Bava Basra 95 ~ The Smallest Ramanujan Taxicab Number

This post is for tomorrow’s page of Talmud to be studied, which is page 1,729 of the Babylonian Talmud. Print it up now and enjoy, and Shabbat Shalom from Talmudology.

The number of tomorrow’s daf, (Bava Basra) 95, has some special mathematical properties. For example, it is a Thabit number, (also called a 3-2-1 number) which is an integer that is of the form 3 · 2ⁿ - 1. But there is another mathematical curiosity about tomorrow’s page number. Starting from the beginning, it is page number 1,729 of the Babylonian Talmud. And 1,729 is the smallest Ramanujan Taxicab Number, a number that can be written as the sum of two cubes: (1³ + 12³=1729.) In two different ways: (9³ + 10³=1729).*

[*These numbers are also known as Hardy-Ramanujan numbers. Also, to be precise, they are numbers that can be can be written as the sum of two cubes using positive integers. Let’s keep going.]

Here is one version of the story of how these numbers were discovered:

Curious properties sometimes lurk within seemingly undistinguished numbers. 1729 sparked one of maths most famous anecdotes: a young Indian, Srinivasa Ramanujan, lay dying of TB in a London hospital. G.H. Hardy, the leading mathematician in England, visited him there. 'I came over in cab number 1729,' Hardy told Ramanujan. 'That seems a rather dull number to me.'

'Oh, no!' Ramanujan exclaimed. '1729 is the smallest number you can write as the sum of two cubes, in two different ways.' Most of us would use a computer to figure out that 1³ + 12³ = 9³ + 10³ = 1729. Ramanujan did it from his sickbed without blinking.

Mathematicians have mined his theorems ever since. ..Far more than just another number theory, 1729 is the first of the 'Ramanujan numbers' or taxicab numbers. Mathematicians are competing to search for more of them (with higher powers) and testing the strength of new computing technology. The search is seen as mathematics' current greatest challenge. Only recently, a lost bundle of Ramanujan's notebooks turned up in a Cambridge library setting maths off on a new voyage of discovery.

Ramanujan, a largely self-taught mathematician, seemed to solve problems instinctively and said his formulas came to him in the form of visions from a Hindu goddess. During the height of British colonialism, he left his native India to become a protégé of mathematician G.H. Hardy at Cambridge University in England.
— Emory University News Center, October 22, 2015.

In case you are wondering, this is the only page of the Talmud that is a taxi-cab number. (There is a machloket achronim [debate] as to whether 2 is a taxicab number. Some lists include it. Others don’t. Personally, I don’t think it counts, but my opinion on the matter is of zero mathematical importance.) The next one is 87,539,319.

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Talmudology on the Parsha, Nitzavim~ I Have a Dream

דברים 30:12

כִּי הַמִּצְוָה הַזֹּאת אֲשֶׁר אָנֹכִי מְצַוְּךָ הַיּוֹם לֹא־נִפְלֵאת הִוא מִמְּךָ וְלֹא רְחֹקָה הִוא׃

לֹא בַשָּׁמַיִם הִוא לֵאמֹר מִי יַעֲלֶה־לָּנוּ הַשָּׁמַיְמָה וְיִקָּחֶהָ לָּנוּ וְיַשְׁמִעֵנוּ אֹתָהּ וְנַעֲשֶׂנָּה׃

Surely, this instruction which I enjoin upon you this day is not too baffling for you, nor is it beyond reach.It is not in the heavens, that you should say, “Who among us can go up to the heavens and get it for us and impart it to us, that we may observe it?”

Rashi, citing the statement of Avdimi bar Chama bar Dosa (Eruvin 55a) comments:

לא בשמים הוא. שֶׁאִלּוּ הָיְתָה בַשָּׁמַיִם, הָיִיתָ צָרִיךְ לַעֲלוֹת אַחֲרֶיהָ לְלָמְדָהּ

IT IS NOT IN HEAVEN — for were it in heaven it would still be your duty to go up after it and to learn it.

However, elsewhere (Bava Metziah 59b) the Talmud is very clear: when it comes to Jewish law, we keep “the heavens” out of it. When Rabbi Eliezar found himself losing a halakhic battle with his colleagues, he arranged for a series of miracles to prove that his ruling was correct. Here is what happened next:

עמד רבי יהושע על רגליו ואמר (דברים ל, יב) לא בשמים היא מאי לא בשמים היא אמר רבי ירמיה שכבר נתנה תורה מהר סיני אין אנו משגיחין בבת קול שכבר כתבת בהר סיני בתורה (שמות כג, ב) אחרי רבים להטות

Rabbi Yehoshua stood on his feet and said: It is written: “It is not in heaven” (Deuteronomy 30:12). The Gemara asks: What is the relevance of the phrase “It is not in heaven” in this context? Rabbi Yirmeya says: Since the Torah was already given at Mount Sinai, we do not regard a Divine Voice, as You already wrote at Mount Sinai, in the Torah: “After a majority to incline” (Exodus 23:2).

Rabbis who Dream and Decide

It is therefore somewhat surprising that this principle was forgotten when some rabbis declared that they had received halakhic rulings in their dreams. Some of them were noted by Ze’ev Zuckerman in his Otzar Pila’ot Hatorah, and this week on Talmudology we will take a closer look at rabbis who claim to have had God tell them directly how to rule.

First, let’s note that after Rabbi Eliezer’s claim of support via miracles, the earliest example of paksening (ruling) via dreams can be found in the writings of Natronai Ben Hilai Hacohen, known as Natronai the Gaon, who lived in Mesopotamia in the late 9th century and headed the Yeshiva in Sura. He was asked whether a person who converts out of Judaism may legally inherit his father’s property. Nope. “כך הראוני מן השמים שמשומד אינו ירוש אביו.” “This is what was taught to me from heaven: an apostate may not inherit his father.”

The Rashba

Shlomo ben Avraham ibn Aderet (1235-1310) was a Spanish rabbi who left a great many responsa (actually more than 3,000 according to this source). I counted at least 19 that have the phrase שהראוני מן השמים “as shown to me from heaven” in them. Here is the first responsum in which this phrase appears, shown in the red box.

שו"ת הרשב"א - א בני ברק, תשי"ח - תשי"ט

The Ra’avad

Abraham ben David (best known by his acronym Ra’avad, c.1125-1198) lived in Provence and is famous for his (sometimes quite hostile) commentary on the Mishneh Torah of Maimonides. In the Laws of the Lulav (8:8) Maimonides outlined the blemishes that render a myrtle (hadas) as useless. However, according to Maimonides, “a myrtle branch whose top is cut off is acceptable.” But that wasn’t how the Ra’avad ruled. And he had it on good authority:

הדס שנקטם וכו'. כתב הראב"ד ז"ל כבר הופיע רוח הקודש בבית מדרשנו מכמה שנים והעלינו שהוא פסול כסתם מתני'. ודברי רבי טרפון שאמר אפילו שלשתן קטומים כשר ענין אחר הוא ולא שנקטם ראשו והכל ברור בחבורנו ומקום הניחו לי מן השמים עכ"ל

The Holy Spirit (רוח הקודש) has appeared in our Bet Midrash (study hall) over a number of years and has ruled that such a myrtle is forbidden…

Shut Min Hashamayim - The Responsa From Heaven

The thirteenth century French kabbalist Jacob HaLevi of Marvège (יעקב הלוי ממרויש) took this heaven thing and cranked the volume up to 11. He wrote a series of responsa whose halakhic decisions, he claimed, were revealed to him in his dreams. He called the work, appropriately, “שאלות ותשובות מן השמים - Questions and Answers From Heaven. In a fascinating article on the work, the late Israel Ta-Shema (1936-2004) wrote that it was cited as early as 1215 (in a book called Hamanhig by Avraham Hayarechi). It was used widely during the middle ages and “many important poskim [religious authorities] relied on it when ruling.”

The Magid Mesharim - The Preacher of RIGHTEOUSNESS

Not to be outdone, no less a personality than Yosef Karo (or Caro, 1488-1575), the author of the authoritative Shulchan Aruch, (Code of Jewish Law) also claimed to have been visited by heavenly creatures who would urge him on to new spiritual heights. He wrote a book about these encounters which he called Maggid Mesharim - The Preacher of Righteousness. Writing in the Jewish Encyclopdia, here is how Louis Ginzberg explained the book:

This book is a kind of diary in which Caro during a period of fifty years noted his discussions with his heavenly mentor, the personified Mishnah. …The discussions treat of various subjects. The maggid enjoins Caro to be modest in the extreme, to say his prayers with the utmost devotion, to be gentle and patient always. Especial stress is laid on asceticism; and Caro is often severely rebuked for taking more than one glass of wine, or for eating meat. Whenever Caro did not follow the severe instructions of his maggid, he suddenly heard its warning voice. His mentor also advised him in family affairs (p. 21b), told him what reputation he enjoyed in heaven, and praised or criticized his decisions in religious questions…

The present form of the "Maggid Mesharim" shows plainly that it was never intended for publication, being merely a collection of stray notes; nor does Caro's son Judah mention the book among his father's works. It is known, on the other hand, that during Caro's lifetime the cabalists believed his maggid to be actually existent …. The "Maggid Mesharim," furthermore, shows a knowledge of Caro's public and private life that no one could have possessed after his death; and the fact that the maggid promises things to its favorite that were never fulfilled—e.g., a martyr's death—proves that it is not the work of a forger, composed for Caro's glorification...

Some Halachik rulings determined by dreams

  1. Is Balbuta Kosher?

    Balbuta was some kind of fish that shed its scales as it grew. (Perhaps it was this fish). Rabbi Ephraim of Regensburg (1110-1175) ruled that it was kosher, as had Rashi and his two famous grandsons Rashbam and Rabbenu Tam. According to the account of R. Baruch of Mainz (1150-1221) the night after R. Ephraim made his fishy ruling, he [Ephraim] had a dream

    “that he was being presented with a brimming plate of non-kosher crustaceans by an elderly man with a pleasant countenance, white hair, and a flowing white beard. The elderly man bid R. Ephraim to eat from this plate, but Ephraim adamantly (and even angrily) refused, explaining to the man that these were non-kosher sea creatures. The man responded, “These are as permitted (for consumption) as the non-kosher species (sherazim) that you allowed today.” When R. Ephraim awoke, he understood that Elijah the Prophet had appeared to him, and he refrained away from (eating) those fish from that day on (me-hayom va-hal’ah piresh me-hem)” (From here.)

  2. Lung adhesions and kashrut

    R. Isaiah di Trani, known as the Rid (c.1180-c1250) ruled that certain lung adhesions that were found in a slaughtered animal rendered it treif, and as a result its meat could not be eaten. While he recognized that in general one may not be guided by dreams when reaching halakhic decisions (c.f. Sanhedrin 30a “דברי חלומות לא מעלין ולא מורידין”), the Rid also noted that Elijah the prophet had appeared to him in a dream and that Elihah supported the Rid’s position.

תשובות הריד, ירושלים 1975, #112

3. Paying a worker from the foods he collects

The Mishnah (Bava Metziah 118a) rules that a worker who is paid to collect straw and chafe (which is the husk surrounding a seed, and is generally discarded,) may refuse payment in the form of these items, since they are difficult to trade or exchange for other foods. In the Middle Ages the question arose as to whether this ruling is restricted to wheat and chafe mentioned specifically in the Mishnah, or is generalisable to other low quality items a worker is paid to collect.

One of the great medieval talmudists used a dream to decide the issue. Mordechai ben Hillel, known simply as “the Mordechai” (c.1250-1298) was a German posek whose rulings to this day are printed at the back of the standard editions of the Talmud. And here is his one of them:

מרדכי מסכת בבא קמא פרק ארבעה אבותֿ

ולמורי ר' מאיר נראה בחלום דוקא בתבן ובקש אבל במידי דאכילה כגון חטין ושעורין ואמר טול מה שעשית בשכרך שומעין לו, וכן פסק להלכה

My teacher R. Meir saw in a dream that only wheat and chafe can specifically be rejected by the worker. But regarding other edible commodities, such as wheat and barley, the hirer may say to the worker “take your wages from this produce.”

4. Is refraining for pride one of the 613 Mitzvot?

Among the earliest works of Jewish Law is that of Moses ben Jacob of Coucy, a 13th century French tosafist and disciple of Rabbi Yechiel of Paris. In 1247 he completed his Sefer Mitzvot Gadol, and he needed to decide whether the sin of pride (גאוה) was one of the 248 negative commandments found in the Torah. He decided it was, and listed it as “Negative Prohibition #64”:

ספר מצוות גדול לאוין, ס״ד

השמר לך פן תשכח את ה' אלהיך אזהרה שלא יתגאו בני ישראל כשהקדוש ברוך הוא משפיע להם טובה ויאמרו שבריוח שלהם ועמלם הרויחו כל זה ולא יחזיקו טובה להקב"ה מחמת גאונם שעל זה עונה זה המקרא ואומר גם בפ' ואתחנן ובתים טובים מלאים כל טוב אשר (מאת) [לא מלאת] וגומ' ואכלת ושבעת השמר לך פן תשכח וגו' וזה הפי' שפירשתי מפורש בסמוך פן תאכל ושבעת ובתים טובים תבנה וישבת ובקרך וצאנך ירביון וכסף וזהב ירבה לך וגומ' ורם לבבך ושכחת את ה' אלהיך המוציאך מארץ מצרים וגו' ואמרת בלבבך כחי ועוצם ידי עשה לי את החיל הזה וזכרת את ה' אלהיך כי הוא הנותן לך כח לעשות חיל ומכאן (ב) אזהרה שלא יתגאה האדם במה שחננו הבורא הן בממון הן ביופי הן בחכמה אלא יש לו להיות ענו מאד ושפל ברך לפני ה' אלהי' ואנשי' ולהודות לבוראו שחננו זה

Beware lest you forget the Lord your God." [Deuteronomy 4:23] This is a warning for the Israelites not to become arrogant when God blesses them with prosperity. They should not claim that all their success is due to their own efforts and hard work, thereby neglecting to acknowledge God's goodness due to their pride. This is what the verse addresses, as it also says in the portion of Va'etchanan, "Houses filled with all good things that you did not fill..." [Deuteronomy 6:11] and continues, "And you will eat and be satisfied, beware lest you forget the Lord your God." This interpretation is further explained nearby, "Lest you eat and be satisfied, and build good houses and live in them, and your cattle and sheep increase, and you gather silver and gold in abundance, and your heart becomes haughty, and you forget the Lord your God who brought you out of the land of Egypt..." and "You will say in your heart, 'My strength and the power of my hand made me all this wealth,' but you shall remember the Lord your God, for it is He who gives you the strength to make wealth." From here (b), there is a warning not to be arrogant about what God has granted, whether it is wealth, beauty, or wisdom. Rather, one should be very humble and lowly before the Lord, their God, and before people, and give thanks to their Creator for granting them these qualities.

Rather surprisingly, Moses then described how he had arrived this interpretation of the verse (Deut. 4:23) השמר לך פן תשכח - “Beware lest you forget the Lord your God."

וכשהגעתי להשלים ע"כ הלאוין וארא בחלום במראית הלילה הנה שכחת את העיקר השמר לך פן תשכח את ה' והתבוננתי עליו בבקר והנה יסוד גדול הוא ביראת השם הואלתי לחברו בעזרת יהיב חכמתא לחכימין

When I reached the completion of the prohibitions and saw in a dream at night that I had forgotten the principle, "Beware lest you forget the Lord," I considered it in the morning, and behold, it is a great foundation in the fear of the Lord. Therefore, I decided to include it, with the help of the One who grants wisdom to the wise…

Lo Bashamayim In Theory and Practice

There are many more examples I could share but let’s conclude with Ephraim Kanarfogel, University Professor of Jewish History, Literature and Law at Bernard Revel Graduate School of Jewish Studies and at Stern College for Women. He concludes his fascinating paper Dreams as a Determinant of Jewish Law and Practice in Northern Europe During the High Middle Ages (from where some of these examples were taken), with this thought:

In sum, the (surprisingly) positive or receptive attitude that a number of Tosafists expressed with respect to the potential impact of dreams on the halakhic process, as well as the differences between them about how such dreams should be evaluated and classified, had much in common with the surrounding host culture, even as the Tosafist attitudes were clearly a function of their own rabbinical and mystical sensibilities. As leading students and teachers of talmudic law, the Tosafists were surely cognizant of the principle, lo ba-shamayim hi, “it is not in heaven.” As religious authorities of their age, however, they were more than willing to entertain the possibility that heavenly, dream-like contra-texts could nonetheless contribute to the halakhic enterprise, and to Jewish life and practice more broadly.

Shabbat Shalom and sweet dreams (חלומות פז) from Talmudology

עד הניצחון


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Talmudology on the Parsha, Ki Tavo~ Kri, Ketiv and Hemorrhoids

In this week’s parsha, we read about the rewards for following the word of God. And then we read about the punishments for not doing so. Here is one of the latter:

דברים כח: 15,27

וְהָיָה אִם־לֹא תִשְׁמַע בְּקוֹל יְהֹוָה אֱלֹהֶיךָ לִשְׁמֹר לַעֲשׂוֹת אֶת־כל־מִצְותָיו וְחֻקֹּתָיו אֲשֶׁר אָנֹכִי מְצַוְּךָ הַיּוֹם וּבָאוּ עָלֶיךָ כל־הַקְּלָלוֹת הָאֵלֶּה וְהִשִּׂיגוּךָ׃

…יַכְּכָה יְהֹוָה בִּשְׁחִין מִצְרַיִם ובעפלים [וּבַטְּחֹרִים] וּבַגָּרָב וּבֶחָרֶס אֲשֶׁר לֹא־תוּכַל לְהֵרָפֵא…

But if you do not obey the Lord your God to observe faithfully all His commandments and laws which I enjoin upon you this day, all these curses shall come upon you and take effect…The Lord will strike you with the Egyptian inflammation, with hemorrhoids, boil-scars, and itch, from which you shall never recover.

The word translated as hemorrhoids is written “עפלים,” but that is not what you will hear being chanted. Instead, you will hear the word “טְּחֹרִים.” If you have you wondered why, you are in luck, because this week in Talmudology on the Parsha we will discuss the kri and the ketiv. Oh, and also hemorrhoids.

A Quick Introduction to Kri & Ketiv

There are two traditions that we have about the written Torah, also known as the Five Books of Moses. There is the way the word is written - known as the ketiv, from the Hebrew k-t-v (כ–ת–ב), meaning, well, written, And there is the way that the word is actually pronounced, known as the kri, from the Hebrew k-r-i (ק–ר–י), meaning read.

If Jewish services are familiar to you, then so too is the kri-ketiv. There is one that is said often, and certainly each time we read it in the Torah. It is the name of God, spelled in the Torah in Hebrew as י–ה–ו–ה. It is pronounced something like Yehowah, from where we get the word Jehovah, (as in Witnesses). But whenever we encounter that word in the Torah, or as part of Jewish prayer, we pronounce it Adonai (lit. my Lord). See. It’s a kri-ketiv.

Emanuel Tov, Professor Emeritus of Bible at the Hebrew University (and the editor-in-chief of the Dead Sea Scrolls publication project) is probably the world's leading authority on the textual criticism of the Hebrew. In his classic work Textual Criticism of the Hebrew Bible (I have the second edition, but a third is now available,) he noted that there are anywhere from 848 to 1566 instances of kri-ketiv, depending on which text you consult. (He and other academics rather annoyingly calls them Ketib-Qere, but I suppose if you are the world expert you get to do that kind of thing.)

The notion of the Ketib and Qere in the manuscripts of [the masoretic text] derives from a relatively late period, but the practice was already mentioned in the rabbinic literature…For example, b. Erub. 26 a motes that in 2 Kgs 20:4 “it is written ‘the city,’ but we read ‘court.’ Manuscripts and editions likewise indicate: Ketib העיר, “the city,” Qere חצר, “court.” (p59.)

The Aleppo Codex, (c. 920 CE) Ki Tavo. The subject matter of this post is found in the black box, and the note on the keri is found in the marginalia to its right.

The Origins of the Keri-Ketiv

Summarizing the scholarship, Emanuel Tov suggested four possible origins of the kri-ketiv:

  1. They are corrections

  2. They are variant spellings

  3. They are marginal corrections that later became variant spellings

  4. They are reading traditions

Most scholars adhere to the third reason. “If that view is correct,” he wrote, “most of the Ketib-Qere interchanges should be understood as an ancient collection of variants. Indeed, for many categories of Ketib-Qere interchanges similar differences are known between ancient witnesses [i.e. very old manuscripts].

Sometimes the keri-ketiv avoids profanation, such as the perpetual reading of God’s four-letter name as Adonai. And sometimes they serve “as the replacement of possibly offensive words with euphemistic expressions.” This is what is going on in this week’s parsha, where ובעפלים (and with hemorrhoids) is replaced with וּבַטְּחֹרִים (and with tumors). The Talmud makes this cleaning up of the text explicit:

מגילה כה, ב

תָּנוּ רַבָּנַן: כל הַמִּקְרָאוֹת הַכְּתוּבִין בַּתּוֹרָה לִגְנַאי — קוֹרִין אוֹתָן לְשֶׁבַח, כְּגוֹן: ״יִשְׁגָּלֶנָּה״ — יִשְׁכָּבֶנָּה, ״בַּעֲפוֹלִים״ — בַּטְּחוֹרִים, ״חִרְיוֹנִים״ — דִּבְיוֹנִים, ״לֶאֱכוֹל אֶת חוֹרֵיהֶם וְלִשְׁתּוֹת אֶת מֵימֵי שִׁינֵּיהֶם״ — לֶאֱכוֹל אֶת צוֹאָתָם וְלִשְׁתּוֹת אֶת מֵימֵי רַגְלֵיהֶם

The Sages taught in a baraita: All of the verses that are written in the Torah in a coarse manner are read in a refined manner. For example, the term “shall lie with her [yishgalena]” (Deuteronomy 28:30) is read as though it said yishkavena, which is a more refined term. The term “with hemorrhoids [bafolim]” (Deuteronomy 28:27) is read bateḥorim. The term “doves’ dung [chiryonim]” (II Kings 6:25) is read divyonim. The phrase “to eat their own excrement [choreihem] and drink their own urine [meimei shineihem]” (II Kings 18:27) is read with more delicate terms: To eat their own excrement [tzo’atam] and drink their own urine [meimei ragleihem].

So that explains why the word ובעפלים is read as וּבַטְּחֹרִים. But why are these kinds of swellings mentioned among the curses that await the Israelites if they fail to heed the word of God? Is that the best punishment that God can come up with? Well, it turns out that ophalim likely referenced a truly awful punishment, one that would instill dread and fear. I am talking about bubonic plague.

More than You ever wanted to know about Biblical Hemorrhoids

Let’s fast forward to the Book of Samuel. Having entered the Promised Land, the people of Israel began a long military campaign against its inhabitants, the foremost of which were the Philistines. But they lost not only their battles, but also their Ark, which had been brought to the battlefield in a last-ditch attempt at victory. The captured Ark was taken to Ashdod and placed in a temple to Dagon. God then directed his anger against the Philistines in a most unusual way. He destroyed the idols in the temple and then “struck Ashdod and its territory with swellings” (I Sam 5:6). When the Ark was moved to Gath, another outbreak of “swellings” followed: “The hand of the Lord came against the city, causing great panic; He struck the people of the city, young and old, so that swellings broke out among them” (I Sam 5:9).”

Having understood the terrible danger of keeping the Ark captive, the Philistines sent it back to Israel, but were counseled by their priests not to “send it away without anything; you must also pay an indemnity to Him.” This reparation took a most unusual form: “five golden swellings and five golden mice” (I Sam 6:4). Just what these swellings were is not clear, but there are two possibilities. The first is they were lymph glands in the groin, swollen from infection from bubonic plague. The second is they were hemorrhoids. Both possibilities are hinted to in the Hebrew text and its many translations.

Plague and Bubos

These two quite distinctive words in our parsha - עפלים and טְּחֹרִים have led to the differing explanations of the epidemic. The identification of the Philistine epidemic as bubonic plague privileges the written text, עפלים ophalim. Bubonic plague got its name from the buboes, which are swellings in the axillae and groin. These are the lymph nodes that swell with bacteria and the body’s own dead cells white cells. Bubonic plague is caused by a bacterium called Yersinia Pestis, which is found in fleas that primarily feed on mice and rats, though they can also leap to humans. It swept through Europe as the Black Death in a series of deadly waves that began around 1347, killing a third of the population. But it was also around long before then; fragments from an ancestor of Yersina Pestis have been detected in samples over 3,000 years old.

The Hebrew Bible doesn’t mention the role of rodents in spreading the epidemic, but the Greek translation known as the Septuagint does. This translation was composed around the third century B.C.E. for the Jews of Alexandria, and it adds a detail not found in the Hebrew original: “And the Ark was seven months in the country of the Philistines, and their land brought forth swarms of mice.” These “swarms of mice,” missing from the Hebrew text, are a key to identifying the epidemic. Rodents play a key role in the transmission of bubonic plague. It was these swarms of mice (or really rats, which are the primary host for the rat flea that carries the plague bacteria Yersinia) that were responsible for spreading the plague among the Philistines, causing the lymphatic swellings that characterize the bubonic plague.

One of the first people to identify the outbreak as bubonic plague was the Swiss naturalist Johan Jakob Scheuchzer, who died in 1733. Scheuchzer’s many works included the four-volume Latin Physica Sacra, where he noted that ophalim were buboes. “I therefore come to the conclusion,” he wrote, “that the disease which cased so many deaths among the Philistines was real plague.” But Sheuchzer’s written works were predated by the artist Nicolas Poussin (1594– 1665), whose painting The Plague of Ashdod became “the most imitated and celebrated plague painting of the seventeenth century.”

Nicolas Poussin, The Plague of Ashdod, 1630. From here.

Poussin’s painting shocks. At the foot of the painting lie a dead woman and child, their skin already a pallid green. Another child tries in vain to suckle from the breast of her dead mother. From there we are drawn to the onlookers and those in the throes of death, while in the background bodies are carried away. All around are the rodents, fearless as they come out of their lairs into the daylight. Several figures are pinching their noses to keep out the awful odor from the buboes that had ruptured, while a group looks in dismay at the broken idols in what had been the temple of Dogon. Poussin knew of what he painted for in 1630, the same year in which he began this work, Italy suffered a terrible outbreak of the plague.

Poussin was one of several artists who depicted the Philistine plague. Mice can be seen scurrying over the bodies of four dead Philistines in the lavishly illustrated Crusader Bible created in the mid- thirteenth century. “The victims here lie heaped,” wrote the art historian Otto Neustatter, “but otherwise show no specific signs of the plague, the great ravages of which swept over Europe a century later. Rats, however, swarm from every nook and cranny of the crowded city buildings and attack the bodies and faces of the victims.” And in a woodcut in the Lutheran Lubeck Bible, printed in 1491, “the mice play an especially prominent part.” Although the bacterium that caused bubonic plague was not identified until the mid- nineteenth century, the association of rodents in spreading the disease had long been acknowledged, starting perhaps with the Hebrew Bible itself.

So what were Tehorim?

While modern germ hunters gave primacy to the written text ophalim, rabbinic interpretations of the story focused on the word that was read in its place, tehorim, and first, they had to establish its precise meaning. However, over the centuries there has been little agreement. For Josephus, a first- century Roman Jew, the plague was “dysentery or flux; a sore distemper, that brought death upon them very suddenly.” A millennium later, the medieval French commentator Rabbi Shlomo ben Yitzhak (d.1105) had a different idea. Rashi, as he was known by his acronym, was certain that tehorim affect the rectum, but he then needed to explain how this condition was associated with rodents. So he came up with this: “mice enter through rectum, disembowel the innards, and leave.” Two centuries later, another French exegete Levi ben Gershon (Gersonides) focused on the reason for this choice of divine retribution: “Hemorrhoids are very painful, and they bleed a great deal. And how much more so these, that were sent by God to cause them agony. As a result, they would be forced to send the Ark of God away.” In contrast, David Altschuler of Prague (d. 1769) thought that tehorim was the name of a kind of vermin, while the nineteenth-century philologist Marcus Jastrow wrote that the word is derived from the root ט–ח–ר (t-h-r,) meaning to strain.

Later scholars added their own take on the plague of hemorrhoids. Chaim Yosef Azulai (d. 1806), a prominent rabbi and author was born in Jerusalem, but traveled extensively throughout Europe. In his commentary, he wrote that the Philistines had erred, believing in “their own power and the might of their hands.” They were therefore punished with hemorrhoids “that made them appear like women, since they were in pain and were bleeding as women did.”

חומת אנך שמואל א, 5:6

ויך אותם בטחורים. לפי שטעו לומר שכחם ועוצם ידם עשתה זאת הוכו בטחורים שנדמו לנשים בהיותם כואבים ויוצא הדם כי דרך נשים להם

Some contemporary commentaries have tried to combine the two possibilities into a single narrative. The multivolume Olam Hatanach [The World of the Bible] noted that hemorrhoids may be caused by constipation, and that among the causes of this “the medical literature has identified the buboes found in bubonic plague. Thus, the difference between the keri [what is read] and the ketiv [what is written] is the difference between the ophalim [swellings] as a cause of the illness, and tehorim [hemorrhoids] which were its result.” However, this attempt at reconciliation is forced. Bubonic plague may cause constipation, and just as often it may result in diarrhea. To suggest that hemorrhoids are so identified with bubonic plague that they would be specifically mentioned as a feature of the outbreak seems mistaken.

And what of the odd gifts that the Philistines sent, those “five golden hemorrhoids and five golden mice”? This too has its origin not in the original Hebrew but in the Septuagint translation. In Hebrew there were five ophalim or swellings, meaning perhaps five orbs or balls. But in the Greek translation we read, “According to the number of the lords of the Philistines, five buttocks of gold, for the plague was on you, and on your rulers.” From this Greek version of the Hebrew we move to the Latin. In the late fourth century, Jerome produced a Latin translation of the Hebrew Bible known as the Vulgate, which is still used by the Catholic Church. This translation gave us the quinque anos aureos, “five golden behinds,” which was then translated in the King James Bible as “five golden emerods.” The Revised Version of the Bible, first published in 1884, replaced the word emerods with tumors.

In this week’s parsha, God warns his people about the consequences of not obeying his commands. Earlier in the Torah we read of God bringing rivers of blood, darkness, lightening and the parting of the sea as displays of his limitless power. Now, for a change, God threatens to punish in a most intimate and private way, perhaps known only to the unfortunate subject of his anger. Reader beware.

{Want even more on this topic? Try this post. You are welcome.]

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Bava Basra 84a ~ “Why are Sunsets Red?” asked the Rabbi and the Scientist

Photo by the Talmudology. Sunset from Clearwater Florida, Jan 29, 2020.

Sunset from Clearwater Florida, Jan 29, 2020. Photo from the Talmudology archive.

We are studying the tractate Bava Basrsa (The Last Gate), which is currently dealing with the circumstances under which the sale of goods may be voided.  The Mishnah (83b) ruled that if there is agreement to sell red wheat (שחמתית) and it was found to be white (לבנה), both the seller and the buyer have legal grounds to retract. The Talmud then discusses the names for these colors: what we call red and white are called "like the sun" and "like the moon." Rav Pappa (the Babylonian sage who died in 375CE) took this a step further:

בבא בתרא פד,א

בצפרא דחלפא אבי וורדי דגן עדן בפניא דחלפא אפתחא דגיהנם – ואיכא דאמרי איפכא

In the morning it becomes red as it passes over the site of the roses of the Garden of Eden, [whose reflections give the light a red hue]. In the evening the sun turns red because it passes over the entrance of Gehenna, whose fires redden the light. And there are those who say the opposite [in explaining why the sun is red in the morning and the evening, i.e., in the morning it passes over the entrance of Gehenna, while in the evening it passes over the site of the roses of the Garden of Eden.]

Shmuel ben Meir, known as Rashbam (d. ~1158) explained that "our eyes are not able to discern the colors very well because in the middle of the day the light is blinding. But in the morning and the evening, when the sun is less bright, we can see the redness of the sun."

 מאור עינינו אינו ברור כל כך מתוך אור היום שמכהה עינינו אבל צפרא ופניא שהיום חשוך ניכר אדמומית החמה ורב פפא לפרש משנתנו בא אמאי מקרי שחמתית

According to Rav Pappa, the true color of the sun is red - but this true color can be seen only when the sun is at its least intense - in the evening and the morning. We have all experienced Rav Pappa's description: who cannot be moved by the sight of a blazing red sunrise or sunset? But what is the scientific explanation of these colors?

דְּאָמַר רַבִּי חִיָּיא בַּר אַבָּא אָמַר רַבִּי יוֹחָנָן: מִצְוָה לְהִתְפַּלֵּל עִם דִּמְדּוּמֵי חַמָּה. וְאָמַר רַבִּי זֵירָא: מַאי קְרָאָה — ״יִירָאוּךָ עִם שָׁמֶשׁ וְלִפְנֵי יָרֵחַ דּוֹר דּוֹרִים״

Rabbi Chiyya bar Abba said that Rabbi Yochanan said: It is a mitzva to pray with the reddening of the sun. And Rabbi Zeira said: What is the verse that alludes to this? “Let them fear You with the sun and before the moon, generation after generation” (Psalms 72:5)…
— Berachot 29b
 
The sequence above shows the setting Sun dipping toward the western horizon. As the Sun sinks lower, its color becomes more reddened. From here.

The sequence above shows the setting Sun dipping toward the western horizon. As the Sun sinks lower, its color becomes more reddened. From here.

 

Why sunrise & sunset are red - the science

Here is the scientific explanation. At sunrise and sunset the light from the sun is not directly overhead, but from its position on the horizon it must pass through more of the atmosphere to reach our eyes, as you can see here.

From here.

From here.

You may recall that ever since Newton and his prism we have known that white light is made up of many different wavelengths, or colors of light (Figure 1 below). As the sun’s white light passes through our atmosphere, the shorter wavelengths of light are scattered (Figure 2). And the longer the path through our atmosphere, the more the shorter wavelengths of light are scattered away from the original white sun beam. All of that scattered light (Figure 3) is from the shorter, blue end of the spectrum, which is what colors the sky blue (whatever else your dad may have told you). The remaining unscattered light is at the red end of the spectrum, and that’s why the sun appears red at sunrise and sunset, and why the clouds that reflect it are colored red.

From here.

From here.

The Color of the Sun in Space, and on Earth

According to NASA experts (who really are rocket scientists, among other things), the sun emits all colors of the visible light spectrum. And when you mix all these colors together you get...white. If you were to look at the sun from high in space, (perhaps aboard the International Space Station), it would indeed appear to be a pure white.  Like this:

It was in the seventeenth century that Isaac Newton used a prism to split the sun's light into its constituent colors. Before then it was raindrops that did the same thing, forming a rainbow as a result.

Isaac Newton divided  a ray of sunlight with a prism in a series of experiments published in 1672.  Lego recreation is from here.

Here on Earth, the atmosphere plays a role in the color of the sun. Since shorter wavelength blue light is scattered more efficiently than longer wavelength red light, we lose some of the blue tint of the sun as sunlight passes through the atmosphere. In addition, all wavelengths of visible light passing through our atmosphere are attenuated so that the light that reaches our eyes does not immediately saturate the cone receptors. This allows the brain to perceive color from the image with a little less blue – yellow.
— NASA

The Cultural determinants of the Sun's Color

On their website, the NASA scientists claim that "sometimes the display color of the Sun is culturally determined. If a kindergartener in the USA colors a picture of the Sun, they will usually make it yellow. However, a kindergartener in Japan would normally color it red!"  The rabbis of the Talmud had their own cultural explanation of the colors of the sun.  As we have seen, after suggesting that the color of the sun may actually be white (because that is the color of a patch of skin with zora'at, usually identified as a kind of leprosy), the Talmud then explains the cause of the red sunrises and sunsets:  

ולמאי דסליק דעתין מעיקרא הא קא סמקא צפרא ופניא בצפרא דחלפא אבי וורדי דגן עדן בפניא דחלפא אפתחא דגיהנם

In the morning it becomes red as it passes over the site of the roses of the Garden of Eden, whose reflections give the light a red hue. In the evening the sun turns red because it passes over the entrance of Gehenna, whose fires redden the light...

Without the scientific understanding we have today, the Talmud claimed that the red color of sunrise and sunset was due to the light filtering though the red roses of the Garden of Eden, and fires of Hell.

is the Garden of Eden real or metaphorical?

It would seem that the Talmud's description of the locations of the Garden of Eden and the Gates of Hell is to be taken literally, for it is given as an explanation for physical phenomena.  But here is where things can get tricky. The famous rabbi Joseph Hayyim of Baghdad (1834–1909) wrote a work that is widely read by Sephardic Jews to this day called Ben Ish Hai. He also  published three volumes of responsa between 1901 and 1905 called Rav Pe’alim. (A fourth volume was posthumously published in 1912.) In an undated question, R. Hayyim was asked about the location of the Garden of Eden. In one tradition, the garden was located “on the other side of the world,” somewhere below the equator in the southern hemisphere. However, the questioner continued, the world has been circumnavigated, and the Garden of Eden has not been identified. Where then is it located?

In his answer, R. Hayyim digressed into the truth claims of science, and then returned to the location of the Garden of Eden. He noted that although it may be located on the Earth itself, it existed on a different spiritual plane and would therefore not be perceived by the human senses. I suppose many moderns would agree with the suggestion that the Garden of Eden is not to be found in a geographic location. But today's page of Talmud reminds us that at least in talmudic Babylon, the Garden of Eden was not just a metaphor.  It determined the very colors of the sun.

The Poet and the Scientist

Science is not the only way of understanding the world. Artists, poets, philosophers and religions all add different kinds of knowledge about the very same physical world that science explains. Science explains that a red sunrise is a result of physics. Rabbi Chiyya explained that it is because the sun reflects the red roses of the Garden of Eden. Which explanation most satisfies your mind? And which most satisfies your heart?

In philosophy [i.e.science] one must proceed from wonder to no wonder, that is, one should continue one’s investigation until that which we thought strange no longer seems strange to us; but in theology, one must proceed from no wonder to wonder, that is…[until] that which does not seem strange to us does seem strange, and that all is wonderful.
— Isaac Beekman. Journal tenu par Isaac Beekman de 1604 a 1634. Ed C de Waard. The Hague: M Nijhoff, 1939-53. vol 2, p375.
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