The case of the square inside the circle

Eruvin 76 presents the geometry of a square inside a circle. The math seems badly wrong at the commentators’ first glance, leading to lots and lots of interpretation.

The Mishnah on Eruvin 76a says that for a window to possibly bridge two courtyards, it needs to be at least 4 by 4 tefahim and within 10 tefahim of the ground.

משנה. חלון שבין שתי חצירות, ארבעה על ארבעה בתוך עשרה - מערבין שנים. ואם רצו - מערבין אחד. פחות מארבעה על ארבעה, או למעלה מעשרה - מערבין שנים ואין מערבין אחד.

The Gemara then gives us the ruling of Rabbi Yohanan about a circular window:

אמר רבי יוחנן: חלון עגול צריך שיהא בהיקפו עשרים וארבעה טפחים, ושנים ומשהו מהן בתוך עשרה, שאם ירבענו נמצא משהו בתוך עשרה.

Rabbi Yohanan said: A circular window needs 24 tefahim in its circumference. And two plus a bit from those need to be within ten [tefahim from the ground], so that if you make a square, some of it will be within ten.

This is difficult to understand.

Nisht Shabbos geredt...

Today, Daf Yomi discusses appropriate conversation on Shabbat. The Gemara on 113a–b interprets the following verses from the end of Isaiah 58:

(יג) אִם תָּשִׁיב מִשַּׁבָּת רַגְלֶךָ עֲשׂוֹת חֲפָצֶיךָ בְּיוֹם קָדְשִׁי וְקָרָאתָ לַשַּׁבָּת עֹנֶג לִקְדוֹשׁ ה׳ מְכֻבָּד וְכִבַּדְתּוֹ מֵעֲשׂוֹת דְּרָכֶיךָ מִמְּצוֹא חֶפְצְךָ וְדַבֵּר דָּבָר:
(יד) אָז תִּתְעַנַּג עַל ה׳ וְהִרְכַּבְתִּיךָ עַל <במותי> בָּמֳתֵי אָרֶץ וְהַאֲכַלְתִּיךָ נַחֲלַת יַעֲקֹב אָבִיךָ כִּי פִּי ה׳ דִּבֵּר:

(13) If you restrain your foot on the Shabbat, and from doing business on My holy day; and you call the Shabbat a delight, and God's holy day honored; and you honor it from doing your own ways, seeking business, and speaking about things; (14) then you will feel delight in God, and I will have you ride upon the high places of the world, and I will feed you the portion of Jacob your father; for the mouth of God has spoken.

The Gemara learns something from each phrase in the second half of verse 13, including that “your speech on Shabbat should not be like your speech during the week.”

And now for something completely different

Today, Daf Yomi begins the ninth perek, Amar Rabbi Akiva. It's hard to see those words at the top of every daf without a voice in my head bursting into the song.

This is one of those perakim where the Mishnah goes off on a tangent. The first four mishnayot contain seven statements that all start with the same word, minnayin:

משנה א — אָמַר רַבִּי עֲקִיבָא, מִנַּיִן לַעֲבוֹדָה זָרָה שֶׁמְּטַמְּאָה בְמַשָּׂא כַּנִּדָּה. שֶׁנֶּאֱמַר (ישעיה ל) תִּזְרֵם כְּמוֹ דָוָה צֵא תֹּאמַר לוֹ. מַה נִּדָּה מְטַמְּאָה בְמַשָּׂא, אַף עֲבוֹדָה זָרָה מְטַמְּאָה בְמַשָּׂא:

משנה ב — מִנַּיִן לַסְּפִינָה שֶׁהִיא טְהוֹרָה. שֶׁנֶּאֱמַר (משלי ל) דֶּרֶךְ אֳנִיָּה בְלֶב יָם. מִנַּיִן לַעֲרוּגָה שֶׁהִיא שִׁשָּׁה עַל שִׁשָּׁה טְפָחִים שֶׁזּוֹרְעִין בְּתוֹכָהּ חֲמִשָּׁה זֵרְעוֹנִין, אַרְבָּעָה בְּאַרְבַּע רוּחוֹת הָעֲרוּגָה וְאֶחָד בָּאֶמְצַע. שֶׁנֶּאֱמַר (ישעיה סא) כִּי כָאָרֶץ תּוֹצִיא צִמְחָה וּכְגַנָּה זֵרוּעֶיהָ תַצְמִיחַ, זַרְעָהּ לֹא נֶאֱמַר, אֶלָּא זֵרוּעֶיהָ:

משנה ג — מִנַּיִן לְפוֹלֶטֶת שִׁכְבַת זֶרַע בַּיּוֹם הַשְּׁלִישִׁי שֶׁהִיא טְמֵאָה. שֶׁנֶּאֱמַר (שמות יט) הֱיוּ נְכוֹנִים לִשְׁלשֶׁת יָמִים. מִנַּיִן שֶׁמַּרְחִיצִין אֶת הַמִּילָה בַּיּוֹם הַשְּׁלִישִׁי שֶׁחָל לִהְיוֹת בַּשַּׁבָּת. שֶׁנֶּאֱמַר (בראשית לד) וַיְהִי בַיּוֹם הַשְּׁלִישִׁי בִּהְיוֹתָם כֹּאֲבִים. מִנַּיִן שֶׁקוֹשְׁרִין לָשׁוֹן שֶׁל זְהוֹרִית בְּרֹאשׁ שָׂעִיר הַמִּשְׁתַּלֵּחַ. שֶׁנֶּאֱמַר (ישעיה א) אִם יִהְיוּ חֲטָאֵיכֶם כַּשָּׁנִים כַּשֶּׁלֶג יַלְבִּינוּ:

משנה ד — מִנַּיִן לְסִיכָה שֶׁהִיא כַשְּׁתִיָּה בְּיוֹם הַכִּפּוּרִים. אַף עַל פִּי שֶׁאֵין רְאָיָה לַדָּבָר, זֵכֶר לַדָּבָר, שֶׁנֶּאֱמַר (תהלים קט) וַתָּבֹא כַמַּיִם בְּקִרְבּוֹ וְכַשֶּׁמֶן בְּעַצְמוֹתָיו:

There's nothing unusual about that in the Mishnah. The question is, how did these mishnayot end up in this perek?

Letting your animals rest

The fifth and sixth chapters of Shabbat discuss what items may be carried in public on the body of a person or animal, as clothing or as jewelry, and are thus excluded from the prohibition of hotsa'ah.

If you were to ask me how these laws should be organized, I would say that the Mishnah should start by discussing what items may be worn by people, followed by what items may be worn by an animal. But the fifth perek deals with animals, and the sixth perek deals with people. Why is that?

The Yalkut Bi'urim in the Mesivta offers a few answers from the aharonim. I suggest that the Mishnah begins with the more interesting, “haviva leih” topic.

The prohibition of hotsa'ah for animals is unique in its sources and in its application.

“A keli sheni cannot cook”

Disclaimer: nothing in this post should be taken as practical. As Rav Eliezer Melamed explains,

התשובה הכללית, שבכלי ראשון הדבר אסור ובכלי שני מעיקר הדין מותר, אולם בפועל רק בכלי שלישי מותר.

In general, even though putting food in a keli sheni is permitted in principle, in practice we often allow only a keli shelishi. This post discusses the principle, not the practice.

Why is a keli sheni different from a keli rishon? Isn't possible to have a keli sheni that is just as hot as a keli rishon and cooks food just as easily?

The safek of bein ha-shemashot

Shabbat 34–35 discusses the laws of bein ha-shemashot, the period of twilight between sunset and full darkness. This time has a status of safek, uncertainty, when it comes to laws that depend on the time being day or night. There was no way I was going to skip a sugya on uncertainty.

A berayta on 34b states:

תנו רבנן: בין השמשות ספק מן היום ומן הלילה, ספק כולו מן היום, ספק כולו מן הלילה - מטילין אותו לחומר שני ימים.

Bein ha-shemashot is a three-sided safek: it might be fully day, it might be fully night, and it might be some combination of the two. In any question of halakhah we treat it stringently, as either one, or the other, or both of the days that it bridges.

There are two main shittot on understanding the side of the safek that bein ha-shemashot could be both days. Rabbeinu Tam understands the safek to be that any moment between sunset and nightfall could be the dividing line for when the previous day ends and the new day begins. The Ritva (as understood by some aharonim based on a comment on Yoma 47b) understands the safek to be that the entire period of bein ha-shemashot might be ruled as both days intertwined, just as an adroginus might be ruled both male and female.

In this post I discuss Rashi's shittah on how this safek works. It's a shittah whose meaning is, well...uncertain.

Adjusting a timer on Shabbat

If you're looking for the laws of a timer on Shabbat, click right on through to the article by Rabbi Michael Broyde. This post discusses a related hava amina that caught my interest while learning today's daf.

The Mishnah on Shabbat 29b quotes a dispute about setting up a vessel to drip oil into your lamp:

לֹא יִקֹּב אָדָם שְׁפוֹפֶרֶת שֶׁל בֵּיצָה וִימַלְאֶנָּה שֶׁמֶן וְיִתְּנֶנָּה עַל פִּי הַנֵּר בִּשְׁבִיל שֶׁתְּהֵא מְנַטֶפֶת, אֲפִלּוּ הִיא שֶׁל חֶרֶס. וְרַבִּי יְהוּדָה מַתִּיר. אֲבָל אִם חִבְּרָהּ הַיּוֹצֵר מִתְּחִלָּה, מֻתָּר, מִפְּנֵי שֶׁהוּא כֶלִי אֶחָד.

The explanation of most commentators is that you may come to take the oil from the vessel, and thus violate the prohibition of extinguishing, mekhabbeh. Rashi here:

שתהא מנטפת — ויתקיים הנר, שתהא השמן מטפטף כל שעה לתוך הנר, וטעמא משום גזרה, שמא יסתפק הימנו, וכיון שהקצהו לנר - חייב משום מכבה, ואפילו אותה שפופרת של חרס דמאיסא ליה גזרינן.

A squeeze on the Beit Yosef

This week, our topic in afternoon seder has been sehitah, squeezing liquid out of a solid on Shabbat. We came across an Eglei Tal that cites a Tosafot from today's Daf Yomi. It seems like Daf Yomi material comes up elsewhere in my day surprisingly often.

The Eglei Tal is “shocked” at the Beit Yosef.

The square root of two

The Gemara on Shabbat 8a discusses a kavveret, a round basket made of reeds.

A drawing of a kavveret from the Steinzaltz Talmud (PDF)

The kavveret can be its own domain:

אמר אביי: זרק כוורת לרשות הרבים, גבוהה עשרה ואינה רחבה ששה - חייב, רחבה ששה - פטור. רבא אמר: אפילו אינה רחבה ששה - פטור. מאי טעמא - אי אפשר לקרומיות של קנה שלא יעלו למעלה מעשרה.

A house for hobbits

The Gemara on Shabbat 7a quotes the following statement:

והאמר רב גידל אמר רב חייא בר יוסף אמר רב: בית שאין בתוכו עשרה, וקרויו משלימו לעשרה - על גגו מותר לטלטל בכולו, בתוכו אין מטלטלין בו אלא ארבע אמות.

Soncino translates:

R. Gidal said in the name of R. Hiyya b. Joseph in Rab's name: In the case of a house, the inside of which is not ten [hand breadths in height] but its covering makes it up to ten, it is permitted to carry on the roof over the whole [area]; but within, one may carry only four cubits.

A diagram might help:

Tractate Shabbat: In and out and in and out...

Massekhet Shabbat discusses, of course, the laws of Shabbat. The beginning of the massekhet is structured chronologically, starting with the laws of Friday afternoon, then candle lighting on Friday evening, then cooking and insulating Friday night. The basics of the 39 melakhot don't come up until the middle of the seventh perek. The rest of the 24 perakim then flow from topic to topic.

But amidst this structure, a surprising topic dominates the first half of the massekhet: hotsa'ah, the melakhah of carrying between a private and public domain. Eight out of the first eleven chapters of the massekhet contain mishnayot about hotsa'ah, and it is the sole topic of five of those chapters: 5, 6, 8, 9, and 11. And most strangely, the very first mishnah of the massekhet is a total non sequitur to the rest of the first perek—a mishnah about, you guessed it, hotsa'ah.

Adding to the surprise, when the Mishnah lists the 39 melakhot in the seventh perek, hotsa'ah is last on the list. And the first Tosafot on the first amud calls it a melakhah geru'ah, an "inferior" melakhah.

So why the focus on hotsa'ah? Why does it get so many chapters? Why is it tacked on to the beginning of the tractate?

Ge’ullah and tefillah

The first half of Masekhet Berakhot covers two main topics, the Shema with its blessings and the Amidah. One subject arises multiple times as a glue that joins the two topics together (five times, to be exact, according to the Bar Ilan Responsa Project: on 4b, 9b, 10b, 26a, and 30a). This is the requirement to be somekh ge’ullah li-tfillah—that we connect the redemption at the end of the Shema’s blessings, “ge’ullah,” to the start of the Amidah, “tefillah.” The Halakhah gives this requirement high priority.

What is the reason for semikhat ge’ullah li-tfillah? And why is it so important?

Beginning with Berakhot

The Talmud Bavli begins with an important question: תנא היכא קאי? Literally, "where was the Tanna standing" when he started this discussion?

The question applies directly to the opening line of the Mishnah, about the times for keri'at Shema at night. The Gemara answers that the Tanna was coming from the verse in the Torah that requires keri'at Shema twice a day.

But the question also applies to the first perek, the first massekhet, and the first seder. Why do we begin the Talmud here? Why with Shema? Why with Massekhet Berakhot? Why with Seder Zera'im?