Chullin 113b~ Gender Fluidity, Male Lactation and Mordechai

Baby mil bottle.jpeg

[Editor’s note: Today is the Jewish Festival of Purim, on which there is a tradition to create and recite Purim Torah. (These spoofs are usually very clever and witty, and may require a deep knowledge of rabbinic texts. Like this anonymous one from Eddie Reichman.) But this post is not Purim Torah, although it may read as such if you have drunk a little too much alcohol. And drinking too much alcohol is definitely a Purim tradition. So drink up and read on…and I swear I am not making this stuff up.]

Milk Producing Male Goats of The Talmud (MPMGOTT)

In the one-page-a-day of Talmud (Daf Yomi) cycle we are currently learning about the prohibition of cooking meat and milk together. There are several teachings that are derived from the three places in the Torah where we read “You shall not cook a kid in its mother’s milk” (לא תְבַשֵּׁל גְּדִיח בַּחֲלֵב אִמּוֹ) Here is one of them, attributed to Shmuel that we read yesterday:

חולין קיג, ב

בחלב אמו” ולא בחלב זכר

“…In its mother’s milk” indicates that one is not liable for cooking meat in the milk of a male goat

A male goat that grows udders and produces milk? Here is how the great exegete Rashi (1040-1105) explains the Talmud:

ולא בחלב זכר - שהיה לו חלב מועט מן הדדים כגון אם נשתנה והיו לו דדים

“And not in the milk of a male goat”: This means that there was a small amount of milk from the udder. For example if the male goat changed and grew udders.

To understand what on earth is going on here, we need to take a detour into the strange world of biologic gender fluidity. So strap in and here we go.

Clown_fish_in_the_Andaman_Coral_Reef.jpg

Fish

In their helpful 2003 paper Group Sex, Sex Change, and Parasitic Males: Sexual Strategies Among the Fishes and Their Neurobiological Correlates (published, obviously, in the Annual Review of Sex Research) the authors note that there is “tremendous sexual diversity exhibited by fishes” Consider for example the clownfish, also known as the anemonefish. They are sequential hermaphrodites, and first develop into males. These colorful fish thrive unharmed in the poisonous tentacles of the sea anemone, and while several fish may live within the same anemone, there is only one pair that mate. Should the dominant egg-laying female die, one of the largest males steps up does what needs to be done. He changes into a female. This male-to-female change is called protandry. Other fish, like the sea wrasse, are all born female, and as the need arises change into a male. This trick is carried out in at least 500 species of fish, and is called protogyny.

Birds

The male Northern Cardinal (Cardinalis cardinalis) is a bright red color with a black mask over its beak and eyes. The female is a drab olive color, with a grey mask. In 2008 the ornithological world was rocked when a bird was sighted that was half-red and half-olive. Meaning it was half-male and half-female. The bird, sighted in the Black Hawk Forest Nature Preserve in northwestern Illinois, “was perched in a cockspur hawthorn tree.” Its right side was male, and its left, female. The cardinal evaded capture so it was not possible to analyze its genetic makeup. To be clear, this was not a bird that changed sex; it was one that appeared to be both sexes.

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Split sex Cardinal.jpg

Humans

We all should have been taught in school that our gender is determined by which sex chromosomes we receive. If we get two female chromosomes -XX- (one from mom and one from dad) we are female, and if we get one X from mom and a Y from dad -XY- we are male. But like all things, it’s a little more complicated than that. In the 1980s, British researchers discovered the sex-determining gene on a tiny bit of the male Y chromosome and named it the sry gene. That gene tells the body to develop into a male or female appearing body. Sometimes the sry gene sneaks off of the Y gene and makes its way into the DNA of an XX female. As a result, she will develop male anatomy while genetically remaining an XX female. (Please read that sentence again, just to be sure you have understood it.) And sometimes the sry gene on an XY genetic male can mutate and not work. In that case, the genetic male appears to have the organs of a female, which is what occurs in Swyer syndrome. (You can hear more about the amazing sex-changing effects of sry in this fascinating podcast.)

Ready for more? In a small community in the Dominican Republic there have been a number of cases in which little girls grow a penis and turn into little boys. (Again, please re-read that sentence.) These observations were first reported to the scientific community in 1974, and are caused by a deficiency of the steroid 5a-Reductase. Here is how the BBC explained what is going on when they reported about it in 2015.

When you are conceived you normally have a pair of X chromosomes if you are to become a girl and a set of XY chromosomes if you are destined to be male. For the first weeks of life in womb you are neither…Then, around eight weeks after conception, the sex hormones kick in. If you're genetically male the Y chromosome instructs your gonads to become testicles and sends testosterone to a structure called the tubercle, where it is converted into a more potent hormone called dihydro-testosterone. This in turn transforms the tubercle into a penis. If you're female and you don't make dihydro-testosterone then your tubercle becomes a clitoris…the reason [some genetic males] don't have male genitalia when they are born is because they are deficient in an enzyme called 5-alpha-reductase, which normally converts testosterone into dihydro-testosterone.

So the boys, despite having an XY chromosome, appear female when they are born. At puberty, like other boys, they get a second surge of testosterone. This time the body does respond and they sprout muscles, testes and a penis.

So there you have it. Little girls, brought up as little girls, turn into boys, who develop male genitalia, and live as men. You see, they were never really girls in the XX sense. They were XY boys whose lack of sex hormones caused them to look like girls. Which brings us to yesterday’s page of Talmud and the strange case of…

That male goat that produced milk

We have seen that there is great deal of natural gender fluidity in the animal world (and if for no other reason, this should make us more sensitive and understanding of those people who want to change their birth gender). But what about that milk-producing male goat? Well according to the website dedicated to “Goat Milk Stuff,” as bizarre as it seems, “there have even been bucks that have been known to give milk (yes, all bucks have teats, and no, a milking buck is not normal).” This was not a case of a male-to-female transformation. It was a case of male lactation.

Writing in the 13th century in his classic commentary on the Talmud called Bet Habechirah, Menachem ben Solomon Meiri, known as the Meiri(1249–1306) wrote that he had seen examples of male milk-producing goats:

בית הבחירה. מכון התלמוד הישראלי השלם.ירושלים, תשל׳ד 432

בית הבחירה. מכון התלמוד הישראלי השלם.ירושלים, תשל׳ד 432

There are a few male [goats] in whom the works of creation are slightly changed and whose nipples become larger such that they produce a little milk. And we have seen them with our own eyes...
— Meiri, Bet Habechirah Chullin, 432

So too, did Khalifa al Nuaimi, a shepherd in the United Arab Emirates: Here is the 2009 report from The National, a newspaper in the United Arab Emirates.

As one of his prized male goats trotted up for some feed, he noticed the animal had seemingly developed a large udder. While he could not quite believe his eyes, the luckless creature proceeded to produce milk on demand, much like his female companions in the pen.

The local farmer made the discovery four days ago at his goat pen in Masakin, a suburb of Al Ain, the government news agency, WAM, reported yesterday. The animal's male organs are said to have been pushed back by the udder, described as "big and bulky". Mr al Nuaimi got a half-litre of good-quality milk from the goat. Dr Martin Wyness, of the British Veterinary Centre in Abu Dhabi, said it was unusual but not unheard of for male mammals to produce milk. "It's absolutely possible," he said.

what may be happening

The structure of the cells involved in producing milk in the male goat has been studied using immunofluorescence and electron microscopy techniques. It turns out they are smaller but higher in number than those found in normal males, which suggests that the anterior pituitary gland, which controls their function is probably acting in a weird way.

Another explanation of the milk-producing male goats of the Talmud (MPMGOTT) is that it is linked to estrogen-like compounds in the plants upon which they were feeding.

“It is now known that more than 50 plant species contain estrogen mimics known as phytoestrogens. Although the mechanisms are not completely understood, several plant secondary metabolites…can mimic the effects of steroidal estrogens. These non-steroidal compounds have similar overall structures or active sites as natural steroidal estrogen and can compete for binding sites on estrogen receptor proteins. Thus, plant compounds can have effects similar to endogenous estrogens”

This comes from an intriguing 2008 paper, Male lactation: why, why not and is it care? published in Trends in Ecology and Evolution. It points out that there are other mammalian species in which the male has been known to lactate, including sheep, rats, free-ranging Dayak fruit bats in Malaysia and the masked flying fox bats of Papua New Guinea. Male lactation was also recorded “in World War II prisoner of war camps when malnourished detainees were later liberated and provided with adequate nutrition. During the period of limited food supply, the prisoners suffered liver, testicular and pituitary atrophy” which messed things up. Once fully nourished, the lactation quickly ended.

But whatever the cause, Shmuel was neither drunk nor hallucinating when, in yesterday’s page of Talmud, he claimed that male goats can produce milk. Because sometimes they do.

mordechai lactating on demand

Male lactation. It’s not just for goats and bats. Human males might do it too. Here is a story told in the Talmud (Shabbat 53b) and knowing what we now do, perhaps it not as fanciful as it might seem.

שבת נג,ב

מעשה באחד שמתה אשתו והניחה בן לינק ולא היה לו שכר מניקה ליתן ונעשה לו נס ונפתחו לו דדין כשני דדי אשה והניק את בנו

There was an incident where a man’s wife died, and she left him a son to nurse, and he did not have money to pay for a wet-nurse. And a miracle was performed on his behalf, and he developed breasts like the two breasts of a woman, and he nursed his son.

That’s a pretty impressive miracle, although it may seem a little less miraculous now that we understand so much about the role of the anterior pituitary gland. This father is not identified in the Talmud, but another lactating male is. And his name was Mordechai, the hero of the Purim story we read today. In the Book of Esther (2:7) we read וַיְהִ֨י אֹמֵ֜ן אֶת־הֲדַסָּ֗ה - that Mordechai “raised” or “sustained” Esther. Let’s pickup the story in Beresheet Rabbah (30:8), compiled between 300 and 500 CE.

מָרְדְּכַי זָן וּפִרְנֵס, אָמַר רַבִּי יוּדָן פַּעַם אַחַת חִזֵּר עַל כָּל הַמֵּנִיקוֹת וְלֹא מָצָא לְאֶסְתֵּר לְאַלְתָּר מֵינִיקָה, וְהָיָה מֵינִיקָהּ הוּא, רַבִּי בֶּרֶכְיָה וְרַבִּי אַבָּהוּ בְּשֵׁם רַבִּי אֱלִיעֶזֶר בָּא לוֹ חָלָב וְהָיָה מֵינִיקָהּ. כַּד דָּרַשׁ רַבִּי אַבָּהוּ בְּצִבּוּרָא גָּחוֹךְ צִבּוּרָא לְקָלֵיהּ,

But did Mordecai really feed and sustain Esther? R. Yudan said: On one occasion he went round to all the wet nurses but could not find one for Esther, so he himself suckled her. R. Berekiah and R. Abbahu said in the name of R. Eleazar: Milk came to him and he suckled her [and he never even tried to find a wet nurse]. When R. Abbahu taught this publicly, the congregation laughed

They laughed. Of course they did. It sounded like Purim Torah. But what a happy coincidence it is that we learned the passage of the lactating male goat one day before we read the Megillah, the Book of Esther, from where the rabbis describe Mordechai as doing the same thing. Now that’s some real Purim Torah.

happy purim from Talmudology

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From the Talmudology Archives: Queen Esther's Fight or Flight Reaction

In honor of the festival of Purim, which being celebrated either now (in Australia) tomorrow, or on Friday (if you live in a very old walled city), we are reposting this from the Talmudology archives. Enjoy.

אסתר 4:4

וַ֠תָּבוֹאינָה נַעֲר֨וֹת אֶסְתֵּ֤ר וְסָרִיסֶ֙יהָ֙ וַיַּגִּ֣ידוּ לָ֔הּ וַתִּתְחַלְחַ֥ל הַמַּלְכָּ֖ה מְאֹ֑ד וַתִּשְׁלַ֨ח בְּגָדִ֜ים לְהַלְבִּ֣ישׁ אֶֽת־מָרְדֳּכַ֗י וּלְהָסִ֥יר שַׂקּ֛וֹ מֵעָלָ֖יו וְלֹ֥א קִבֵּֽל׃

When Esther’s maidens and eunuchs came and informed her, the queen was greatly agitated. She sent clothing for Mordecai to wear, so that he might take off his sackcloth; but he refused.

The meaning of the verse seems straightforward enough. Esther learned that throughout the empire, Jews were fasting, weeping and wailing, (although she did not yet know why). This greatly upset or"agitated" her.  But in the Talmud, Rav (d. ~247) and his student Rabbi Yirmiyah are not content with this straightforward reading. 

מגילה טו, א

ותתחלחל המלכה מאי ותתחלחל אמר רב שפירסה נדה ור' ירמיה אמר שהוצרכה לנקביה 

What is the meaning of the word ותתחלחל? Rav said: It means that she started to menstruate. R. Yirmiyah said: that her bowels were loosened.

Esther before Ahasuerus by Jacopo Tintoretto (1519-94). From The Royal Academy of Arts, London.

Esther before Ahasuerus by Jacopo Tintoretto (1519-94). From The Royal Academy of Arts, London.

FIGHT OR FLIGHT

Any of us who have have experienced moments of intense fear or anxiety can understand R. Yermiah's explanation. In moments of sudden severe stress, the body's sympathetic nervous system ("fight or flight") goes into overdrive and releases epinephrine (AKA adrenaline). This prepares us for battle: our heart rate increases, blood is diverted away from the digestive system and towards the muscles, and our pupils dilate, to allow for better vision. At the same time the  parasympathetic nervous system ("rest and digest") is partially activated, which results in urination and defecation (or at least the urge to do so). 

Brain circuits involved in fear and anxiety. A schematic view of major brain circuits involved in fear and anxiety. External auditory, visual, olfactory, or somatosensory stimuli are relayed by the thalamus to the amygdala and cortex. The basolatera…

Brain circuits involved in fear and anxiety. A schematic view of major brain circuits involved in fear and anxiety. External auditory, visual, olfactory, or somatosensory stimuli are relayed by the thalamus to the amygdala and cortex. The basolateral complex (BLA) of the amygdala is the input side of the system, which also receives contextual information from the hippocampal formation (entorhinal cortex, hippocampus, and ventral subiculum). After intra-amygdala processing of the emotional stimuli, the central nucleus of the amygdala (CeA), on the output side, activates the locus ceruleus (LC) and central and peripheral noradrenaline systems (via corticotropin-releasing factor [CRF] neurons), and the hypothalamus (paraventricular nucleus [PVN] and lateral hypothalamus [LH]). The bed nucleus of the stria terminalis (BNST, part of the “extended amygdala”) is also a control center for the neuroendocrine system by integrating information originating from both the hippocampus and the amygdala. In addition, the CeA directly activates various midbrain regions or nuclei responsible for different aspects of the fear/anxiety response: freezing or escape (periaqueductal gray [PAG]), increased respiratory rate (parabrachial nucleus [PBN]), startle (caudal reticulopontine nucleus of the reticular formation [RPC]), and the dorsal motor nucleus of the vagus (DMN) in the medulla, which (together with the lateral hypothalamus) is responsible for the increase in heart rate and blood pressure associated with emotional events. The prefrontal cortex (PFC) processes more elaborate (“cognitive”) information; it modulates the physiological, neuroendocrine, and behavioral responses (via the amygdala), and it is also involved in the extinction of fear- and anxiety-related conditional responses. ACTH, adrenocorticotropic hormone; ANS, autonomous nervous system; BP, blood pressure; GABA, γ-aminobutyric acid; Glu, glutamate; NA, noradrenaline (neurotransmitter) or nucleus ambiguus (structure); NTS, nucleus tractus solitarius. From Steimer, T. The biology of fear- and anxiety-related behaviors. Dialogues in Clinical Neuroscience - Vol 4 . No. 3 . 2002, 231-249.

Queen Esther's Stress

As we saw in Megillah, Rav opined that fear can induce menstrual bleeding. In Sotah, the Talmud further delineates the effect of stress on menstruation.

סוטה כ, ב

למימרא דבעיתותא מרפיא אין דכתיב ותתחלחל המלכה מאד ואמר רב שפירסה נדה והא אנן תנן חרדה מסלקת דמים פחדא צמית ביעתותא מרפיא

Does fright loosen the womb [and causes a woman to menstruate]? Yes, as the verse states (Esther 4:4) "...and the Queen [Esther] became very afraid" about which Rav explained:" she began to menstruate."

But haven't we learned elsewhere in a Mishnah (Niddah 39a) that fear suspends the discharge of menstrual blood? In fact, fear that is not sudden contracts [the womb and prevents bleeding], but sudden fear loosens [the womb and causes early menstrual bleeding].

Here are some of the things that the rabbis of the Talmud believed could induce menstruation:

  1. Carrying a heavy load (Tosefta Niddah 9:1)

  2. Jumping (ibid)

  3. Sudden fright (Niddah 71a, and Niddah 39a)

  4. Yearning for intercourse (Niddah 20b)

  5. Garlic, onions and peppers (Niddah 63b)

Let's take a look at the medical literature and see whether or not it supports Rav's assertion.

Data from both animal and human research indicate that psychological stress is associated with altered menstrual function.
— Barsom S, et al. Association between psychological stress and menstrual cycle characteristics in perimenopausal women. Women’s Health Issues 14 (2004) 235-241

The Effect of Stress on Menstrual Function

In a review from the Department of Biological Sciences at Ohio University, researchers acknowledged that stress is difficult to define. However, one final common pathway of stressors is the low availability of dietary energy. Ovulation - which is the first part of the cascade that leads to menstruation - has been blocked in hamsters "by food restriction, pharmacological blockers of carbohydrate and fat metabolism, insulin administration (which shunts metabolic fuels into storage), and cold exposure (which consumes metabolic fuels in thermogenesis)." Women athletes frequently experience a lack of menstruation, which is found in up to 65% of competitive young runners. But what about psychogenic causes of a disturbed menstrual cycle - after all, Rav taught that it was fear that caused Esther's presumably early onset of menstruation? While not adressing this directly, the Ohio University researchers had this to say about the relationship between psychological stressors and amenorrhea (the lack of menstruation. Remember that word - it will come up again):

Associations between psychological disturbances and amenorrhea or infertility have long been interpreted as a causal relationship, but prospective studies demonstrating that psychogenic factors contribute to reproductive dysfunction in women are almost completely lacking . Early psychoanalytic conclusions that psychological conditions underlie involuntary infertility in women have been criticized recently on several grounds: first, the same psychological conditions have been found in analyses of fertile women; second, other women with very serious psychic problems conceive with ease; and third, couples with an unfulfilled desire for a child do not show psychological disorders any more frequently than do couples without fertility disorders. Even the direction of causality is questionable, because there are grounds for believing that infertility and its medical treatment cause the depression and anxiety observed in some infertility patients. These findings have led to the recommendation that the term ‘psychogenic infertility’ should be withdrawn from use because it is simplistic and anachronistic.

Menstruation and Incarceration

Some of the rabbis viewed Esther's association with King Achashverosh as being coerced: she was brought to his palace against her will, and remained there in a similar state. So with only a bit of a stretch, we might turn to a 2007 paper published in Women's Health Issues which addressed the influence of stress on the menstrual cycle among newly incarcerated women.  Researchers analyzed 446 non-pregnant women who answered a number of detailed questions about their menstrual cycles.  They found that 9% reported amenorrhea (I told you what that meant two paragraphs ago) and that a third reported menstrual irregularities.  

Incarcerated women have high rates of amenorrhea and menstrual irregularity and the prevalence may be associated with certain stresses. Further research on the causes and consequences of menstrual dysfunction in this underserved population is needed.
— Allsworth J. et al. The influence of stress on the menstrual cycle among newly incarcerated women. Women's Helath Issues 2007; (17) 202-209.

As might be expected, the stressors of the incarcerated women in this study included drug and alcohol problems and sexual abuse. These are not the same stressors that faced Queen Esther - who was held in such esteem by her kingly husband that he promised her (Esther 5:6) "up to half of the kingdom."  But this work does show how stress may impact the menstrual cycle.  

A Longitudinal Study of Psychological Stress and Menstruation

The final study we will review comes from a cohort of predominantly white, well educated married women of whom 505 were "invited to participate join a special survey focusing on midlife and menopause." Rather than ask about stress and current menstruation, the researchers performed a two-year analysis. Here's what they found:

In analyzing stress levels and cycle characteristics across 2 years...women with marked increases in their level of stress (n =30) are shown to have decreased length (0.2 days/cycle) of menstrual cycle intervals and decreased duration of bleed (0.1 day/cycle) compared with increases in these measures (2.9 days/cycle for cycle interval; 0.3 days/cycle for duration of bleed) among women with no marked change in stress level (n =103); t-tests indicate that these differences are significant (p < .05).

Some of the differences that the researchers found in this group were really small - "0.3 days/cycle for duration of bleeding" but if you are into statistics this difference can be significant (that's what those t-tests are all about). But these statistical associations were not powerful, and the researchers concluded that "the results of this investigation...suggest that, in the long term, stressful life events have little relationship to the length of menstrual cycle intervals and the duration of menstrual bleeding in perimenopausal women."

The three studies we've reviewed (even that last one with its weak findings) all suggest that there is indeed some relationship between psychological stress and menstruation.  Generally, the effect of stress is to increase the length of the menstrual cycle which may result in amenorrhea.  This finding  is also mentioned in Sotah 20b:   "פחדא צמית - chronic fear contracts [the uterus and prevents menstruation]."  But according to Rav, stress caused Esther to menstruate sooner - the opposite of most modern research findings.  Single events should be used with caution when trying to build a general explanatory model, but Rav, and the other rabbis of the Talmud were onto something when they noted that both acute and chronic fear (which is of course just one type of stress) -  can effect a women's menstrual cycle.  

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Happy Pi Day2019, and Happy Birthday Albert Einstein

WHAT IS PI DAY, AND WHEN IS IT CELEBRATED?

From here.

From here.

Today, March 14, is celebrated as Pi Day by some of the mathematically inclined in the US. Why? Well, in most of the world, the date is written as day/month/year. So in Israel, all of Europe, Australia, South America and China, today's date, March 14th, would be written as 14/3. 

But not here in the US. Here, we write the date as month/day/year; it's a uniquely American way of doing things. (Like apple pie. And guns.) So today's date is 3/14. Which just happen to be the first few digits of pi, the ratio of the circumference of a circle to its diameter.

And that's why each year, some (particularly geeky) Americans celebrate Pi Day on March 14 (3/14). The year 2015 was Pi'ish than all others, since the entire date (when written the way we do in the US, 3/14/15) reflects five digits of pi, and not just the first three: 31415. Actually we got even more geeky: This day in 2015 at 9:26 and 53 seconds in the morning, the date and time, when written out, represented the first ten digits of Pi: 3141592653.

So that's why Pi Day is celebrated here in the US -  and probably not anywhere else. (It has even be recognized as such by a US Congressional Resolution. Really. I'm not making this up. And who says Congress doesn't get anything done?) 

PI IN THE BIBLE

In the ּBook of Kings (מלאכים א׳ 7:23) we read the following description of  a circular pool that was built by King Solomon. Read it carefully, then answer this question: What is the value of pi that the verse describes?

מלכים א פרק ז פסוק כג 

ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקוה שלשים באמה יסב אתו סביב 

And he made a molten sea, ten amot from one brim to the other: it was round, and its height was five amot, and a circumference of thirty amot circled it.

Answer: The circumference was 30 amot and the diameter was 10 amot. Since pi is the ratio of the circumference of a circle to its diameter, pi in the Book of Kings is 30/10=3. Three - no more and no less.

There are lots of papers on the value of pi in the the Bible. Many of them mention an observation that seems to have been incorrectly attributed to the Vilna Gaon.  The verse we cited from מלאכים א׳ spells the word for line as קוה, but it is pronounced as though it were written קו.  (In דברי הימים ב׳ (II Chronicles 4:2) the identical verse spells the word for line as קו.)  The ratio of the numerical value (gematria) of the written word (כתיב) to the pronounced word (קרי) is 111/106.  Let's have the French mathematician Shlomo Belga pick up the story - in his paper (first published in the 1991 Proceedings of the 17th Canadian Congress of History and Philosophy of Mathematics, and recently updated), he gets rather excited about the whole gematria thing:

A mathematician called Andrew Simoson also addresses this large tub that is described in מלאכים א׳ and is often called Solomon's Sea. He doesn't buy the gematria, and wrote about it in The College Mathematics Journal.

A natural question with respect to this method is, why add, divide, and multiply the letters of the words? Perhaps an even more basic question is, why all the mystery in the first place? Furthermore, H. W. Guggenheimer, in his Mathematical Reviews...seriously doubts that the use of letters as numerals predates Alexandrian times; or if such is the case, the chronicler did not know the key. Moreover, even if this remarkable approximation to pi is more than coincidence, this explanation does not resolve the obvious measurement discrepancy - the 30-cubit circumference and the 10-cubit diameter. Finally, Deakin points out that if the deity truly is at work in this phenomenon of scripture revealing an accurate approximation ofpi... God would most surely have selected 355/113...as representative of pi...

Still, what stuck Simoson was that "...the chroniclers somehow decided that the diameter and girth measurements of Solomon's Sea were sufficiently striking to include in their narrative." (If you'd like another paper to read on this subject, try this one, published in B'Or Ha'Torah - the journal of "Science, Art & Modern Life in the Light of the Torah." You're welcome.)

PI IN THE TALMUD

The Talmud echoes the biblical value of pi in many places. For example:

תלמוד בבלי מסכת עירובין דף יד עמוד א 

כל שיש בהיקפו שלשה טפחים יש בו רחב טפח. מנא הני מילי? - אמר רבי יוחנן, אמר קרא : ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקו שלשים באמה יסב אתו סביב 

"Whatever circle has a circumference of three tefachim must have a diameter of one tefach."  The problem is that as we've already noted, this value of pi=3 is not accurate. It deviates from the true value of pi (3.1415...) by about 5%. Tosafot is bothered by this too.

תוספות, עירובין יד א

והאיכא משהו. משמע שהחשבון מצומצם וכן בפ"ק דב"ב (ד' יד:) גבי שני טפחים שנשתיירו בארון ששם ספר תורה מונח שהיא בהיקפה ששה טפחים ופריך כיון דלאמצעיתו נגלל נפיש ליה משני טפחים וכן בתר הכי דמשני בספר דעזרה לתחלתו נגלל ופריך אכתי תרי בתרי היכי יתיב משמע דמצומצם לגמרי וקשיא דאין החשבון מדוקדק לפי חכמי המדות

Tosafos can't find a good answer, and concludes "this is difficult, because the result [that pi=3] is not precise, as demonstrated by those who understand geometry." 

PI IN THE RAMBAM

In his commentary on the Mishnah (Eruvin 1:5) Maimonides makes the following observation:

פירוש המשנה לרמב"ם מסכת עירובין פרק א משנה ה 

צריך אתה לדעת שיחס קוטר העיגול להקפו בלתי ידוע, ואי אפשר לדבר עליו לעולם בדיוק, ואין זה חסרון ידיעה מצדנו כמו שחושבים הסכלים, אלא שדבר זה מצד טבעו בלתי נודע ואין במציאותו שיודע. אבל אפשר לשערו בקירוב, וכבר עשו מומחי המהנדסים בזה חבורים, כלומר לידיעת יחס הקוטר להקיפו בקירוב ואופני ההוכחה עליו. והקירוב שמשתמשים בו אנשי המדע הוא יחס אחד לשלשה ושביעית, שכל עיגול שקוטרו אמה אחת הרי יש בהקיפו שלש אמות ושביעית אמה בקירוב. וכיון שזה לא יושג לגמרי אלא בקירוב תפשו הם בחשבון גדול ואמרו כל שיש בהקיפו שלשה טפחים יש בו רוחב טפח, והסתפקו בזה בכל המדידות שהוצרכו להן בכל התורה.

...The ratio of the diameter to the circumference of a circle is not known and will never be known precisely. This is not due to a lack on our part (as some fools think), but this number [pi] cannot be known because of its nature, and it is not in our ability to ever know it precisely. But it may be approximated ...to three and one-seventh. So any circle with a diameter of one has a circumference of approximately three and one-seventh. But because this ratio is not precise and is only an approximation, they [the rabbis of the Mishnah and Talmud] used a more general value and said that any circle with a circumference of three has a diameter of one, and they used this value in all their Torah calculations.

So what are we to make of all this? Did the rabbis of the Talmud get pi wrong, or were they just approximating pi for ease of use?  After considering evidence from elsewhere in the Mishnah (Ohalot 12:6 - I'll spare you the details), Judah Landa, in his book Torah and Science, has this to say:

We can only conclude that the rabbis of the Mishnah and Talmud, who lived about 2,000 years ago, believed that the value of pi was truly three. They did not use three merely for simplicity’s sake, nor did they think of three as an approximation for pi. On the other hand, rabbis who lived much later, such as the Rambam and Tosafot (who lived about 900 years ago), seem to be acutely aware of the gross innacuracies that results from using three for pi. Mathematicians have known that pi is greater than three for thousands of years. Archimedes, who lived about 2,200 years ago, narrowed the value of pi down to between 3 10/70 and 3 10/71 ! (Judah Landa. Torah and Science. Ktav Publishing House 1991. p.23.)

HAPPY BIRTHDAY, EINSTEIN

Today, March 14, is not only Pi Day. It is also the anniversary of the birthday of Albert Einstein, who was born on March 14, 1879. As I've noted elsewhere, Einstein was a prolific writer; one recent book (almost 600 pages long) claims to contain “roughly 1,600” Einstein quotes. So it's hard to chose one pithy quote of his on which to close.  So here are two.  Happy Pi Day, and happy birthday, Albert Einstein.

As a human being, one has been endowed with just enough intelligence to be able to see clearly how utterly inadequate that intelligence is when confronted with what exists.
— Letter to Queen Elisabeth of Belgium, September 1932
One thing I have learned in a long life: That all our science, measured against reality, is primitive and childlike — and yet it is the most precious thing we have.
— Banesh Hoffman. Albert Einstein: Creator and Rebel. Plume 1973
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Chullin 105b ~ The Healing Effects of Alcohol

חולין קה, ב

לכרסם דחמרא שיכרא דשיכרא מיא דמיא לית ליה תקנתא והיינו דאמרי אינשי בתר עניא אזלא עניותא

The treatment for catarrh caused by the foam of wine is beer; the treatment for catarrh caused by the foam of beer is water; and for catarrh caused by the foam of water there is no remedy. And this is in accordance with the adage that people say: Poverty follows the poor. [Not only does a pauper have nothing to drink other than water, but there also is no treatment for the disease caused by his beverage.]

Beer and Health image.png

In today’s page of Talmud we read that the disease known as karsom (כרסם) was caused by the “foam” that floats above wine, beer or water. Karsom is translated by the Soncino, Koren and ArtScroll Talmuds as catarrh, that green phlegmy discharge from our noses and mouths when we come down with a heavy cold. In his dictionary, the great philologist of rabbinic literature Marcus Jastrow notes that there is another spelling of the word, barsom, (ברסם) “a dripping like balsam, whence catarrh of the head.” And Rashi describes it as “nasal mucus” (רירין הבאין מן החוטם). In any event, the cure for one type of this mucus was beer, which raises the question - can ingesting alcohol cure disease?

We are not going to examine the ongoing debate as to whether a regular glass of wine is good for you or not. At best the evidence is mixed, with any positive effects being highly dependent on not drinking “too much.” Alcohol may be cardioprotective, but only at a moderate dose and frequency of ingestion. On the other hand, even at a low dose, alcohol does some pretty terrible things to your immune system and ability to repair damaged tissue.

...even after a single acute or binge exposure, alcohol leads to tissue damage. In gastric mucosa and in bone, alcohol exposure alters basic signaling processes. In the repair of skin damage following injury or surgery, alcohol disrupts signaling in a broader context, in multiple tissue types. The derangement of the inflammatory response by alcohol leads to altered cytokine and chemokine production by multiple cell types and this, in turn, influences the responses of other cell types.
— Jung et al. Alcohol Exposure and Mechanisms of Tissue Injury and Repair. Alcohol Clin Exp Res. 2011 ; 35(3): 392–399.
Habitual light to moderate alcohol intake (up to 1 drink per day for women and 1 or 2 drinks per day for men) is associated with decreased risks for total mortality, coronary artery disease, diabetes mellitus, congestive heart failure, and stroke. However, higher levels of alcohol consumption are associated with increased cardiovascular risk.
— O'Keefe et al. Alcohol and Cardiovascular Health: The Dose Makes the Poison...or the Remedy. Mayo Clin Proc.2014;89(3):382-393.

Alcohol has been used as a medicine for over 5,000 years and when thee alternative was drinking water contaminated with bacteria, alcohol provided a safer (and certainly more enjoyable) way to remain hydrated, since it is a natural antiseptic. Juniper essential oil for example, which is obtained from Juniper berries is both antimicrobial and antifungal. It is also an essential ingredient of gin. “Juniper is such an important aspect of gin” we learn on this useful website, “that quite literally, it is not only the primary botanical used in gin but by law, it needs to be the predominant flavour in anything seeking to be classified as gin.”

alcohol and the discovery of the cause of CHolera

In the 1850s, London (and much of Europe) suffered a series of cholera outbreaks, and no-one knew what caused them. But John Snow (1813-1858), anesthesiologist to Queen Victoria had a hunch. He drew a map of the deaths around the Broad Street pump, which, he suspected was somehow involved in transmitting whatever it was that was spreading the disease.

 
Snow map detail.png
 

There were a large cluster of deaths in the immediate vicinity of the Broad Street Pump; that made sense if the pump was supplying contaminated water. However, there were far fewer deaths than would be expected at the brewery, which lay at the corner of Broad Street and Hopkin Street. Snow dug deeper, and this is what he found:

 
John Snow. On the Mode of Communication of Cholera. London, John Churchill 1855. p42.

John Snow. On the Mode of Communication of Cholera. London, John Churchill 1855. p42.

 

The men had been saved by their allotted drinks of beer, which came from a separate well and not from the one on Broad Street. This explanation did much to bolster Snow’s suspicions. On September 8, 1854 he famously removed the pump handle which prevented the pump from being used and, so the story goes, the cholera epidemic was averted.

Alcohol and Influenza

The Talmud had suggested wine would fight some infections. In the last century physicians had a similar idea. In 1913 in New York, a physician named John Hopkirk published a small book: Influenza. Its History, Nature, Cause and Treatment. To cure some of the many complications of influenza (including pneumonia and otitis media) Hopkirk wrote that “it will always be necessary…to administer port or champagne…there is no finer pick-me-up after an attack of influenza than good “fiz”.” During the Great Flu Epidemic of 1918 a few years later, physicians reverted to a similar strategy. Writing in the London Times on November 1, 1918, Britain’s chief medical officer had limited advice: wear small face masks, eat well, and drink a half bottle of light wine.

Purim in next week

When celebrating the festival of Purim, the Talmudic sage Rava recommends (Megillah 7b) that a person drink until they are so inebriated that they cannot distinguish between the phrases “cursed is Haman” (the enemy of the Jews), and “blessed be Mordechai” (one of the key figures in their salvation). Perhaps in doing so, we can remain sober enough to remember that from the time of the Talmud until today alcohol was thought to prevent and cure all manner of disease. But only in moderation.

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