, and of which the sukkah roof is a cross section parallel to the base. The exact area covered by shade would be derived from the height of the sukkah, the height of the sun from the ground, and the angle of the sun's rays, which would provide the angle at which the pyramid deviates from the perpendicular at any given time of the day. The first two would of course be constant for every sukkah; the second would be constant but would need to be individually determined for each sukkah; the third would of course need to be determined from an astronomical ephermeris or almanac, and would change throughout the day.

Avromi said...

Firstly, yasherkoach - sounds good.

Secondly, Ritva wonders about this, because in the middle of the day, when the sun is directly above, the shade will be from the s’chach and not from the walls? Ritva offers two answers. One answer is that the sun is only directly above in the summer months when the sun travels in middle of the sky. In the month of Tishrei, however, when the sun is always to the side, there will be no shade from the s’chach even in the middle of the day. The second answer of the Ritva is that since in the middle of the day the walls do not provide shade, there will also not be any shade from the s’chach. The Aruch LaNer expresses his bewilderment to this answer, as the reality is that there is shade in the middle of the day. The Aruch LaNer offers a means of explaining the answer of the Ritva.

Thirdly, how do you explain the Steipler's extra two tefachim?