THOUGHTS ON THE DAILY DAF
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Rosh Kollel: Rav Mordecai Kornfeld
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ERUVIN 11-15 - sponsored by a generous grant from an anonymous donor. Kollel Iyun Hadaf is indebted to him for his encouragement and support and prays that Hashem will repay him in kind.
1) VIEWING A CROOKED "KORAH" AS STRAIGHT
OPINIONS: The Tana Kama in the Mishnah (13b) says that a Korah must be
strong enough to hold a brick. Rebbi Yehudah argues and says that even if
the Korah is made of straw, we view it "as if it is metal."
2) THE VALUE OF "PI"
The Mishnah continues and says that if the Korah is bent, we view it "as if
it is straight," and if it is spherical (lengthwise), we view it "as if it
Is this last statement of the Mishnah a continuation of Rebbi Yehudah's
opinion? Or does the Tana Kama agree that "as if" can be applied in this
(a) The ROSH points out that the Gemara uses different phrases when it asks
questions on the statements in the Mishnah. First, when citing Rebbi
Yehudah's statement that if the Korah was made of straw we view it as if it
was made of metal, the Gemara asks, *Mai Ka'mashma Lan* ("What is this
statement teaching us" -- Rebbi Yehudah already said that the Korah does not
have to be strong). Then, when it cites the statement that if the Korah was
bent we view it as straight, the Gemara asks, *Peshita* ("That is obvious").
Later, when it mentions the third statement of the Mishnah that we view a
round Korah as if it were square, the Gemara asks *Ha Su Lamah Li* ("Why is
it necessary to mention this as well?")
HALACHAH: The SHULCHAN ARUCH 363:20 rules like the Rosh and the Rambam (a),
and applies the logic of "as if" to a bent or round Korah.
The Rosh explains that the first question addressed specifically the opinion
of Rebbi Yehudah. However, the second statement, that we view a bent Korah
as if it were straight, is "obvious" -- that is, it is even more logical to
apply the "as if" reasoning in this case. If so, the Tana Kama of Rebbi
Yehudah may ascribe to it as well. In fact, the Gemara concludes that the
Mishnah is teaching a Halachah that was also taught by Rebbi Zeira, and it
is logical to assume that Rebbi Zeira was explaining the Halachic opinion
(i.e. the Tana Kama rather than Rebbi Yehudah). When the Gemara discusses
the thrid statement of the Mishnah, that we view a round Korah as if it were
square, the Gemara asks *Ha Su Lamah Li* -- this Halachah is *identical* to
the previously mentioned one. That is, here too the Tana Kama applies the
logic of "as if." (This is the ruling of the RAMBAM, Hilchos Shabbos 17:26,
(b) RASHI in our Sugya (DH Peshita) explains that the logic of "as if"
applies *equally* to a bent Korah and to a weak Korah. It is Rebbi Yehudah,
then, who made both statements, and the Tana Kama *never* applies the logic
of "as if." (This is also the approach of Rav Yehonasan m'Lunil; see,
however, the Bach there.) The RITVA cites a Yerushalmi that seems to support
Rashi's interpretation of the Mishnah.
QUESTION: The Gemara says that the circumference of a circle is three times
greater than its diameter. How do we reconcile this Gemara with the known
fact that the ratio of the circumference of a circle to its diameter is
slightly more than three (Pi=3.14159...)?
(a) The TOSFOS HA'ROSH explains that the Gemara itself is addressing this
issue. Why does the Gemara ask "from where do we learn" that the
circumference of a circle is three times greater than the diameter? We do
not need a verse to teach us a mathematical fact! The Gemara must be asking
from where do we learn that we may use a slightly *inexact* value for
determining the circumference of a circle. The Gemara learns from the verse
that one may round off the relationship of the diameter of a circle to its
circumference for all Halachic purposes, and assume it to be three. This is
learned from the verse which describes the circumference of the Yam Shel
Shlomo as *three* times its diameter.
Similarly, the RAMBAM (Perush ha'Mishnayos; see also Hil. Tum'as Mes 12:7)
writes that Pi is actually an irrational number. "The exact relationship of
the diameter to its circumference cannot be known and it is not possible to
speak of it... and its actual value cannot be perceived." He writes that the
value which is commonly used in calculations is 3 1/7 (3.142857...). The
Tana'im of the Mishnah rounded this number and expressed it in terms of the
nearest whole integer (3).
(c) It has been said in the name of the Vilna Ga'on (and more reliably, in
the name of one Dr. Adler, a Jewish professor of mathematics in Germany)
that in the verse (Melachim I 7:23) that the Gemara cites, there is a Kri
and a Kesiv; a word is pronounced differently than it is spelled. The word
in the verse is written "v'Kaveh" (with a "Heh" at the end), but it is
pronounced "v'Kav (with no "Heh"). The Gematria (numerical value) of the
word "Kav" is 106, and the Gematria of the word "Kaveh" is 111. The ratio of
the K'siv (111) to the K'ri (106), or 111/106, is 1.0471698. This value is
an extremely close representation of the relationship of the real value for
pi to 3 (111/106 = 3.1415094/3).
Hence, the difference between the actual value of pi and its practical value
is expressed by the difference between the Kesiv (the actual, but unread
word) and the Kri (the word as we use it) of the verse discussing pi!
3) A "LECHI" PLACED THREE "TEFACHIM" AWAY FROM THE WALL OF THE "MAVOY"
OPINIONS: Rava says that a Lechi that was placed over three Tefachim away
from the wall is invalid, because "Gedi'in Bok'in Bo," young goats walk
though the area.
(a) TOSFOS (10b, DH v'Oseh) seems to explain that the Lechi is invalid when
distanced more than three Tefachim from the wall because the rule of Lavud
cannot be applied to it, and therefore the Lechi is not connected to the
The difference between these two reasons manifests itself in a case where a
wide Lechi (such as one that is four Tefachim wide) was placed a distance of
more than three Tefachim away from the wall, such that the distance between
it and the wall is less than the width of the Lechi itself. According to Rav
Yehonasan, the Lechi will be valid, because the airspace between the Lechi
and the wall is smaller than the Lechi. According to Tosfos, though, the
Lechi is invalid because Lavud cannot be applied. (Tosfos, ibid., indeed
says explicitly that such a Lechi will be invalid because of the problem of
(b) RAV YEHONASAN M'LUNIL explains that the Lechi is invalid because the
airspace on each side of the Lechi is larger than the Lechi, and therefore
the Lechi becomes Batel ("Asi Avira d'Hai Gisa u'd'Hai Gisa v'Ka Mevatel
The TEVU'OS SHOR brings proof from the Gemara here to the opinion of Tosfos.
Tosfos says that the Lechi that is far away from the wall is invalid because
Lavud cannot function to connect it to the wall. We see that Tosfos requires
the Lechi to be attached to the wall. Rav Yehonasan, on the other hand, does
not require the Lechi to be attached to the wall, and that is why he says
that the problem is that the airspace on each side of it invalidates it.
According to Rav Yehonasan, why does the Gemara say that the problem is that
young goats can walk through the space, thus making it unattached to the
wall? It does not have to be attached to the wall according to Rav
REBBI AKIVA EIGER answers that the reason of "Gedi'in Bok'in Bo" that the
Gemara gives is necessary to explain why *Raban Shimon ben Gamliel*
invalidates this Lechi. According to Raban Shimon ben Gamliel, Lavud (up to
*four* Tefachim) makes it as if there is no airspace between the Lechi and
the wall, and thus there is no airspace to annul the Lechi. Why, then, is
the Lechi invalid according to Raban Shimon ben Gamliel? Says the Gemara,
because young goats walk through that space and thus Lavud cannot work to
take away the airspace. Once Lavud is not applied, the reasoning that "air
on either side annuls it" can be applied to invalidate the Lechi.