Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Friday, January 29, 2010

Twins, Mathematics and Widow

Unexpected Birth of Twins

by: Meoros HaDaf HaYomi

Our Mishna concerns a person who wants to distribute his estate before his demise. According to Rashbam (s.v. Haomer im), he could be healthy and just wants to grant his future child a certain portion through the offices of a third party or he could be moribund (shechiv mera) and not be expecting to witness his child’s birth, in which case we must obey his wish as it is a mitzvah to execute such a person’s orders. At any rate, the person in question commanded that if his wife bears a son, he gets a maneh (100 zuz) from the estate and if she bears a daughter, the daughter should receive 200 zuz. The Mishna then adds that if she bears “a male and a female,” the son gets a maneh and the daughter 200 zuz.

The Rosh assumes that the Mishna means that she bore twins (Responsa of the Rosh, Kelal 81:2). Rashbam disagrees (s.v. Hachi garsinan im zachar; see Maharsha) and explains that the Mishna merely means that the father expressed both eventualities, but does not discuss the birth of twins. The halachah was ruled according to the Rosh (Shulchan ‘Aruch, C.M. 253:27) and the poskim discuss more questions arising from the unexpected birth of twins.

A Question of Mathematics

About 700 years ago a person commanded just before his demise that if his wife bore a son, he should get two thirds of his estate while the rest should be given to his brothers – the child’s uncles, whereas if she bore a daughter, the daughter should receive one third with the rest going to his brothers. The widow bore twins, a son and a daughter, and the question arose as to how to apportion the estate. If we succeed in understanding the father’s intention, we must divide the estate into sevenths. The son gets four sevenths, the uncles two sevenths altogether and the daughter one seventh. The father, after all, apparently wanted to leave his son twice as much as the uncles – originally giving him two thirds as opposed to one third for the uncles – and the uncles twice as much as his daughter, originally giving her one third and the uncles two thirds. We have no choice, then, but to apportion one seventh to the daughter, two sevenths to the uncles and four sevenths to the son.

This hypothetical solution was suggested to the Rosh (ibid), who ordered the whole estate to be given to the son as the father made no mention of twins! The Rosh assumes that when the father commanded “if my wife bears a son [or daughter],” he meant only a son or only a daughter and the birth of twins therefore invalidates the father’s condition. The son inherits the entire estate as a daughter does not inherit if there is a son and the halachah was ruled accordingly (Shulchan ‘Aruch, ibid, 253:28).

Donating 18 rotel for Lag BaOmer

A certain childless person recently vowed that if his wife would bear a child, he would donate 18 rotel of wine or liquor to be distributed at the tomb of Rabbi Shimon bar Yochai in Meiron on Lag BaOmer. Such donations have long been customary as a segula to merit Heavenly favor and are meant to provide sustenance and merrymaking for the many thousands visiting the tomb on that day. A rotel, approximately three liters, was a common measure in the Ottoman era and persists among the descendants of families that settled in Eretz Yisroel centuries ago.

Within a year the person’s wife bore twins and some insisted that he must donate 36 rotel for the double kindness. In fact, however, he had only to give 18, as that was how much he vowed.

HALACHOS FROM THE DAF

Widow vs. Daughter

The Gemora discusses an aspect in the inheritance not mentioned in the Mishna - the widow. Where does she fit into all of this? Would it make a difference if there is a small amount of money or a large amount? Does the money that supports the widow detract from the sons’ portion?

The Shulchan Aruch (Even Ha'ezer Siman 93 Sief 4) has different opinions in a case where there is a widow and daughters, and there isn’t enough to support both the widow and the daughters. The Mechaber is of the opinion that the widow gets supported and the daughters go collecting and of course, the sons too (Bais Shmuel quoting Ran). However the Mechaber cites another opinion (Tosfos) that differentiates between cases where there is a widow and son or daughter, and cases where there is a widow and son and daughter. It is important to note that the widow getting supported is a takanah (rabbinical enactment), while inheritance is m’doiraisa (biblical commandment).

Widow and son or daughter: The child inherits the money and the widow and child support themselves with that. Even if the daughter would get married (and the money belongs to her husband) and even if the married daughter dies, the widow still gets supported from that money.

Widow and son and daughter: In a case of a small inheritance we learned in the previous Mishna that the daughters get supported and the sons go begging. That is a takanah for the daughters that they get supported and not the sons. Therefore in a case where there is not enough money to support both the sons and the daughters, and there is a widow involved, and her getting supported is also a takanah, the problem arises which takanah is stronger? The answer is - the widow’s. She alone gets supported until she collects her kesuvah.
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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?
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