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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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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Talmudology on the Parsha, Vayakhel: How The Menorah Became the Emblem of The State of Israel

שמות 31:17–22

וַיַּ֥עַשׂ אֶת־הַמְּנֹרָ֖ה זָהָ֣ב טָה֑וֹר מִקְשָׁ֞ה עָשָׂ֤ה אֶת־הַמְּנֹרָה֙ יְרֵכָ֣הּ וְקָנָ֔הּ גְּבִיעֶ֛יהָ כַּפְתֹּרֶ֥יהָ וּפְרָחֶ֖יהָ מִמֶּ֥נָּה הָיֽוּ

וְשִׁשָּׁ֣ה קָנִ֔ים יֹצְאִ֖ים מִצִּדֶּ֑יהָ שְׁלֹשָׁ֣ה ׀ קְנֵ֣י מְנֹרָ֗ה מִצִּדָּהּ֙ הָֽאֶחָ֔ד וּשְׁלֹשָׁה֙ קְנֵ֣י מְנֹרָ֔ה מִצִּדָּ֖הּ הַשֵּׁנִֽי

שְׁלֹשָׁ֣ה גְ֠בִעִ֠ים מְֽשֻׁקָּדִ֞ים בַּקָּנֶ֣ה הָאֶחָד֮ כַּפְתֹּ֣ר וָפֶ֒רַח֒ וּשְׁלֹשָׁ֣ה גְבִעִ֗ים מְשֻׁקָּדִ֛ים בְּקָנֶ֥ה אֶחָ֖ד כַּפְתֹּ֣ר וָפָ֑רַח כֵּ֚ן לְשֵׁ֣שֶׁת הַקָּנִ֔ים הַיֹּצְאִ֖ים מִן־הַמְּנֹרָֽה׃

וּבַמְּנֹרָ֖ה אַרְבָּעָ֣ה גְבִעִ֑ים מְשֻׁ֨קָּדִ֔ים כַּפְתֹּרֶ֖יהָ וּפְרָחֶֽיהָ׃

וְכַפְתֹּ֡ר תַּ֩חַת֩ שְׁנֵ֨י הַקָּנִ֜ים מִמֶּ֗נָּה וְכַפְתֹּר֙ תַּ֣חַת שְׁנֵ֤י הַקָּנִים֙ מִמֶּ֔נָּה וְכַפְתֹּ֕ר תַּֽחַת־שְׁנֵ֥י הַקָּנִ֖ים מִמֶּ֑נָּה לְשֵׁ֙שֶׁת֙ הַקָּנִ֔ים הַיֹּצְאִ֖ים מִמֶּֽנָּה׃

כַּפְתֹּרֵיהֶ֥ם וּקְנֹתָ֖ם מִמֶּ֣נָּה הָי֑וּ כֻּלָּ֛הּ מִקְשָׁ֥ה אַחַ֖ת זָהָ֥ב טָהֽוֹר׃

And he made the Menorah of pure gold: of beaten work made he the Menorah; its shaft, and its branches, its bowls, its bulbs, and its flowers, were of the same piece: and six branches going out of its sides; three branches of the candlestick out of the one side of it, and three branches of the Menorah out of the other side of it: three bowls made after the fashion of almonds in one branch, a bulb and a flower; and three bowls made like almonds in another branch, a bulb and a flower: so throughout the six branches going out of the Menorah. And in the Menorah were four bowls made like almonds, its bulbs, and its flowers: and a bulb under two branches of the same, and a bulb under two branches of the same, and a bulb under two branches of the same, according to the six branches going out of it.. Their bulbs and their branches were of the same: all of it was one beaten work of pure gold.

The 1948 Search for an Emblem of the State of Israel

Immediately after the establishment of Israel, the Provisional State Council appointed a committee to create its official flag and national emblem.  The committee publicized the search in a small newspaper announcement.

Among the few responses included one from the well known graphic designers Valish and Strosky. It featured the Menorah – the oldest Jewish symbol that can be positively identified, and that is first described in this week’s parsha. Their model of the Menorah was based on the one depicted on the Arch of Titus in Rome., and the row of seven gold stars is taken from Herzl’s own proposal for a flag.  These seven stars symbolized the seven-hour workday that Herzl had envisioned for Jewish workers.  In July 1948  the committee rejected Valish and Strosky’s proposal.

One doesn’t chose a national emblem and flag every day
— David Ben Gurion

Another newspaper notice was published, and this time there was more interest in the challenge. The committee received 131 entries, but only a few have been preserved in the State archives. Here are a some of them.

Graphic artists Gabriel and Maxim Shamir (whose proposal was ultimately selected), submitted a design. It depicted a stylized Menorah in modern form, specifically to break with tradition. Instead of curves there were six right angles rather than curves, and the heavy base was replaced with a tiny unsteady one, in an intentional dissociation from the traditional Jewish symbol.

In December 1948 the committee felt the Shamirs had the most promising design, but they wanted several changes, like adding the word “Israel” underneath.  A month later, at the seventh meeting of the committee, they reevaluated the modern design they had requested. Being a committee, they changed their minds again, and asked that the Menorah on the Arch of Titus be used - the same Menorah that had been depicted on the earlier design of Valish and Storsky.  Why?  According to Professor Alec Meroshi, of the Open University in Israel, it was because of the symbolism:

“It was a visual metaphor for a concept that was popular at the time…just as the fall of the Jewish state in 70 CE found visual expression in the relief depicting Titus’ triumphal procession on the arch…so would the rebirth of the Jewish state and the termination of exile be symbolized by the return of the menorah to its homeland, if not to the Temple, then to the state of Israel that had just been established.  The menorah was being removed from the arch, where it served as a symbol of defeat and degradation, and placed on the most honored spot of all – in the emblem of the State of Israel ” .

After some further minor revisions, the proposal was unanimously accepted on February 10th, 1949. The following day the provisional government published its “Proclamation of the Emblem of the State of Israel.”

Some of those first Israelis interpreted the design as as a victory for secular, socialist and democratic values over religious ones.  But the combination of the Menorah and olive branches in the Shamir design actually had graphic precedents – from the vision of the prophet Zechariah, which is read on Shabbat Channukah and Pa’arshat Beha’alotecha:

זכריה ד

וַיֹּ֣אמֶר אֵלַ֔י מָ֥ה אַתָּ֖ה רֹאֶ֑ה וָאֹמַ֡ר רָאִ֣יתִי ׀ וְהִנֵּ֣ה מְנוֹרַת֩ זָהָ֨ב כֻּלָּ֜הּ וְגֻלָּ֣הּ עַל־רֹאשָׁ֗הּ וְשִׁבְעָ֤ה נֵרֹתֶ֙יהָ֙ עָלֶ֔יהָ שִׁבְעָ֤ה וְשִׁבְעָה֙ מֽוּצָק֔וֹת לַנֵּר֖וֹת אֲשֶׁ֥ר עַל־רֹאשָֽׁהּ׃ וּשְׁנַ֥יִם זֵיתִ֖ים עָלֶ֑יהָ אֶחָד֙ מִימִ֣ין הַגֻּלָּ֔ה וְאֶחָ֖ד עַל־שְׂמֹאלָֽהּ׃

And he said to me, What seest thou? And I said, I have looked, and behold a menorah all of gold, with a bowl upon the top of it, and seven lamps to it, and seven pipes to the seven lamps, which were upon the top of it: and there are two olive trees by it, one upon the right side of the bowl, and the other upon the left side of it.

Zechriah had seen the Menorah in the Second Temple which was completed in 521 C.E. This was apparently the same Menorah that was captured some 500 years later by Titus and carried off to Rome.  And so the emblem of the State of Israel may well replicate the actual Menorah in the Bet Hamikdash, one that in turn is based on the description in this weeks’ parsha.

We don’t like it

Public reaction to the new emblem was swift and extreme; it was criticized by both the religious and the secular. On February 13, 1948, the very next day after the winning emblem had been announced, Gershon Schoken, editor of Haaretz wrote:

This proposal…is nothing but a horror from an aesthetic viewpoint…the execution is so vulgar and amateurish that no self-respecting commercial firm would even consider selecting it as its trademark…

Israel’s Chief Rabbi, Yitchak Halevi Herzog (and the grandfather of the current President of the State if Israel) was also annoyed.

What our government has done today is wrong…it has copied the depiction of the Menorah on the Arch of Titus, which was apparently the work of foreigners, and is not entirely in accordance with the sacred prescriptions…

It might be surprising to learn that the Emblem of Israel was initially controversial, but great decisions require compromise and understanding. What better message could there be for the State of Israel today?

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