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‘Arachin and a Bar Mitzvah in Adar

May 25, 2015

On the subject of ‘Arachin, we should bring up the Jewish version of of the twins paradox. According to modern physics, it could be that one twin will age much slower than the other if he stays in an accelerated frame of reference for a significant amount of time, either by flying around space in a rocket ship, or by hanging out in a region of a strong gravitational pull. This has been proven many times through experimentation. There is a different paradox mentioned in Shulhan ‘Aruch with regards to turning bar mitzvah (Orah Hayim 55). Take two children, possibly twins, one born at the conclusion of the first Adar, and the other right at the begining of the second. Thirteen years later, there may only be one Adar, and thus the younger boy will become a man on the first of that Adar, whereas the elder will become a man at the end of that month. This seeming contradiction is so radical, it was never actually proposed by our sages. As the Beth Yosef points out, this is a ruling of the Agur, and it is based on two similar cases mentioned in Tractate ‘Arachin and codified in the Mishneh Torah.

On page 18b of ‘Arachin we find the following:

Our Rabbis taught: The year mentioned in connection with 1. consecrated animals, 2. the year stated in connection with houses in a walled city, 3. the two years in connection with the field of possession, 4. the six years of the Hebrew slave, 5. as well as those of a son or daughter [their ages with regard to ‘arachin], are to be understood as from me’eth l’eth[, exact increments of time]. 

As explained by Rashi and others, each of these subjects’ ages is determined by how old it actually is, as opposed to which calendar years it has experienced. Sometimes, the Torah considers something as being, for example, “two years” in duration if it spans parts of two calendar years, like a king who reigned some months both before and after Nisan is considered as having reigned two years. This teaches us that at least for these subjects, their ages are determined by how old they themselves are, and gain years every time the starting date (the birthday) rolls around each year. The state can have a law that all those born in 1999 should now be in 10th grade, but each individual will only be licensed to drive after his own birthday. School grade follows the calendar year of birth, but the license follows the actual age of the person. There are many other halachoth that use calendrical cut-off dates for determining something’s “year. ” The first chapter of Rosh Hashana describes, for example, how the first three years of fruit trees are determined by objective dates like 1 Tishrei and 15 Sh’vat.

The Gemara brings a proof for each of the five halachoth enumerated above:

How do we know that with regard to consecrated animals? — R’ Aha bar Jacob said: Scripture said, “A lamb of in its first year” means in ‘its own first year’, not that of the calendar. As to the year mentioned in connection with houses in a walled city, Scripture said: “Within a whole year  of its sale,” means in its own year of sale, not of the calendar[, does the original owner have the right to buy back the property]. With regard to the two years of the field of possession, it is written: According to the number of crop-years shall he sell unto you, implying that a man could potentially eat three crops in two years. [The sale takes into account the usual circumstances, but because it does not actually devolve on crops, it leaves open the potential for years with multiple crops.] With regard to the six years of a Hebrew slave, Scripture said: “Six years he shall serve, and in the seventh…” implying that at times he may still be at work during the seventh year [i.e. he goes free sometime in seventh year].

Now here is the section (ibid, 31b) that declares the paradoxical rule for determining when to observe the anniversary of a day in the next year’s only Adar with regards to selling and re-buying houses:

R’ Abba bar Memel said: If one sold two houses in a walled city, one on the fifteenth day of I Adar, and the other on the first day of II Adar, then as soon as the first day of Adar in the next year has arrived, the year is complete for the sale of the first day of II Adar, but for the sale of the fifteenth of I Adar the year does not become complete before the fifteenth of Adar in the next year.

R’ Abba also explicated a similar rule regarding certain consecrated animals: 

If two lambs were born to someone, one on the fifteenth of I Adar, and the other on the first of II Adar, then the one born on the first of II Adar has its year completed as soon as the first day of Adar of the next year has arrived, whereas for the one born on the fifteenth day of I Adar, the year is not complete before the fifteenth day of Adar in the next year.

Notice that the Gemara does not record that this surprising rule should apply to the other three halachic subjects mentioned above, including ‘arachin, which also depend on the person’s age. The Agur lived during the Renaissance; surely the question of how to calculate when someone born in the a leap year turns 20 in an ordinary year came up before hand, and we would expect R’ Abba’s paradoxical ruling to also apply to people’s ages. But it does not explicitly do so. Not only that, the Gemara continues with a discussion that implies that this paradoxical ruling should be strictly limited to house purchases and the age of consecrated animals:

For what purpose was that second [case] taught? Is it not identical with the first? — You might have said: There [the reason for the change] is that it is written: ‘a full [year]’, but here, in connection with which ‘full’ is not written, it does not apply; therefore we are informed that there is an inference from the analogous ‘year’,’year’ words mentioned in both scriptural sources.

That, it is a special teaching that this paradox applies to these cases, and because of its novelty, we could not just extend it to other cases.

There is also a good argument for not extending this paradox to the other halachoth: Rabbi Judah the Prince’s opinion. In the next line of the Gemara, he holds that for this case of the house in a walled city, we really should count the year in an objective manner that does not allow for paradoxes (ibid., 31b):

Our Rabbis taught: [It is written], ‘a full year’: Rabbi Says. He counts three hundred and sixty-five days according to the number of days in the solar year; but the Sages say: He counts twelve months from day to day, and if the year is intercalated it is intercalated to his advantage.

I would have thought that for the laws of redeeming a house in the first year and the age of consecrated animals, the Rabbis specifically followed the Hebrew calendar dates, allowing for R’ Abba’s paradox, but with regards to the other laws, they would agree with Rabbi Judah the Prince’s opinion, that we count years using an objective measure, one that does not allow for logical contradictions. The practical application: When we need to determine how old a person is with regard to his bar/bat mitzvah or ‘erech or the duration of a Hebrew’s indentured servitude, we look at his birthday or start of service according to the solar calendar. This would prevent any paradoxes in these cases.

I have had an interest in topics such as these. Yes, the ruling of the Agur has been around for 500 years, but what did they do the first few thousand years before that? The begining of an answer is that in the olden days, they did not place so much attention to when children came of age, and bar mitzvah’s were not celebrated the way they are now. Keep in mind that the halacha also maintains that one exhibit certain physical signs of maturity to achieve adulthood, and that unless a young man was both trying to undertake a public function and exhibited obvious signs of maturity, such as facial hair, they did not bother checking when exactly he turned bar mitzvah. All that they cared about was that the boy started keeping all his personal commandments, and this even started sometime before he was to turn thirteen. Like with regard to many other commandments, in the olden days they did not attempt to precisely define every moment in time. An important rule can also be derived from this case: sometimes, the fact that a question was not asked, or the fact that such an obvious answer was never suggested, might be the key to deciding between two opinions. This has ramifications, for example, with regard to keeping a second day of a festival within the land of Israel. 


From → halacha, logic, original

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