Bava Metzia 24a ~ Torture

This post is for the page of Talmud to be studied tomorrow, Shabbat.

Print it up today and enjoy tomorrow.

בבא מציא כד, א

מר זוטרא חסידא אגניב ליה כסא דכספא מאושפיזא חזיא לההוא בר בי רב דמשי ידיה ונגיב בגלימא דחבריה אמר היינו האי דלא איכפת ליה אממונא דחבריה כפתיה ואודי

Mar Zutra the Pious was involved in an incident in which a silver cup was stolen from his host. Later, Mar Zutra saw a certain student wash his hands and dry them on his friend's garment. Mar Zutra said: "this is the one who stole the cup, for he has no consideration for his friend's property. Mar Zutra bound the student to a post and coerced him, and he confessed to the crime (Bava Metzia 24a).

This is an incredible passage. When I first encountered it I wasn't certain I had understood it correctly. But there it was, in black and white. The Pious Mar Zutra had, in essence, tortured a confession out of a student.

Courtesy of Wikimedia.

Courtesy of Wikimedia.

The phrase that describes this is כפתיה ואודי "they bound him and he confessed." The root of the word to bind is כפת, which is used in rabbinic literature to mean to tie or to bind. Rabbi Asher ben Yechiel (Germany ~1250-1327), known as the Rosh, is certain that the suspect was tortured. In his commentary on this passage he wrote וכפתיה בשוטי עד דאודי "he flogged him with rods until he confessed." (As in חושך שבטו שונא בנו ואהבו שחרו מוסר "spare the rod and spoil the child," from Proverbs 13:24.) Rabbi Betzalel ben Avraham Ashkenazi (Israel ~1520-1594) in his commentary called Shitah Mekubetzet agrees that coercion was used, although he is unsure if it was physical or psychological:

כפתוהו ואודי. יש מפרשים כפתוהו על העמוד והלקוהו בשוטים. ויש מפרשים כפתיה בדברים שנדוהו אם לא יודה האמת

Some explain that he was tied to post and flogged. Others explain that he was verbally coerced (and threatened with excommunication) until he confessed.

False Confessions

In a 2010 paper published in the Stanford Law Review, Brandon Garett notes that DNA testing has now exonerated over forty people who falsely confessed to rapes and murders. He wonders how an innocent person could convincingly confess to a crime he never committed. For example, in 1990  Jeffrey Deskovic a seventeen-year-old, was convicted of rape and murder. Deskovic was a classmate of the fifteen-year-old victim, had attended her wake, and was eager to help solve the crime. During one of several police interrogations he “supposedly drew an accurate diagram,” which depicted details concerning “three discrete crime scenes” which were not ever made public. "In his last statement, which ended with him in a fetal position and crying uncontrollably," wrote Garrett, "he reportedly told police that he had “hit her in the back of the head with a Gatoraid [sic] bottle that was lying on the path.” Police testified that, after hearing this, the next day they conducted a careful search and found a Gatorade bottle cap at the crime scene."

Scholars increasingly study the psychological techniques that can cause people to falsely confess and have documented how such techniques were used in instances of known false confessions.
— Garrett, B.L. The Substance of False Confessions. Stanford Law Review 2010. 62 (4): 1051-1119.

Deskovic was convicted of rape and murder and served more than fifteen years of a sentence of fifteen years to life. Then in 2006, new DNA testing not only excluded him, but also matched the profile of a murder convict who subsequently confessed and pleaded guilty. So how did Deskovic know all the details of the crime to which he confessed? Here is what the District Attorney noted in the post-exoneration inquiry:

...Given Deskovic’s innocence, two scenarios are possible: either the police (deliberately or inadvertently) communicated this information directly to Deskovic or their questioning at the high school and elsewhere caused this supposedly secret information to be widely known throughout the community.

Another paper, this time in the North Carolina Law Review, analyzed 125 cases of "proved interrogation-induced false confessions, which, the authors note with some pride, is "the largest cohort of interrogation-induces false confession cases ever identified and studied in the literature." It makes terrifying reading.  

It is of course really hard to study in the laboratory the psychological effects of torture and coercion and how they produce false confessions.  But scientists try anyway. For example, a very recent paper from a team from the New School for Sociological Research in New York and the University of California studied the effect of sleep deprivation on false confessions.  When compared to those who had rested, participants were over four times more likely to sign a false statement if they were deprived of one night's sleep.  In another recent peer-reviewed paper, (Constructing Rich False Memories of Committing Crime) psychologists used suggestive retrieval techniques on some rather nice Canadian undergraduates. They found that up to 70% of those interviewed 

were classified as having false memories of committing a crime (theft, assault, or assault with a weapon) that led to police contact in early adolescence and volunteered a detailed false account. These reported false memories of crime were similar to false memories of noncriminal events and to true memory accounts, having the same kinds of complex descriptive and multisensory components.

They continue: 

Our finding that young adults generated rich false memories of committing criminal acts during adolescence supports the notion that false confessions and gross confabulations can take place within interview settings. The Innocence Project has shown that about 25% of false convictions are attributable to faulty confession evidence...The kind of research presented here is essential in the quest to help prevent memory-related miscarriages of justice.

Back to Mar Zutra the Pious

We know little about Mar Zutra, but for those studying the one-page-a-day Daf Yomi cycle, the last place we learned his teachings was in Bava Kamma. On Shabbat, when using a stone from a wall to wipe himself after using the bathroom, Mar Zutra the Pious would then return the stone to its place in the wall. He would later instruct his servant to cement the stone back into place, so as not to damage the wall.  He was, then, a man who acted to preserve the property rights of others, even in the most intimate of circumstances, when he knew no one would be watching.  And there's another story about Mar Zutra's piety - this one with more bearing on today's teaching in the Talmud. In the tractate Nedarim, we are taught the following:  

דמר זוטרא חסידא כי מחייב בר בי רב שמתא משמית נפשיה ברישא והדר משמת בר בי רב וכי עייל לביתיה שרי לנפשיה והדר שרי ליה ואמר רב גידל

When Mar Zutra the Pious placed excommunicated a student, Mar Zutra first excommunicated himself, and only then the student.  On arriving home, he lifted the ban from himself and then from the disciple.

Tosafot offers two explanations for this rather unusual behavior. First, he excommunicated himself so as not to forget that he had done so to a student. This would force him to recall his student, and when the time came, he would lift the ban. The second proposal offered by Tosafot is that Mar Zutra acted in this way as a sort of penitence: excommunicating another person was an extreme measure, and Mar Zutra reminded himself of this by imposing the same punishment on himself.

תוספות נדרים דף ז, ב 

פר"ת שזה היה עושה כדי שלא ישכח להתיר הנידוי של בר בי רב אבל עכשיו שמשמת נפשיה מתוך כך שהיה זכור להתיר שלו זכור יהיה נמי להתיר של בר בי רב ור"י פירש דלכפרה היה עושה כך שלא יענש במה שמנדה צורבא מדרבנן כי בקושי יש לנדותו

Do you recall the explanation of today's passage from Rabbi Betzalel ben Avraham Ashkenazi in his commentary called Shitah Mekubetzet with which we opened?  He wrote that in order to coerce the student to confess, Mar Zutra threatened the suspect with...excommunication.  And so perhaps we can now better understand the severity of this coercion, for Mar Zutra himself went to extraordinary lengths to avoid imposing it.

Mar Zutra was a complex man, who would use methods we call torture to extract a confession.  The Talmud also points to his sensitivities.  But do the latter ever forgive the former?

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Talmudology on the Parsha, Vayikrah: Unicorns

ויקרא 1:1-2

וַיִּקְרָ֖א אֶל־מֹשֶׁ֑ה וַיְדַבֵּ֤ר יְהֹוָה֙ אֵלָ֔יו מֵאֹ֥הֶל מוֹעֵ֖ד לֵאמֹֽר׃

דַּבֵּ֞ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ וְאָמַרְתָּ֣ אֲלֵהֶ֔ם אָדָ֗ם כִּֽי־יַקְרִ֥יב מִכֶּ֛ם קרְבָּ֖ן לַֽיהֹוָ֑ה מִן־הַבְּהֵמָ֗ה מִן־הַבָּקָר֙ וּמִן־הַצֹּ֔אן תַּקְרִ֖יבוּ אֶת־קרְבַּנְכֶֽם׃

And the Lord called to Moshe, and spoke to him out of the Tent of Meeting, saying,Speak to the children of Yisra᾽el, and say to them, If any man of you bring an offering to the Lord, of the cattle shall you bring your offering, of the herd, and of the flock.

In context, the word adam - אדם – in this verse means person. But the Midrash expounds and takes the word to mean Adam, as in primordial man. Here is that midrash:

ויקרא רבה 2:7

אָמַר רַבִּי בֶּרֶכְיָה אָמַר לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא לְאָדָם זֶה, אָדָם, יְהֵא קָרְבָּנְךָ דּוֹמֶה לְקָרְבָּנוֹ שֶׁל אָדָם הָרִאשׁוֹן שֶׁהָיָה הַכֹּל בִּרְשׁוּתוֹ וְלֹא הִקְרִיב מִן הַגְּזֵלוֹת וּמִן הַחֲמָסִים, אַף אַתָּה לֹא תַקְרִיב מִן הַגְּזֵלוֹת וְלֹא מִן הַחֲמָסִים, וְאִם עָשִׂיתָ כֵן (תהלים סט, לב): וְתִיטַב לַה' מִשּׁוֹר פָּר.

[“When a man [adam] among you sacrifices.”] Rabbi Berekhya said: The Holy One blessed be He said to this man: ‘Man, let your offering be similar to the offering of Adam the first man; everything was in his domain and he did not sacrifice from that which was stolen or extorted. You, too, do not sacrifice from that which was stolen or extorted. If you do so: “It will please the Lord more than a bull”’ (Psalms 69:32).

Rashi liked this midrash, so he cited it in his commentary on the Torah:

רשי, שׁם

אדם. לָמָּה נֶאֱמַר? מָה אָדָם הָרִאשׁוֹן לֹא הִקְרִיב מִן הַגָּזֵל — שֶׁהַכֹּל הָיָה שֶׁלּוֹ — אַף אַתֶּם לֹא תַּקְרִיבוּ מִן הַגָּזֵל (ויקרא רבה)

אדם — Why is this term for “man” employed here? Since אדם also means Adam, its use suggests the following comparison: what was the characteristic of the first man (אדם הראשון)? He did not offer sacrifice of anything acquired by way of robbery, since everything was his! So you, too, shall not offer anything acquired by way of robbery (Leviticus Rabbah 2:7).

The Keli Yakar, a commentary written by Shlomo Ephraim ben Aaron Luntschitz (1550-1619) liked another midrash, found in the Talmud (Shabbat 28b). So he connected the two:

כלי יקר שם

וזה"ש (שבת כח:) שור שהקריב אדה"ר קרן אחת היה לו במצחו לכך נזדמן לו שור בעל קרן אחת כי היה דומה אל האדם שהיה קרן א' ר"ל שהיה יחידי בעולם ולא גזל משום אדם, ולא נתעורר משום אדם, כ"א מעצמו דהיינו מכם ע"כ עלה קרבנו לרצון נמצא שקרבן לה' הפסיק הענין. ואח"כ אמר מן הבהמה וגו' להוציא זרע פשתן אלא יעשה כהבל שהביא מבכורות צאנו. ומה שאמר תקריבו קרבנכם היינו מחלביהן החלק המובחר שאדם בוחר לעצמו הנקרא קרבנכם אותו תקריב לגבוה ונקט קרבנכם לשון רבים כפירש"י לומר שב' מקריבין בהמה

This is what is referred to [in the Talmud Shabbat 28b] “the ox that Adam sacrificed had but a single horn on its forehead,” mirroring Adam who was a single person in the world…

And here is the talmudic discussion as found in Shabbat:

תלמוד בבלי שבת כח, ב

מִדְּקָאָמַר קֶרֶן אַחַת הָיְתָה לוֹ בְּמִצְחוֹ, שְׁמַע מִינַּהּ טָהוֹר הָיָה, דְּאָמַר רַב יְהוּדָה: שׁוֹר שֶׁהִקְרִיב אָדָם הָרִאשׁוֹן קֶרֶן אַחַת הָיְתָה לוֹ בְּמִצְחוֹ, שֶׁנֶּאֱמַר: ״וְתִיטַב לַה׳ מִשּׁוֹר פָּר מַקְרִין מַפְרִיס״. ״מַקְרִין״ תַּרְתֵּי מַשְׁמַע! אָמַר רַב נַחְמָן בַּר יִצְחָק — ״מַקְרָן״ כְּתִיב

… as Rav Yehuda said in a similar vein: The ox that Adam, the first man, sacrificed as a thanks-offering for his life being spared, had a single horn on its forehead, as it is stated: “And it shall please the Lord better than a horned [makrin] and hooved ox” (Psalms 69:32). The word makrin means one with a horn. The Gemara asks: On the contrary, makrin indicates that it has two horns. Rav Naḥman bar Yitzḥak said: Despite the fact that it is vocalized in the plural, it is written mikeren without the letter yod to indicate that it had only a single horn….

Rabbi Yehudah does not suggest just what animal this might have been, but that doesn’t stop us from trying to do so.

How about a unicorn? To understand this suggestion we need a little more background.

THE RE'EM IN THE BIBLE

The word ראם, re'em appears several times in the Hebrew Bible. Here, for example, is a verse from Deuteronomy (33:17) which describes the offspring of Joseph.

דברים לג: יז

בְּכ֨וֹר שׁוֹר֜וֹ הָדָ֣ר ל֗וֹ וְקַרְנֵ֤י רְאֵם֙ קַרְנָ֔יו בָּהֶ֗ם עַמִּ֛ים יְנַגַּ֥ח יַחְדָּ֖ו אַפְסֵי־אָ֑רֶץ וְהֵם֙ רִבְב֣וֹת אֶפְרַ֔יִם וְהֵ֖ם אַלְפֵ֥י מְנַשֶּֽׁה׃

Like a firstling bull in his majesty, He has horns like the horns of the re'em; With them he gores the peoples, The ends of the earth one and all. These are the myriads of Ephraim, Those are the thousands of Manasseh. 

The re'em is specifically identified by the great translator of the Bible Oneklos (~35-120 CE) as one of the species singled out in the Torah as being kosher:

דברים יד: ד–ה

 זֹ֥את הַבְּהֵמָ֖ה אֲשֶׁ֣ר תֹּאכֵ֑לוּ שׁ֕וֹר שֵׂ֥ה כְשָׂבִ֖ים וְשֵׂ֥ה עִזִּֽים׃ אַיָּ֥ל וּצְבִ֖י וְיַחְמ֑וּר וְאַקּ֥וֹ וְדִישֹׁ֖ן וּתְא֥וֹ וָזָֽמֶר׃

These are the animals that you may eat; the deer, the gazelle, the roebuck, the wild goat, the dishon, the antelope, the mountain sheep.

Onkelos translates that word דִישֹׁ֖ן into Aramaic as רֵימָא - the re'em. And then there is this passage from the Book of Job (39:9-12):

איוב לט:ט–יב

הֲיֹ֣אבֶה רֵּ֣ים עָבְדֶ֑ךָ אִם־יָ֝לִ֗ין עַל־אֲבוּסֶֽךָ׃ הֲ‍ֽתִקְשָׁר־רֵ֭ים בְּתֶ֣לֶם עֲבֹת֑וֹ אִם־יְשַׂדֵּ֖ד עֲמָקִ֣ים אַחֲרֶֽיךָ׃

Most English versions of this passage translate the word re'em as "wild ox"and so read: 

Would the wild ox agree to serve you? Would he spend the night at your crib?  Can you hold the wild ox by ropes to the furrow? Would he plow up the valleys behind you?

But not the King James Bible. It goes in an entirely different direction: 

Will the unicorn be willing to serve thee, or abide by thy crib? Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?

So according to the King James Bible, the re'em is a unicorn. Why on earth would the translators have chosen, of all creatures, the mythical unicorn as the re'em?

“The men who [produced the King James Bible], who pored over the Greek and Hebrew texts, comparing the accuracy and felicity of previous translations, arguing with each other over the finest details of chapter and verse, were many of them obscure at the time and are generally forgotten now, a gaggle of fifty or so black-gowned divines whose names are almost unknown but whose words continue to resonate with us.
— Adam Nicoloson. God's Secretaries: The Making of the King James Bible. Harper Collins 2005. xi

THE RE'EM IS A UNICORN. OR MAYBE NOT.

Well, they didn't. They merely followed the Septuagint, the Greek translation of the Hebrew Bible from the third century BCE. And the Septuagint translated the Hebrew re'em as μονόκερως - monokeros, or "one horned". Which is why the King James Bible translated it as a unicorn, from the Latin uni meaning "single" and cornu meaning "horn". And since, according to the Talmud, the Septuagint was created at the command of Ptolemy II by seventy-two Jewish sages, you could claim that the King James translation was following a long Jewish tradition.

“King Ptolemy once gathered 72 Elders. He placed them in 72 chambers, each of them in a separate one, without revealing to them why they were summoned. He entered each one’s room and said: “Write for me the Torah of Moshe, your teacher”. God put it in the heart of each one to translate identically as all the others did.
— TB Megillah 9a-b

This translation made its way into later rabbinic commentary. For example, R. Dovid Kimche (1160-1235), in his dictionary of the Hebrew language called Sefer Hashorashim, wrote that the re'em has only one horn. And Abraham Yagel, (1553 – 1623), the Italian rabbi and exegete, mentioned a one-horned re'em that had been captured and brought to Portugal:

Book IV, ch. 45: 108a בית יער הלבנון 

ובימנו הובא בארץ פורטוגאלי מן האי האינדי׳ ראם אחד במצודה צדו אותו ומראה צורתו הביאו אח׳כ עוברי אורחות ימים והוא גדול מהפיל ומזרין בקסקשיו בכל עורו וקרן חזות עב על חוטמו אשר בו לחם מלחמות עם הפיל ועם שאר החיות

And in our days a re'em was brought to Portugal from India having been ambushed and trapped, and afterwards sea travellers reported how it looked. It is larger than an elephant and its scales cover all its skin. It has a thick horn on its nose which it uses in fights with the elephant and with other creatures...

As Natan Slifkin points out, what Yagel what was actually describing was a rhinoceros: "It was given to King Manuel of Portugal by Alfonso de Albuquerque, governor of Portuguese India. This was the first rhinoceros to be brought to Europe since Roman times, and it caused quite a sensation." Quite so.

But before we conclude that the re'em was a rhinoceros, there are a couple of problems. First, although it was once found in the Land of Israel, the rhinoceros remains so far discovered only go back to the Mousterian era, which ended about 35,000 years ago. That's quite a few years before the biblical period. Thus it is very unlikely that there were rhinoceri in Israel in the biblical period. And second, the re'em in the Bible is described as having two horns.  Two. "וְקַרְנֵ֤י רְאֵם֙ קַרְנָ֔יו" His horns are like the horns of the re'em" (Deut.33:17). So there are challenges identifying the rhinoceros as a unicorn.

Other One-horned creatures “witnessed” by the rabbis

One of the earliest rabbinic texts to discuss rhinoceri (or unicorns) is Shiltei Hagiborim, (#52), written by the physician-polymath Abraham Portaleone and first published in 1612, the year of his death. He enthusiastically cited Aristotle and Pliny who had testified to having seen one-horned animals:

You should know that I have not simply imagined these descriptions [of one-horned animals] without supporting testimony. For Aristotle wrote that the wild donkey has a single horn and non-cloven hooves. In addition, Pliny in chapter twenty-one of his eighth book wrote that in India there are ox like creatures with a single horn on their heads, and with hooves that are not cloven….

In his work on the Shulhan Arukh known as the Pri Hadash, Rabbi Hezekiah da Silva (1659–1698) cited Portalene’s remarks, and expanded upon them.

פרי חדש יורה דעה סימן פ

ועוד ראיתי בספר שלטי הגיבורים בפרק נ"ב [נה, ד] שחברו חכם רופא אחד מהדור שלפנינו שהאריך בענין זה, והביא בשם חכמי האומות מכמה בעלי חיים שהם בעלי קרן אחד והם טמאים, והעידו שחמור הבר יש לו במצחו קרן אחד והוא קלוט ברגליו ובהודו נמצאים שוורים שיש להם קרן אחד במצחם ופרסותיהם קלוטות, וכן יולדו שם בעלי חיים אכזריים דומין בגופן לסוסים ובראשם לאיל ורגליהם דומין לרגלי הפיל, והוסיפו עוד כי זנב הבעלי חיים האלה הוא דומה לזנב החזיר יערי ורוב הפעמים הולכים הלוך וגעו וממצחם יוצא קרן אחד שחור ארוך שתי אמות, וכיוצא בזה רבים אתם. וכל אילו העניינים אינם מבודים מן הלב שכולם אין ספק בדבר שהם עדי ראייה ולא שייך בזה למימר אשר פיהם דיבר שוא

…They testified that the wild donkey has one horn in its forehead and does not have cloven hooves. In India there are oxen that have one horn on their foreheads and their hooves are not cloven, and there are dangerous animals whose bodies are similar to horses and whose heads are similar to rams and whose feet are similar to those of elephants…. And all these things are not impossible, for there is no doubt that they are eyewitnesses accounts and it is not appropriate to think of them as the testimony of those “whose mouths speak lies” (Psalms 144:8)

RABBI YEHUDAH AND THE GREEKS

Perhaps then, the single horned animal that according to Rabbi Yehudah was sacrificed by Adam was the mythical unicorn. Rabbi Yehudah, also known as Yehudah bar Ilai, lived in the Galilee in the second century, some five hundred years after the Greek translation of the Hebrew Bible which introduced the re'em as μονόκερως - monokeros, or one horned. And he knew his Greek. In fact he held the Greek language in such a special esteem that he even allowed a Torah to be written in it:

מגילה ט,א

א"ר יהודה אף כשהתירו רבותינו יונית לא התירו אלא בספר תורה 

And it is taught in another baraita that Rabbi Yehuda said: Even when our Rabbis permitted Greek, they permitted it only in a Torah scroll, and not for other books of the Bible, which must be written only in Hebrew.

And so the rabbis linked the opening of this week’s parsha to a mythical animal sacrificed by the mythical first human. It is a wonderful flight of rabbinic fancy, on which the famous Rabbi Shmuel Eidels (d.1631) had this to say in his famous Chidushei Maharsha (Chullin 60a):

ולכך כשחזר בתשובה הקריב שור שהיה לו קרן א' מורה על עיקר האחדות

…when Adam repented of sin he sacrificed an animal with one horn to signify God’s unity

Perhaps what we need today is not a sign of God’s unity, but the unity of his people Israel.

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New York Lecture: This Tuesday March 19th at Weil Cornell

If you are in the area, do come and join!

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Talmudology on the Parsha, Pekudei: Happy Pi Day

This weeks parsha, Pekudei, contains additional details about the construction of the Mishkan. We are told how much gold was used:

38:24 שמות

כל־הַזָּהָ֗ב הֶֽעָשׂוּי֙ לַמְּלָאכָ֔ה בְּכֹ֖ל מְלֶ֣אכֶת הַקֹּ֑דֶשׁ וַיְהִ֣י ׀ זְהַ֣ב הַתְּנוּפָ֗ה תֵּ֤שַׁע וְעֶשְׂרִים֙ כִּכָּ֔ר וּשְׁבַ֨ע מֵא֧וֹת וּשְׁלֹשִׁ֛ים שֶׁ֖קֶל בְּשֶׁ֥קֶל הַקֹּֽדֶשׁ׃

All the gold that was applied for the work in all the work of the holy place, even the gold of the offering, was twenty nine talents, and seven hundred and thirty shekels, after the shekel of the sanctuary.

We read how the Ephod, a sort of priestly apron, was made:

39:2 שמות

וַיַּ֖עַשׂ אֶת־הָאֵפֹ֑ד זָהָ֗ב תְּכֵ֧לֶת וְאַרְגָּמָ֛ן וְתוֹלַ֥עַת שָׁנִ֖י וְשֵׁ֥שׁ משְׁזָֽר׃

And he made the efod of gold, blue, and purple, and scarlet, and fine twined linen.

And when it was all finally completed, Moses looked at the finished product, and was pleased. He was very pleased:

39:43 שמות

וַיַּ֨רְא מֹשֶׁ֜ה אֶת־כל־הַמְּלָאכָ֗ה וְהִנֵּה֙ עָשׂ֣וּ אֹתָ֔הּ כַּאֲשֶׁ֛ר צִוָּ֥ה יְהֹוָ֖ה כֵּ֣ן עָשׂ֑וּ וַיְבָ֥רֶךְ אֹתָ֖ם מֹשֶֽׁה׃ {פ}

And Moses saw all the work, and, behold, they had done it as the Lord had commanded, even so had they done it: and Moses blessed them.

The haftarah for this week’s reading is from The First Book of Kings (מלכים א 7:51-8:21) and echoes the theme of the parsha. It describes the completion of the first Temple, which was built by King Solomon. Here is the opening verse:

וַתִּשְׁלַם֙ כל־הַמְּלָאכָ֔ה אֲשֶׁ֥ר עָשָׂ֛ה הַמֶּ֥לֶךְ שְׁלֹמֹ֖ה בֵּ֣ית יְהֹוָ֑ה וַיָּבֵ֨א שְׁלֹמֹ֜ה אֶת־קדְשֵׁ֣י ׀ דָּוִ֣ד אָבִ֗יו אֶת־הַכֶּ֤סֶף וְאֶת־הַזָּהָב֙ וְאֶת־הַכֵּלִ֔ים נָתַ֕ן בְּאֹצְר֖וֹת בֵּ֥ית ה׳

So was ended all the work that King Solomon made for the house of the Lord. And Solomon brought in the things which David his father had dedicated; the silver, and the gold, and the vessels, he did put in the treasuries of the house of the Lord…

In keeping with the topic of the Temple and its vessels, and noting today’s date, we will focus on another special piece of equipment in Solomon’s Temple. It was a large round bowl, and it is mentioned in the same chapter as the haftarah. Read it carefully, then answer this question: What is the value of pi that the verse describes?

מלכים א פרק ז פסוק כג 

ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקוה שלשים באמה יסב אתו סביב

And he made a molten sea, ten amot from one brim to the other: it was round, and its height was five amot, and a circumference of thirty amot circled it.

Answer: THREE.

The circumference was 30 amot and the diameter was 10 amot. Since pi is the ratio of the circumference of a circle to its diameter, pi in the Book of Kings is 30/10=3. Three - no more and no less. Which brings us to today’s date and the math that is celebrated on it.

WHAT IS PI DAY, AND WHEN IS IT CELEBRATED?

From here.

Today, March 14, is celebrated as Pi Day by some of the mathematically inclined in the US. Why? Well, in most of the world, the date is written as day/month/year. So in Israel, all of Europe, Australia, South America and China, today's date, March 14th, would be written as 14/3. 

But not here in the US. Here, we write the date as month/day/year; it's a uniquely American way of doing things. (Like apple pie. And guns.) So today's date is 3/14. Which just happen to be the first few digits of pi, the ratio of the circumference of a circle to its diameter.

And that's why each year, some (particularly geeky) Americans celebrate Pi Day on March 14 (3/14). The year 2015 was more Pi'ish than all others, since the entire date (when written the way we do in the US, 3/14/15) reflects five digits of pi, and not just the first three: 31415. Actually we got even more geeky: This day in 2015 at 9:26 and 53 seconds in the morning, the date and time, when written out, represented the first ten digits of Pi: 3141592653.

So that's why Pi Day is celebrated here in the US -  and probably not anywhere else. (It has even been recognized as such by a US Congressional Resolution. Really. I'm not making this up. And who says Congress doesn't get anything done?) 

Pi in the Bible

We have just seen how the value of pi that we would derive from the bowl in Solomon’s Temple is three (and not 3.1415….). There are lots of papers on the value of pi in the the Bible. Many of them mention an observation that seems to have been incorrectly attributed to the Vilna Gaon.  The verse we cited from מלאכים א׳ spells the word for line as קוה, but it is pronounced as though it were written קו.  (In דברי הימים ב׳ (II Chronicles 4:2) the identical verse spells the word for line as קו.)  The ratio of the numerical value (gematria) of the written word (כתיב) to the pronounced word (קרי) is 111/106.  Let's have the French mathematician Shlomo Belga pick up the story - in his paper (first published in the 1991 Proceedings of the 17th Canadian Congress of History and Philosophy of Mathematics, and recently updated), he gets rather excited about the whole gematria thing:

Another mathematician, Andrew Simoson also addresses this large bowl that is described in מלאכים א׳, the First Book of Kings and is often called Solomon's Sea. He doesn't buy the gematria, and wrote about it in The College Mathematics Journal.

A natural question with respect to this method is, why add, divide, and multiply the letters of the words? Perhaps an even more basic question is, why all the mystery in the first place? Furthermore, H. W. Guggenheimer, in his Mathematical Reviews...seriously doubts that the use of letters as numerals predates Alexandrian times; or if such is the case, the chronicler did not know the key. Moreover, even if this remarkable approximation to pi is more than coincidence, this explanation does not resolve the obvious measurement discrepancy - the 30-cubit circumference and the 10-cubit diameter. Finally, Deakin points out that if the deity truly is at work in this phenomenon of scripture revealing an accurate approximation ofpi... God would most surely have selected 355/113...as representative of pi...

Still, what stuck Simoson was that "...the chroniclers somehow decided that the diameter and girth measurements of Solomon's Sea were sufficiently striking to include in their narrative." (If you'd like another paper to read on this subject, try this one, published in B'Or Ha'Torah - the journal of "Science, Art & Modern Life in the Light of the Torah." You're welcome.)

PI IN THE TALMUD

The Talmud echoes the biblical value of pi in many places. For example:

תלמוד בבלי מסכת עירובין דף יד עמוד א 

כל שיש בהיקפו שלשה טפחים יש בו רחב טפח. מנא הני מילי? - אמר רבי יוחנן, אמר קרא : ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקו שלשים באמה יסב אתו סביב 

"Whatever circle has a circumference of three tefachim must have a diameter of one tefach."  The problem is that as we've already noted, this value of pi=3 is not accurate. It deviates from the true value of pi (3.1415...) by about 5%. Tosafot is bothered by this too.

תוספות, עירובין יד א

והאיכא משהו. משמע שהחשבון מצומצם וכן בפ"ק דב"ב (ד' יד:) גבי שני טפחים שנשתיירו בארון ששם ספר תורה מונח שהיא בהיקפה ששה טפחים ופריך כיון דלאמצעיתו נגלל נפיש ליה משני טפחים וכן בתר הכי דמשני בספר דעזרה לתחלתו נגלל ופריך אכתי תרי בתרי היכי יתיב משמע דמצומצם לגמרי וקשיא דאין החשבון מדוקדק לפי חכמי המדות

Tosafos can't find a good answer, and concludes "this is difficult, because the result [that pi=3] is not precise, as demonstrated by those who understand geometry." 

PI IN THE RAMBAM

In his commentary on the Mishnah (Eruvin 1:5) Maimonides makes the following observation:

פירוש המשנה לרמב"ם מסכת עירובין פרק א משנה ה 

צריך אתה לדעת שיחס קוטר העיגול להקפו בלתי ידוע, ואי אפשר לדבר עליו לעולם בדיוק, ואין זה חסרון ידיעה מצדנו כמו שחושבים הסכלים, אלא שדבר זה מצד טבעו בלתי נודע ואין במציאותו שיודע. אבל אפשר לשערו בקירוב, וכבר עשו מומחי המהנדסים בזה חבורים, כלומר לידיעת יחס הקוטר להקיפו בקירוב ואופני ההוכחה עליו. והקירוב שמשתמשים בו אנשי המדע הוא יחס אחד לשלשה ושביעית, שכל עיגול שקוטרו אמה אחת הרי יש בהקיפו שלש אמות ושביעית אמה בקירוב. וכיון שזה לא יושג לגמרי אלא בקירוב תפשו הם בחשבון גדול ואמרו כל שיש בהקיפו שלשה טפחים יש בו רוחב טפח, והסתפקו בזה בכל המדידות שהוצרכו להן בכל התורה.

...The ratio of the diameter to the circumference of a circle is not known and will never be known precisely. This is not due to a lack on our part (as some fools think), but this number [pi] cannot be known because of its nature, and it is not in our ability to ever know it precisely. But it may be approximated ...to three and one-seventh. So any circle with a diameter of one has a circumference of approximately three and one-seventh. But because this ratio is not precise and is only an approximation, they [the rabbis of the Mishnah and Talmud] used a more general value and said that any circle with a circumference of three has a diameter of one, and they used this value in all their Torah calculations.

So what are we to make of all this? Did the rabbis of the Talmud get pi wrong, or were they just approximating pi for ease of use?  After considering evidence from elsewhere in the Mishnah (Ohalot 12:6 - I'll spare you the details), Judah Landa, in his book Torah and Science, has this to say:

We can only conclude that the rabbis of the Mishnah and Talmud, who lived about 2,000 years ago, believed that the value of pi was truly three. They did not use three merely for simplicity’s sake, nor did they think of three as an approximation for pi. On the other hand, rabbis who lived much later, such as the Rambam and Tosafot (who lived about 900 years ago), seem to be acutely aware of the gross innacuracies that results from using three for pi. Mathematicians have known that pi is greater than three for thousands of years. Archimedes, who lived about 2,200 years ago, narrowed the value of pi down to between 3 10/70 and 3 10/71 ! (Judah Landa. Torah and Science. Ktav Publishing House 1991. p.23.)

HAPPY BIRTHDAY, EINSTEIN

Today, March 14, is not only Pi Day. It is also the anniversary of the birthday of Albert Einstein, who was born on March 14, 1879. As I've noted elsewhere, Einstein was a prolific writer; one recent book (almost 600 pages long) claims to contain “roughly 1,600” Einstein quotes. It's hard to choose just one pithy quote of his on which to close.  So here are two.  Happy Pi Day. Happy birthday, Albert Einstein. And Shabbat Shalom from Talmudology

As a human being, one has been endowed with just enough intelligence to be able to see clearly how utterly inadequate that intelligence is when confronted with what exists.
— Letter to Queen Elisabeth of Belgium, September 1932
One thing I have learned in a long life: That all our science, measured against reality, is primitive and childlike — and yet it is the most precious thing we have.
— Banesh Hoffman. Albert Einstein: Creator and Rebel. Plume 1973
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