Daf Yomi Megillah: "From Chamtan to Teveria" as a Paradigm for Quantification or Lack Thereof of Halachic Shiurim

Whew!

A particular section of gemara Megillah caught my attention when I was learning through it for Rif Yomi, about how far away a village can be from a walled city to be considered part of it, so as to read the megillah on the 15th of Adar. Citing from Alfasi:

אמר ר' יהושע בן לוי כרך וכל הסמוך לו וכל הנראה עמו נידון ככרך וקורין בחמשה עשר ועד כמה אמר רבי ירמיה כמחמתן לטבריא והיינו מיל ולימא מיל הא קמ"ל דשיעורא דמיל כמחמתן לטבריא:

Rabbi Yehoshua ben Levi said: A large city, all that neighbors it, and all that is seen with it {from a distance} is judged to be the large city and reads on the 15th {if it is a walled city from the time of Yehoshua bin Nun}.
And until how far?
Rabbi Yirmeya said: As from Chamtan to Teveria, and this is a mil.
So let him have said a mil?!
This informs us that the measure of a mil is as from Chamtan to Teveria.

There is a slight girsological difference between the Rif, cited above, and the text of the gemara:

דאמר רבי יהושע בן לוי כרך וכל הסמוך לו וכל הנראה עמו נידון ככרך
עד כמה אמר רבי ירמיה ואיתימא רבי חייא בר אבא כמחמתן לטבריא מיל
ולימא מיל
הא קא משמע לן דשיעורא דמיל כמה הוי כמחמתן לטבריא

There are a few slight differences, but the only one I find of possible interest is that Rif has כמחמתן לטבריא והיינו מיל while our gemara has כמחמתן לטבריא מיל.

This statement can be interpreted in one of a few possible ways. One way is:

"until how far?
Rabbi Yirmiyah said: the same as the {convenient measurement of} the distance between Chamtan and Teveria. And this happens to be a mil."

If so, the question of why mention Chamtan and Teveria is a nice one. If there is a definite exact shiur of one mil, why bother to mention the cities?

Another way is:

"until how far?
Rabbi Yirmiyah said: Well, speaking from experience, we know of one such kerach which reads megillah on the 15th, and that is Teveriah, and we know that Chamtan also reads on the 15th because of it's proximity to Teveriah, following the rule laid out by Rabbi Yehoshua ben Levi. And they are about a mil apart. So, while we don't have an exact upper limit, we know at the least that it extends to one mil."

Indeed, we find out a bit later in the gemara that Teveriah was considered a kerach even though it was not a walled city, because of its natural defenses, and so they did read the megillah on the 15th. And applying Rabbi Yehoshua ben Levi's statement, they did so in Chamtan as well.

If so, the setama digmara's question is a bit harder to understand. Why mention Chamtan and Teveriah? This is the basis for his estimation of a mil, so it is natural for Rabbi Yirmiyah to have mentioned it.

However, the setama's reaction is: OK, you gave me a hard number, a concrete measure. Why bother to also give an example of two town's distance from another. Therefore, the setama understood it as still more definition of this hard number, this concrete measure. You might not know what a mil is, and so Rabbi Yirmiyah mentioned these two towns as a way of obtaining a hard number for this abstract concept of mil. That Teveriah happened to have read on the 15th is quite possibly beside the point.

This would then be a shift from an "organic" definition of this shiur to a more mathematical one. Or perhaps it is no shift at all, if we agree with the setama's interpretation of Rabbi Yirmiyahu's statement.

Indeed, Rabbi Yehoshua ben Levi's formulation was also somewhat organic, such that it is somewhat surprising that it worked out to be exactly one mil. He had stated

כרך וכל הסמוך לו וכל הנראה עמו נידון ככרך

which means that the walled city, and all that adjoins it, and all that it seen with it {say, from a distance} is judged like the walled city. How fortuitous that this worked out to be exactly one mil! I wonder, though -- how come Rabbi Yehoshua ben Levi did not simply say "one mil?!"

Rather, I believe this represents the paradigm shift mentioned above, from a natural definition to a concrete mathematical one. The natural definition could well be that anything that surrounds the city or can be seen with it is conceptually, within people's minds, considered part of the city. And therefore the halachic status would apply to those areas as well. The mathematical one of specifically one mil seems somewhat arbitrary, motivated by a desire to scientifically and systematically assign classifications, which would "ease" halachic determinations and thus actual practice. Similar to the way a kezayis was basically a kezayis, and everyone knew more or less what that was, whereas nowadays people measure matzah portions with a ruler or have books saying exactly how large of portion of each common food item constitutes a kezayis.

I found an interesting reference to this:

Chammath חמת In Talmud Babli, Megillah, 6a, it says, that Chammath is the same with Chamtan; and ibid. fol. 2 b, it says, "From Chamtan to Tiberias there is a distance of 1 mill." I presume this to be identical with the Emaus of Josephus, and that its situation was near the present hot spring of Tiberias; for although it is more than a mill from Tiberias, it must be observed that this is now situated farther to the north than it was in the time of the Talmud. I farther believe that Chammath is identical with the Levitical town of Naphtali חמת דאר Chammath Dor, literally "the hot springs from fire," (דאור=דאר*) in reference to the hot springs found there, of Joshua 21:32. In I Chron. 6:61, it is called: Chammon.

* This would require a Chaldee construction, in which the Daleth is the preposition "of the."—Translator.

I wonder if that town's location in Talmudic times is known with any precision, which would help with all this. I would guess (and this is just a guess) that the town was not exactly 1 mil away to the cubit and handbreadth, that it was a bit more or a bit less, and that would be acceptable. Perhaps it was exactly on mil. But if not, the alternative would be that this distance is definitional of a mil, and thus exactly this and no more would be considered part of the kerach for this purpose and perhaps for other halachic purposes as well. For example, 12 mil leInyan Shabbat.

Of course, all this is not halacha lemaaseh.