Zevachim 74a ~ Talmudic Probability Theory II

Our first deep dive into the math surrounding Talmudic Probability Theory was back in February 2015 when we were studying Ketuvot.  Today's Daf Yomi addresses the same theme, and thanks to some clever work by a contemporary mathematician we are able to provide some new insights today's page of Talmud.

Don't touch that goat

The reason we even get into this subject is a Mishnah that opens the eighth chapter of Zevachim, and which we studied just four days ago. There, the Mishnah rules on the problem of animals that must not be sacrificed getting mixed up with groups of those same animals that may be sacrificed. We have already learned that under usual circumstances, when a forbidden object falls into a majority of similar objects that are permitted, the prohibition is annulled, so that if one draws any object it is permitted (Zevahim 72a). However, the prohibition against idol worship is so strong that the usual rule allowing the minority object to be annulled in favor of the majority is not in play. This is made explicit in the definitive Shulchan Aruch, the Code of Jewish Law: 

שולחן ערוך יורה דעה 140:1

עֲבוֹדַת כּוֹכָבִים וּמְשַׁמְּשֶׁיהָ וְתִקְרָבְתָּהּ, אוֹסְרִים בְּכָל שֶׁהוּא, שֶׁאִם נִתְעָרֵב אֶחָד מֵהֶם, אֲפִלּוּ בְּאֶלֶף, כֻּלָּן אֲסוּרוֹת

Objects used for idol worship or their accessories are forbidden in any amount. So even if one of these objects was mixed into a group of one thousand, it is forbidden to derive any benefit from the entire group.

What about a 40:60 split?

Here is today's page of Talmud:

זבחים עד, א

אמר רב טבעת של עבודת כוכבים שנתערבה במאה טבעות ופרשו ארבעים למקום אחד וששים למקום אחר פרשה אחת מארבעים אינה אוסרת אחת מששים אוסרת

Rav says: With regard to a ring used in idol worship that was intermingled with one hundred permitted rings, and then forty of them became separated to one place, and the other sixty became separated to another place, so that they are now two distinct groups of rings, if one ring from the group of forty became separated from them and then became intermingled with other rings, it does not render them prohibited. But if one ring from the other sixty became separated from its group and became mixed with other rings, it renders them prohibited.

The talmudic reasoning here is not straightforward, (even with a lengthy attempt by Rashi) which is why we have to thank Rabbi Nahum Eliezer Rabinovitch (b.1928), the Rosh Yeshiva of the hesder Yeshivah Birkat Moshein Ma'ale Adumim.  (He also has a PhD. in the Philosophy of Science from the University of Toronto, published in 1973 as Probability and Statistical Inference in Ancient and Medieval Jewish Literature.)  In a paper published in 1969, Rabbi Rabinovitch reconstructs what he he calls "a plausible line of reasoning."

Screen Shot 2018-06-19 at 1.53.11 PM.png
Rabinovitch N.L. Probability in the Talmud. Biometrika 1969, 56 (2): 437-441

Rabinovitch N.L. Probability in the Talmud. Biometrika 1969, 56 (2): 437-441

As we have noted before, James Franklin, in his book on the history of probability theory, wrote that codes like the Talmud (and the Roman Digest that was developed under Justine c.533) "provide examples of how to evaluate evidence in cases of doubt and conflict.  By and large, they do so reasonably. But they are almost entirely devoid of discussion on the principles on which they are operating." But it is unfair to expect the Talmud to have developed a notion of probability theory as we have it today. That wasn't its interest or focus. Others have picked up this task, and have explained the statistics that is the foundation of  talmudic probability. For this, we have many to thank, including the Rosh Yeshiva, Rabbi Rabinovitch שליט׳א.

(The [Roman] Digest and) the Talmud are huge storehouses of concepts, and to be required to have an even sketchy idea of them is a powerful stimulus to learning abstractions.
— James Franklin. The Science of Conjecture: Evidence and Probability Before Pascal, 349.

[For more on Rabbi Rabinovitch and tamludic probability, see our post here, from where some of this is taken.]

Print Friendly and PDF

Zevachim 70b ~ The Prosecution (& Punishment) of Animals

Tractate Zevachim addresses the laws of sacrifices. Chapter eight, which we started learning today, opens with the case of a group of animals awaiting sacrifice that became intermingled with an identical animal that is forbidden to sacrifice. That causes a major problem:

 כל הזבחים שנתערבו בחטאות המתות או בשור הנסקל אפילו אחת בריבוא ימותו כולן נתערבו בשור שנעבדה בו עבירה או

MISHNA: All the offerings that were intermingled with animals from which deriving benefit is forbidden... for example an ox that was sentenced to be stoned, even if the ratio is one in ten thousand, deriving benefit from them all is prohibited and they all must die...

Sentencing an animal to death? Putting animals on trial? That's quite a concept. We have discussed this before, when learning Sanhedrin and Bava Kamma. But that was a year ago, so let's remind ourselves of the odd judicial notion of putting animals on trial for their alleged crimes.

סנהדרין טו, א

 שור הנסקל בעשרים ושלשה: שנא' השור יסקל וגם בעליו יומת כמיתת הבעלים כך מיתת השור

An ox that may be punished with stoning is tried by a court of twenty-three judges: As it is stated "the ox shall be stoned and its owner shall be put to death" (Ex. 21:29). The juxtaposition teaches that in the manner in which the owner is put to death, so too is the ox put to death.  

In Sanhedrin, the case of an ox that sodomizes a person is discussed. The bovine in question stands trial, and if found guilty is executed. We have already encountered the trial of oxen in another context, that time concerning an ox that gored a person to death:

בבא קמא צ, א 
תנו רבנן שור תם שהמית והזיק דנין אותו דיני נפשות ואין דנין אותו דיני ממונות מועד שהמית והזיק דנין אותו דיני ממונות וחוזרין ודנין אותו דיני נפשות קדמו ודנוהו דיני נפשות אין חוזרין ודנין אותו דיני ממונות 

The rabbis taught: a tam ox that killed a person and inflicted damages, is tried first for the capital case and is not tried for the damages. A muad ox that killed a person and inflicted damages is tried first for the damages and is then tried for the capital case.  

The notion that an animal should be tried for a crime is a completely foreign one to our modern sensibilities. Animals do not commit crimes; they act on instinct. When those instincts lead to a conflict with human society animals might be removed, or killed. But tried for a crime? Isn’t that an odd notion? Not so much, it turns out.

On the prosecution of ANIMALS

In her review article The historical and contemporary prosecution of animals, Professor Jen Girgen noted that the formal prosecution of animals existed for centuries. Aristotle (d.322 BCE) mentioned animal trials in Athens, although there is no direct evidence of them having taken place in ancient Greece. The earliest known records of animal trials are from the mid-13th century. For example, in France in 1386, a pig was put on trial for the death of a child:

  
The defendant was brought before the local tribunal, and after a formal trial she was declared guilty of the crime. True to lex talionis, or "eye-for-an- eye" justice, the court sentenced the infanticidal malefactor first to be maimed in her head and upper limbs and then to be hanged. A professional hangman carried out the punishment in the public square near the city hall. The executioner, officially decreed to be a "master of high works," was issued a new pair of gloves for the occasion in order that he might come from the discharge of his duty, metaphorically at least, with clean hands, thus indicating that, as a minister of justice, he incurred no guilt in shedding blood.

In medieval times, animals were tried in two different court systems. The Church handled cases in which animals were a public nuisance (usually because they ate a farmer’s crops) while secular courts judged cases involving the physical injury or death of person.  Apparently these trials were taken seriously: “The community, at its own expense, provided the accused animals with defense counsel, and these lawyers raised complex legal arguments on behalf of the animal defendants. In criminal trials, animal defendants were sometimes detained in jail alongside human prisoners. Evidence was weighed and judgment decreed as though the defendant were human.”  Animals that faced these trials included swans, rodents, dolphins (dolphins!) grasshoppers, and, in 1713, a nest of termites, which was I suppose fair enough. The termites were munching their way through a monastery, devouring the friars' food, destroying their furniture, and even threatening to topple the walls of the monastery. 

The ox is to be executed, not because it had committed a crime, but rather because the very act of killing a human being- voluntarily or involuntarily-had rendered it an object of public horror.
— JJ Finkelstein. The ox that gored. Transactions of the American Philosophical Society, Vol. 71, No. 2 (1981), pp. 1-89

The animals that faced prosecution would rarely appear in court on their trial day (because, I suppose, they had other things on their mind) so they usually lost the case by default.  Here’s a fairly typical example. In 1575 weevils were helping themselves to the vineyards in a picturesque hamlet in France, and were brought to trial:

The plaintiff and the two lawyers appointed as counsel for the beetle defendants presented their respective sides of the case…Pierre Rembaud, the beetles' newly appointed defense counsel, made a motion to dismiss the case. Rembaud argued that, according to the Book of Genesis, God had created animals before human beings and had blessed all the animals upon the earth, giving to them every green herb for food. Therefore, the weevils had a prior right to the vineyards, a right conferred upon them at the time of Creation… While the legal wrangling continued, the townspeople organized a public meeting in the town square to consider setting aside a section of land outside of the Saint Julien vineyards where the insects could obtain their needed sustenance without devouring and destroying the town's precious vineyards. They selected a site named "La Grand Feisse" and described the plot "with the exactness of a topographical survey."…However, the weevils' attorney declared that he could not accept, on behalf of his clients, the offer made by the plaintiffs. The land…was sterile and not suitable to support the needs of the weevils. The plaintiff’s attorney insisted that the land was, in fact, suitable and insisted upon adjudication in favor of the complainants. The judge decided to reserve his decision and appointed experts to examine the site and submit a written report upon the suitability of the proposed asylum.

How did this case end? We have no idea.  The last pages of the court records were (I kid you not) eaten by insects.  

The Source- our Hebrew Bible

The impetus for all this, according to historians, was our own Hebrew Bible, or more precisely, the passage from Exodus 21:28.

 וְכִי-יִגַּח שׁוֹר אֶת-אִישׁ אוֹ אֶת-אִשָּׁה, וָמֵת סָקוֹל יִסָּקֵל הַשּׁוֹר, וְלֹא יֵאָכֵל אֶת-בְּשָׂרוֹ, וּבַעַל הַשּׁוֹר, נָקִי
"If a bull gores a man or woman to death, the bull is to be stoned to death, and its meat must not be eaten. But the owner of the bull will not be held responsible.

The Jewish scholar Bernard Jackson, (who seems to have spent his entire career studying the legal history of the goring ox,) noted this connection.  “The stoning of the goring ox”, he wrote

… may well have been the parent, rather than the child, of the idea of divine punishment of animals .... [O]nce the concept of divine punishment of animals became established, it could then be transferred back to the legal sphere as a primarily penal notion.

What sense can we make of these medieval trials – and what sense can be made of the earlier Talmudic law that also placed animals on trial for their actions? Girgen suggests a number of possible ways to explain these trials, which seem to have become increasingly popular in the middle ages. 

  1. Rehabilitation of the offending animal. This is not a satisfying explanation, since “these proceedings usually ended with the execution of the animal.” That left little opportunity for rehabilitation.  
  2. Retribution, which is another word for revenge.  Indeed, this is precisely the notion reflected in the biblical law of “an eye for an eye”- although of course that was not the way the rabbis of the Talmud interpreted the verse.  Under Roman law, the Torah law of  עין תחת עין was called lex talionis – the law of retaliation.  This need to retaliate was, according to Justice Oliver Wendell Holmes, a key feature of early legal systems, which were “…grounded in vengeance.” 
  3. Revenue for the king.  This would only explain cases in which the animal was impounded or confiscated from the owner and given over to the king or local lord. But this did not happen when the animal was executed – which apparently was a frequent outcome of these trials.
  4. The elimination of a social danger. Now, this begins to sound familiar. In the US and other western countries, vicious dogs are, after all, put down, and when this happens we breathe a collective sigh of relief.  So by sentencing a dangerous animal to death, the courts were making life safer for everyone else.
  5. Deterrence – that is, “to dissuade would-be criminals - both animal and human-from engaging in similar offensive acts”.  As the legal scholar Nicholas Humphrey noted, "if word got around about what happened to the last pig that ate a human child, might not other pigs have been persuaded to think twice?” That implies endowing animals with an agency that we would consider today to be quite fanciful. So perhaps the deterrent effect was not aimed at other animals, but rather at other humans – deterring them from committing these kinds of horrible crimes.  
  6. Establishing control in a disorderly world. Perhaps these trials were a search for order in a world of chaos.  “Just as today,” wrote Professor Humphries “when things are unexplained, we expect the institutions of science to put the facts on trial ... the whole purpose of the legal actions was to establish cognitive control.".  The good professor continues:  
What the Greeks and mediaeval Europeans had in common was a deep fear of lawlessness: not so much fear of laws being contravened, as the much worse fear that the world they lived in might not be a lawful place at all. A statue fell on a man out of the blue; a pig killed a baby while its mother was at Mass; swarms of locusts appeared from nowhere and devastated the crops .... To an extent that we today cannot find easy to conceive, these people of the pre-scientific era lived every day at the edge of explanatory darkness.

By defining events as crimes rather than as natural occurrences, they could be placed within a legal context – and controlled. The late JJ Finkelstein of Yale University (d. 1974) wrote one of the most detailed studies of the ox that gored (called, rather unimaginatively, The Ox that Gored). On page 24 of his 86-page essay he addressed this aspect:

[T]he "crime" of the ox that gored a person to death is not just to be found in the fact that it had "committed homicide.". . .The real crime of the ox is that by killing a human being-whether out of viciousness or by an involuntary motion, it has objectively committed a de facto insurrection against the hierarchic order established by Creation.  

Trials of animals in more recent Times

Animal trials continued well into the twentieth century. In 1906 in Switzerland a dog was sentenced to death for killing a man, while his masters – who had used the dog to help them rob the man - were sentenced to life in prison. In 1924, Pep, a Labrador retriever, was accused of killing Pennsylvania Governor Gifford Pinchot's cat. 

The dog was tried (without the assistance of counsel) in a proceeding led by the Governor himself.  Governor Pinchot found Pep responsible for the cat's death and sentenced the dog to life imprisonment in the Philadelphia State Penitentiary. Pep died of old age, still incarcerated, six years later… And in 1927, a dog was reportedly tried and incarcerated by a Connecticut justice of the peace for "worrying the cat of a neighbor lady.”

In fact, “trials” of dangerous animals continue to this day. Depending on where you live, a judge may rule an animal to be dangerous if it has attacked others, and may order it destroyed.  This is what happened in New Jersey in 1991, when Taro, a 110 lb Japanese Akita dog was sentenced to death by a judge in Bergen County, after it had apparently attacked its owner’s niece. Taro’s owner appealed the verdict and the dog remained on death row for three years, until the order to execute the dog was upheld.  That’s when newly elected Governor Christin Todd Whitman issued an executive order and reprieved the dog, which by now had been imprisoned for more than one thousand days at a cost to the state of more than $100,000. Taro was exiled from New Jersey, and died in her sleep five years later. 


What do we talk about when we talk about punishment?

What is it that we want to see happen when we call for a criminal to be “punished”?  This simple question has been answered by legal scholars and judges who have written about theories of punishment, but we knew little about what the average citizen wants to see happen when a punishment is imposed. 

In a series of experiments published in 2002, psychologists from Princeton and Northwestern University studied the motivation underlying use of punishment in a group of students; that is to say, in people with no special legal training or background. What are the motives of ordinary people when they wish to punish a criminal? (Ok, they weren’t exactly “ordinary people, since they were Princeton University students, but still…)The two specific motives they contrasted were just deserts and deterrence. The “just desserts” theory is the belief that when punishing a criminal, our concerns should not be about future outcomes like rehabilitation, but rather about providing a punishment appropriate for the given crime. “Although it is certainly preferable that the punishment serve a secondary function of inhibiting future harmdoing, its justification lies in righting a wrong, not in achieving some future benefit. The central precept of just deserts theory is that the punishment be proportionate to the harm.”  So what motivates the theory of punishment in ordinary people? Does it come from a deservingness perspective, in which the focus is on atoning for the harm committed, or from a utilitarian, deterrence perspective, in which the focus is on preventing future harms against society? 

The psychologists found that in sentencing hypothetical criminal perpetrators, their student subjects responded to factors associated with the “just deserts theory” and ignored those associated with deterrence. This desire to see a criminal get his just desserts is also found when animals are put on trial.  More recent work by the psychologists Geoffrey Goodwin and Adam Benforado also addressed the way in which we view punishment as retribution.  They asked volunteers (found on-line using something called Amazon's Mechanical Turk interface) about a number of different scenarios in which animals had killed or injured people. In five different studies the results demonstrated "...clear evidence for the existence of retributive motives and for a broader conception of the viable targets of retribution."


Back to the goring, Or SODOMIZING ox

In the view of J.J. Finkelstein, the Yale scholar, “the system of categorization reflected in the biblical statement of the laws of the goring ox is essentially the same as our own… the cosmic apprehension of the biblical authors, the way in which the Bible perceives and classifies the world of experience, is in every fundamental respect identical with ours, that is, with that of the civilization we usually describe as "Western.” Once we understand that animal trials were not just an interesting quirk mentioned in today’s page of Talmud, but were – and still are - a common part of the judicial process, Finkelstein’s claim view is entirely plausible.  This, together with the insights from the field of psychology about what motivates people to punish others, leads us to a remarkable conclusion.  Moderns, like those before us, seek to punish, not to rehabilitate the criminal or deter others from committing a crime, but because the criminal “deserves to be punished”. It matters not one bit if that criminal is a human, a dog, or an insect.  

[Repost from Bava Kamma 90a]

Print Friendly and PDF

Zevachim 62b ~ To the Right. Always to the Right

זבחים נד,ב

כל פינות שאתה פונה לא יהו אלא דרך ימין...

All turns that you make must be towards the right

Homer Simpson Lefty Store.jpeg

Today's page of Talmud teaches that when walking up the ramp to the top of the Altar in the Temple, the Cohen must make a right turn at the top. Following that, every turn he makes must be a right turn. But why a right turn?

The importance of the right side in Judaism

In the Talmud and in normative Jewish practice, the preference to favor the right over the left is everywhere. Here are just a few. (How many more can you think of?)

  • Rav Ashi rules that Tefillin must placed it on the left arm, because it is weaker than the right and the action of placing them should be performed with the stronger right hand (מנחות לז, א).

  • The Talmud teaches that a right-handed person who writes with her left hand on Shabbat has not violated the prohibition against writing. It doesn't count. Maimonides (הלכות שבת 11:14) agrees:

הַכּוֹתֵב בִּשְׂמֹאלוֹ אוֹ לְאַחַר יָדוֹ בְּרַגְלוֹ בְּפִיו וּבְמַרְפֵּקוֹ פָּטוּר

  • According to Rava, walking should start with the right leg, and not the left (יומא יא, ב)

  • As we know from studying Zevachim, the entire service in the Temple in Jerusalem must be performed with the right hand (ביאת המקדש 5:18 )

  • The rite of חליצה must be performed with the right leg and a right shoe (יבמות קד, א).

  • The mezuzah can only be placed on the right side of the door (רמבם הל׳ מזוזה 6:12).

  • The best student of a rabbi should walk on the rabbi's right side, relegating the second best to the left (יומא לז, א).

  • After observing his teacher Rabbi Yehoshua, Rabbi Akiva taught that the left hand should be used after using the bathroom, out of respect to the right hand (ברכות סב,ב). When challenged as to why Rabbi Akiva was impertinent enough to report on which hand his teacher wiped himself he replied תורה היא וללמוד אני צריך - "this too is Torah, and I must study it".

לֵ֤ב חָכָם֙ לִֽימִינ֔וֹ וְלֵ֥ב כְּסִ֖יל לִשְׂמֹאלֽוֹ׃

A wise man’s mind tends toward the right hand, a fool’s toward the left.

— Kohelet 10:2

It's not Just Judaism

In Islam

The importance of all things right handed is found in other religions. For example, when Muslims perform any of the following, it is mustahabb [مستحبّ‎, - "recommended"] to start on the right or use the right hand.

  • putting on one's garment and pants and shoes

  • entering the mosque, using the siwaak [ a kind of toothpick]

  • putting on kohl [an ancient blue eye cosmetic]

  • clipping the nails

  • trimming the mustache

  • combing the hair plucking the armpit hair

  • shaving the head

  • saying salaam at the end of prayer

  • washing the limbs when purifying oneself

  • exiting the toilet, eating and drinking

  • shaking hands

  • touching the Black Stone [ٱلْحَجَرُ ٱلْأَسْوَد‎, al-Ḥajaru al-Aswad, a rock set into the eastern corner of the Kaaba, the ancient building located in the center of the Grand Mosque in Mecca, Saudi Arabia. Legend has it that the rock dates back to Adam and Eve.]

  • Conversely, the Bukhari Sharif , one of the six major hadith collections of Sunni Islam rules along the lines of Rabbi Akiva:

"... when you urinate, do not touch your penis with your right hand. And when you cleanse yourself after defecation, do not use your right hand."

The right hand of the Messenger of Allah (peace and blessings of Allah be upon him) was for his purification and food, and his left hand was for using the toilet and anything that was dirty...
— Sunan Abi Dawood (33)

in christianity

in hinduism

  • Offerings, such as flowers or garlands, are carried with both hands on the right side of the body.

  • "Pointing with the forefinger of the right hand or shaking the forefinger in emphasis while talking is never done. This is because the right hand possesses a powerful, aggressive pranic force, and an energy that moves the forces of the world."

  • Vāmācāra ( वामाचार, meaning "left-handed attainment" in Sanskrit) describes the "Left-Hand Path" or "Left-path" It is used to describe a particular mode of worship that is heterodox to standard Vedic teachings.

  • In Benares, the holiest of the seven sacred cities and sitting on the Ganges, "pilgrims circumambulate with their right hands towards the center, as Krishna is alleged to have done at the sacred mountain."

Well, you get the point.  Judaism, along with all the major religions (and some you've never heard of) emphasize the dominance of the right hand in all things holy. Or mundane.

The Ngaga of southern Borneo believe everything in the after-world is reversed, “sweet” becoming “bitter”, “straight” becoming “crooked”, and “right” becoming “left”. Likewise the Toraja of Celebes (Sulawesi) believed the dead do everything backwards, even pronouncing words backwards... the dead therefore use their left hand...
— I. C. Mcmanus. Right Hand, Left Hand: The Origins of Asymmetry in Brains, Bodies, Atoms and Cultures. Phoenix 2003, p27.

 and It's not just religions

There are lots of things that have chirality - meaning they have a mirror image but cannot be mapped onto that mirror image by rotations and translations. They exist in left or right-handed versions. Let's start with in easy example. Um, your hands. Although your right hand mirrors your left, your right hand cannot (comfortably) fit into a handed-glove.

From here.

From here.

Here's another example. Bend your fingers and extend your thumb as below. You've made two mirror images that cannot be mapped onto each other. (Go on. Give it a try. See what I mean?) That's chirality.

If we extend this to molecules, they are left or right-handed, meaning they are mirror images but they cannot be superimposed on each other. These are isomers. Like this:

From here.

From here.

And here is where things start to get really weird. Nearly everything in the universe - from chemicals and medications to fundamental particles and even galaxies themselves have a right-handed or left-handed preference. No, really. 

Let's start with the essential building blocks of life: amino acids and sugars. Almost all amino acids (not you, glycine) used by life on earth (but not necessarily elsewhere in the universe) are left-handed.  Right-handed amino acids exist of course. They're just not utilized by any life form on earth. Any.  If you sit in a lab and cook up an amino acid from its ingredients, you will make an equal amount of the left and right handed variates. That's just good old chemistry at work. But life on earth can only use half the mixture: the L form. Some bacteria can actually convert right-handed amino acids into the left-handed version, but they can’t use the right-handed ones as is.

Like amino acids, sugars also come in two isomers, but those that are used by life forms on earth are the right-handed variety. All the enzymes that living things use to manipulate amino acids and sugars only work on left-handed amino acids and right-handed sugars. They simply can't use the opposites. Why did life turn out this way? Truth is, nobody knows.  

Medications also exhibit chirality. For example, propranolol is commonly used to help control high blood pressure. Some of you reading this may be taking it. The left form (L-propranolol) is the one that helps. The right form (known as D-propranolol) is inactive. (The Latin for left and right is laevus and dexter, respectively.)

Quinine is an antimalarial drug. It has an isomer called quinidine, and quinidine has no anti-malarial action. But it's a great drug to reduce arrhythmias of the heart. One compound, with two isomers, each with their own remarkable and very different healing properties.

Now consider muons, a fundamental particle in our universe. It is kind of like an electron, but about 200 times heavier. Muons have an average life-expectancy of 2.2 microseconds (so don't expect any kind of long-term relationship) after which time they decay into an electron, a neutrino, and an anitneutirno. The direction that the electron will come out depends on the direction in which the muon spins. Now you would expect there to be equal amounts of electrons that are ejected spinning one way or another. But there aren't.  What happens is that 99.9% of muons decay in a right-handed fashion.

And while we are on the subject of decaying muons, let's talk about those neutrinos, which are a weird fundamental particle with the smallest mass of any known thing. They too, have a preference for the right or left. All neutrinos are left handed, while all anti-neutrinos (whatever that means) are right handed.

Left and right handed galaxies. From here.

Left and right handed galaxies. From here.

Ready for more? Statistically speaking our universe should contain an equal amount of left and right handed galaxies (as noted in how they spin). But this should not occur. In an analysis of over 2,600 nearby spiral galaxies and a later analysis of 15,000 more, Michael Longo demonstrated that that left-handed spirals are more common in the northern hemisphere, above the northern galactic pole. And although the signal is less strong, right-handed spirals appear more frequently in the south.

It's good to be a leftie

About 10-13% of humans are left-handed. (Captive chimpanzees are more left-handed than us, with an approximate 2:1 ratio of righties to lefties. In us it's more like 8:1) But aside from the problem of not finding scissors that work for you, being a leftie gives you some pretty good advantages.

...not only left-handers are over-represented in confrontational sports, but the closer the physical interaction of the opponents such as in boxing, fencing, judo, or karate, the greater the prevalence of left-handers. In basketball, football, handball, table tennis, tennis, and volleyball, for instance, competitors stand some distance apart and do not confront directly. But even in these sports, there are more than the expected number of left-handers...
— Grouios G. et al. Do left-handed competitors have an innate superiority in sports? Perception and Motor Skills, 2000:90;1273-1282

At the undergraduate level they are more likely to take part in a whole range of events, from judo and fencing and soccer and volleyball. But when it comes to non-confrontational sports like cycle racing, running or swimming, the proportion of left handers fall back to that of the general population. Lefties make up about 10% of the population, but 23% of all Wimbledon tennis champions were lefties.

There is a lot more evidence that lefties have many advantages over (us) righties. In a complicated test of spatial skills which you can read about here, 47 lefties demonstrated faster and more accurate spatial skills than the 50 righties, along with strong executive control and mental flexibility. And in this study of 100 lefties and 100 righties, the left-handed demonstrated greater creativity than the right-handed on all 4 scales of the Torrance test which examines creative thinking.

Obama writes with his left hand.jpg

And lefties appear to be smarter that righties.  In a study of some 300 gifted children, left (-or mixed-handedness) occurred more frequently in those who were mathematically or verbally precocious (for our readers in the US, this meant an SAT-M score of more than 700 and an SAT-L score of more than 630). Of the last 15 US presidents, seven (about 47%) have been left-handed.  That's almost 1 in 2! Oh, and compared with righties, college-educated left-handers in the US earn 10-15% more.

Leonardo da Vinci was a lefty, as were Michelangelo, Isaac Newton, and Albert Einstein.

Despite these, and many other advantages, our cultures have stigmatized those who are left-handed. We all know that the word sinister (meaning something harmful or evil is going to happen) comes from the Latin sinister meaning left.  But there are more examples of anti-left associations in other languages too. Adroit, meaning clever or skillful comes from the French word for right droite, meaning dextrous. In German, linkisch means awkward, and it comes from the German links, meaning left. And so it goes on.

Back to the Jewish Bible

Left-handed people are mentioned only three times in Tanach, and all come from the tribe of Benjamin:

  • There were the 700 men from the tribe of Benjamin who could use a sling with deadly accuracy (שופתים 20:16):

מִכֹּ֣ל ׀ הָעָ֣ם הַזֶּ֗ה שְׁבַ֤ע מֵאוֹת֙ אִ֣ישׁ בָּח֔וּר אִטֵּ֖ר יַד־יְמִינ֑וֹ כָּל־זֶ֗ה קֹלֵ֧עַ בָּאֶ֛בֶן אֶל־הַֽשַּׂעֲרָ֖ה וְלֹ֥א יַחֲטִֽא׃

  • There were the ambidextrous men who came to fight for King David at Ziklag, who were from the tribe of Benjamin (דברי הימים א, 12:2)

נֹ֣שְׁקֵי קֶ֗שֶׁת מַיְמִינִ֤ים וּמַשְׂמִאלִים֙ בָּֽאֲבָנִ֔ים וּבַחִצִּ֖ים בַּקָּ֑שֶׁת מֵאֲחֵ֥י שָׁא֖וּל מִבִּנְיָמִֽן׃

  • And perhaps most famously there was the left-handed Ehud ( אֶת־אֵה֤וּד בֶּן־גֵּרָא֙ בֶּן־הַיְמִינִ֔י אִ֥ישׁ אִטֵּ֖ר יַד־יְמִינ֑וֹ) who assassinated the Moabite king Eglon (שופתים 3:12-30). Because Ehud was left-handed he hid his dagger on his right side. In this way he got past the body search outside the throne room, where the guards looked for a weapon on the left. As for the rest, well, read on:וַיִּשְׁלַ֤ח אֵהוּד֙ אֶת־יַ֣ד שְׂמֹאל֔וֹ וַיִּקַּח֙ אֶת־הַחֶ֔רֶב מֵעַ֖ל יֶ֣רֶךְ יְמִינ֑וֹ וַיִּתְקָעֶ֖הָ בְּבִטְנֽוֹ׃ וַיָּבֹ֨א גַֽם־הַנִּצָּ֜ב אַחַ֣ר הַלַּ֗הַב וַיִּסְגֹּ֤ר הַחֵ֙לֶב֙ בְּעַ֣ד הַלַּ֔הַב כִּ֣י לֹ֥א שָׁלַ֛ף הַחֶ֖רֶב מִבִּטְנ֑וֹ וַיֵּצֵ֖א הַֽפַּרְשְׁדֹֽנָה׃ Reaching with his left hand, Ehud drew the dagger from his right side and drove it into [Eglon’s] belly. The fat closed over the blade and the hilt went in after the blade—for he did not pull the dagger out of his belly—and the filth came out.

All of this is really strange because of course the name of this tribe  - Benjamin - literally means "the son of the right" בן ימין.  

Back to Zevachim

Today's daf yomi page of Talmud has a very short instruction:"All turns that you make must be towards the right." But this phrase reveals a profound truth about who we are as humans, and of the very stuff from which we are made.  In culture after culture, in religions after religion, and in the very structure of our universe, there are left or right-handed preferences and predilections, many of which we simply cannot currently explain. Our religious and cultural preferences for the right likely stems from the simple fact that left-handedness is eight times less common. Unfortunately, a suspicion of the other, of those who are not like the majority, is a common trait that in one way or another we all share. But it needn't be so. The other, those in the minority, teach us and enrich our lives. Heck, they are often even smarter and quicker than the majority.  We are all better off with them.

Print Friendly and PDF

Zevachim 54b ~ How High is Jerusalem?

זבחים נד, ב

דרש רבא מאי דכתיב (שמואל א יט, יח) "וילך דוד ושמואל וישבו בנויות ברמה" וכי מה ענין נויות אצל רמה? אלא שהיו יושבין ברמה ועוסקין בנויו של עולם אמרי כתיב (דברים יז, ח) וקמת ועלית אל המקום מלמד שבית המקדש גבוה מכל ארץ ישראל וארץ ישראל גבוהה מכל ארצות

Rava taught: What is the meaning of that which is written concerning David: “And he and Samuel went and dwelt in Naioth. And it was told Saul, saying: Behold, David is at Naioth in Ramah” (I Samuel 19:18–19)? But what does Naioth have to do with Ramah? They are in two distinct places. Rather, this means that they were sitting in Ramah and were involved in discussing the beauty [benoyo] of the world, i.e., the Temple. David and Samuel said: It is written: “Then you shall arise, and get you up unto the place which the Lord your God shall choose” (Deuteronomy 17:8). This teaches that the Temple is higher than all places in Eretz Yisrael. And Eretz Yisrael is higher than all countries. 

This passage is unequivocal in its meaning: Jerusalem - that is, the Temple Mount -  is the highest place in Israel, and Israel itself is the highest place on earth. Now you don't need me to tell you that this is not a true statement. But I will anyway. It's not true. When I lived in Efrat it would often snow there while in Jerusalem, a mere twenty minutes away, there would be no snow. Why? Because Efrat is at a higher elevation than is Jerusalem. And if you have looked out from the Bet Midrash of the Hebrew University's Mount Scopus campus you will look down on the Temple Mount some three hundred feet below.

There is another passage in the Talmud that teaches the same point but uses some additional verses from the Book of Jeremiah to prove (as it were) that the Land of Israel is higher than all other places on earth. Here it is:

Picture of a mountain.jpeg

סנהדרין פז, א 

ועלית מלמד שבית המקדש גבוה מא"י וא"י גבוה מכל הארצות אל המקום בשלמא בית המקדש גבוה מא"י דכתיב ועלית אלא א"י גבוה מכל הארצות מנא ליה דכתיב לכן הנה ימים באים נאם ה' (לא יאמר) חי ה' אשר העלה את בני ישראל מארץ מצרים כי אם חי ה' אשר העלה ואשר הביא את זרע בית ישראל מארץ צפונה ומכל הארצות אשר הדחתים שם וישבו על אדמתם

"And you shall go up" [Deut 17:8] This teaches that the Holy Temple is higher than all other places in Israel...And from where do we now that Israel is higher than all other lands? From the verses [Jeremiah 23: 7-8] "Therefore, behold the days come, saith the Lord, that they shall no more say, The Lord liveth, which brought up the children of Israel out of the land of Egypt,' But the Lord liveth, which brought up and which led the seed of the house of Israel out of the north country, and from all the countries whither I have driven them; and they shall dwell in their own land."

Rashi points to yet another verse from the Book of Jeremiah (16:23) that teaches that Israel is the highest place on earth.

רשי, זבחים נד, ב

וארץ ישראל גבוהה מכל הארצות - לא מיבעיא לן הכא ולאו מהכא נפקא לן אלא מקרא אחרינא דכתיב (ירמיהו טז כג) לא יאמר עוד חי וגו' כי אם חי ה' אשר העלה ואשר הביא את בני ישראל מארץ צפון ומכל המקומות אשר הדחתים שם וגו

So it's not just a one-off statement. The Talmud in at least two places, and Rashi in a third, claim that Israel is the highest place on earth. But after a quick check in your reference book or internet search engine of choice you will see this is not correct. It's not even close. (I'm talking to you, Denver).

it's true; Google said so

Here are some other places, randomly chosen that are physically higher than Jerusalem.

Location Elevation (feet)
Jerusalem 2,424
Mount of Olives 2,710
Hebron 3,051
Efrat 3,150
Ben Nevis (UK) 4,413
Denver, Colorado 5,280
Johannesburg, South Africa 5,751
Mount Everest 29,029

Maharsha to the Rescue?

The Maharsha, R. Shmuel Eidels (1555 – 1631) in his commentary to Kiddushin 69a  suggests that since the Earth is a sphere, Israel and Jerusalem can be seen as if they were its "center."

מהרש"א חידושי אגדות מסכת קידושין דף סט עמוד א

 שהעולם הוא כתפוח ומקום בהמ"ק הוא מרכז עולם וכן א"י ולכך אמרו בא"י כיון דהוא מקום הממוצע אוירו מזוג ומחכים ויותר מקום המקדש שע"כ היו שם בלשכת הגזית חכמי סנהדרין וק"ל

Perhaps the Maharsha means that the spherical earth spins on its axis and that is the highest point, just like you might see a model of the earth on a bookshelf that spins on an axis with the North Pole at the top. But that cannot be, because the axis of the rotation of the Earth does not pass through Israel. It passes through the North Pole.  

No No. It is all metaphorical

The Talmud's claim is measurably incorrect, and several commentators suggest a metaphorical explanation. For example, the mystically inclined Maharal of Prague, Rabbi Yeduah Loew, wrote that Jerusalem is, spiritually speaking, the highest point on Earth (באר הגולה, הבאר הששי). Elsewhere, the Maharal suggests that just as water flows from the peaks of mountains down into valleys, it is Torah teachings that flow down from the spiritual capital Jerusalem to water the rest of the world.  Perhaps it is this that gives Israel and its capital a shot at the claim of being the most spiritually elevated.  Perhaps. But it's a claim that is contingent on the behavior of all those who live there.

אמר ר' יוסי: מבקש אתה לראות פני השכינה בעולם הזה? עסוק בתורה בארץ ישראל"

(מדרש תהלים, תחילת פרק ק"ה).

Rav Yosi said: Do you desire to see the face of the Divine in this world? 

Then study Torah in the Land of Israel.

[Partial repost from Sanhedrin 87. Want more on this topic? Then try this nice essay from Dr Nissin Elikim in Hebrew.]

 

Print Friendly and PDF