Bava Metzia 2a ~ Garments, Game Theory and the Principal of Contested Sums

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.

We open the new masechet of Bava Metzia with two people claiming ownership of a garment. One claims that it belongs entirely to her, and the other claims he owns half of the garment.  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  our Mishnah, 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." It turns out that this principal is found in other contested divisions, like a case in Ketuvot 93a, in which a man dies, leaving debts totaling more than his estate. The Mishnah explains how the estate should be divided up among his three wives, each of who has a claim. And it uses the same principal as the one found in today's Mishnah: the Contested Garment Consistent.

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)…

Aumann likes to think of it this way:

Here is how he explains what is going on in the Mishnah in Ketubot.

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 principal 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.  

Happy learning, and שנה טובה, a happy New Year from Talmudology.

 

 

Bava Kamma 115b ~ Drinking Snake Venom

בבא קמא קטו, ב

והתניא מים שנתגלו הרי זה לא ישפכם ברשות הרבים ולא יגבל בהן את הטיט ולא ירבץ בהן את הבית ולא ישקה מהם את בהמתו ולא בהמת חבירו

It was taught in a Baraisa: water that was left uncovered should not be spilled out in a public area, nor should one knead clay with it, nor should one lay in the dust with it, nor should one give it to his animal, nor the animal of his friend, to drink. (Bava Kamma 115b)

Don't Drink That Water!

The rabbis of the Talmud were very worried indeed about the health effects of water that had been left uncovered.  This concern was codified by Maimonides, and later by Ya'akov ben Asher, the Rosh, (d. 1340) in his famous halakhic work called the Arba'ah Turim

טור יורה דעה הלכות מאכלי עובדי כוכבים סימן קטז 

דברים האסורים משום סכנה
  יש דברים שאסרום חכמים משום סכנה כגון משקין שנתגלו שיש לחוש שמא שתה מהן נחש והטיל בהן ארס אפי' אם שתו מהן אחרים ולא הוזקו אין לשתות מהן  שיש נחש שהארס צף למעלה ויש שארס שלו מפעפע עד אמצעית המשקה  ויש שהארס שלו שוקע לשולי הכלי לפיכך אפי' שתו ממנו אחרים ולא הוזקו אין לשתות מהן דשמא ארס של הנחש ששתה מהן שוקע ואלו המשקין שיש בהן משום גילוי מים יין חלב ודבש ושום כתוש 

Tur, Yoreh De'ah 116. Things that are Prohibited Because they are Dangerous

There are things that the rabbis of the Talmud prohibited because they are dangerous. For example, liquids that were left uncovered, because of the possibility that a snake drank from the water and expelled some of its poison into them. Even if others had drunk from the liquid, and not been injured, one should not drink from them.  For some snake venom floats on the surface, and some sinks to the middle and some moves to the edges of the vessel. Therefore, even if others had drunk and had suffered no harm, one should not drink from them, for perhaps the venom from the snake that had drunk the water had sunk to the bottom. The following liquids should not be drunk if they were left overnight in an uncovered vessel: water, wine, milk, honey, and crushed garlic...

The normative Code of Jewish Law, the שולחן ערוך agreed, but added an important caveat:

שולחן ערוך יורה דעה הלכות מאכלי עובדי כוכבים סימן קטז סעיף א 

משקים שנתגלו, אסרום חכמים דחיישינן שמא שתה נחש מהם והטיל בהם ארס. ועכשיו שאין נחשים מצויים בינינו, מותר

The rabbis forbade drinking from liquids that were left uncovered,. They were concerned that a snake may have drunk from them and expelled some of its poison into them. But now that snakes are not commonly encountered, this is permitted. (Shulchan Aruch Yoreh De'ah 116:1)

So today it is permitted for us to drink from an uncovered pot, but only in a place that does not have a problem with poisonous snakes.  Which is not helpful. There are poisonous snakes in nearly every state in the US, resulting in about 2,000 human envenomations each year, and we have noted before that Israel has its own problem with snakes, including the Palestinian Viper.  The World Health Organization estimates that snakes kill between 20,000 and 94,000 people per year. So exactly where this leniency of the Shulchan Aruch might apply is not clear.

But is drinking snake venom indeed dangerous? Maybe not. In 2012 India Today reported that police in New Delhi had seized about half a liter of snake venom to be used "in high-end raves planned for Valentine's Day in and around the national capital." Apparently the venom, when ingested, produces a euphoric state. Who knew?

Video evidence - Drinking Cobra Venom

It is really hard to find any peer-reviewed scientific studies about people drinking snake venom, because, um, it's a silly thing to do.  But that doesn't mean it hasn't been done. So where could we turn to find people doing silly things? YouTube of course. (Warning. This video involves spitting. Not by the snakes.)

Want more? Ok then. Here's another one. This time it involves drinking the venom directly from spitting snake. Apparently, these kind of human interest stories are popular in India. 

Why it is safe to drink snake venom

If you are a diabetic and take insulin, or know someone who does, you may have wondered why the drug has to be injected. It would, after all, be much less bothersome to swallow an insulin pill than to inject insulin several times a day.  The reason is that insulin is a protein, and like all proteins, it is easily broken down by heat and, more importantly, by the acid environment in the stomach.  Our gastrointestinal tracts evolved to break down proteins into their building blocks - and they perform a wonderful job doing precisely that.

Like insulin, snake venom is a complex protein. And so, like insulin, it too is easily broken down in the very acidic environment of your stomach.  Of course, if intact venom gets into your bloodstream, it could kill you. But if you drink venom, then the intact protein never does get into your bloodstream. You don't need to be an Indian snake charmer to safely drink snake venom. You just need a working digestive system.

HOW SNAKES DRINK

 In case you were wondering how we know how snakes drink, here is a diagrammatic view of the apparatus used to record the kinematics and water transport during drinking. The video camera was placed to the left. LED, light-emitting diode. From Cundall, D. Drinking in snakes: kinematic cycling and water transport. The Journal of Experimental Biology. 2000; 203, 2171–2185.

 In case you were wondering how we know how snakes drink, here is a diagrammatic view of the apparatus used to record the kinematics and water transport during drinking. The video camera was placed to the left. LED, light-emitting diode. From Cundall, D. Drinking in snakes: kinematic cycling and water transport. The Journal of Experimental Biology. 2000; 203, 2171–2185.

The Talmud was concerned that snakes leave venom in water from which they drank, and that a person drinking from that water would then suffer from envenomation. As we have seen, this concern has no biological basis, although theoretically, if there was an open cut or ulcer in the mouth, ingested venom could get into the bloodstream and then cause its havoc.  But there is another reason why the talmudic concern is overstated.  Snakes, you see, don't leave any venom when they drink water.  As you may have noted from watching the first video, it takes a lot to get a snake to expel its venom - like sticking a blue pen in its mouth.  Venom is a snake's most precious commodity, and it has evolved to protect that commodity. Snakes only release venom when they are in danger, or ready to strike their prey, and not otherwise. Want a great example? The venomous rattlesnake. That species has evolved a warning rattle to tell would-be predators that if they get any closer, they will be bitten. This only makes evolutionary sense if it was in the snake's best interest to do everything possible to conserve its venom.

In a fascinating article on how snakes drink published in The Journal of Experimental Biology, David Cundall notes that a snake's tongue does not carry or move water, and that "in many snakes, the tongue does not visibly move during drinking." That leads to the conclusion that snakes are suction drinkers. And that makes them even less likely to leave any venom behind in the water.

As far as is known, all snakes are suction drinkers, and the only critical structural variations that might be predicted to influence drinking performance are the relative dimensions and shapes of the mandibles and their suspensorial elements and the arrangements of intermandibular muscles and connective tissues.
— Cundall, D. Drinking in snakes: kinematic cycling and water transport. The Journal of Experimental Biology. 2000; 203, 2171–2185.

So let's put this all together:

  1. Snakes don't release their venom unless they are threatened or hunting. 
  2. Snakes use suction when they drink water. Their mouths are not open, which is needed when they are expelling venom.
  3. Snake venom is not dangerous when drunk.
  4. (If somehow venom did get into the water, it would be greatly diluted.)

So there is no danger if you were to drink from water from which a venomous snake had drunk. None.

Rashi's Two Explanations of Today's Passage

In today's page of Talmud, we are warned not to drink water left standing, because of the danger of a venomous snake having drunk from it.  That danger, as we have seen, does not exist.  But the Talmud also warns us not to use this water to sprinkle on a dirt floor to keep the dust down. According to Rashi, the concern is that a person might cut her foot on a sharp stone left on the floor, which would then allow the venom that was in the water that was sprinkled on that floor to enter the bloodstream. Now that is an incredibly unlikely event, but it is certainly possible, and Rashi's point is absolutely correct. The danger is only if there is an open wound that would allow the venom to enter the blood stream. (שלא יעבור עליהם אדם יחף ויכנס ארס של נחש ברגלו ע"י מכת צרור וימות.)  It is fascinating to compare Rashi's explanation here with his explanation of the the identical passage found in Avodah Zarah (30b).  

 לא ישפכם: שמא יעבור אדם יחף ויעמוד הארס בין קשרי אצבעותיו וכיון שנכנס מעט ונוקב   בבשר שוב אין לו רפואה. רשי, עבודה זרה ל, ב

There, Rashi notes that if "venomous" water was sprinkled on the floor, a person might step on it and absorb the venom through the skin of his toe joints. Once that happens, "שוב אין לו רפואה" - there is no medical treatment. What Rashi may not have known is that snake venom is not dangerous if it gets on your skin, because it is not absorbed from there into the bloodstream.  So his explanation in Avodah Zara is not correct, unlike his explanation of the passage in today's daf.

Bye Bye Bava Kamma

And that brings us to the end of Talmudology on Bava Kamma, which we will finish learning next Tuesday. We've discussed all kinds of topics:

Whether wolves can be tamed

Whether donkeys could break pottery with their braying

The talmudic and legal liability for dog bites

Whether a man is liable for injuring his wife during intercourse

How animals feel pain

Liability in bullfighting

Deaths from falling

Whether a goose has a scrotum

Whether kosher and non-kosher animals might cross-breed

Whether garlic is good for you

Whether honey is bad for you

How animals faced trial

And more besides.  Now it is time to turn to the next tractate. I'll see you on the opening page of Bava Metziah,  when we will discuss game theory and the work of the Israeli Nobel prize winner Robert Aumann.

Bava Kamma 105b ~ Teaching By Humiliation

בבא קמא קה, ב

אמר ליה תדורא...

Rabbah said to Rav Amram : "Scatterbrain" 

As a medical student in London, humiliation came with the territory. There I was, on rounds on General Surgery Firm. At its head, the consultant surgeon.  Followed (in their correct pecking order) by two senior registrars, three or four registrars, several senior house officers and house officers, nurses, physiotherapists, and a couple of medical students.  We gathered around the bed of some poor patient who had recently undergone surgery. The consultant surgeon turned to me: "Mr. Brown" he said, looking at me atop of his professorial reading glasses, "how long is the anal canal?" Everyone else smiled, relieved to know they had not been asked this, rather challenging question. I had no idea, despite having once known this useful fact to pass my anatomy exams. "Thirty centimeters, sir" I replied, hopefully.  "Correct," said the surgeon, as he surveyed the menagerie of staff trailing him.  "If you are an elephant." And so ended my surgical career.

Teaching By Humiliation in the Talmud

The rabbis of the Talmud were not shy to call out those they felt were slow-witted or annoying. After Rabbi Yehudah HaNasi was asked a relatively innocent question by Levi, the great editor of the Mishnah replied כמדומה לי שאין לו מוח בקדקדו - "it appears to me that Levi has no brains in his head," an insult he repeated on at least one other occasion. Rabbi Tarfon had enough of  Rabbi Elazar when he told him "How long will you pile up meaningless  words and bring them against us." He even used the same insult against Rabbi Akivah. Rabbi Akivah! (See ילקוט שמעוני תורה פרשת בהעלותך רמז תשכה.) Rabbi Yishmael was called "a date palm" (and not in a good way) by Rabbi Eliezer (see ספרא תזריע פרשה ה).  One of my favorites, though, came from Rabbi Dosa who called his  younger brother "the first-born of Satan" (and you thought your kids had issues).  I could go on, but you get the point. These guys could be really insulting.

Pimping in the Medical Literature

For the reader who is not medically trained, here's a new word: pimping. It's a real word that is OK to use in polite company (maybe).  According to the esteemed Journal of the American Medical Association, pimping is

a series of difficult and often intentionally unanswerable questions posed to a medical student or house staff in quick succession. The objective of pimping is to teach, motivate, and involve the learner in clinical rounds while maintaining a dominant hierarchy and cultivating humility by ridding the learner of egotism.

There is an art to pimping, according to Fredrick Brancati, the man generally thought to have invented the term in its medical content. Here is an excerpt from his classic 1989 paper, called, what else, The Art of Pimping:

Pimp questions should come in rapid succession and should be essentially unanswerable. They may be grouped into five categories:
1. Arcane points of history.These facts are not taught in medical school and are irrelevant to patient care—perfect for pimping. For example, who performed the first lumbar puncture? Or, how was syphilis named?
2. Teleology and metaphysics.These questions lie outside the realm of conventional scientific inquiry and have traditionally been addressed only by medieval philosophers and the  editors of the National Enquirer. For instance, why are some organs paired?
3. Exceedingly broad questions. For example, what role do prostaglandins play in homeostasis? Or, what is the differential diagnosis of a fever of unknown origin? Even if the intern begins making good points, after 4 or 5 minutes he can be cut off and criticized for missing points he was about to mention. These questions are ideally posed in the final minutes of rounds while the team is charging down a noisy stairwell.
4. Eponyms. These questions are favored by many old-timers who have assiduously avoided learning any new developments in medicine since the germ theory. For instance, where does one find the semilunar space of Traube? 
5. Technical points of laboratory research. Even when general medical practice has become a dim and distant memory, the attending physician-investigator still knows the details of his research inside and out. For instance, how active are leukocyte-activated killer cells with or without interleukin 2 against sarcoma in the mouse model? Or, what base sequence does the restriction endonuclease EcoRI recognize?
....pimping can create a hostile environment among the team members, suppress creativity or intellectual curiosity because of fear of embarrassment, and dehumanize students at the expense of maintaining medical hegemony.
— McCarthy, CP. McEvoy, JW. Pimping Medical Education. JAMA 2015; 314 (22). 2347-2348.

 Last year an Australian team published a paper titled "Teaching by humiliation” and mistreatment of medical students in clinical rotations. They found that 74% had experienced and 83% had witnessed teaching by humiliation during their adult clinical rotations; smaller proportions had experienced (29%) or witnessed (45%) it during their pediatric rotations, which just proves what everyone already knows.  Pediatricians are all nice. All this pimping comes with a down side. "Students’ responses to these practices" wrote the Australian researchers, "ranged from disgust and regret about entering the medical profession to endorsement of teachers’ public exposure of a student’s poor knowledge. Reported victims and perpetrators included junior medical staff, who were subjected to the practices as much as students and were equally likely to be the perpetrators, alongside senior medical and nursing staff."

As a deeply ingrained cultural, institutionalised practice, mistreatment requires focused action to replace the existing culture with one of compassion, tolerance and respect.
— Scott, KM. et al. “Teaching by humiliation” and mistreatment of medical students in clinical rotations: a pilot study. Medical Journal of Australia 2015; 203(4): 1-6

Talmudic Insults and Respect for the talmid

In today's page of Talmud, Rabbah called Rav Amram תדורא, a scatterbrain. In fact he called him a scatterbrain again (in the next tractate we will learn), so I guess he really meant it.  This epithet seems to have been the "moron' of its day. Rabbi Hiyya bar Abba called Rebbi Zeira a scatterbrain, and  even the great Abayye must have felt a little miffed when he was called a scatterbrain by Rava bar Hannan.  

It seems demeaning to use language like this, and out of place given the words of the Mishnah (Avot 2:10) יהי כבוד חבירך חביב עליך כשלך - "let your friend's honor be as important to you as your own." Rabbi Yair Chaim Bachrach (Germany, 1638-1732) addressed talmudic insults in his book of responsa called Chavvot Yair, first published in 1699. Apparently things were getting out of hand in Germany, where the talmudic art of humiliating had evolved. Yeshivah students now also yelled and gesticulated rather enthusiastically as they sparred with their learning partners:

 מש"כ קפיצה וסיפוק וריקוד תוך הפלפול איש נגד רעהו שזה גורם בלי ספק שחבירו ימהר לעשות כמעשהו וירקוד ג"כ כנגדו וירים קולו בצעקה גדולה ומרה יותר ולא ישמע איש שפת חבירו ואין זה רק מנהג יהוא וכל המרבה בה ה"ז משוגע 

Students jump and dance around each other in the middle of expounding a subject, and this will cause, without doubt, that other students will do the same and will leap and raise their voices in a louder and more bitter cry. No one will be able to listen to the voice of his partner. This is nothing other than a ridiculous custom, and anyone who does this often is a mesgugah...  

Rabbi Bachrach then rose to the defense of those who used talmudic insults, claiming that they did so with only good intentions. They did it, he said, in order to bring out the very best they could in those they insulted. Hmmm. I'm not convinced.

Insults don't work, not for medial students and not for any students.  Ad hominem attacks are also unlikely to elevate the quality of an argument. In this final run up to the US presidential elections we are likely to see more of both forms of  disrespect, though they usually say more about the person uttering them than the person against whom they are directed.  

תנו רבנן: שלשה שונאין זה את זה, אלו הן: הכלבים, והתרנגולין, והחברין. ויש אומרים: אף הזונות. ויש אומרים: אף תלמידי חכמים שבבבל
The rabbis taught: three groups hate each other: Dogs, roosters, and sorcerers. Some say: so do prostitutes. And others say: so do the sages in Babylon...
— פסחים דף קיג עמוד ב