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.

Zedekiah’s Cave

Today was one of those Daf Yomi coincidence days.

Last night I made plans to go to Zedekiah's Cave today, near Damascus Gate in Jerusalem. It's pretty cool. Literally cool, actually – it's a nice temperature down there out of the sun. The inside of the cave has an area of about two football fields ("football" still means "American football" to this oleh hadash) and averages the height of a four-story building. Who knew that such a huge, quiet space exists down there under the Arab markets?

So that's one thing I did today on Jerusalem Day. And guess what? By total coincidence, the cave is also mentioned on today's daf, Eruvin 61b!

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.”

Tying knots on Shabbat

Daf Yomi now begins the fifteenth perek of Shabbat, which starts by dealing with knots. Tying and untying knots are two of the thirty-nine melakhot.

Two mishnayot on 111b discuss the knots that are prohibited by the Torah and by the rabbis:

משנה. ואלו קשרים שחייבין עליהן: קשר הגמלין, וקשר הספנין. וכשם שהוא חייב על קישורן - כך הוא חייב על היתרן. רבי מאיר אומר: כל קשר שהוא יכול להתירו באחת מידיו אין חייבין עליו.

משנה. יש לך קשרין שאין חייבין עליהן כקשר הגמלין וכקשר הספנין. קושרת אשה מפתח חלוקה, וחוטי סבכה, ושל פסקיא, ורצועות מנעל וסנדל, ונודות יין ושמן, וקדירה של בשר. רבי אליעזר בן יעקב אומר: קושרין לפני הבהמה בשביל שלא תצא.

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?

How far does borer go?

One of the 39 melakhot in the mishnah on 73a is borer, “separating” a mixture of waste and food. This is one of the melakhot in siddura de-pat, the process of making bread.

In general, as the rishonim learn from Shabbat 74a–b, you may only select from a mixture under three conditions: (1) you remove the food from the waste, and not vice versa; (2) you remove the food by hand; (3) you remove it for immediate eating. When any of these conditions are missing, a penalty of karet is at stake. Each condition is very detailed, and I don't plan to cover them here.

One of the major questions with borer is how far its application goes. What kinds of mixed items are included in the prohibition? Just waste from food? Or even forks from knives?

At one extreme, there is the Talmud Yerushalmi, Shabbat 7:2, which quotes Rabbi Yudan's limited view of borer:

אמר רבי יודן יש שהוא בורר צרורות כל היום ואינו מתחייב יש שהוא נוטל כגרוגרת ומיד מתחייב היך עבידה היה יושב על גבי כרי וברר צרורות כל היום אינו מתחייב נטל לתוך ידו כגרוגרת ובירר חייב

It sounds like the only way to transgress borer is to clear the very last stone from a pile of grain. You have to entirely purify the food from its waste. Unlike what happened with zoreh, this is a case where you'd be happy for the Rema to pick up the Yerushalmi, at least if you like kulot.

At the other extreme, we have the “great question” of Rabbi Yehiel Michel Epstein, in Arukh ha-Shulkhan, O"H 319:8. He assumes that borer applies to literally “everything,” even a collection of non-food items. Were it indeed so, he objects, “we could not find our hands and feet!”

Insulating food Friday evening

The fourth perek of Shabbat (47b–51b) discusses hatmanah, insulating hot food on Shabbat. Materials that add their own heat may not be used. Why not?

Rava establishes on Shabbat 34a–b that there are two rabbinic decrees against hatmanah. One decree applies to insulating materials that add heat, which may not even be used from Friday going into Shabbat. The other decree applies to materials that insulate without adding heat, which may be used on Friday but not once Shabbat starts. The fourth perek then defines which materials add heat and which don't.

Making a keli unusable on Shabbat

The mishnah on Shabbat 42b states:

אין נותנין כלי תחת הנר לקבל בו את השמן, ואם נתנוה מבעוד יום - מותר. ואין ניאותין ממנו, לפי שאינו מן המוכן.

One may not place a keli under a lamp, on Shabbat, in order to catch the oil that may drip.

Rav Hisda says the principle also applies to a placing a keli under a hen to catch a newly hatched egg:

אמר רב חסדא: אף על פי שאמרו אין נותנין כלי תחת תרנגולת לקבל ביצתה - אבל כופה עליה כלי שלא תשבר.

Rav Yosef explains Rav Hisda on 43a:

רב יוסף אמר: היינו טעמא דרב חסדא - משום דקא מבטל כלי מהיכנו.

By causing a new egg, which is muktsah, to rest on the keli, you are mevattel keli me-heikhano, “nullifying the readiness of the keli.”

Abaye raises a number of cases against Rav Yosef that also involve bittul keli me-heikhano at first glance, including supporting a broken beam in the ceiling with a bench, placing a keli under a leaking roof, and using an overturned basket as a step for baby chicks to enter and exit their coop.

What is this prohibition of bittul keli me-heikhano?

“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?

Making aliyah from Babylonia

Shabbat 41a mentions Rabbi Zeira's disagreement with Rav Yehudah about making aliyah:

רבי זירא הוה קא משתמיט מדרב יהודה, דבעי למיסק לארעא דישראל. דאמר רב יהודה: כל העולה מבבל לארץ ישראל עובר בעשה, שנאמר +ירמיהו כז+ בבלה יובאו ושמה יהיו. אמר: איזיל ואשמע מיניה מילתא, ואיתי ואיסק.

Rav Yehudah believed that “anyone who goes up from Babylonia to Israel transgresses a positive commandment.” But Rabbi Zeira disagreed and made up his mind to make aliyah, and so for some time he avoided Rabbi Yehudah.

This opinion of Rav Yehudah is quoted on Ketubbot 111a, along with a second statement:

אמר רב יהודה אמר שמואל: כשם שאסור לצאת מארץ ישראל לבבל, כך אסור לצאת מבבל לשאר ארצות.

Rav Yehudah says in Shemuel’s name that, just as you may not leave Israel for Babylonia, you may not leave Babylonia for other countries.

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.

The extra Hanukkah candle

Hanukkah time! Now that it gets dark around 5pm, it feels like the holiday is just around the corner, even though it's over six weeks away. But if you learn Daf Yomi, it's already here! It starts on Shabbat 21!

This post is based on shi'urim that Rav Reuven Taragin gave at Camp Moshava IO during the summer of 2010.

Rava on 21b says that you need "another lamp" in addition to the Hanukkah nerot:

אמר רבא: צריך נר אחרת להשתמש לאורה.

The continuation (by Rava himself?) discusses exceptions:

ואי איכא מדורה - לא צריך, ואי אדם חשוב הוא, אף על גב דאיכא מדורה - צריך נר אחרת.

What is the purpose of this ner aheret?

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.

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?