Sukkot

Talmudology for Sukkot~ Take Two Etrogim, and Call Me in the Morning; The Citron as Medicine

The Midrash tells a story of a man who was so generous with his charitable donations that he had no money left to feed his own family. Out of ideas, he did what I suppose anyone in his position would have done. He went to gather up discarded etrogim [the citron taken as part of the four species on the Festival of Sukkot] and went to see a king.

ויקרא רבה לו:ה

, וְנִתְבַּיֵּישׁ לֵילֵךְ לְבֵיתוֹ הָלַךְ לוֹ לְבֵית הַכְּנֶסֶת, חָמָא תַּמָּן מִן אִלֵּין אֶתְרוֹגַיָא דְּמֵינוּקַיָא מְקַלְקְלֵי בְּיוֹם הוֹשַׁעְנָא, וּתְנִינַן תַּמָּן מִיָּד הַתִּינוֹקוֹת שׁוֹמְטִין לוּלָבֵיהֶן וְאוֹכְלִים אֶתְרוֹגֵיהֶם, נְסַב מִנְּהוֹן וּמְלָא יָת סַקָּא וְהָלַךְ לִפְרשׁ בַּיָּם הַגָּדוֹל, עַד שֶׁהִגִּיעַ לִמְדִינַת הַמֶּלֶךְ, כֵּיוָן שֶׁהִגִּיעַ שָׁם אַרָעַת שַׁעְתָּא וְאִשְׁתְּכַח מַלְכָּא חָשֵׁשׁ מֵעוֹי, אָמְרִין לֵיהּ בְּחֶלְמָא אַסְוָתָךְ אֱכֹל מִן אִלֵּין אֶתְרוֹגִין דִּיהוּדָאי מַצְלִין עִמְּהוֹן בְּיוֹם הוֹשַׁעְנָא וְאַתְּ מִתְּסֵי, פִּשְׁפְּשִׁין בְּהַהוּא שַׁעְתָּא לְכָל אִלְפַיָא וּלְכָל מְדִינְתָּא וְלָא אַשְׁכְּחוּן, אָזְלִין וְאַשְׁכְּחוּן לְהַהוּא גַבְרָא יָתֵיב עַל סַקָּא, אָמְרִין לֵיהּ אִית גַּבָּךְ כְּלוּם, אֲמַר לָהֶם גְּבַר מִסְכֵּן אֲנָא וְלֵית גַּבִּי כְּלוּם לִמְזַבְּנָא, פִּשְׁפְּשׁוּ בְּסַקָּא וְאַשְׁכְּחוּן מִן אִלֵּין אֶתְרוֹגִין, וַאֲמָרִין לֵיהּ אִלֵּין מָה הֵן, אֲמַר לוֹן מִן אִלֵּין דִּיהוּדָאי מַצְלֵי בְּיוֹם הוֹשַׁעְנָא, אַטְעָנוּן סַקָּא וְאַעֲלוּהָ קֳדָם מַלְכָּא, אָכַל מַלְכָּא אִלֵּין אֶתְרוֹגַיָיא וְאִתְּסֵי. פַּנּוּן שַׂקָּא וּמְלָאוּהָ דִינָרִין…

…He was ashamed to go to his home. He went to the synagogue and saw there some of the citrons that the children away... He took some of them and filled a sack, and embarked on a voyage in the Mediterranean Sea until he reached the province of the king. When he arrived there, it happened to be that the king had an intestinal illness. They said to him in a dream: ‘Your cure is to eat from those citrons with which the Jews pray on the day of the hoshana, and you will be cured.’ At that time, they searched all the ships and all the provinces, but could not find any. They went and found that man sitting on the sack. They said to him: ‘Do you have anything?’ He said to them: ‘I am a poor man and I have nothing to sell.’ They searched the sack and found those citrons. They said to him: ‘What are they?’ He said to them: ‘From those with which the Jews pray on the day of the hoshana.’ They loaded the sack and took it in before the king. The king ate those citrons and he was cured. They emptied the sack and filled it with dinars..

The etrog as medicine? Yes. People once believed, and many still believe today, that the etrog has medicinal uses. So in honor of Sukkot, let’s talk about some of them.

The Etrog in Ma’aseh Tuviah

The etrog as a medicine appears in one of the first Jewish encyclopedias, written by Tuviah Hacohen. He studied in a yeshivah in Cracow, and at the age of twenty-six, entered the University of Frankfurt, where he began to study medicine. Despite being taken under the wing of Fredrick William, the elector of Brandenburg, and receiving a stipend from him, anti-Jewish sentiment prevented Tuviah from graduating. As a result, he left for the University of Padua, where he graduated with a degree in medicine in 1683 and soon found employment as a physician in Turkey. He published his only work, Ma’aseh Tuviah (The Work of Tuviah), in Venice in 1708 and moved in 1715 to Jerusalem, where he died in 1729.

Tuviah Cohen has long been a favorite of historians of science and Judaism. Perhaps this is because he was a reformer of sorts, ready to sweep away old superstitions and replace them with scientific knowledge. Perhaps it is because his book, Ma’aseh Tuviah, was “ ... the best-illustrated Hebrew medical work of the pre-modern era,” full of wonderful drawings about astronomy and anatomy. Perhaps it is because his book is so clearly printed and a pleasure to read in the original. Or perhaps it is because Cohen was so adamantly opposed to Copernicus that he called him the “Firstborn of Satan”—which made his the first Hebrew work to attack Copernicus and his heliocentric system.

In any event, Tuviah wrote about the wonderful healing properties of the etrog.

Ma'aseh Tuviah, Venice 1708, 146a.

Because in homes that have abundant medicines they also have the five special fruits through with the Land of Israel was blessed, I will write in praise of the of etrog [פרי עץ הדר] which is more beautiful than any other fruit…. both the peel and the fruit itself are delicious to eat, and it also has many wonderful properties [סגולות נפלאות]. The peel alleviates all internal pain and strengthens the muscles. while the white of the fruit strengthens the internal organs. Its bitter taste is good for the liver, and cures thirst. The seeds are also good for internal pain as an an aid for digestion…it is as good as theriac for any person who is ill, and it is particularly beneficial for children with viral infections [ויראוליס] like smallpox. The wood of the tree itself does not have these qualities though without doubt it imparts them to the fruit, which is why the fruit never falls far from the tree [התפוח אינו נופל רחוק מן העץ]. And so if there is a scarcity of the fruit, cut some wood from the etrog tree and boil. It will strengthen the body and a serve to heal the soul.

The Etrog as a Cure for Cholera

We have had occasion in the past to talk about Hayyim Palagi (there are many different ways to spell his last name, 1788– 1868) who was a rabbi and leader of the Jewish community in Izmir (Smyrna), Turkey, though his influence was felt far beyond. Writing about the 1865 cholera outbreak in Turkey, Rabbi Palagi recalled how the Jews had fled Izmir.

In our town of Izmir in 5625 [= 1865] there was an outbreak of cholera, just like the outbreak of 5592 [= 1832] and many fled. The few who remained in the town were expelled by the mayor on the advice of physicians, and left for a nearby mountainside where men, women and children camped, and remained for about three weeks. There was not a single case of cholera the entire time,and the outbreak in the town eventually ended. During that time, I was particular with my prayers, and I prayed to God in the merit of Abraham who was called “a mountain” . . . that the merit of our ancestors would protect us and that we would not fall ill. And so it was. Praise be to God, for his loving kindness endures forever.

I am lucky to own a copy of one of his many works, called Refuah Vehayyim, published in Izmir in 1874. (It even contains three handwritten annotations in the margins written by Rabbi Palagi’s youngest son Yosef.) And here is what you can find on page 12b (though alas, there are no marginalia).

Sefer Refuah Vehayyim, Izmir 1874. 12b. (Chapter 4 #2).

It is written in the name of our teacher Rabbi Hayyim Vital, that to cure cholera take distilled water and the resin of the (?) mastic tree…and take half a cup of the size used for kiddush…and boil it with the resin and give it to the patient. And this is guaranteed.

And it is writtn in the Sefer Otzar Hayyim that this works with etrog peel…

Later in the book, Rabbi Palagi wrote that the etrog can be used for stomach aches in general, and not just those associated with cholera. However, it cannot be any old citron; it must be an etrog used for the mitzvah of lulav and etrog on Sukkot:

Sefer Refuah Vehayyim, Izmir 1874. 51b

For a stomach ache: the remedy is to eat etrogim with were used for the mitzvah of lulav and etrog during the holiday and through Hoshanah Rabbah. For they are used in prayer, and they heal…sometimes they are hard to digest, in which case they should be peeled and then boiled, and then that water should be drunk.

But wait - there’s more

In another of his many books Mo’ed Lekol Chai, Rabbi Palagi recommended the etrog as a means for easing the pains and dangers of childbirth. He cited another work in which this suggestion appeared, though in a slightly different and shorter form. (That work is Nazir Shimshon, published by Ya’akov Shimshon Shabtai Sinigaliah in Pisa in 1783. It is on page 38.)

When a women is pregnant, she should take the etrog on Hosha’ana Rabbah and afer removed the pittom [style] she should distribute charity to the poor each according to her means, and she should pray that God should should save her and that her child should be born healthy.

The reason for this is that there is an opinion that the Tree of Knowledge was an etrog, and when Eve ate from it, Death came into the world. We know that many women die during childbirth, and therefore they should undertake this ritual and say the following prayer:

Master of the Universe, you know that because Chava [Eve] ate from the Tree of Knowledge she sinned and brought Death to the world as well as the pains of childbirth. Had I been there at that time I would not have eaten from it and I would not have benefitted from it in any way, just as I did not want to blemish the etrog during the Festival [of Sukkot] But now I have blemished it, because now it is no longer a mitzvah to take it. I would never want to disobey your mitzvot. Please accept my prayer and my supplication that I should not die as a result of this child or as a result of childbirth. Save me, grant me an easy labor without pain or hardship and let no harm befall me or my child, for you are the God who saves…

And so any man whose woman whose wife is pregnant during Sukkot should arrange for her to take the etrog and give it to his wife and she should follow this procedure. She should say this prayer word for word and conclude by saying “let this infant bring contentment and not pain, and may it be born to a good and peaceful life. Amen.”

Hayyim Pilagi, Mo'ed Lekol Chai Jerusalem 1976 #25.

The Etrog increases Male potency

The etrog. It’s not just for women. In the anonymous collection of segulot called Sefer Refuot published in Vienna in 1926, we find the following recommendation:

Sefer Refuot, Vienna 1926

For increased virility, take four drahms of the tongue of an ox together with half a handful of etrog peel and half a drahm of girofilo

Good to know.

Not so Fast - Chaim Bachrach and his objection

Rabbi Yair Hayyim Bachrach (1638-1702) better known by his famous work the Chavot Yair, was a leading posek of his generation, and led the communities of Worms and Mainz. In his commentary on the Tur (הלכות לולב #664) he also noted the custom of pregnant women biting off the pitum of the etrog, and he was not happy about it. Not at all.

Jewish Etrogs, and Greek Etrogs

The belief in the medicinal properties of the etrog was not unique to our ancestors alone. The Greeks believed it too. In fact, it was they who gave the fruit we know as an etrog a name that reflects just this; they called it Citrus Medica, “the medical citrus" and that is the Latin name of the species to this day. Citrus Medica.

Gaius Plinius Secundus (AD 23/24–79) better known as Pliny the Elder held the cirton tree in very high esteem as demonstrated by this passage in his Natural History (Book XII chapter 7):

The citron tree, called the Assyrian, and by some the Median apple, is an antidote against poisons. The leaf is similar to that of the arbute, except that it has small prickles running across it. As to the fruit, it is never eaten, but it is remarkable for its extremely powerful smell, which is the case, also, with the leaves; indeed, the odour is so strong, that it will penetrate clothes, when they are once impregnated with it, and hence it is very useful in repelling the attacks of noxious insects. The tree bears fruit at all seasons of the year; while some is falling off, other fruit is ripening, and other, again, just bursting into birth. Various nations have attempted to naturalize this tree among them, for the sake of its medical properties, by planting it in pots of clay, with holes drilled in them, for the purpose of introducing the air to the roots;

The Chinese Etrog

To this day, the etrog is used as a medicine in China. They grow several different varieties including the world’s largest citrus, the “Ning’er Giant. And, as the photo below shows, it really is giant.

It is the custom of pregnant women to bite off the tip of the etrog and it is mentioned in the Tzenah Urenah.How fortunate we are that this custom has been utterly uprooted.

 

“Ning’er Giant” citron weighing about 17lb (8kg), held in the gentle hands of the farmer who grew it, Li Hua Zhong, near Ning’er Yunan. (Photo credit David Karp, 18 October 2011.)

 

Some varieties are grown for their antioxidant properties, while others release insulin, which may be of use in Type II diabetes. In fact, according to a 2012 Review on Phytochemical and Pharmacological Properties of Citrus medica Linn, the etrog will cure just about anything.

Result shows that Citrus medica Linn. possesses analgesic, hypoglycaemic, anticholinesterase, anticancer, antidiabetic, hypocholesterolemic, hypolipidemic, insulin Secretagogue, anthelmintic, antimicrobial antiulcer and estrogenic properties.

And presumably, all without any side effects! The Jinguu variety from southern Yunnan is used to treat respiratory disorders, whereas the Qingpi variety, grown in the Provinces of Zhejiang and Jianxi is used for its more general medicinal effects.

Citrus Fruits and the First Randomized controlled Medical Trial

The citrus (but not the etrog, sadly) made a surprising appearance in the first randomized controlled clinical trial that humanity conducted. In the 18th century, sailors in the British Navy, went without fresh fruit for long periods of time. Citrus fruits contain the essential Vitamin C also known as ascorbic acid. Without it you develop a very nasty disease called scurvy. There is lethargy, the hair and teeth fall out, the gums bleed spontaneously, and bruising appears. Without treatment, you die. So yes, it is very nasty.

Sailors were often at sea for months at a time, without access to fruit containing Vitamin C. In the 18th century, it is estimated that more British sailors died from scurvy than died in battle.

For reasons we won’t go into here, a Scottish naval Surgeon named James Lind (1716-1794) had a hunch that the disease was cured by a lack of whatever it was that citrus fruits contained. So he took 12 sailors with scurvy and fed them various experimental diets that included one enriched with oranges and lemons (but not etrogs), and compared them to a similar group of sailors who ate a regular Royal Navy diet. The results were startling.

On the 20th of May 1747, I selected twelve patients in the scurvy, on board the Salisbury at sea. Their cases were as similar as I could have them. They all in general had putrid gums, the spots and lassitude, with weakness of the knees. They lay together in one place, being a proper apartment for the sick in the fore-hold; and had one diet common to all, viz. water gruel sweetened with sugar in the morning; fresh mutton-broth often times for dinner; at other times light puddings, boiled biscuit with sugar, etc., and for supper, barley and raisins, rice and currants, sago and wine or the like. Two were ordered each a quart of cyder a day. Two others took twenty-five drops of elixir vitriol three times a day … Two others took two spoonfuls of vinegar three times a day … Two of the worst patients were put on a course of sea-water … Two others had each two oranges and one lemon given them every day … The two remaining patients, took … an electary recommended by a hospital surgeon … The consequence was, that the most sudden and visible good effects were perceived from the use of oranges and lemons; one of those who had taken them, being at the end of six days fit for duty … The other was the best recovered of any in his condition; and … was appointed to attend the rest of the sick. Next to the oranges, I thought the cyder had the best effects…

The most sudden and visible good effects were perceived from the use of oranges and lemons; one of those who had taken them being at the end of six days fit for duty … The other was the best recovered of any in his condition; and being now deemed pretty well, was appointed nurse to the rest of the sick.

Lind demonstrated that citrus fruits prevented and cured scurvy, and the first randomized controlled clinical trial, now the gold standard for evaluating new drugs, was born. Even Rabbi Bachrach would not have objected to that.

The etrog, whose Latin name means a medicine, has long been a symbol of healing, not only in our own tradition, but in others, often just as ancient. How fitting that we take it this year, a year of pain and sorrow for the Jewish People, and pray for the release of our bothers and sisters in captivity, the safety of our soldiers, and a speedy end to this most terrible and most just of wars. We all need some healing.

עד הניצחון

אַחֵינוּ כָּל בֵּית יִשְׂרָאֵל

הַנְּתוּנִים בַּצָּרָה וּבַשִּׁבְיָה

הָעוֹמְדִים בֵּין בַּיָּם וּבֵין בַּיַּבָּשָׁה

הַמָּקוֹם יְרַחֵם עֲלֵיהֶם

וְיוֹצִיאֵם מִצָּרָה לִרְוָחָה

וּמֵאֲפֵלָה לְאוֹרָה

וּמִשִּׁעְבּוּד לִגְאֻלָּה

הָשָׁתָא בַּעֲגָלָא וּבִזְמַן קָרִיב

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Talmudology Redux ~ Could the Vilna Gaon Have Stayed Awake Over Sukkot?

The Vilna Gaon, (lit. The Genius of Vilna) lived from 1720-1797, and next week, the 19th of Tishrei, is the Hebrew anniversary of his death. He was one of the leading talmudic and halakhic authorities of his time. His works are widely studied to this day, and his legal opinions are often cited. Today’s question is: did the Vilna Gaon stay awake for several consecutive days one Sukkot? Here is the background:

The Vilna Gaon.

In January 1788 the Vilna Gaon was involved in the kidnapping of a young Jewish man who had converted to Christianity. For his role in the kidnapping Rabbi Eliyahu (the given name of the Gaon) was arrested and held for over a month.  The case was later tried, and on September 15, 1789 (sic) the Gaon of Vilna, together with others involved in the kidnapping, was sentenced to twelve weeks in jail.  Although it is unclear how long he was imprisoned, he was there over Sukkot, and the Lithuanian authorities were hardly in the practice of providing imprisoned Jews with a sukkah.  But since one is not permitted to sleep outside of the sukkah, what was the Gaon to do?  Simple.  He’d stay awake, and by doing so he would not transgress the prohibition of sleeping outside the sukkah.  Here’s how the episode is described in the work Tosefet Ma’aseh Rav published in 1892. 

Our Leader, teacher and Rabbi may he rest in peace, when he was imprisoned on Sukkot, tried with all his strength, and walked from one place to another, and held his eyelids open, and made an extraordinary effort not to sleep outside the sukkah – not even a brief nap – until the authorities released him to a sukkah.

We don’t know for how many nights the sixty-nine year-old Rabbi Eliyahu stayed awake, but is such a claim even plausible? As it turns out, it is.

The World Record for Staying Awake

The world record for staying awake is an amazing eleven days. Eleven days – that’s 264 hours (and 24 minutes to be precise) without sleep. It was set in 1965 by Randy Gardner, who was then seventeen years old. Gardner seems to have suffered little if any harm by his marathon period of sleep deprivation. But don’t try and beat the record. The Guinness Book of Records no longer has an entry for staying awake – because it is considered too dangerous an ordeal to undertake. (You can hear a review of sleep deprivation stunts in general and a wonderful interview with Gardner himself here.)

The Health Risks of Sleep Deprivation

What are the health risks of prolonged sleep deprivation? A 1970 study of four volunteers who stayed awake for 205 hours (that’s eight and a half days!) noted some differences in how the subjects slept once they were allowed to do so, but follow-up testing of the group conducted 6-9 months after the sleep deprivation showed that their sleep patterns were similar to the pre-deprivation recordings.

Sleep deprivation reduces learning, impairs performance in cognitive tests, prolongs reaction time, and is a common cause of seizures. In the most extreme case, continuous sleep deprivation kills rodents and flies within a period of days to weeks. In humans, fatal familial or sporadic insomnia is a progressively worsening state of sleeplessness that leads to dementia and death within months or years.
— Lulu Xie et al. Sleep Drives Metabolite Clearance from the Adult Brain. Science 2013. 342.317

Although Randy Gardner and these four volunteers seem to have suffered no long-term health consequences of staying awake for over a week, scientists have long noted that sleep deprivation is rather bad for the body. Or to be more precise, the bodies of unfortunate laboratory rats who are not allowed to sleep. In these animals, prolonged sleep deprivation causes the immune system to malfunction. This results in infection and eventual lethal septicemia. The physiologist who kept these rats awake noted that there are “far-reaching physical implications resulting from alterations in immune status [which] may explain why sleep deprivation effects are risk factors for disease and yet are not well defined or specifically localized.” In other words, sleep deprivation makes rats really sick, but we don’t know how, or why…

One possible explanation was suggested in 2013 by a group from the University of Rochester Medical Center. They demonstrated that during sleep, the space between the cells of the brain (the interstitial space) increased by up to 60%, allowing toxic metabolites to be cleared. This raises the question of whether the brain sleeps in order to expel these toxic chemicals, or rather it is the chemicals themselves that drive the brain to switch into a sleep state.

The extracellular (interstitial) space in the cortex of the mouse brain, through which cerebral spinal fluid moves, increases from 14% in the awake animal to 23% in the sleeping animal, an increase that allows the faster clearance of metabolic waste products and toxins. From Suzana Herculano-Houzel. Sleep it out. Science 2013: 342; 316

Not having any sleep is bad for your health - but so too is going without enough sleep. Chronic restriction of sleep to six hours or less per night can produce cognitive performance deficits equivalent to up to two nights of total sleep deprivation. So be sure to get a full night's rest.

Hard, But Not Impossible

The world record set by Randy Gardner has implications for a talmudic decision. In the tractate Shavuot (26b) Rabbi Yochanan ruled that since it was impossible to stay awake for more than three days, any vow to do so is considered to have been a vow made in vain – and punishment follows swiftly.  Here is how the ArtScroll Talmud explains this ruling, (based on the explanation of the Ran).

Since it is impossible for a person to go without sleep for three days, the man has uttered a vain oath. Hence, he receives lashes for violating the prohibition (Exodus 20:7): לא תשא את שם ה׳ אלוקיך לשוה, You shall not take the Name of Hashem, your God, in vain. And since the oath -being impossible to fulfill -has no validity, he is not bound by it at all and may sleep immediately.

Maimonides codified this law and also assumed that it is impossible to stay awake for three consecutive days. 

רמב"ם הלכות שבועות פרק ה הלכה כ

נשבע שלא יישן שלשת ימים, או שלא יאכל כלום שבעת ימים וכיוצא בזה שהיא שבועת שוא, אין אומרין יעור זה עד שיצטער ויצום עד שיצטער ולא יהיה בו כח לסבול ואח"כ יאכל או יישן אלא מלקין אותו מיד משום שבועת שוא ויישן ויאכל בכל עת שירצה

If a person swore that he would not sleep for three days, or would not eat anything for seven days, or something similar, this is considered a false oath. We do not tell the person to stay awake until it is impossible to do so, or fast for as long as possible until the discomfort is too great to bear, and then allow him to eat or sleep. Rather he is punished with lashes immediately for making a false oath, and is then allowed to sleep or eat as much as he wants…

Based on Randy Gardner’s feat, Rabbi Yochanan was incorrect when he ruled that it was impossible to stay awake for three days. It's certainly not impossible, but that hardly means it's a good idea to try. 

It also means that the story of the Gaon of Vilna’s sleepless nights in that cold prison might indeed have occurred. Still it is best not to disrupt your usual sleep patterns. Perhaps that is why Rabbi Chaninah ben Chachina'i in Masechet Avot  (3:4) taught that one who stays awake at night "will forfeit with his life."  Now that's a warning to heed.

רבי חנינא בן חכינאי אומר הנעור בלילה ... הרי זה מתחייב בנפשו

HAPPY SUKKOT FROM TALMUDOLOGY

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From the Talmudology Archives: ~ Gauss, Tosafot, and Counting the Sukkot Sacrifices

We are currently celebrating the seven-day festival (or eight outside Israel) of Sukkot (Tabernacles). When the Temple in Jerusalem stood, it was a time when a large number of animals were sacrificed. A very large number. For each of the seven days of the festival, in addition to two rams, fourteen lambs and one goat there were a number of bulls that were sacrificed. Thirteen on the first day, twelve on the second, eleven on the third, ten on the fourth, nine on the fifth, eight on the sixth and finally seven bulls on the last day.

במדבר 29:12-34

וּבַחֲמִשָּׁה עָשָׂר יוֹם לַחֹדֶשׁ הַשְּׁבִיעִי מִקְרָא־קֹדֶשׁ יִהְיֶה לָכֶם כָּל־מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ וְחַגֹּתֶם חַג לַה׳ שִׁבְעַת יָמִים׃ 

וְהִקְרַבְתֶּם עֹלָה אִשֵּׁה רֵיחַ נִיחֹחַ לַה פָּרִים בְּנֵי־בָקָר שְׁלֹשָׁה עָשָׂר אֵילִם שְׁנָיִם כְּבָשִׂים בְּנֵי־שָׁנָה אַרְבָּעָה עָשָׂר תְּמִימִם יִהְיוּ…׃ 

וּבַיּוֹם הַשֵּׁנִי פָּרִים בְּנֵי־בָקָר שְׁנֵים עָשָׂר אֵילִם שְׁנָיִם כְּבָשִׂים בְּנֵי־שָׁנָה אַרְבָּעָה עָשָׂר תְּמִימִם׃… 

וּבַיּוֹם הַשְּׁלִישִׁי פָּרִים עַשְׁתֵּי־עָשָׂר אֵילִם שְׁנָיִם כְּבָשִׂים בְּנֵי־שָׁנָה אַרְבָּעָה עָשָׂר תְּמִימִם׃… 

and so on…

Numbers 29:34

Pablo Picasso: “Bull,” 1945

On the fifteenth day of the seventh month, you shall observe a sacred occasion: you shall not work at your occupations.—Seven days you shall observe a festival of the LORD.— 

You shall present a burnt offering, an offering by fire of pleasing odor to the LORD: Thirteen bulls of the herd, two rams, fourteen yearling lambs; they shall be without blemish. 

The meal offerings with them—of choice flour with oil mixed in—shall be: three-tenths of a measure for each of the thirteen bulls, two-tenths for each of the two rams, 

and one-tenth for each of the fourteen lambs. 

And there shall be one goat for a sin offering—in addition to the regular burnt offering, its meal offering and libation. 

Second day: Twelve bulls of the herd, two rams, fourteen yearling lambs, without blemish… 

Third day: Eleven bulls, two rams, fourteen yearling lambs, without blemish…

and so on… 

So how many bulls would the manager of the Temple inventory have to make ready for the entire festival of Sukkot? Well, you could just add them up, which is not too hard (13+12+11+10+9+8+7=70), but there is another way, which is found in the medieval commentary known as Tosafot, on page 106 of the tractate Menachot. Let’s take a look. 

Another offering, another math problem

We read there that the mincha offering is accompanied by a minimum of a one-issaron measure of flour. But a mincha can also be accompanied by a multiple of that number, up to a maximum of 60 issronot. What happens if a person vows to bring a specific number of issronot of flour to accompany a mincha offering but cannot recall how many he had in mind? What number of issronot of flour should he offer? Well it’s a bit tricky. The sages ruled that a single offering using the full sixty issronot of flour is all that needs to be brought. But the great editor of the Mishnah, Rabbi Yehudah Hanasi disagreed. In a spectacular way. Here is the discussion:

מנחות קו, א

תנו רבנן פירשתי מנחה וקבעתי בכלי אחד של עשרונים ואיני יודע מה פירשתי יביא מנחה של ששים עשרונים דברי חכמים רבי אומר יביא מנחות של עשרונים מאחד ועד ששים שהן אלף ושמונה מאות ושלשים

The Sages taught in a baraita: If someone says: I specified that I would bring a meal offering, and I declared that they must be brought in one vessel of tenths of an ephah, but I do not know what number of tenths I specified, he must bring one meal offering of sixty-tenths of an ephah. This is the statement of the Rabbis. Rabbi Yehuda HaNasi says: He must bring sixty meal offerings of tenths in sixty vessels, each containing an amount from one-tenth until sixty-tenths, which are in total 1,830 tenths of an ephah.

Since there is a doubt as to the true intentions of the vow, Rabbi Yehudah HaNasi covers all the bases and requires that every possible combination of a mincha offering be brought. So you start with one mincha offering accompanied with one issaron of flour, then you bring a second mincha offering accompanied with two issronot of flour, then you bring a third mincha together with three issronot, and so on until you reach the maximum number of issronot that can accompany the mincha - that is until you reach sixty. The total number of Rabbi Yehudah HaNasi’s mincha offerings is then calculated: 1,830.

How did the Talmud arrive at that number? We are not told, and presumably you simply add up the series of numbers 1+2+3+4….+59+60, which gives a total of 1,830. That certainly would work. But Tosafot offers a neat mathematical trick to figure out the sum of a mathematical sequence like this:

שהן אלף ושמונה מאות ושלשים. כיצד קח בידך מאחד ועד ששים וצרף תחילתן לסופן עד האמצע כגון אחד וששים הם ס"א שנים ונ"ט הם ס"א ושלש ונ"ח הם ס"א כן תמנה עד שלשים דשלשים ושלשים ואחד נמי הם ס"א ויעלה לך שלשים פעמים ס"א

How did we arrive at 1,830? Take the series from 1 to 60 and add the sum of the first to the last until you get to the middle. Like this: 1+60=61; 2+59=61; 3+58=61. Continue this sequence until you get to 30+31 which is also 61. You will have 30 sets of 61 (ie 1,830).

Tosafot continues with the math lesson, and lets us know the total number of bulls sacrificed over the seven day festival of Sukkot:

וכן נוכל למנות פרים דחג דעולין לשבעים כיצד ז' וי"ג הם עשרים וכן ח' וי"ב הם עשרים וכן ט' וי"א הם כ' וי' הרי שבעים

This method may also be used to count the number of sacrificial bulls on Sukkot, which are a total of 70. How so? [There are thirteen offered on the first day of sukkot, and one fewer bull is subtracted each day until the last day of sukkot, on which seven bulls are offered.] 13+7=20; 12+8=20; 11+9=20… [There are a total of 3 pairs of 20+ an unpairable 10]= 70.

In mathematical terms, the Tosafot formula for the sum (S) of the consecutive numbers in Rebbi’s series, where n is the number of terms in the series and P is the largest value, is S= n(P+1)/2. Which reminds us of…

Carl Friedrich Gauss

Carl Friedrich Gauss (1777-1855) was one of the world’s greatest mathematicians. He invented a way to calculate the date of Easter (which is a lot harder than you’d think), and made major contributions to the fields of number theory and probability theory. He gave us the Gaussian distribution (which you might know as the ”bell curve”) and used his skills as a mathematician to locate the dwarf planet Ceres. The British mathematician Henry John Smith wrote about him that other than Isaac Newton, “no mathematicians of any age or country have ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied.”

There is a delightful (though possibly apocryphal) story about Gauss as a bored ten-year old sitting in the class of Herr Buttner, his mathematics teacher. There are at least 111 slightly different versions of the story, but here is one, as told by Tord Hall in his biography of Gauss:

When Gauss was about ten years old and was attending the arithmetic class, Buttner asked the following twister of his pupils. “Write down all the whole numbers from 1 to 100 and add their sum…The problem is not difficult for a person familiar with arithmetic progressions, but the boys were still at the beginner’s level, and Buttner certainly thought that he would be able to take it easy for a good while. But he thought wrong. In a few seconds, Gauss laid his slate on the table, and at the same time he said in his Braunschweig dialect: “Ligget se” (there it lies). While the other pupils added until their brows began to sweat, Gauss sat calm and still, undisturbed by Buttner’s scornful or suspicious glances.

How had the child prodigy solved the puzzle so quickly? He had added the first number (1) to the last number (100), the second number (2) to the second from last number (99) and so on. Just like Tosafot suggested. The sum of each pair was 101 and there were 50 pairs. And so Gauss wrote the answer on his slate board and handed it to Herr Buttner. It is 5,050.

THE Number of bulls=70

Gauss was raised as a Lutheran in the Protestant Church, and so he did not learn of this method from reading Tosafot. But it is delightful to learn that the same mathematical method that launched Gauss into his career as a mathematician predated him by at least four-hundred years and can be found on page 106a of Menachot, where it also applies to the festival of Sukkot.

Happy Sukkot from Talmudology

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From the Talmudology Archives: The Vilna Gaon’s Sleepless Nights over Sukkot

Tonight is the start of the joyous festival of Sukkot (Tabernacles) in which we remember our time in the wilderness by conducting all of our daily activities outside, in makeshift booths. In honor of Sukkot, here is a Talmudology encore presentation that involves vows, sleep, and the Vilna Gaon’s refusal to sleep in prison over Sukkot.

Let’s start with the Talmud in Nedarim, the tractate that deals with vows.

נדרים טו א

והא"ר יוחנן שבועה שלא אישן שלשה ימים מלקין אותו וישן לאלתר

...Rabbi Yochanan said "An oath that I will not sleep for three days" - we lash him [since he took an oath in vain] and he may sleep immediately...(Nedarim 15a)

How long can you go without sleep? If you are like me, staying awake for just one night can be very challenging.  I worked my share of night shifts in the emergency department for over fifteen years (amounting to hundreds of overnight shifts) but it never got any easier with time. We all push ourselves when we need to, but is there a physiological limit to the amount of time that you can stay awake?

The World Record for Staying Awake

The world record for staying awake is an amazing eleven days. Eleven days – that’s 264 hours (and 24 minutes to be precise) without sleep. It was set in 1965 by Randy Gardner, who was then seventeen years old. Gardner seems to have suffered little if any harm by his marathon period of sleep deprivation. But don’t try and beat the record. The Guinness Book of Records no longer has an entry for staying awake – because it is considered too dangerous an ordeal to undertake. (You can hear a review of sleep deprivation stunts in general and a wonderful interview with Gardner himself here.)

The Health Risks of Sleep Deprivation

A 1970 study of four volunteers who stayed awake for 205 hours (that’s eight and a half days!) noted some differences in how the subjects slept once they were allowed to do so, but follow-up testing of the group conducted 6-9 months after the sleep deprivation showed that their sleep patterns were similar to the pre-deprivation recordings.

Although Randy Gardner and these four volunteers seem to have suffered no long-term health consequences of staying awake for over a week, scientists have long noted that sleep deprivation is rather bad for the body. Or to be more precise, the bodies of unfortunate laboratory rats who are not allowed to sleep. In these animals, prolonged sleep deprivation causes the immune system to malfunction. This results in infection and eventual lethal septicemia. The physiologist who kept these rats awake noted that there are “far-reaching physical implications resulting from alterations in immune status [which] may explain why sleep deprivation effects are risk factors for disease and yet are not well defined or specifically localized.” In other words, sleep deprivation makes rats really sick, but we don’t know how, or why…

One possible explanation was suggested in a 2013 by a group from the University of Rochester Medical Center. They demonstrated that during sleep, the space between the cells of the brain (the interstitial space) increased by up to 60%, allowing toxic metabolites to be cleared. This raises the question of whether the brain sleeps in order to expel these toxic chemicals, or rather it is the chemicals themselves that drive the brain to switch into a sleep state.

The extracellular (interstitial) space in the cortex of the mouse brain, through which cerebral spinal fluid moves, increases from 14% in the awake animal to 23% in the sleeping animal, an increase that allows the faster clearance of metabolic waste products and toxins. From Suzana Herculano-Houzel. Sleep it out. Science 2013: 342; 316

Not having any sleep is bad for your health - but so too is going without enough sleep. Chronic restriction of sleep to six hours or less per night can produce cognitive performance deficits equivalent to up to two nights of total sleep deprivation. So be sure to get a full night's rest.

How long did the Vilna Gaon stay awake?

And now, with this background, we can turn to Sukkot. In his book on the Vilna Gaon, Eli Stern reviewed an episode in which the Gaon (d. 1797) was jailed on charges of kidnapping. (It’s a long story, but the Vilna Gaon was involved in the kidnapping of a young Jewish man who had converted to Christianity.) This episode occurred in January 1788, after which the Gaon was arrested and held for over a month.  The case was later tried, and on September 15, 1789 (sic) the Gaon of Vilna (together with others involved in the kidnapping) was sentenced to twelve weeks in jail.  Although it is unclear how long he was imprisoned, he was there over Sukkot, and the Lithuanian authorities were hardly in the practice of providing imprisoned Jews with a sukkah.  But since one is not permitted to sleep outside of the sukkah, what was the Gaon to do?  Simple.  He’d stay awake, and by doing so he would not transgress the prohibition of sleeping outside the sukkah.  Here’s how the episode is described in the work Tosefet Ma’aseh Rav published in 1892. 

Our Leader, teacher and Rabbi may he rest in peace, when he was imprisoned on Sukkot, tried with all his strength, and walked from one place to another, and held his eyelids open, and made an extraordinary effort not to sleep outside the sukkah – not even a brief nap – until the authorities released him to a sukkah.

We don’t know for how long the sixty-nine year-old Elijah stayed awake, but any suggestion that he was awake for the entire holiday of Sukkot seems to be far fetched (though as we have seen, not entirely impossible).

Hard, But Not Impossible

As we read in the Talmud, Rabbi Yochanan ruled that since it impossible to stay awake for more than three days, any vow to do so is considered to have been a vow made in vain – and punishment follows swiftly.  Here is how the ArtScroll Talmud explains this ruling, (based on the explanation of the Ran).

Since it is impossible for a person to go without sleep for three days, the man has uttered a vain oath. Hence, he receives lashes for violating the prohibition (Exodus 20:7): לא תשא את שם ה׳ אלוקיך לשוא, You shall not take the Name of Hashem, your God, in vain. And since the oath -being impossible to fulfill -has no validity, he is not bound by it at all and may sleep immediately.

We have seen however, that while it’s not a good idea to do so on any kind of regular basis, it is certainly possible to stay up for longer than three days. (Back in the 1970s, some volunteers would even do so for as little as $100). Maimonides codified this law and also assume that it is impossible to stay awake for three consecutive days. 

רמב"ם הלכות שבועות פרק ה הלכה כ

נשבע שלא יישן שלשת ימים, או שלא יאכל כלום שבעת ימים וכיוצא בזה שהיא שבועת שוא, אין אומרין יעור זה עד שיצטער ויצום עד שיצטער ולא יהיה בו כח לסבול ואח"כ יאכל או יישן אלא מלקין אותו מיד משום שבועת שוא ויישן ויאכל בכל עת שירצה

Based on what we've reviewed, Rabbi Yochanan was incorrect when he stated that it was impossible to stay awake for three days. It's certainly not impossible, but that hardly means it's a good idea to try. 

Sleep deprivation reduces learning, impairs performance in cognitive tests, prolongs reaction time, and is a common cause of seizures. In the most extreme case, continuous sleep deprivation kills rodents and flies within a period of days to weeks. In humans, fatal familial or sporadic insomnia is a progressively worsening state of sleeplessness that leads to dementia and death within months or years.
— Lulu Xie et al. Sleep Drives Metabolite Clearance from the Adult Brain. Science 2013. 342.317

This may explain the teaching of Rabbi Chaninah ben Chachina'i in Masechet Avot  (3:4) who taught that one who stays awake at night "will forfeit with his life."  Now that's a warning to heed.

רבי חנינא בן חכינאי אומר הנעור בלילה ... הרי זה מתחייב בנפשו

Happy Sukkot from Talmudology 

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