Avodah Zarah 51a ~ The Neck of a Grasshopper

In today's page of Talmud there is a dispute about how far the prohibition against idol worship extends: 

עבודה זרה נא, א

 שחט לה חגב ר' יהודה מחייב וחכמים פוטרים

If one slaughtered a locust for an idol, Rabbi Yehuda deems him liable, and the Rabbis deem him exempt from punishment.

According to Rabbi Yehudah the neck of the grasshopper is similar to the neck of an animal; since slaughtering an animal for idol worship is prohibited, so, by analogy, is slaughtering a grasshopper.

ושאני חגב הואיל וצוארו דומה לצואר בהמה...

The neck of the grasshopper resembles the neck of an animal...

What is a neck?

The neck is the bit that connects an animal's head to its body. Grasshoppers have a head and they have a body, so perforce, they have a neck.  Here is what a typical (female) grasshopper looks like:

Diagram of a female grasshopper. From Pfadt, R. The Field Guide to Common Wester Grasshoppers. Wyoming Agricultural Experiment Station Bulletin #912, 1994. p1.

As you can see, the pronotum  sits where the neck should be.  It is the bony upper plate of the first section of the thorax, and when viewed from the side, appears saddle shaped.  Other insects with a pronotum include ladybugs (or ladybirds, as they are quaintly called in Britain and elsewhere), termites, beetles and fleas. The pronotum covers the cervix, the neck proper, which is "a membranous area that allows considerable freedom of movement for protraction and retraction of the insect's head." Like all insects, grasshoppers possess an exoskeleton. Beneath this hard outer shell, lay all the soft squishy bits like the gut and heart, or at least what passes for a heart in an insect.

Rabbi Yehudah's Anatomy Lesson

Rabbi Yehudah declared that the neck of the grasshopper resembled the neck of an animal, by which he meant an animal that was offered as a sacrifice in the Temple. Rashi changes the language just a little, and in so doing suggests the resemblance is even closer. The grasshopper's neck does not just resemble (דומה) an animal's. Rather, they are the same:

דיש לה צואר כבהמה ולהכי מחייב רבי יהודה דכעין שחיטת פנים הוא

The grasshopper has a neck like an animal, which is why Rabbi Yehudah finds that [a person who slaughters a grasshopper like he would an animal] is liable...

Here is the explanation found in the Koren English Talmud:

Most insects possess a head located very close to the body, i.e., the thorax, and therefore lack a visible neck. Nevertheless, some types of grasshopper possess an uncommonly visible pronotum protecting the front of the thorax. This feature has the appearance of a neck, and so even though a grasshopper cannot be truly slaughtered, it can appear to be slaughtered much like animals with necks.

But animal necks and grasshopper necks are nothing like each other. 

The grasshopper neck:

1. Is covered with a protective shell (the pronotum)

2. Does not possess an endoskeleton.

3. Is really the cervix which lies hidden beneath the pronotum.

The animal neck:

1. Is covered with skin or feathers, not a hard protective shell.

2. Has an endoskeleton made of seven cervical vertebrae.

3. Is clearly visible and is not hidden.

It is not clear in what way Rabbi Yehudah equated the neck of a grasshopper with the neck of an animal that was sacrificed in Jerusalem, but his teaching is echoed in Jewish law.  According to Maimonides, such an act is forbidden if it is done as a part of a religious ceremony:

משנה תורה, הלכות עבודה זרה וחוקות הגויים ג׳:ד׳

 שָׁחַט לָהּ חָגָב פָּטוּר אֶלָּא אִם כֵּן הָיְתָה עֲבוֹדָתָהּ בְּכָךְ

And the Shulchan Aruch rules that a grasshopper slaughtered in front of an idol, regardless of whether this was part of a religious ceremony or not, is forbidden to be used by a Jew. 

שולחן ערוך ירוה דעה ס׳קלט, ד

שחט לפניה חגב, נאסר, אפלו אין דרך לעבדה בחגב כלל

As a result, it's probably best not to sacrifice a grasshopper to an idol, even if you can't see its neck.

Avodah Zarah 39a ~ Do Swordfish have Scales?

A fish is only kosher if it possesses both fins and scales. What happens if the fish only grows scales when it matures, or if the scales fall off as it is being netted? On page 39a of Avodah Zarah, this question is addressed in a Beraita.

עבודה זרה לט, א

תנו רבנן אין לו עכשיו ועתיד לגדל לאחר זמן כגון הסולתנית והעפיץ הרי זה מותר יש לו עכשיו ועתיד להשיר בשעה שעולה מן הים כגון אקונס ואפונס כטספטייס ואכספטייס ואוטנס מותר

The Sages taught: If a fish does not currently possess scales but will grow them after a period of time, such as the sultanit and afiyatz fish, it is permitted. Likewise, if it has scales now but will shed them when it is caught and rises from the sea, such as akunas and afuna, ketasfatiyas and akhsaftiyas and otanas fish, it is permitted.

The identity if these species is not certain. The Schottenstein Talmud, for example, leaves these names untranslated. But according to some, the כטספטייס, the ketasfatiyas, is the swordfish. This is the translation found in the Soncino Talmud, and here is the helpful note from the Koren Talmud:

Is it true?

Let's assume that the identification of the כטספטייס, the ketasfatiyas as the swordfish is correct. All fish will shed some scales when they are thrashing about in a net or fighting at the end of a line. In this regard the swordfish is no different from any other fish. But at first blush, the suggestion that it would lose all its scales when pulled from the water seems rather unlikely. Thanks to modern science, we can better understand the Beraita's claim. It's not that the swordfish loses its scales when removed from the water; rather, the scales of the adult fish are buried deep in the skin, giving it the appearance of having lost its scales.  

“There is some confusion about whether [swordfish] scales become smaller or are replaced by a single scale type in adults and much confusion about the disappearance of scales altogether”

— Govoni, JJ. West, MA. Zivotofsky, D. Zivotofsky AZ. Bowser PR. Collette BB. Ontogeny of Squamation in Swordfish, Xiphias gladius. Copeia, 2004(2), pp. 391–396.

The swordfish and its "disappearing" scales

Dr. Ari Zivotofsky is a Senior Lecturer in Bar-Ilan's Interdisciplinary Science Program. Aside from arguing cases about the status of Jerusalem in front of the U.S. Supreme Court, he has spent considerable time and energy pondering both the kashrut of the swordfish, and the anatomy of swordfish scales. He was one of several authors who published a study in 2004 with the playful title Ontogeny of Squamation in Swordfish, Xiphias gladius. Their study noted that "scales first appear on the abdomen of larval Xiphias at 6 mm standard length. Thereafter, large scales with a single spine increase in number anteriorly and posteriorly in a row along the abdomen and ventral margin." 

An earlier paper from 1982 noted that swordfish develop two types of scales as larvae and juveniles: large, multi-spined row and rostral scales; and small single-spined scales. As the fish matures from larva to juvenile to adult, its scales persist, but become more buried in the dermis, the skin of the fish. It is not that these scales are receding. Rather, the thickness of the dermis increases. You can see this in the photomicrograph below:

Photomicrographs of the integument and scales of Xiphias gladius. (A) The integument with scale (S), epidermis (Ed), and dermis with stratum spongiosum (SSp), stratum compactum (SCm) of a 22.2 mm larvae (scale bar 63 m). (B) The integument of a 330 cm adult (scale bar 45 m). From Govoni, JJ. et al. Ontogeny of Squamation in Swordfish, Xiphias gladius. Copeia, 2004(2), pp. 391–396. 

  Zivotofsky notes that swordfish scales continue to grow and are most certainly not resorbed: 

The confusion in the literature about the presence or absence of scales on adult Xiphias owes to the thickening of the dermis above the scale as larval and juvenile Xiphias grow. The result is that only the tips of the scale spines protrude in adults. Scales are often fractured and abraded when fish are caught and processed by the fishery. The cuticular layer of the integument is also covered with a thick layer of mucus, secreted by a network of mucous canals within the epidermis. This mucus lubricates the integument and renders scale spines less conspicuous. 

And so modern biology supports the claim, found in today's daf, that when adult swordfish are caught they appear to be without scales.  

So is the swordfish Kosher?

The presence of tiny scales does not automatically give a fish a kosher status. Biological evidence of tiny or buried scales may, or may not be of consequence in Jewish law. Way back in 1968, Rabbi Moses Tendler of Yeshiva University wrote a polemic in The Jewish Observer, arguing that under no circumstances could the swordfish be considered kosher.  Among the "facts - halachic and scientific" on which he based his opinion was this: "With growth the scales disappear and the larger fish including those sold in the market have no scales." We have seen that this is not the case.  Later, he wrote that "in no place in the Talmud or the responsa literature is there any reference to a deviant: a fish that has scales as a juvenile but not as an adult." This may indeed be so. But as we have seen, the swordfish does not lose its scales. It buries them.

The kosher status of the swordfish is a complex question. It involves anatomy, biology, history, halakhic responsa and local tradition.  If you want to learn more, you can read Rabbi Tendler's 1968 article here. Avi Zivotofsky published a lengthy (53 pages!) and comprehensive history of the question in 2008. He focused less on the scientific issues and more on the historical and halakhic ones, and you can read it here. Print them both up and enjoy reading them over Shabbat, together with a tasty fish dip. Like herring, or ketasfatiyas.   

Scales of Xiphias gladius. (A) Photograph of the ventral aspect of a pre-served larvae 114 mm long (scale bar 1.5 mm). (B) Photograph of a cleared and stained biopsy of the lateral flank of a 150 mm larvae (scale bar 0.3 mm). (C) Photograph of a cleared and stained biopsy of the lateral flank of a 102 cm juvenile (scale bar 0.6 mm). From Govoni, JJ. et al. Ontogeny of Squamation in Swordfish, Xiphias gladius. Copeia, 2004(2), pp. 391–396. 

Ketuvot 15a ~ Talmudic Probability Theory

תלמוד בבלי כתובות דף טו עמוד א 

  א"ר זירא: כל קבוע כמחצה על מחצה דמי ..מנא ליה לר' זירא הא? ...מתשע חנויות, כולן מוכרות בשר שחוטה ואחת בשר נבלה, ולקח מאחת מהן ואינו יודע מאיזה מהן לקח - ספיקו אסור, ובנמצא - הלך אחר הרוב, 

R. Zera said: Any doubt about something that is fixed in its place is considered be a fify-fifty chance... Where does he learn this from ? [From a Baraisa which teaches the following. Consider a town in which] there are nine shops, all of which sell kosher meat, and one store that sells meat that is not kosher. If a person bought meat from one of these [ten] stores but he cannot recall from which, his doubt means that the meat is forbidden. But if he found a piece of meat [in the street and he cannot tell from which store it came] he may follow the majority [and assume the meat is kosher]...

As Dov Gabbay and Moshe Koppel noted in their 2011 paper, there is something odd about talmudic probability. If we find some meat in an area where there are p kosher stores and q non-kosher stores, then all other things being equal, the meat is kosher if and only if p > q.This is clear from the parallel text in Hullin (11a) where the underlying principle is described as זיל בתר רובא – follow the majority. Or as Gabbay and Koppel explain it:

“Given a set of objects the majority of which have the property P and the rest of which have the property not-P, we may, under certain circumstances, regard the set itself and/or any object in the set as having property P.
”

— Gabbay and Koppel 2010

In other words, what happens is that if there are more kosher stores than there are treif, the meat is considered to have become kosher. It's not that the meat is most likely to be kosher and may therefore be eaten.  Rather it takes on the property of being kosher. 

We encountered another example of talmudic probability theory only a week ago, on Ketuvot 9a. There, a newly-wed husband claims that his wife was not a virgin on her wedding night. The Talmud argues that his claim needs to be set into a context of probabilities:

1. She was raped before her betrothal.

2. She was raped after her betrothal.

3. She had intercourse of her own free will before her betrothal.

4. She had intercourse of her own free will after her betrothal.

Since it is only the last of these that renders her forbidden to her husband (stay focussed and don't raise the question of a husband who is a Cohen), the husband's claim is not supported, based on the probabilities. Here is how Gabbay and Koppel explain the case - using formal logic:

Oh, and the reference to Bertrand's paradox? That is the paradox in which some questions about probability - even ones that seem to be entirely mathematical, have more than one correct solution; it all depends on how you think about the answer. One if its formulations goes like this: Given a circle, find the probability that a chord chosen at random will be longer than the side of an inscribed equilateral triangle. Turns out there are three correct solutions. Gabbay and Koppel claim that just like that paradox, the solution to many talmudic questions of probability will have more than one correct answer, depending on how you think about that answer.

Rabbi Nahum Eliezer Rabinovitch (1928-2020) was the Rosh Yeshiva of the hesder Yeshivah Birkat Moshe in Ma'ale Adumim.  (He also had 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.)  Rabbi Rabinovitch seemed to have been the first to point out the relationship between Bertrand's paradox and talmudic probability theory in his 1970 Biometrika paper Combinations and Probability in Rabbinic Literature. There, the Rosh Yeshiva wrote that "the rabbis had some awareness of the different conceptions of probability as a measure of relative frequencies or a state of general ignorance."

James Franklin, in his book on the history of probability theory, notes that codes like the Talmud (and the Roman Digest that was developed under Justinian around 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 late Rosh Yeshiva, Rabbi Rabinovitch.

“(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.

Pesachim 9b ~ Talmudic Probability Theory

Our new tractate Pesachim, deals with all things Paschal. (Well, nearly all). What happens if there were nine piles of matzah and one pile of forbidden leavened bread known as chametz, and along came a mouse and took a piece from one of the piles and carried it into a house that had already been searched for chametz. Must the house be searched a second time? To find an answer, the Talmud quotes a Baraiasa that deals with an analogous question.

פסחים ט, ב 

דִּתְנַן: תֵּשַׁע חֲנוּיוֹת, כּוּלָּן מוֹכְרִין בְּשַׂר שְׁחוּטָה, וְאַחַת מוֹכֶרֶת בְּשַׂר נְבֵלָה, וְלָקַח מֵאַחַת מֵהֶן, וְאֵינוֹ יוֹדֵעַ מֵאֵיזֶה מֵהֶן לָקַח — סְפֵיקוֹ אָסוּר.

With regard to nine stores in a city, all of which sell kosher meat from a slaughtered animal, and one other store that sells meat from unslaughtered animal carcasses, and a person took meat from one of them and he does not know from which one he took the meat, in this case of uncertainty, the meat is prohibited.

וּבַנִּמְצָא — הַלֵּךְ אַחַר הָרוֹב

And in the case of meat found outside, follow the majority.

What this boils down to is this. If most stores in the city sell kosher meat then a piece of meat that is found in the city (that is “outside”) is assumed to be kosher, since the majority of the stores sell only kosher meat. But if a person bought meat from one of the ten stores, but he cannot recall whether or not it was from a kosher store, the meat may not be eaten. In this latter case, we assume that there were simply an equal number of kosher and non-kosher stores. There is a 50-50 chance that the meat comes from a non-kosher store, and it may not be eaten.

By analogy, if the mouse took the morsel from one of the piles, the legal status of the morsel is that of an equally balanced uncertainty concerning whether it was taken from a pile of matzah or a pile of chametz. Consequently, the owner is required to go back and search the house all over again.

Talmudic Probability

As Dov Gabbay and Moshe Koppel noted in their 2011 paper, there is something odd about talmudic probability. If we find some meat in an area where there are p kosher stores and q non-kosher stores, then all other things being equal, the meat is kosher if and only if p > q.This is clear from the parallel text in Hullin (11a) where the underlying principal is described as זיל בתר רובא – follow the majority. Or as Gabbay and Koppel explain it:

Given a set of objects the majority of which have the property P and the rest of which have the property not-P, we may, under certain circumstances, regard the set itself and/or any object in the set as having property P.

In other words, what happens is that if there are more kosher stores than there are non-kosher, the meat is considered to have become kosher. It's not that the meat is most likely to be kosher and may therefore be eaten.  Rather it takes on the property of being kosher. 

We encountered another example of talmudic probability theory when we studied the tractate Ketuvot. There, a newly-wed husband claims that his wife was not a virgin on her wedding night. The Talmud argues that his claim needs to be set into a context of probabilities:

1. She was raped before her betrothal.

2. She was raped after her betrothal.

3. She had intercourse of her own free will before her betrothal.

4. She had intercourse of her own free will after her betrothal.

Since it is only the last of these that renders her forbidden to her husband (stay focussed and don't raise the question of a husband who is a Cohen), the husband's claim is not supported, based on the probabilities. Here is how Gubbay and Koppel explain the case - using formal logic:

Oh, and the reference to Bertrand's paradox? That is the paradox in which some questions about probability - even ones that seem to be entirely mathematical, have more than one correct solution; it all depends on how you think about the answer. One if its formulations goes like this: Given a circle, find the probability that a chord chosen at random will be longer than the side of an inscribed equilateral triangle. Turns out there are three correct solutions. Gubbay and Koppel claim that just like that paradox, the solution to many talmudic questions of probability will have more than one correct answer, depending on how you think about that answer.

Rabbi Nahum Eliezer Rabinovitch, who died in May of this year at the age of 92 was the Rosh Yeshiva of the hesder Yeshivah Birkat Moshe in Ma'ale Adumim.  (He also had 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.)  Rabbi Rabinovitch seems to have been the first to point out the relationship between Bertrand's paradox and talmudic probability theory in his 1970 Biometrika paper Combinations and Probability in Rabbinic Literature. There, the Rosh Yeshiva wrote that "the rabbis had some awareness of the different conceptions of probability as a measure of relative frequencies or a state of general ignorance."

James Franklin, in his book on the history of probability theory, notes 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 late mathematician and Rosh Yeshiva, Rabbi Rabinovitch.

“(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.