The Solar Eclipse

Friday March 20 - An Astronomic Trifecta, +1

Tomorrow, Friday March 20, 2015, is a very important day for astronomers. That's because three events will coincide: the Spring (Vernal) equinox, a super-moon (in which either a full moon or a new moon occurs during the moon's closest approach to Earth) and...a solar eclipse. (And then of course on Friday night it is ראש הודש ניסן – the start of the month of Nissan.) We will discuss the eclipse, which unfortunately will only be visible over north Africa, Israel and most of Europe, as you can see in the animation. (For those in North America, there will be nothing to see, since the eclipse will occur during the night.  If you live there, the next solar eclipse will be on August 21, 2017.  You may stop reading this, and return to this page in two and-a-half years.)

In Israel, and over most of Europe, this solar eclipse will be partial, with the moon taking only a little bite out of the sun's disc. (To experience a full solar eclipse you'll need to be somewhere in the north Atlantic or on Denmarks's Faroe Islands, which are about 200 miles northwest of Scotland.) In Jerusalem the eclipse will begin at 11:16am.  At its maximum (11:58am)  there won't be any noticeable darkening, but if the sky is clear, you'll see something like this:

The Talmud on Eclipses

תלמוד בבלי סוכה דף כט עמוד א 

תנו רבנן: בזמן שהחמה לוקה - סימן רע לעובדי כוכבים, לבנה לוקה - סימן רע לשונאיהם של ישראל, מפני שישראל מונין ללבנה ועובדי כוכבים לחמה...

תנו רבנן: בשביל ארבעה דברים חמה לוקה: על אב בית דין שמת ואינו נספד כהלכה, ועל נערה המאורסה שצעקה בעיר ואין מושיע לה, ועל משכב זכור, ועל שני אחין שנשפך דמן כאחד

“Our Rabbis taught, A solar eclipse is a bad omen for idolaters; a lunar eclipse is a bad omen for Israel, because Israel reckons [its calendar] by the moon, and idolaters by the sun...

Our Rabbis taught, A solar eclipse happens because of four things:
1. When an Av Bet Din [head of the Rabbinic Court] died and was not properly eulogized;
2. If a betrothed girl cried out aloud in the city and there was no-one to save her [from being raped];
3. Because of homosexuality; and
4 If two brothers were killed at the same time.”

— Sukkah 29a

That's what we have - four causes of a solar eclipse.  And how does Rashi explain this passage?       לא שמעתי טעם בדבר  - "I have not heard any explanation for this." 

The Real Cause of a Solar Eclipse

יערות דבש, דרוש י’ב

Another attempt to explain the Talmud was offered by Jonatan Eybeschutz (d. 1764). In 1751 Eybeschutz was elected as chief rabbi of the Three Communities (Altona, Hamburg, and Wandsbek), and was later accused of being a secret follower of the false messiah Shabtai Zevi. In January 1751, Eybeschutz gave a drasha Hamburg in Hamburg in which he addressed the very same problem that the Maharal had noted: if a solar eclipse is a predictable event, how can it be related to human conduct? His answer was quite different: The Talmud in Sukkah is not actually addressing the phenomenon that we call a solar eclipse. According to Eybeschutz, the phrase in Sukkah "בזמן שהחמה לוקה" actually means - "when there are sunspots."

Inventive though this is, it is as implausible as the suggestion of the Maharal. In the first place, sunspots were almost (but not quite impossible) to see prior to the invention of the telescope. They were described in March 1611 by a contemporary of Galileo named Christopher Scheiner (though Galileo lost no-time in claiming that he, not Scheiner was the first to correctly interpret what they were.) Because sunspots were so difficult to see with the naked eye, it seems unlikely that this is what the rabbis in Gemara Sukkah were describing.

Courtesy of NASA

Christopher Scheiner, Rosa Ursina sive Sol (Bracciai 1626-1630)

Second, according to Eybeschutz, sunspots "have no known cause, and have no fixed period to their appearance".  We can't fault Eybeschutz  for his first claim, but - even by the science of his day - his second was not correct. In fact both Scheiner and Galileo knew  - and wrote - that sunspots were permanent (at least for a while) and moved slowly across the face of the sun.

Sidebar: Eybeschutz, Sunspots and Copernicus

It's interesting to note that Galileo got very excited about the discovery that the spots moved across the face of the sun. This suggested (though it did not prove) that the sun itself was spinning. Galileo had also discovered that Jupiter was orbited by moons. Both of these discoveries now added further support to the Copernican model in which the Earth was spinning on its own axis, and was not the center of all the movement of objects in the sky. But Eybeschutz did not believe Copernicus was correct: "Copernicus and his supporters have made fools of themselves when they declare that the Earth orbits [the Sun]. They have left us with a lie, and the truth will bear itself witness that the Earth stands still for ever."  Eybeschutz wanted to have sunspots explain away a talmudic mystery, but he dismissed the evidence that they provided in other matters - namely, that the earth moves.  

Was the Plague of Darkness a Solar Eclipse? 

Since we are only a couple of weeks before פסח, we will end with another look at an old theory, in which the Plague of Darkness was caused not by a miracle, but rather by a (conveniently timed) solar eclipse.  In 1916 Eduard Mahler (d. 1945)  suggested this explanation in his Handbuch der Jüdischen Chronologie, (Vienna 1887).  According to Mahler, there was a solar eclipse visible in Egypt on Thursday March 13, 1335 BC. Since this was the only such eclipse, it would date the Exodus as occurring on March 27th, 1335 BC.

However, there's an obvious problem: the Torah describes the darkness lasting for three days. But a solar eclipse is over in a matter of minutes.  Mahler has in interesting answer: instead of reading the verses (in Exod. 10) like this:

(22) there was a thick darkness in all the land of Egypt for three days. (23) They did not see each other, or get up from their places for three days.

read them like this:

(22)  there was a thick darkness in all the land of Egypt. (23) For three days they did not see each other, or get up from their places for three days.

The eclipse lasted only a few minutes, but its effect on the Egyptians lasted three days. And what about the Jews in Goshen -why was there no Plague of Darkness there? Because they lived outside of the totality -  the area in which the complete eclipse occurred -  and would not have noted any significant darkening. Now there are some problems with this theory - like the fact that according to NASA, the solar eclipse to which Mahler referred seems to have been only a partial eclipse throughout Egypt. Still, it makes for a good discussion. Try that at your Seder Table.

Ketuvot 41 ~ Good Dog. Bad Dog.

“Az a yid hot a hunt, iz oder der hunt keyn hunt nit, oder der yid iz keyn yid nit

If a Jew has a dog, either the dog is no dog, or the Jew is no Jew”

— Sholem Aleichem. Rabtshik. Mayses far Yidishe Kinder. Ale Verk. Warsaw 1903.

From today's daf:

תלמוד בבלי כתובות דף מא עמוד ב 

ר' נתן אומר: מנין שלא יגדל אדם כלב רע בתוך ביתו, ולא יעמיד סולם רעוע בתוך ביתו? שנאמר: ולא תשים דמים בביתך

Rabbi Natan said: From where do we learn that a person should not raise a bad dog in his house, and should not place a rickety ladder in his house? [From the Torah, where] it states "You shall not place blood in your house" (Deut 22:8).

[First, a disclaimer. I've owned dogs all of my married life, and currently own two of them. Still, I'll try to be as objective as possible.] 

Jews and dogs don't traditionally get along. In Bava Kamma 93a, Rabbi Eliezer does not mince his words: רבי אליעזר הגדול אומר: המגדל כלבים כמגדל חזירים .למאי נפקא מינה? למיקם עליה בארור

“Rabi Eliezer the Great said: Soemone who breeds dogs is like someone who breeds pigs. What is the practical outcome of this comparison? To teach that those who breed dogs are cursed...”

— Bava Kamma 83a

The American Veterinary Medical Association estimates that in the US there are about 43 million households that own almost 70 million dogs; that means over one-third of the households in the US own a dog.  (Fun Fact: Cats are owned by fewer households in the US, but are more often owned in twos or more. That means that there are more household cats - some 74 million - than there are dogs.) In the UK, a 2007 study estimated that 31% of all households owned a dog.

Bad Dogs

There are some really bad dogs. In a 10 year period from 2000-2009, one paper identified 256 dog-bite related fatalities in the US. Of course that's a tiny number compared to the overall number of dogs owned, but that's still 256 to many; the tragedy is compounded when you read that over half the victims were less than ten years old. 

Partaken, GJ. et al. Co-occurrence of potentially preventable factors in 256 dog bite–related fatalities in the United States (2000–2009). Journal of the American Veterinary Medical Association 2013. 243:12: 1726-1736.

Fatalities from dog bites are rare. Dog bites are not. Over my career as an emergency physician I must have treated hundreds of patients with dog bites. And my experience is pretty typical. One recent study estimated that more than half the population in the US will be bitten by an animal at some time, and that dogs are responsible for 80-90% of these injuries. 

Good Dogs

Although Jews are thought not to have a historical affinity for dogs, one theologian has reassessed the evidence. In his 2008 paper Attitudes toward Dogs in Ancient Israel: A Reassessment, Geoffrey Miller  suggests that in fact dogs were not shunned in Israelite society. He notes that the remains of over a thousand dogs were discovered in a dog cemetery near Ashkelon dating from about the 5th century BC. It was described as "by far the largest animal cemetery known in the ancient world" by Lawrence Stager who also pointed out that during this period, Ashkelon was a Phoenician city - not a Jewish one. Miller surveys several mentions of dogs in the Bible and the Book of Tobit, and concludes that at least some Israelites "valued dogs and did not view them as vile, contemptible creatures." Joshua Schwartz from Bar-Ilan University surveyed Dogs in Jewish Society in the Second Temple Period and in the Time of the Mishnah and Talmud (a study that marked "...the culmination of several years of study of the subject of dogs...").  He found that while "most of the Jewish sources from the Second Temple period and the time of the Mishnah and Talmud continue to maintain the negative attitude toward dogs expressed in the Biblical tradition" there were some important exceptions. There were sheep dogs (Gen. Rabbah 73:11) and hunting dogs (Josephus, Antiquities 4.206) and guard dogs (Pesahim 113a), and yes, even pet dogs (Tobit, 6:2), though Schwartz concedes that "it is improbable that dogs in Jewish society were the objects of the same degree of affection as they received in the Graeco-Roman world or the Persian world."  

“תלמוד ירושלמי (ונציה) מסכת תרומות פרק ח דף מו טור א /ה”ג

זמין חד רבן ואייתיב כלבא גביה אמר ליה ביזיון אנא חייב לך אמר ליה רבי טיבו אנא משלם ליה שביין עלון לקרתא עאל חד מינהון בעא מינסב איתתי ואכל ביציו

A certain person invited a sage to his home, and [the householder] sat his dog next to him. [The sage] asked him, ‘How did I merit this insult?’ [The house-holder] responded, ‘My master, I am repaying him for his goodness. Kidnappers came to the town, one of them came and wanted to take my wife, and the dog ate his testicles.’”

— PT Terumot 8:7

Whatever your feeling about dogs, lets's be sure to remember that they serve alongside soldiers in the IDF, where they save lives. In 1969, Motta Gur (yes, the same Mordechai "Motta" Gur who commanded the unit that liberated the Temple Mount in the Six Day War, and who uttered those amazing words "The Temple Mount is in our hands!" הר הבית בידינו‎,) wrote what was to become a series of children's books called Azit, the Canine Paratrooper (later turned into a popular feature film with the same title. And now available on Netflix. (Really. It is available on Netflix.)  But IDF dogs don't just feature in fiction. They are a fact, and an amazing addition to the IDF, where they make up the Oketz unit.  Here's a news report (in Hebrew) about the amazing work these dogs - and their handlers- perform. Keep them in your prayers.

Happy Pi Day, Happy Birthday Albert Einstein

What is Pi Day, and When is it Celebrated?

Tomorrow, March 14, is celebrated by many in the US as Pi Day.  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, tomorrow'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 tomorrow's date will be 3/14. Which just happen to be the first few digits of pi, the ratio of the circumference of a circle to its diameter.

“3.14159265358979323846264338327950288419716939937510”

— The First 50 Digits of Pi

And that's why each year, some (particularly geeky) Americans celebrate Pi Day on March 14 (3/14).  But this year, 2015, is more 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 you can go even more geeky: Tomorrow, at 9:26 and 53 seconds in the morning, the date and time, when written out, represent 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?) 

But tomorrow is Shabbat, so we will celebrate Pi Day a day early (Pie Day מוקדם), following the פסק of my colleagues at the National Institutes of Health, (where this kind of thing is taken really seriously):

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 mot. 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 of pi... 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 over Shabbat 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

Tomorrow, 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.  Shabbat shalom, Happy Pi Day, and happy birthday, Albert Einstein.

“The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed. It was the experience of mystery — even if mixed with fear — that engendered religion. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which only in their most primitive forms are accessible to our minds: it is this knowledge and this emotion that constitute true religiosity. In this sense, and only this sense, I am a deeply religious man...
”

— Albert Einstein. Ideas and Opinions. New York. Crown 1954. p11.

“There could be no greater calamity than a permanent discord between us and the Arab people. Despite the great wrong that has been done to us, we must strive for a just and lasting compromise with the Arab people. Let us recall that in former times no people lived in greater friendship with us than the ancestors of these Arabs.”

— Shaviv and Rosen (eds). General Relativity and Gravitation. Wiley. p.242.

Ketuvot 36 ~ The Aylonit Syndrome and Turner's Syndrome

“ איילונית - אין לה לא קנס ולא פיתוי
​ There is no fine for the rape or seduction of an Aylonit

”

— Ketuvot, 36a

Aylonit Syndrome

An Aylonit is a woman who is congenitally unable to have childern.  In the fifth chapter of Niddah (47b) the Mishnah describes the signs which suggest that a woman is an Aylonit:

תלמוד בבלי נדה דף מז עמוד ב 

...בת עשרים שנה שלא הביאה שתי שערות, תביא ראיה שהיא בת עשרים שנה - והיא איילונית, לא חולצת ולא מתיבמת

A woman who is twenty years old and has not grown two pubic hairs..is classified as an Aylonit...

Earlier in our current tractate, Ketuvot (11a), the Talmud suggested the etymology of the word Aylonit:  "איילונית - דוכרנית דלא ילדה - an Aylonit [is given this name] as if she is a ram [דכר is the Aramic translation of the Hebrew word איל– a ram] which [being a male] cannot give birth"

In the last tractate that we studied (Yevamot 80b) the Talmud gives four other signs of this condition, which are codified by Maimonides:

רמב"ם הלכות אישות פרק ב הלכה ו 

ואלו הן סימני אילונית, כל שאין לה דדין, ומתקשה בשעת תשמיש, ואין לה שיפולי מעיים כנשים, וקולה עבה ואינה ניכרת בין איש לאשה

These are the signs that a woman is an Aylonit: She has not developed breasts, she has difficulty during sexual intercourse [that is, she has a diminished libido], the mons pubis is lacking, and she has such a deep voice that it is indistinguishable from that of a man...(Mishneh Torah, Hil. Ishus, 2:6)

There are many reasons for a woman to be infertile, but because the Talmud lists a number of signs other than infertility, we are able to narrow down the possible causes in the special case of the Aylonit. As many have previously noted, the cause of the Aylonit is likely to be what, (since 1938) we now call Turner's Syndrome.  

Turner's Syndrome

In 1938 an American endocrinologist names Henry Turner published a paper describing a newly observed syndrome in seven female patients. (A syndrome is a series of medical abnormalities which occur together.) It consisted of a triad of infantilism, a webbed neck, and a deformity of the elbow. It was found only in female patients, and was associated with delayed or absent sexual development. We now know (and Turner did not) that it is caused by a genetic aberration in which the patient has a missing X chromosome. Instead of carrying 44 regular and two X chromosomes, a woman with (what we now call) Turner's Syndrome has one missing X chromosome. (It gets a little more complicated: in some cases of Turner's Syndrome the woman has only part of one of the X chromosomes missing. And in others, the women's cells contain a mixture of both normal - 45XX - and abnormal - 45X - chromosomes. This is called mosaicism. But let's keep our focus.)

Sex chromosome analyses in Turner's Syndrome.  Here the 22 pairs of autosomes are grouped according to size and the sex chromosomes placed at the end; in this case, there is only one X chromosome.  From Saenger and Bondy. Turner Syndrome. In Sperling M. (ed.) Pediatric Endocrinology. Pittsburgh PA, Elsevier 2014.

Turner's Syndrome occurs in about 1 out of every 2,000 live-born girls. In addition to infertility in most, there are liver problems, high blood pressure, cardiac disorders and various metabolic disorders. Most of the girls with Turner's Syndrome have skeletal abnormalities and a short stature. In girls with the 45X variant, there is ovarian failure and hence infertility, although the cause is not yet clear.    

The variable appearance of Turner syndrome. Both of these 7-year-old girls with short stature have the 45X variant of Turner syndrome. The girl on the left was diagnosed at birth due to prominent neck webbing and low-set and posteriorly rotated ears. She also has micrognathia and a low posterior hairline. In contrast, the girl on the right was diagnosed at age 7 due to short stature without “classical” stigmata of Turner syndrome, and she is more typical of the clinical presentation of the majority of girls with Turner syndrome diagnosed in the 21st century.  From Saenger and Bondy. Turner Syndrome. In Sperling M. (ed.) Pediatric Endocrinology. Pittsburgh PA, Elsevier 2014. 

“Girls and women with Turner syndrome may have low self-esteem and more shyness and social anxiety than controls. In a population-based study of 566 French women with Turner syndrome, low self- esteem was associated with hearing impairment and limited sexual experience, whereas age at first sexual intercourse was related to age at puberty and paternal socioeconomic class.”

— Levitsky, L. Turner Syndrome. Current Opinion Endocrinology, Feb 2015

A study of Polish women with Turner's Syndrome, found that these women had less "...interest in males, less frequent sexual activity, later initiation of sexual life and a less frequent orgasm rate." Other studies found that women with this syndrome were less likely to establish a relationship with a partner, and were less sexually active than women from the general population. All this suggests that the Talmud's description in which they suffer from "difficulties during intercourse" (מתקשה בשעת תשמיש) may be correct.   

Let's remember that behind these scientific findings are real women with the same range of  sensitivities, feelings, hopes and aspirations as those of us who have two functioning sex chromosomes.  Let's give the last word to Harley Gould, a researcher at the National Institutes of Health:

“Moreover, it is important to remember that society continues to dis- criminate against people that are different, and that being short, or infertile, or looking different impose quite a social burden on individuals... Our demonstration of very similar academic, employment...suggests that genomic imprinting of X-linked genes has little to do with functioning in school or socially...We would like to add to that concept the positive observation that many individuals with Turner Syndrome display excellent coping skills, including perseverance in the face of adversity and equability of temperament.”

— Harley Gould et al. High Levels of Education and Employment Among Women with Turner Syndrome. Journal of Women's Health 2013. 22:(3) 230-235.