Bava Basra 20a ~ A Baby Born After Eight Months

Getty Images

A Baby at the Window

In today’s page of Talmud we read a list of objects which, if placed in an opening between rooms, blocks the tumah (ritual impurity) from passing from one room into the next. Among that list is a baby born after only eight months of gestation:

בבא בתרא כ, א

 עשבין שתלשן והניחן בחלון או שעלו מאליהן בחלונות ומטלוניות שאין בהן שלש על שלש והאבר והבשר המדולדלין בבהמה ובחיה ועוף ששכן בחלון ועובד כוכבים שישב בחלון ובן שמנה המונח בחלון והמלח וכלי חרס וספר תורה כולם ממעטין בחלון 

Grass that was plucked and placed in an opening, or grass that grew by itself in an opening; scraps of fabric that are smaller than three by three fingerbreadths; a partially severed limb or a piece of flesh hanging from a domestic or a wild animal; a bird resting in an opening; an idol worshipper sitting in an opening; a baby born after only eight months of gestation lying in an opening; salt, earthenware vessels and a Torah scroll -all of these reduce the size of the opening and so prevent the tumah from passing through it.

The Talmud then questions this ruling about the premature child lying on a window between two rooms, one if which contains a source of tumah. Won't the mother of the baby carry the child away? How then can we suggest it will be a barrier to the tumah? The Talmud, as always, has a solution: the case is regarding a child born prematurely on Shabbat. Such a child is mukzteh, that is, it is in a category of objects that must not be moved on Shabbat: 

דתניא בן שמנה הרי הוא כאבן ואסור לטלטלו בשבת

For it was taught in a Braisa. A baby born at eight months of gestation is treated like a stone [on Shabbat, because it is muktzeh.]

The premature baby is given the status of a stone because it was not considered to be viable, and as a non-viable human being it does not contract ritual impurity. So that's why the premature baby is listed along with grass, idol worshippers, and the severed limbs of cattle as preventing the transmission of tumah. Got it?

When we studied Yevamot we came across another case which pivoted on the viability of babies born at seven vs. eight months of gestation. The question there was about proving the paternity of a child, and the discussion hinges on the belief that while a child born after seven months of gestation would be viable, a child born at eight months gestation would not be so.  Rashi noted the following: בר תמניא לא חיי -  "an eight month fetus cannot survive." And so now we can ask, where on earth does this notion come from? 

Seven vs Eight Months of gestation in antiquity

Homer's Iliad, written around the 8th century BCE,  records that a seven month fetus could survive. But it is not until Hippocrates (c. 460-370 BCE, or some 500 years before Shmuel), that we find a record of the belief that a fetus of eight months' gestation cannot survive, while a seventh month fetus (and certainly one of nine months gestation) can.  His Peri Eptamenou (On the Seventh Month Embryo) and Peri Oktamenou (On the Eight-Month Embryo) date from the end of the fifth century BCE, but this belief is viewed with skepticism by Aristotle.

In Egypt, and in some other places where the women are fruitful and are wont to bear and bring forth many children without difficulty, and where the children when born are capable of living even if they be born subject to deformity, in these places the eight-months' children live and are brought up, but in Greece it is only a few of them that survive while most perish. And this being the general experience, when such a child does happen to survive the mother is apt to think that it was not an eight months' child after all, but that she had conceived at an earlier period without being aware of it.

The belief that an eight month fetus cannot survive has a halakhic ramification: Maimonides ruled that if a boy was born prematurely in the eighth month of his gestation and the day of his circumcision (eight days after his birth) fell out on shabbat, the circumcision - which otherwise would indeed occur on Shabbat, is postponed until Sunday, the ninth day after his birth. 

רמב׳ם הל' מילה יד, א

מי שנולד בחדש השמיני לעבורו קודם שתגמר ברייתו שהוא כנפל מפני שאינו חי... אין דוחין השבת אלא נימולין באחד בשבת שהוא יום תשיעי שלהן

A child born after eight months of gestation before being fully formed is treated as a stillbirth because it will not live...and we do not set aside the laws of Shabbat [to circumcise him] but he is circumcised on Sunday, which is the ninth day of his life.

This medical “fact” persisted well into the early modern era. Here is a state–of–the–art medical text published in 1636 by John Sadler.  Read what he has to say on the reasons that an eight month fetus cannot survive (and note the name of the publisher at the bottom of the title page-surely somewhat of a rarity then): 

Saturn predominates in the eighth month of pregnancy, and since that planet is "cold and dry"," it destroys the nature of the childe". That, or some odd yearning of the child to be born in the seventh but not the eight month (according to Hippocrates) is the reason that a child born at seven and nine months' gestation may survive, but not one born at after only eight months. 

Evidence from Modern Medicine

Today we know that gestational length is of course critical, and that, all things being equal, the closer the gestational length is to full term, the greater the likelihood of survival. We can state with great certainty, that an infant born at 32 weeks or later (that's about eight months) is in fact more likely to survive than one born at 28 weeks (a seven month gestation.) In fact, a seven month fetus has a survival rate of 38-90% (depending on its birthweight), while an eight month fetus has a survival rate of 50-98%. Here is the data, taken from a British study.

Draper, ES, Manktelow B, Field DJ, James D. Prediction of survival for preterm births by weight and gestational age: retrospective population based study British Medical Journal 1999; 319:1093.

More recently, a study from the Technion in Haifa showed that even the last six weeks of pregnancy play a critical role in the development of the fetus. This study found a threefold increase in the infant death rate in those born between  34 and 37 weeks when compared full term babies.  

You can read more on the history of the eight month fetus in a 1988 paper by Rosemary Reiss and Avner Ash.  From what we have reviewed, the talmudic belief that a seven month fetus can survive but an eight month fetus cannot is one that was widely shared in the ancient world, and even in the early modern era.  But all the evidence we have today firmly demonstrates that it is simply not true.

Talmudology on the Parsha: The Fast of Friday, Parshat Chukkat

במדבר 19:1

זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר־צִוָּה יְהֹוָה לֵאמֹר דַּבֵּר  אֶל־בְּנֵי יִשְׂרָאֵל וְיִקְחוּ אֵלֶיךָ פָרָה אֲדֻמָּה תְּמִימָה אֲשֶׁר אֵין־בָּהּ מוּם אֲשֶׁר לֹא־עָלָה עָלֶיהָ עֹל׃

This is the ritual law that God has commanded: Instruct the Israelite people to bring you a red cow without blemish, in which there is no defect and on which no yoke has been laid.

The word חקת is normally translated as “ritual law” or “statute.” But the Aramiac translation of the Torah called Targum Onkelos (composed between about the years 80-120 CE) translated the work using a different word: גזירה, decree.

דָּא גְּזֵרַת אוֹרַיְתָא

This is a decree of the Torah

Over the lachrymose periods of Jewish history, a play on words connected this religious decree of the Torah with another: to burn it.

“On Monday, June 25, 1240 the first public trial against the Talmud and its most popular commentary, that by Rashi, was opened in the royal court in Paris in the presence of many church-dignitaries and noblemen. The Queen Mother Blanche who was in an advanced stage of pregnancy presided. The prosecutor was the convert Donin, the defendant-the Talmud, and its defenders four French Rabbis: Rabbi Yechiel of Paris, Judah ben David of Melun, Samuel ben Solomon of Chateau Thierry and Moses of Coucy.”

— Judah M. Rosenthal. The Talmud on Trial: The Disputation at Paris in the Year 1240. The Jewish Quarterly Review 1956. 47(1), 58–76.

The Burning of the Talmud in 1244, (or maybe 1242, or 1240)

In 1240 Rabbi Yechiel of Paris (the author of many tosafot, and the teacher of the Rabbi Meir of Rothenburg) was forced to defend the Talmud from accusations that togther with Rashi’s commentary, it contained derogatory remarks about Jesus of Nazareth (De blasphemiis humanitatis Xristi). Yechiel was arguing against Nicholas Donin, a Jew who had converted to Christianity, and who was supported by a team of former Jews. On Friday June 6, 1242 the final verdict was delivered. (As Solomon Grayzel noted many decades ago “the exact year of this event is variously given in the sources. The three years suggested are 1240, 1242, and 1244. Graetz after a long discussion of the subject comes to the conclusion that 1242 is the correct date.” So let’s go with that.) On Friday July 13, 1242, wagonloads of the handwritten Talmud were burned in Paris. That was the day before Parshat Chukat was read in shul.

The FAst of Friday, Parshat Chukkat

One contemporary was Rabbi Zedekiah ben Abraham Anaw, the author of the halakhic compendium called Shibbolei Haleket.

שבולי הלקט 263

ועל שאנו עסוקין בהלכות תענית ובענין שריפת התורה כתבנו זה לזכר על מה שאירע בימינו על רוב עונותינו אשר גרמו לנו ונשרפה תורת אלהינו בשנת חמשת אלפים וב' שנים לבריאת עולם ביום ששי פרשת וזאת חקת התורה כעשרים וארבעה קרונות מלאים ספרי תלמוד והלכות והגדות נשרפו בצרפת כאשר שמענו לשמע אוזן וגם מן הרבנים שהיו שם שמענו שעשו שאילת חלום לדעת אם גזירה היא מאת הבורא והשיבו להם ודא גזירת אוריתא ופירושו ביום ו' זאת חקת התורה היא הגזירה ומאותו היום ואילך קבעוהו היחידים עליהם להתענות בו בכל שנה ושנה ביום ששי של פרשת זאת חקת התורה ולא קבעוהו לימי החודש תהא אפרה עלינו לכפרה (כאשה) [כעולה] על מוקדה וערבה לבני יהודה כמנחתה הקריבה כהילכתה

…Let us remember what happened on account of our sins which caused God’s Torah to be burned in the year 5002, on the Friday of parshat Chukkat. Some twenty-four waggons full of copies of the Talmud and halakhic and aggadic works were burned in France…The rabbis who were there reported that they asked in a dream if this was indeed God’s decree (gezerah me’et haboreh). And one of the rabbis there answered “ודא גזירת אוריתא” - this is the decree of the Torah…

From then on the Jews would fast each and every Friday before the reading of parshat Chukkat. It was not fixed as a calendar date, [but the date is flexible, and depends on when Phukkat is read]

This fast is also recorded in by Rabbi Avraham Gombiner (c. 1635-1682) in his commentary on Shulkah Arukh called Magen Avraham:

מגן אברהם אורח חיים תקפ, ס’ק ט׳

כתב התניא ביום הששי פ' חקת נהגו יחידים להתענו' שבאותו היום נשרפו כ' קרונות מלאים ספרים בצרפת ולא קבעו אותו בימי החדש מפני שמתוך שאלת חלום נודע להם שיום הפרשה גורם גזיר' התורה זאת חקת התורה מתרגמי' דא גזירת אורייתא, וגם בשנת ת"ח נחרבו שני קהילו' גדולות באותו היום כמ"ש בסליחו' שחבר בעל השפתי כהן

We find it mentioned in the work Tanya Rabatia [an early anonymous Italian halakhic compendium] that on the Friday of Parshat Chukkat the Jews have a custom to fast, for on that day twenty cartloads of books were burned in France. The fast was not fixed to a certain date because it was made known through a dream that the day of the burning was to occur on “The day of the זאת חקת התורה which is translated [in Onkelos] as דא גזירת אורייתא - “this is the decree of the Torah”.

And in Turkey, the Jews had a custom to stay inside on the Friday of Parshat Chukkat:

חיים פלאגי, מועד לכל חי, סימן ט, ד

וכבאר היטב סימן תק״ם כתב וזה לשונו, כתב התניא כיום השישי פרשת חוקת נהגו היחידים להתענות שבאותו יום נשרפו עשרים קרונות מלאים טסרים כעדפת ולא קבעו אותו מפני החדש מפני שכתוך שאלת חלום נודע להם שיום הפרשה גורם גזירות התורה, זאת חוקת התודה מתדגמינן דא גזירת אורייתא, גם כשנת ת״ח נחרכו שתי קהילות כאותו יום, עכ״ל, ובעירנו אזמיר יע״א, נהירנא מכד הוינא טליא דהיו כמה אנשים סוחרים דהיו נזהרים שלא לצאת אפילו לשוק לעסקיהם כערב שבת חוקת, ומה שהיה להם לעשות כערב שכת היו עושים ומתקנים מיום חמישי, והן עוד היום רבים נזהרים שלא לילך מעיר לכפר כיום הזה, וה׳ שומר את עמו ישראל ובכל מקום ובכל זמן שלא תאונה שום רעה אמן כן יהי רצון

 …In our ciry of Izmir where the young would stroll, there were a number of merchants who were careful not to leave their homes, even to go to the market for business on the Friday of Parshat Chukkat. Whatever they needed to do they did on Thursday. And there were many others who did not leave the city for the villages on that day. My God guard his people Israel in all places and at all times, so that no evil will happen to them, Amen.

This Friday, another sort of fast. Or not

Several days after I finished a draft of this post, Agudath Israel of America issued a Kol Korei. Its rabbinc leadership “…call upon all holy congregations of Klal Yisroel to designate this Friday of the week of Parshas Chukas as a day of great and bitter outcry regarding this decree of the Torah.” And what might that decree be?

Now, we come to matters pertaining to our present time, as in this generation numerous troubles and severe decrees have arisen against the Am Hashem in general and specifically targeting the Torah and its scholars, and the young children learning Torah, both in Eretz Yisroel and in the Diaspora. Policy-makers, with malicious intent, aim to disrupt the sanctity of Torah scholars, requiring the students of our holy yeshivos to abandon their study benches in the beis medrash and enlist in the military. They scheme with various tricks, and their hand is still outstretched, poised to persist. Moreover, decrees are being issued against young children learning Torah, both in Eretz Yisroel and in the Diaspora. All of this is reminiscent of the decree of burning the Torah.

“All of this is reminiscent of the decree of burning the Torah”? In what universe is calling on all of Israel’s citizens to share the responsibility of defending the country “reminiscent of the decree of burning the Torah”? And just what decrees are “being issued against young children learning Torah, both in Eretz Yisroel and in the Diaspora.” Anyone?

The leadership of this organization (one of whose members believes that the polio vaccine is a hoax,) have reached a new low. In his book, the late Princeton philosopher Harry Frankfurt described those whose utterances are a greater enemy of the truth than liars are. Liars at least acknowledge that the truth matters. I have two copies of his book, so let me know if you’d like to borrow one.

Moetzes Gedolei HaTorah of America, Kol Korei released July 9, 2024.

Here’s an idea for Agudath Israel of America. Tomorrow, on Friday of Parshat Chukkat, gather together and pray for the victory of our soldiers, the safety of our people, and the release of the hostages. And then watch this clip of what is possible when those who care about studying Torah combine it with military service. Watch. And learn.

Bava Basra 16b ~ Here Comes the Sun

This post is for the page of Talmud to be studied tomorrow, Thursday July 11th.

בבא בתרא טז, ב 

רבי שמעון בן יוחי אומר אבן טובה היתה תלויה בצוארו של אברהם אבינו שכל חולה הרואה אותו מיד מתרפא ובשעה שנפטר אברהם אבינו מן העולם תלאה הקדוש ברוך הוא בגלגל חמה אמר אביי היינו דאמרי אינשי אידלי יומא אידלי קצירא

Rabbi Shimon ben Yochai said: there was a precious stone that hung from the neck of Abraham our forefather. Any sick person who looked at it was instantly cured.  When Abraham our forefather died, the Holy One, Blessed be He, hung this stone in the orb of the sun. Abaye said, this is what is meant by the popular saying "when the sun is lifted, sickness is lifted"

Abaye, the great Babylonian sage of the fourth century, commented on a statement made Rabbi Shimon ben Yochai about two centuries earlier, and suggested that sunlight helps heal.  This was not the only time Abaye opined about the health benefits of sunlight. We came across another example when we studied Nedarim: 

נדרים  ח, ב

שמש צדקה ומרפא אמר אביי ש"מ חרגא דיומא מסי ופליגא דר"ש בן לקיש דאמר אין גיהנם לעולם הבא אלא הקב"ה מוציא חמה מנרתיקה צדיקים מתרפאין בה ורשעים נידונין בה

“The sun of righteousness, with healing in its rays” (Malachi 3:20)...Abaye said: “We learn from here that the dust of the sun heals”…Rabbi Shimon ben Gamliel said, “there is no hell in the world to come. Rather God takes the sun out of its canopy; the righteous are healed by it and the wicked are punished by it” (Nedarim 8b.)

A HISTORY OF HELIOTHERAPY

In 1903, the Nobel prize for Medicine was awarded to a Dane named Niels Finsen. Finsen had invented a focusable carbon-arc torch to treat – and cure – patients with lupus vulgaris, a painful skin infection caused by tuberculosis.  While this was the start of the modern medical use of phototherapy, using the sun as a source of healing is much, much older. Older even than the Talmud, which mentions it in today’s daf. 

“The Nobel Prize in Physiology or Medicine 1903 was awarded to Niels Ryberg Finsen “in recognition of his contribution to the treatment of diseases...with concentrated light radiation, whereby he has opened a new avenue for medical science”

Perhaps the earliest reference to heliotherapy – that is, using sunlight to heal - is found in Egyptian papyrus records from over 3,500 years ago, which record using the sun, together with ingesting a local weed, to treat skin conditions. The active ingredients of that weed, Ammi majus, were isolated in 1947. These ingredients, together with heliotherapy, were used in the first clinical trials to treat vitiligo, which were conducted, rather fittingly, in Egypt.  Further work determined that it was only a narrow part of the sun’s spectrum that was needed to treat vitiligo, psoriasis, and other skin conditions, and so lamps were developed that produced only narrow band ultraviolet light (UVB). These UVB lamps are now a mainstay of treatment for psoriasis.

“For most white people, a half-hour in the summer sun in a bathing suit can initiate the release of 50,000 IU (1.25 mg) vitamin D into the circulation within 24 hours of exposure”

— — Environmental Health Perspectives 2008:116;4. A162

SUNLIGHT FOR HEALTHY BONES

But ultraviolet light – UVB – can also be extremely dangerous. Too much exposure to sunlight will cause skin cancer, as the light produces molecules that directly damage DNA. Here is the great paradox of sunlight – too much of it will burn and can kill – but get the dose right and it is not only curative, but essential for healthy living. Sunlight is needed to produce vitamin D in the skin, and vitamin D is needed to produce healthy bones. Without it, you will develop rickets, a skeletal deformity that is characterized by bowed legs. 

Typical presentation of 2 children with rickets. The child in the middle is normal; the children on both sides have severe muscle weakness and bone deformities, including bowed legs (right) and knock knees (left). From Holick M. Sunlight and vitamin D for bone health and prevention of autoimmune diseases, cancers, and cardiovascular disease. Am J Clin Nutr 2004;80(suppl):1678S–88S.

SUNLIGHT FOR A HEALTHY IMMUNE SYSTEM

The sun’s light has been shown to have effect the immune system, although many of these effects are only poorly understood. 

When some nerve fibres are exposed to sunlight, they release a chemical called neuropeptide substance P. This chemical seems to produce local immune suppression.  Exposure to the ultraviolet wavelengths in sunlight can change the regulation of T cells in the body which can also modulate autoimmune diseases.

SUNLIGHT TO TREAT MELANOMA?

While sunlight can cause skin cancer, it has been shown to release a hormone called alpha melanocyte-stimulating hormone. This hormone appears to limit the damage to DNA damage from sunlight and so may actually reduce the risk of melanoma (but don't try this as a treatment yet. It's certainly not ready for prime time.)

SUNLIGHT FOR YOUR MOOD

Then there’s sunlight for your mood. Seasonal affective disorder – SAD – is caused by a lack of exposure to sunlight, which most affects those living in the northern latitudes in the winter.  SAD was first described in 1984 by Norman Rosenthal working at the National Institute of Mental Health but why it happens is still something of a mystery.  Rosenthal went on to write several best selling books on SAD and how to beat it. The answer appears to be something to do with sitting in front of a lamp that mimics sunlight (but the evidence that this works is still controversial).

 SUNLIGHT FOR BABIES WITH JAUNDICE

Sunlight is also a great treatment for babies with neonatal jaundice. This condition is very common and is caused when the baby breaks down the fetal hemoglobin with which it was born. A product of that breakdown is bilirubin, and if this is allowed to build up in the tissues it can cause lethargy, difficultly feeding, and in rare and extreme cases, brain damage. However, sunlight (or more precisely, the blue band of the spectrum at 459nm)  breaks down this dangerous bilirubin molecule into a harmless one called biliverdin.  So the best treatment for a newborn baby with mild jaundice is to put them out in the sun.  (Failing that, or if the degree of jaundice is not mild, you can consider phototherapy in the hospital.) 

The absorbance spectrum of bilirubin bound to human serum albumin (white line) is shown superimposed on the spectrum of visible light. Clearly, blue light is most effective for phototherapy, but because the transmittance of skin increases with increasing wavelength, the best wavelengths to use are probably in the range of 460 to 490 nm. Term and near-term infants should be treated in a bassinet, not an incubator, to allow the light source to be brought to within 10 to 15 cm of the infant (except when halogen or tungsten lights are used), increasing irradiance and efficacy. For intensive phototherapy, an auxiliary light source (fiber-optic pad, light-emitting diode [LED] mattress, or special blue fluorescent tubes) can be placed below the infant or bassinet. If the infant is in an incubator, the light rays should be perpendicular to the surface of the incubator in order to minimize loss of efficacy due to reflectance. From Maisels and McDonagh. Phototherapy for Neonatal Jaundice. New England Journal of Medicine 2008.358;920-928.

SUNLIGHT FOR INFECTIOUS DISEASES

 We don't treat infectious diseases with sunlight any more. But it wasn't always that way. Less than eighty years ago sunlight was recommended as a therapy for some patients with tuberculosis. The authors, writing in the journal Diseases of the Chest were cautious:

Even in those cases where the sun can be of great value, it is in no sense a specific cure for any manifestation of tuberculosis. Rest, good food, and fresh air, are still the fundamentals in treating all forms of the disease; and the sun, where it should be used, is only a valuable adjutant...Heliotherapy is not indicated in all cases of tuberculosis. The majority of patients with this disease should never use it...It is not a sure cure for any type of tuberculosis, but is often, especially in some of the extrapulmonary cases, a very valuable—or even necessary—aid.

In today's daf, Abaye once again noted that the sun can heal. His insight were more correct than he could ever have guessed.  

“Bright light therapy and the broader realm of chronotherapy remain underappreciated and underutilized, despite their empirical support. Efficacy extends beyond seasonal affective disorder and includes nonseasonal depression and sleep disorders, with emerging evidence for a role in treating attention-deficit/hyperactivity disorder, delirium, and dementia.”

— — Schwartz and Olds. The Psychiatry of Light. Harvard Review of Psychiatry 2015. 23 (3); 188.S

Bava Basra 14a ~The value of Pi in the Talmud

Today we discuss maths (as it is called in the UK, Ireland and Australia,) or math (as it is called in the US and Canada). We will focus on that most magical of numbers, pi, also known as π. On today’s page of Talmud we find this theorem:

תלמוד בבלי מסכת בבא בתרא יד, א

כֹּל שֶׁיֵּשׁ בְּהֶקֵּיפוֹ שְׁלֹשָׁה טְפָחִים

Elsewhere, the Talmud determined the that value of π is 3 from a verse in the Book of Kings:

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.

 The Talmud in Eruvin uses this verse to teach a general mathematical principle:

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."  

So one of the vessels in the Temple of Solomon was ten amot in diameter and 30 amot in circumference. Since π is the ratio of the circumference of a circle to its diameter (π=C/d), π in the Book of Kings is 30/10=3. Three - no more and no less.

But PI is more than three

However, this value of π =3 is not accurate. It deviates from the true value of π (3.1415...) by about 5%. Tosafot in Eruvin 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

Tosafot opens the objection with these words: “But [pi] is a little more [than 3]. Which means that the value [of pi] is rounded down” Tosafot can't find a good answer to this obvious problem, 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 on which today’s discussion is based, (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.

Is the Value of Pi hidden in the Bible?

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 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.)

Did the rabbis of the Talmud get π wrong?

So what are we to make of all this? Did the rabbis of the Talmud get π wrong, or were they just approximating π 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.)

Still, don't be too hard on the rabbis of the Talmud. The rule that the circumference of an object is three times its diameter is pretty close to being correct, and is usually a good enough approximation. But it is not accurate, and never will be.