Happy Purim ~ “I am my own Grandpa”, plus Gender Fluidity, Male Lactation and Mordechai

This year, the study of tractate Yevamot coincides with the festival of Purim. This means that the following video is required viewing today. Sit back, enjoy, and see if you can follow along.

Editor’s note: Unless you live in Australia, or New Zealand, or Jerusalem, today is the Jewish Festival of Purim, on which there is a tradition to create and recite spoofs called Purim Torah. These spoofs are usually very clever and witty, and may require a deep knowledge of rabbinic texts. 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 Talmud in tractate Chullin there is a discussion of 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:

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.

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 and 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.

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 back to that page in the 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

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 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 it can happen. Just ask those lactating goats. Now that’s some real Purim Torah.

happy purim from Talmudology


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Yevamot 8b ~ Ta’amei Hamitzvot in the British Medical Journal: The Deceased Wife’s Sister Controversy: Part II

Last time on Talmudology

In Jewish law, a man may marry his dead wife’s sister, but in Victorian Britain it remained against the law (unless you were a Duke). But many ignored the law, and there was a strong movement to change it. Here’s what happened next, but first a personal revelation...

My own great grandfather married his dead wife's sister!

It's true.  I have skin in this game.  I am the direct descendent of a man who married his dead wife's sister. My great-grandfather, Solomon Bograchov married, moved to London (from Odessa?) and had two children. But his wife died, and, so the story goes, he called for his wife's younger sister to come to London and marry him.  Which she did. They had three children, one of whom was Johnny, born in London in 1913. And Johnny was my zaide.

For clarity, not all family members are shown.  

Now back to our regularly scheduled programming

Hook's Church Dictionary vs the British Medical Journal on Ta'amei Hamitzvot

Hook’s Church Dictionary, first published in 1842, was a wildly successful reference manual for the clergy of the Church of England. But its 1887 fourteenth edition contained a controversial new entry

The new edition tackled the key social issue that we have already discussed: should the law be changed to allow a man to marry his deceased wife’s sister? Absolutely not, said Hook’s Church Dictionary. And it supported this opinion by comparing it with what we call Yibbum, that is, the act of levirate marriage, which "was not, properly speaking, permitted by the Jewish law at all." (This is partially true, since marrying a husband's brother was forbidden in Leviticus 18:16.) This prohibition "was a general moral law" and so applied to all mankind, and was only to be overridden in the special case of a married man who died without children. In this instance, The Bible (Deut. 25:5-10) requires levirate marriage so as to "protect those agrarian rights which were at the basis of the Hebrew system.” But at its core, the Bible’s prohibition against marrying a brother’s wife was precisely the same as the Church’s prohibition against a man marrying his deceased wife’s sister.  Precisely the same.  And what would happen if that Church prohibition would be changed? It would lead to the end of society as we know it. Really, I’m not making this up; that’s what it said:

“To legalize marriage with a deceased wife’s sister cannot possibly remain a solitary innovation. We shall have …taken the first step in a revolution of the whole of our domestic and much of our social life.”

Which brings us, at long last, to The British Medical Journal.

Writing in The Journal, an anonymous doctor -“a surgeon of twenty-five years standing” -challenged this entry in Hook's Church Dictionary, and he used the best science of his day to do so.  The reasons for God’s laws, wrote the surgeon,  “will be found closely connected with some physiological law…and …what profound knowledge was possessed by the framer of Mosaic law, because the facts upon which the opinion is based have only recently appeared in the annals of science. “

He stated that the science at the basis of the laws of Yibbum was the laws of heredity.  Since children inherit the “proclivities of their parents,” a marriage of close blood relatives (consanguine marriage) would concentrate any undesirable traits, and “cause the race to deteriorate.” But when a man marries his dead wife’s sister, he is not marrying a close relative. In fact, he not marrying a blood relative at all, and any offspring would not carry the concentrated negative traits of their parents.  As a consequence, these marriages should be permitted. (Remember that the author was writing some six decades before the discovery of DNA, and only a few years after Mendel’s (largely ignored) suggestion that there were recessive and dominant “factors” that carry hereditary characteristics.)

But when a man marries a woman who has fathered children with another husband, something else is at work, scientifically speaking. “The fact may be regarded as well established that…traces of the first child’s father are discoverable in all succeeding children of the same mother, whatever the direct paternity of these may be.”

Got that? When a man impregnates a women, some of his traits are carried to all the future children of that woman, regardless of who the next father may be.  It is for this reason that the Bible prohibited a man from marrying his dead bother’s wife - unless that brother had fathered no children. For if the deceased brother had fathered a child, his traits would be carried by his wife in all her future pregnancies.  If a man would then marry his widowed brother’s wife, she would pass on both his traits and those of her former husband in a concentrated form. The effect on heredity would be exactly the same as marrying a close blood relative, since the undesirable traits (this time from two brothers) would be mixed together and passed on.  

By the powers of this science, the surgeon then addressed the issue of the day. He argued that no such effect would occur if a man were allowed to marry his dead wife’s sister. “The father has no similar power of transmitting traces of his former wife to the children of her successor, for the diseases which are occasionally contracted by contagion are quite distinct from the collaterally inherited traits referred to.”

Ta’amei Hamitzvot in the BMJ

It’s all very neat and scientific. Levirate marriage was a special dispensation and when understood through the science of heredity, it made biological sense. Since the dead brother had fathered no children, his traits were not carried by his wife, and she could marry her brother-in-law without being worried that there would be a concentration of bad blood. This same cutting edge science also supported a change in the law that would allow a man to marry his dead wife’s sister.

“The effect produced upon the ovaries by impregnation is not only special upon the particular ovum which becomes developed into the particular child begotten, but general upon the entire mass of at least one, if not both…But where impregnation has failed to take place no such effects can follow....”

But we know that no such effect exists. Not remotely.  (And don’t write to me about infectious conditions; we’re not talking about those.)  Today, we know that the science in The BMJ was wrong. Which makes us question the nature of scientific knowledge itself.  It is, as this example shows,  unreliable.  What is true for science today turns out to be wrong tomorrow. And so, when the Torah and Jewish tradition faces a challenge from the scientific community, the correct response is to ignore the science, because hey, in a few years, there will be another scientific theory that comes along and replaces the one that is troubling to us. Right?

Find out in the next installment, on Talmudology. 

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Yevamot 8b ~ Science, Torah, and The Deceased Wife’s Sister Controversy: Part I

For the last several pages, the Talmud has been analyzing one phrase in the Torah (Lev. 18:18):

וְאִשָּׁ֥ה אֶל־אֲחֹתָ֖הּ לֹ֣א תִקָּ֑ח לִצְרֹ֗ר לְגַלּ֧וֹת עֶרְוָתָ֛הּ עָלֶ֖יהָ בְּחַיֶּֽיהָ׃

Do not take [into your household as a wife] a woman as a rival to her sister and uncover her nakedness in the other’s lifetime.

The Talmud spends a total of twelve pages proving that this verse means that a man is forbidden to take his wife’s sister’s, even when she falls to him for levirate marriage (yibbum) following the death of her husband. This same verse was at the center of a fierce debate in Great Britain in the nineteenth century, which concerned the legality of a man marrying his dead wife’s sister. In telling the story of this debate, we will have to discuss what we mean when we say that science changes. We are also going to look at some Jewish skeptics of science, and their understandings and misunderstandings of the concept of a science that changes

We’re going to do this through the lens of Yevamot, and examine in some depth The British Medical Journal’s understanding of Ta’amei Hamitzvot, the reasons for the commandments in the Torah. We are going to dive deeply. So strap in. (Yes I know. Too many metaphors. Sorry.)

Background – Yevamot 8.

Let’s start by going back to that verse in Leviticus (18:18). The Torah states

וְאִשָּׁ֥ה אֶל־אֲחֹתָ֖הּ לֹ֣א תִקָּ֑ח לִצְרֹ֗ר לְגַלּ֧וֹת עֶרְוָתָ֛הּ עָלֶ֖יהָ בְּחַיֶּֽיהָ׃

Do not take [into your household as a wife] a woman as a rival to her sister and uncover her nakedness in the other’s lifetime.

Based on the word בחייה – “in the other’s lifetime”, the Talmud in today’s page of Talmud (8b) establishes that a man may marry his wife’s sister if, and only if, his wife had died. This is reflected in the Code of Jewish Law, the Shulchan Aruch, which ruled (as did Maimonides) that the prohibition against a man marrying his wife’s sister exists only while his wife is alive. On her death, a man may marry his deceased wife’s sister. 

שולחן ערוך אבן העזר הלכות אישות סימן טו סעיף כו 

אחות אשתו אסורה לו מן התורה כל זמן שאשתו קיימת לא שנא אם היא אחותה מן האב או מן האם ואפי' גירש את אשתו אבל לאחר מיתתה מותר באחותה וכל המגרש אפי' מחמת קול בעלמא נאסר בקרובותיה

His wife's sister is forbidden to him from the Torah, all the while his wife is alive; it makes no difference if (the sister) is paternal or maternal, or even if he has already divorced his wife. However, after her (his wife's) death, he may marry her sister.

Just to be clear – this is not the central focus of Yevamot, which is concerned with levirate marriage, when a man marries his dead brother’s widow. But it is very important since it will touch on issues central to science and Yevamot.  Let’s see how.  

Was Henry illegitimate?

The Duke of Beaufort by Henry Alken. From here.

The Jewish law allowing a man to marry his dead wife's sister was not followed in Victorian England. Quite the opposite - a marriage like this was forbidden. But a debate about this law began with a question about the the legitimacy the Duke of Beaufort. Henry Somerset (d. 1853) the seventh Duke of Beaufort, had married Georgina Fitzroy and had fathered two girls with her. But Georgina died in 1821, and the sad Duke then married her younger half-sister Emily, with whom he had a further six daughters, and a son. (I know this is beginning to sound like a complicated episode of Downton Abbey, but bear with me. It’s worth it.)  That son was Henry Charles FitzRoy Somerset (1824-1899), who later became the 8th Duke of Beaufort. But there was a problem. Perhaps Henry was not a legitimate heir to the House of Somerset, since he was the child of a union of a man and his wife’s sister (or in this case, half-sister.) If the old Duke’s marriage to his dead wife’s (half-) sister was prohibited, then Duke Henry was a bastard child and his inheritance would have to be passed on to other males in the family line. There was a lot at stake.

The solution came with the 1835 Act to render certain marriages valid and to alter the law with respect to certain voidable marriages, introduced by Lord Lyndhurst. This Act retrospectively made any marriage like the old Duke’s valid, but prohibited any such marriages from taking place in the future.  In this way, the present Henry, Duke of Beaufort, was not a bastard child after all; he could inherit the estate, and all was made good.

Except that it wasn’t. The Act did not settle matters at all, and ignited a debate in England that lasted seven decades. 

In addition to regular parliamentary bills and debates, pamphlets, letters, treatises and statements from all sides were published steadily through this period; major journals carried articles from leading figures in the controversy…and at least five novels took marriage with a deceased wife’s sister as their explicit subject
— Wallace, Anne D. “On the Deceased Wife’s Sister Controversy, 1835-1907."

The Chief Rabbi and the Royal Commission

In 1842, and almost every year after that, the British Parliament debated whether to legalize the marriage between a man and his dead wife’s sister. Queen Victoria appointed a Commission to look into the whole thing, and look it did, producing a report of over 150 pages in 1848.  Buried in that report is a letter from the Chief Rabbi Nathan Adler, who made the Jewish position very clear.

...the marriage of a widower with the sister of his deceased wife… is not only not considered as prohibited, but it is distinctly understood to be permitted, and on this point neither the Divine Law, nor the Rabbis, nor historical Judaism leave room for the least doubt.
— Chief Rabbi Nathan Adler, Appendix to the Report of the Commissioners appointed to inquire into the state and operation of the Law of Marriage

It didn’t much matter. The law remained the law, though it seemed that the British public ignored their learned lawmakers.  In one 1849 parliamentary debate, it was estimated that there were some 13,000 such marriages. These marriages in turn produced about 40,000 children, all of whom were, by Victorian standards, bastards.

Things became especially heated in the late 1870s when some 3,000 farmers (all, apparently from Norfolk – what was happening in Norfolk?) signed a petition “praying for the legislation of marriage with a deceased wife’s sister.” And so, in May 1879, the Prince of Wales himself introduced a bill to legalize this marriage in Britain’s Parliamentary upper chamber, the House of Lords. Their lordships droned on, and on, and on (the transcript takes up some eight pages of single space font) until the measure was struck down in a vote: “Contents 81: Not-Contents 101”.

But even in England, things do change, and by the beginning of the twentieth century, Parliament was ready to legalize what many women were already doing with their dead sister’s husband. The Deceased Wife’s Sister’s Marriage Act of 1907 was passed, and British law finally caught up with that of the Talmud.


Next time:

The scientists weigh in on the Marriage Act as we look at The British Medical Journal and its understanding of Ta’amei Hamitzvot and Yibbum.

 

 

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Happy Pi Day 2022, and Happy Birthday Albert Einstein

WHAT IS PI DAY, AND WHEN IS IT CELEBRATED?

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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