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

Ketuvot 93a ~ Game Theory and the Principle of Contested Sums

We are currently studying a series of cases in co-wives claim the money from their ketuvah when the husband dies. It gets complicated.

משנה, כתובות צג, א

  מי שהיה נשוי שלש נשים ומת כתובתה של זו מנה ושל זו מאתים ושל זו שלש מאות ואין שם אלא מנה חולקין בשוה

היו שם מאתים של מנה נוטלת חמשים של מאתים ושל שלש מאות שלשה שלשה של זהב

היו שם שלש מאות של מנה נוטלת חמשים ושל מאתים מנה ושל שלש מאות ששה של זהב

If a man who was married to three wives died, and the kethubah of one was a maneh (one hundred zuz), of the other two hundred zuz, and of the third three hundred zuz, and the estate was worth only one maneh (one hundred zuz), they divide it equally. 

If the estate was worth two hundred zuz, the claimant with the kesuva of the maneh receives fifty zuz,  while the and the claimants of the two hundred and the three hundred zuz each receive three gold denarii (worth seventy-five zuz).

If the estate was worth three hundred zuz, the claimant of the maneh receives fifty zuz, the claimant of the two hundred zuz receives a maneh (one hundred zuz) and the the claimant of the three hundred zuz receives six gold denarii (worth one hundred and fifty zuz)…

In these cases, each surviving wife claims not all, but only part of the deceased husband’s estate. We find a similar contested case in the opening pages of Bava Metziah. Here, two people claim ownership of a garment; one claims she owns all of it, and the other that she owns 50%:

בבא מציעא ב,ב

שנים אוחזין בטלית ... זה אומר כולה שלי וזה אומר חציה שלי ...זה נוטל שלשה חלקים וזה נוטל רביע

Two hold a garment; ... one claims it all, the other claims half. ... Then the one is awarded 3⁄4, the other 1⁄4.

In this case, the Mishnah rules that each swears under oath, and then the garment is divided with 3/4 awarded to one claimant and 1/4 to the other.

Rashi and the Principal of Contested Sums

In his explanation of the case in Bava Metziah, Rashi notes that the claimant to half the garment concedes that half belongs to the other claimant, so that the dispute revolves solely around the second half. Consequently, each of them receives half of this disputed half - or a quarter each.:

זה אומר חציה שלי. מודה הוא שהחצי של חבירו ואין דנין אלא על חציה הלכך זה האומר כולה שלי ישבע כו' כמשפט הראשון מה שהן דנין עליו נשבעין שניהם שאין לכל אחד בו פחות מחציו ונוטל כל אחד חציו

Now of course this is only one way that the garment could be divided between the two claimants. For example, it could be divided in proportion to the two claims, (2/3-1/3), or even split evenly (1/2-1/2).  But instead, and as Rashi explained, the Mishnah ruled using the principal of contested sums. Which is where Robert Aumann comes in.

Game Theory from Israel's Nobel Prize Winner

We have met Robert Aumann before, when we reviewed Israel's glorious winners of the Nobel Prize. For those who need reminding, Aumanm, from the Hebrew University, won the 2005 Nobel Prize in Economics. His work was on conflict, cooperation, and game theory (yes, the same kind of game theory made famous by the late John Nash, portrayed in A Beautiful Mind). Aumann worked on the dynamics of arms control negotiations, and developed a theory of repeated games in which one party has incomplete information.  The Royal Swedish Academy of Sciences noted that this theory is now "the common framework for analysis of long-run cooperation in the social science." The kippah-wearing professor opened his speech at the Nobel Prize banquet with the following words (which were met with cries of  אמן from some members of the audience): 

ברוך אתה ה׳ אלוקנו מלך העולם הטוב והמיטב

If you haven't already seen it, take the time to watch the four-minute video of his acceptance speech. It should be required viewing for every Jewish high school student (and their teachers).

Where was I? Oh, yes. Contested sums.  In 1985, twenty years before receiving his Nobel Prize, Aumann described the theoretic underpinnings of today's Mishnah, as part of a larger discussion about bankruptcy.  His paper, published in the Journal of Economic Theory, is heavy on mathematical notations and light on explanations for non-mathematicians (like me).  Fortunately he later published a paper that is much easier to read and which covers the same material.  The second paper appeared in the Research Bulletin Series on Jewish Law and Economics, published by Bar-Ilan University in June 2002.  "Half the garment" wrote the professor, "is not contested: There is general agreement that it belongs to the person who claimed it all. Hence, first of all, that half is given to him. The other half, which is claimed by both, is then divided equally between the claimants, each receiving one-quarter of the garment." Here is how Aumann visualizes it:

There is another example of this from the Tosefta, a supplement to the Mishnah and contemporary with it. In this new case, one person claims the entire garment, and one claims only one third of it. In this case, the first person gets 5/6 and the second gets 1/6.  

Aumann calls this principal the "Contested Garment Consistent." And this this principle is found in other contested divisions, like our case in Ketuvot 93a, in which a man dies, leaving debts totaling more than his estate.

Aumann likes to think of it this way:

A Nobel Explanation of today’s daf

Here is how he explains what is going on in today’s page of Talmud.

We’ll call the creditor with the 100-dinar claim “Ketura,” the one with the 200, “Hagar” and the one with the 300, “Sara.” Let’s assume, to begin with, that the estate is 200. As per [the table above], Ketura gets 50 and Hagar 75 – together 125. On the principle of equal division of the contested sum, the 125 gotten by Hagar and Ketura together should be divided between them in keeping with this principle. ... In other words, the Mishna’s distribution reflects a division of the sum that Hagar and Ketura receive together according to the principle of equal division of the contested sum...
The division of the estate among the three creditors is such that any two of them divide the sum they together receive, according to the principle of equal division of the contested sum. This precisely is the method of division laid down in the Mishna in Bava Metzia that deals with the contested garment. 

There's a lot more to the paper, including an interesting proof of the principal using fluids poured into cups of different sizes.  But I prefer to focus on another aspect of the paper.  Prof. Aumann notes that, in addition to its own internal logic, the underlying principle of contested sums fits in well with other talmudic passages. 

The reader may ask, isn’t it presumptuous for us to think that we succeeded in unraveling the mysteries of this Talmudic passage, when so many generations of scholars before us failed? To this, gentle reader, we respond that the scholars who studied and wrote about this passage over the course of almost two millennia were indeed much wiser and more learned than we. But we brought to bear a tool that was not available to them: the modern mathematical theory of games.

The actual sequence of events was that we first discovered that the Mishnaic divisions are implicit in certain sophisticated formulas of modern game theory. Not believing that the sages of the Talmud could possibly have been aware of these complex mathematical tools, we sought, and eventually found, a conceptual basis for these tools: the principle of consistency. Of this, the sages could have been, and presumably were, aware. It in itself is sufficient to yield the Mishnaic divisions; and it is this principle that we describe below, bypassing the intermediate step – the game theory.

It’s like “Alice in Wonderland.” The game theory provides the key to the garden, which Alice had such great difficulty in obtaining. Once in the garden, though, Alice can discard the key; the garden can be enjoyed without it.

What a wonderful analogy. Game theory is the key to entering the garden, a key which might not have been available to earlier generations who learned the Talmud. How lucky we are.  

————

Want more on Today’s Daf? Click here to watch Talmudology reader Dr Shalom Kelman explain a (Non) Game Theory approach.

Shabbat Shalom from Talmudology

Yoma 20b ~ From The Talmudology Yom Kippur Archives: Sound Propagation at Night

In discussing the service on Yom Kippur, the holiest day of the Jewish Year, the Talmud notes that the voice of the Cohen Gadol, the High Priest, could be heard from a distance of ten parsangs. In case you were wondering, a parsang is an old Persian measure, and is about 3 miles or almost 5km. This means that the voice of the High Priest could be heard over 30 miles away! The Talmud notes that it could be heard at this distance even during the day, when sound does not travel as far as it does at night. Here it is, in the original:

שקלים כ,א

דְּאָמַר מָר: וּכְבָר אָמַר ״אָנָא הַשֵּׁם״ וְנִשְׁמַע קוֹלוֹ בִּירִיחוֹ. וְאָמַר רַבָּה בַּר בַּר חָנָה אָמַר רַבִּי יוֹחָנָן: מִירוּשָׁלַיִם לִירִיחוֹ עֲשַׂר פַּרְסֵי

וְאַף עַל גַּב דְּהָכָא אִיכָּא חוּלְשָׁא, וְהָכָא לֵיכָּא חוּלְשָׁא. וְהָכָא יְמָמָא, וְהָתָם לֵילְיָא

דְּאָמַר רַבִּי לֵוִי: מִפְּנֵי מָה אֵין קוֹלוֹ שֶׁל אָדָם נִשְׁמָע בַּיּוֹם כְּדֶרֶךְ שֶׁנִּשְׁמָע בַּלַּיְלָה? מִפְּנֵי גַּלְגַּל חַמָּה שֶׁמְּנַסֵּר בָּרָקִיעַ כְּחָרָשׁ הַמְנַסֵּר בַּאֲרָזִים

There already was an incident where the High Priest recited, in his confession that accompanied the placing of hands on his bull on Yom Kippur: Please God, and his voice was heard in Jericho. And Rabba bar bar Chana said that Rabbi Yochanan said: The distance from Jerusalem to Jericho is ten parasangs.

…here it was during the day, when sound does not travel as well, that the High Priest recited his confession… As Rabbi Levi said: Why is a person’s voice not heard during the day in the manner that it is during the night? It is due to the fact that the sound of the sphere of the sun traversing the sky generates noise like the noise generated by a carpenter sawing cedars, and that noise drowns out other sounds…

As we approach Yom Kippur, we might ask if this is true? Does sound really travel further at night? And if so, why?

Yes. It is true

Rabbi Levi is correct. Sound does indeed travel further at night, as you can see below in this helpful graphic. (For the man with the trumpet, think Cohen Gadol. For the dog, think Jericho.)

From here.

The first thing to know is that the speed of sound is dependent on the temperature of the air. Sound moves quicker in warm air and slower in cold air. During the day the sun heats up the earth’s surface, and in particular it heats up the air that is closest to the ground, which is where the sound travels the fastest. But a heat gradient bends the sound waves upwards, much in the same way that a lens bends light rays. (The gradient in which atmospheric temperature decreases with elevation by an amount known as the adiabatic lapse rate.) As a result, the sound waves travels up and away from the listener, and the sounds are quieter.

The reverse happens at night. At night the ground cools quickly. The higher air is warmer than the air close to the ground. The sound further from the ground travels faster at night causing the sound wave to refract back towards the earth. The listener now hears them as louder than they were during the day. It’s physics! (Though it should be noted that some physicists dispute this explanation.)

It’s not just sound waves

Why radio waves travel further at night. From here.

Here’s a fact that Rabbi Levi did not know. It’s not just sound that is heard better at night. Radio waves are heard better at night too, though for an entirely different reason. To be precise, this does not happen with all radio waves, but just those on the AM and short wave frequencies. Because radio waves only travel in straight lines, they do not follow the curvature of the earth’s surface, and so have a natural range of only 30-40 miles. But they can be transmitted up to the ionosphere, where they bounce off of it and down, back to earth. At night, that ionosphere is protected from the electromagnetic radiation that streams from the sun and tends to distort it. And so the radio waves are reflected back down with less interference, which means they travel further and are easier to detect. As a result, some distant AM radio stations (remember those?) can only be heard at night, though the whole thing becomes rather a moot point since nearly everything broadcast can now be found on the internet, for which the ionosphere is not needed.

Noise pollution

We have demonstrated that sound travels further at night, using our knowledge of the properties of sound waves and the phenomenon of refraction. Rabbi Levi knew none of this, but he had something that very few of us today have: a quiet natural environment. What many of us never experience thanks to noise pollution, he experienced each and every night. He, together with the other sages of the Talmud lived in a world that had no noise other than the sound of human voices around a crackling fire and the background music of the natural world. It was an utterly different experience. Our modern world has given us many things to be grateful for, but noise is not one of them.

May you be blessed for a quiet and peaceful year ahead.

גמר טוב

Ketuvot 86b ~ Who Wants to Marry More?

 תלמוד בבלי כתובות פו ב

יותר ממה שהאיש רוצה לישא אשה רוצה להנשא

More than a man desires to wed, a woman desires to be wed.

What happens if a man owes money to both a debtor and to his ex-wife to pay for her כתובה?

In today's daf, the Talmud teaches that if this unlucky person can only repay one of the debts, he should repay the creditor and not his ex-wife. Although this ruling might discourage women from getting married in the first place, we should not be concerned, because "more than a man desires to wed, a woman desires to be wed."  

We've had other occasions to look at sweeping statements made by the rabbis of the Talmud about ways women view marriage. Resh Lakish famously stated (יבמות 118) that "it was better for a women to live with a husband than to live alone" (though you may recall that there were at least four ways to understand this statement of Resh Lakish). We also noted that the late Rabbi J.B. ("the Rav") Soloveitchik believed that this statement reflected "an existential fact." (It also turned out that he was wrong.) While the Rav didn't declare our new psychological insight to be an "existential fact," does it have any validity to it in today's society? Do women really want to be married more than men?

Societal norms change very fast

In 2015 the US Supreme Court heard oral arguments about whether the Constitution guarantees same-sex couples the right to marry. On the one hand, Justice Kennedy pointed out that the traditional  definition of marriage "has been with us for millennia.  And it’s very difficult for the Court to say, oh, well, we ­­— we know better."  On the other hand, gay marriage was then legal in 36 states in the US. (It is now legal in all 50 states, but stay tuned.) The lesson here is that societal norms of about all aspects of marriage are changing very quickly. It may indeed have been true in talmudic times that women wanted to marry more than did men, but our society is vastly different. And with that note of caution, we may proceed.

Who Wants to be Married?

In 2011 the anthropologist Helen Fisher and two colleagues released the "largest and most comprehensive nationally-representative study of single men and women ever done." They surveyed 5,200 single people in the US aged 21 to over 65, and found "a new picture of single Americans emerges that is radically different than it was 50 years ago..." And what of the talmudic claim that women are more eager to marry? It does not seem to be true, (at least in the US).

This national survey clearly shows that men are just as eager to marry as women are; 33% of both sexes want to say “I do.

A 2021 version of the same survey found that “men (42%) are more ready to find a long-term romantic relationship than women (29%).” So today, at least in the US, it is not correct to say that women want to be married more than men.  Some of Fisher's other findings about the attitudes of single men might surprise you too:

Men in every age group are more eager than women to have children.  Even young men. Among those between ages 21 and 34, 51% of men want kids, while 46% of women yearn for young.  Men are less picky too.  Fewer men say it is important to find a partner of their own ethnic background (20% of men vs 29%  of women said this is a “must have” or “very important”); and fewer say they want someone of their own religion (17% of men vs 28% of women said this is a “must have” or “very important”).   Men are also more likely to have experienced love at first sight...

Let's give the last word to Dr Fisher, (who serves as an advisor to Match.com), and remember the danger of assuming that human nature does not change.

My colleagues and I have put over 60 men and women ages 18-57 into a brain scanner to study the brain circuitry of romantic passion.  We found no gender differences.  This..study supports what I have long suspected: that men are just as eager to find a partner, fall in love, commit long term and raise a family.   It’s an illuminating, indeed myth-shattering, new set of scientific data.  And the sooner we embrace these findings, and fling off our outmoded and unproductive beliefs about both sexes, the faster we will find—and keep–the love we want.