Shabbat 12a ~ Killing Lice and Spontaneous Generation

שבת יב, א

 רַבָּה מְקַטַּע לְהוּ. וְרַב שֵׁשֶׁת מְקַטַּע לְהוּ. רָבָא שָׁדֵי לְהוּ לְלָקָנָא דְמַיָּא. אֲמַר לְהוּ רַב נַחְמָן לִבְנָתֵיהּ: קִטְלָן וְאַשְׁמְעִינַן לִי קָלָא דְסָנְווֹתִי

תַּנְיָא, רַבִּי שִׁמְעוֹן בֶּן אֶלְעָזָר אוֹמֵר: אֵין הוֹרְגִין אֶת הַמַּאֲכוֹלֶת בְּשַׁבָּת, דִּבְרֵי בֵּית שַׁמַּאי. וּבֵית הִלֵּל מַתִּירִין

Rabba would kill the lice. And Rav Sheshet would also kill them. Rava would throw them into a cup [lekna] of water and he would not kill them directly with his hands. The Gemara relates that Rav Naḥman would say to his daughters: Kill them, and let me hear the sound of the combs, meaning, you may kill the lice in the usual manner on the comb.

As far as the basic halakha is concerned, it was taught in a baraita that Rabbi Shimon ben Elazar says that Beit Shammai and Beit Hillel disagreed with regard to killing a louse on Shabbat: One may not kill a louse on Shabbat, this is the statement of Beit Shammai; and Beit Hillel permit doing so. In their opinion, a louse is unlike the other creatures for which one is liable for killing them on Shabbat.

648x364_Body-Lice-Infestation.jpg

Later in this tractate (107b), the Talmud derives the prohibition against killing an animal on Shabbat. It is learned from the fact that during the construction of the Tabernacle in the desert, rams were killed and their hides were used for its coverings. Rashi picks up the details:

מתירין - כדמפרש טעמא בפרק שמונה שרצים (לקמן שבת דף קז:) מאילים מאדמים דמשכן מה אילים פרים ורבים אף כל שפרה ורבה וכינה אינה פרה ורבה אלא מבשר אדם היא שורצת

…just as rams reproduce and may not be killed on Shabbat, so too any animal that reproduces may not be killed on Shabbat. However a louse does not reproduce, but grows directly from human flesh.

Other Talmudic Discussions of Spontaneous Generation

Here is another example of an animal that does not reproduce. It is a mysterious mouse, from the Talmud in Chullin.

חולין קכז,א

עכבר שחציו בשר וחציו אדמה שאין פרה ורבה

There is a mouse that is hard made from flesh and half from dirt, and does not procreate

And what exactly is this strange creature, which has come to be called the mud-mouse? Here is the explanation of Rashi:

אין פרה ורבה - כלומר שלא היה מפריה ורביה של עכבר לפי שנוצר מאליו  

It does not procreate: This means it does not sexually reproduce, but instead it spontaneously appears.

And here is Rashi from Chullin127b:

 יש מין עכבר שאינו פרה ורבה  אלא מעצמו נוצר מאדמה כאשפה המשרצת תולעים 

There is a species of mouse that does not reproduce sexually but is spontaneously generated from the earth, just as maggots appear at a garbage site.

The mud-mouse is also mentioned in Sanhedrin (91):

סנהדרין צא, א

צא לבקעה וראה עכבר שהיום חציו בשר וחציו אדמה למחר השריץ ונעשה כלו בשר

Consider the mouse which today is half flesh and half earth, and tomorrow it has become a creeping thing made entirely of flesh.  

Clearly, Rashi and the rabbis of the Talmud believed in spontaneous generation. That is clear from the example of today’s page of Talmud (Shabbat 12), Sanhedrin, and Chullin. Here is the opening of the Wiki article on the subject:

Spontaneous generation or anomalous generation is an obsolete body of thought on the ordinary formation of living organisms without descent from similar organisms. Typically, the idea was that certain forms such as fleas could arise from inanimate matter such as dust, or that maggots could arise from dead flesh.

EVERYONE BELIEVED IT

How could the esteemed rabbis of the Talmud believed in this crazy idea of spontaneous generation? The answer is simple. Everyone believed it. Everyone, from the time of Aristotle until Louis Pasteur. Here is Aristotle (d. 322 BCE):

So with animals, some spring from parent animals according to their kind, whilst others grow spontaneously and not from kindred stock; and of these instances of spontaneous generation some come from putrefying earth or vegetable matter. [History of Animals 539a, 18-26.]

“Aristotle’s theory of spontaneous generation was as influential as his other teachings in philosophy and natural history; it was accepted with reverence, not only among his contemporaries but well into modern times.
— Jan Bondeson. The Feejee Mermaid and other Essays in Natural and Unnatural History. Cornell University Press 1999. p194

The great Roman poet Ovid (43 BCE-17/18 CE) is best known for his work Metamorphosis. It’s a bit of a long read (almost 12,000 lines contained in 15 books), and in it he mentions spontaneous generation three times. Actually, given its length, he probably mentions everything at least three times. Here is an example, from Metamorphosis I, 416-437.

So, when the seven-mouthed Nile retreats from the drowned fields and returns to its former bed, and the fresh mud boils in the sun, farmers find many creatures as they turn the lumps of earth. Amongst them they see some just spawned, on the edge of life, some with incomplete bodies and number of limbs, and often in the same matter one part is alive and the other is raw earth. In fact when heat and moisture are mixed they conceive, and from these two things the whole of life originates. And though fire and water fight each other, heat and moisture create everything, and this discordant union is suitable for growth. So when the earth muddied from the recent flood glowed again heated by the deep heaven-sent light of the sun she produced innumerable species, partly remaking previous forms, partly creating new monsters.

Spontaneous generation was an accepted theory throughout the middle ages and was found in the writings of Arab naturalists, such as Averroes. Sir Francis Bacon, (d.1626) the English "philosopher, statesman, scientist, jurist, orator, and author" accepted the theory. And so did Willam Harvey, who discovered the circulation of the blood,  - at least under certain circumstances.  And why not believe is spontaneous generation? Before the invention of the microscope, it certainly explained how worms, fleas, bees and other insects could appear out of nowhere.

WELL, NOT QUITE EVERYONE

In his commentary to the Mishnah on about the mud mouse (Chullin 127), Maimonides has this to say:

והויות העכבר בלבד מן האדמה עד שימצא קצתו בשר וקצתו עפר וטיט והוא ענין מפורסם מאד אין מספר לרוב המגידין לי שראו זה אע"פ שמציאות בעל חיים כזה דבר מתמיה ולא נודעת בו טענה בשום פנים

The case of the mouse which uniquely grows from the earth so that it is half-flesh and half dust and mud is very well known. There is no end to the countless numbers of those who have told me that they have seen it, even though the existence of this creature is astonishing, and there is no known explanation for it.

Maimonides did not reject the idea that the mouse grows directly from the earth, but he seems very sceptical of the idea. Still, it was a widely accepted explanation for centuries before, and centuries after Maimonides. For example, let’s consider…

JAN BAPTISTA VAN HELMONT AND THE RECIPE TO GROW A MUD-MOUSE

Jan Baptista van Helmont (1580-1644) knew a thing or two about science. Although still deeply embedded in alchemy, his many observations led the way to the scientific revolution. He was the first to suggest that the stomach contained somethings to aid in digestion (what we call today enzymes and acids). And according to the Science History Institute, “he discovered that chemical reactions could produce substances that were neither solids nor liquids and coined the term gas to describe them.” “I call this spirit,” he wrote, “hitherto unknown, by the new name of gas…"(Hunc spiritum, incognitum hactenus, nero heroine Gas voco). This laid the groundwork for Robert Boyle’s later research on gases.

Spontaneous generation also occupied Van Helmont’s scientific worldview. Like everyone else, he believed in it, because it explained observations like fleas appearing around rotting meat or mice appearing in a farmer’s barn of grain. He was so certain of the reality of spontaneous generation that he provided a recipe to grow mice de novo.

“If a dirty shirt is stuffed into the mouth of a vessel containing wheat, within a few days, say 21, the ferment produced by the shirt, modified by the smell of the grain, transforms the wheat itself, encased its husk into mice.

PASTEUR'S EXPERIMENTS

Then came the microscope. Using one, in October 1676, Leeuwenhoek reported finding tiny micro-organisms in lake water. Now perhaps there was another explanation for how things were created, although not much progress was made for a couple of hundred more years.  It was Louis Pasteur (d.1895) who finally disproved the theory of spontaneous generation with some elegant experiments. He boiled a meat broth in a flask like this, with its neck pointed downwards.

Sanhedrin 91. Spntaneous Generation.jpeg

Boiling sterilized the mixture, and with the neck pointing down, no organisms could contaminate the broth. As a result, there was no growth of bacteria or could inside the flask. He did the same using a flask with a neck that was upturned. This allowed the broth to become contaminated with organisms in the outside air, and the mixture soon became cloudy. Spontaneous generation had been disproven.

THE RABBI WHO TRIED TO GET IT RIGHT, BUT GOT IT WRONG

Israel Lipschutz of Danzig (1782-1860) wrote a very important two-part commentary on the Mishnah called Tiferet Yisrael. In it, R. Lipschutz got very excited about this whole mouse thing:

ואני שמעתי אפיקורסים מלגלגין על בריה זו שנזכרת כאן ובסנהדרין [דצ"א א']. ומכחישים ואומרים שאינה במציאות כלל לכן ראיתי להזכיר כאן מה שמ"כ בספר אשכנזי שחיבר חכם אחד מפורסם בחכמי האומות. ושמו. לינק. בספרו הנקרא אורוועלט חלק א' עמוד 327. שנמצא בריה כזאת בארץ מצרים במחוז טחעבאיס. ונקראת העכבר ההיא בלשון מצרים דיפוס יאקולוס . ובל"א שפרינגמויז. אשר החלק שלפניה ראש וחזה וידיה מתוארים יפה. ואחוריה עדיין מגולמים ברגבי ארץ. עד אחר איזה ימים תתהפך כולה לבשר. ואומר מה רבו מעשיך ה

I have heard heretics mocking the existence of this creature, mentioned here and in the Talmud Sanhedrin. They deny its existence and claim it is not in any way real. So I have found it appropriate to mention here what is published in a German book written by one of the wisest and most well-known of any nationality, named Link. In his book Urwelt (Part I p327) he states that such a creature was indeed found in the district of Thebais in Egypt. In Egyptian this mouse is called Dipus Jaculus, and in German it is called the spring-mouse. Its head, chest and front paws are well-formed, but its rear is still unformed and is just bits of earth. But after a few days, the mouse becomes made entirely of flesh. And I said “Lord, how great are your works!” (Ps.104:24)

So according to R. Lipschutz all the scoffers were wrong, and as proof he cites his contemporary, the well respected naturalist Johan Heinrich Link (1738–1783), whose Die Urwelt und das Altertum, erläutert durch die Naturkunde (Prehistoric times and antiquity, explained by natural history) was first published in Berlin between 1820 and 1822. Great. A mid-19th century rabbi and scholar quoting a German naturalist in support of a statement made by the rabbis of the Talmud. Science and Judaism at their best!

Well no. Not so fast.

In a paper devoted to this topic, Dr. Sid Leiman noted that the passage cited by R. Lipschutz only appeared in the first edition of Link’s book, and was removed from later ones. But more importantly, R. Lipschutz misread the context of the passage he was citing. Rather than attesting to the reality of the mud-mouse, Link was quoting from a passage in the book Bibliotheca historica by Diodorus Siculas, a Greek historian of the first century. It was Diodorus who was describing what his contemporaries believed. But what about that reference to the Latin and German names for the mouse? Diodorus wrote in Greek and could not not have thought that Dipus Jaculus (Latin) is an Egyptian phrase. Let’s have Prof. Leiman explain:

What happened is that Link added a footnote to the Diodorus passage, in an attempt to account for the belief in the existence of this strange creature in antiquity. Link’s note reads (in translation): “The Springmaus (Dipus Jaculus), which dwells in Upper Egypt and is characterized by very short forelegs, doubtless could lead one to conclude that it is a not yet fully developed creature.” Link was suggesting that the very existence of the Springmaus, or jerboa, a small, leaping kangaroo-like rodent found to this day in the arid parts of North Africa, and characterized by long hindfeet and short forelegs, may have misled the ancients into thinking that the different parts of the body of some mice fully matured at different times…The upshot of this was that Lipschutz was persuaded, quite mistakenly, that the mouse described by the rabbis as being half flesh and half earth was alive and well in nineteenth-century Egypt, as attested by no less a scholar than Professor Link!…

One would like to think that Rabbi Israel Lipschutz, whose seminal work is everywhere characterized by intellectual honesty, would have retracted his garbled reading of Link if only the error had been brought to his attention.

However, an earlier Italian rabbi, Isaac Lampronti, tried to bring the whole spontaneous generation thing up to date.

Isaac Lampronti - Bringing the talmud Up to Date

Issac Lampronti (1679– 1756) was an Italian Jew who studied medicine at Padua. He completed his studies at the age of twenty-two and returned to his home town of Ferrara in northern Italy. There he became a rabbi and eventually rose to become the head of the yeshivah in the city, all while continuing to practice medicine. Lampronti introduced a curriculum of dual learning in his yeshivah, but he is best known for his lengthy alphabetical encyclopedia of Jewish law, Pahad Yizhak (The Fear of Isaac), in which each entry contained material from the Mishnah, Talmud, later commentaries, and the responsa literature, in addition to updates from contemporary science. (The first two volumes, published in 1750 and 1753, covered the first four letters of the Hebrew alphabet. These were the only parts published during Lampronti’s lifetime, and publication of the remaining volumes was not completed until 1888.)

Lampronti brought this discussion up to date by declaring that this talmudic rule was based on faulty science.

Lampronti discussed the talmudic rule that lice could be killed on the Sabbath, an act normally forbidden under the general prohibition of hunting on the day of rest. As we have seen, the Talmud had reached this conclusion based on a belief that lice are spontaneously created from dust and therefore did not have the usual status of other creatures that reproduce sexually. As a result, the usual prohibition against killing them on the Sabbath did not apply. Lampronti brought this discussion up to date by declaring that this talmudic rule was based on faulty science. Because naturalists had now concluded that every living creature must come from an egg, the legal status of lice must be changed, and Lampronti ruled therefore that they may not be killed on the Sabbath. “Every careful person who cares for his life will stay far from these creatures, and not kill either a flea or a louse, and will not place himself in a situation in which he may have to bring a sin offering [for violating the Sabbath]. In this matter I believe that if the sages of Israel understood the proofs offered by the Gentiles, they would revisit their ruling and accept the [Gentile] opinions, as they did regarding the dispute about whether the heavenly sphere is fixed and the constellations revolve.”

Lampronti here referenced the talmudic passage (Pesachim 94b) about the structure of the universe, which we have discussed elsewhere on Talmudology. “The Jewish sages say, the galgal is fixed and the mazzalot revolve, and the Gentile sages say the galgal revolves and the mazzalot are fixed.” The Talmud concluded that “their words appear more reasonable than our words,” and Lampronti understood this conclusion to be an example of the intellectual honesty of the sages, who were open to changing their opinions when faced with new evidence.

WRONG, BUT FOR THE RIGHT REASONS

The rabbis of the Talmud were not fools for believing in spontaneous generation. They would have been fools had they not. If was an explanation for many natural phenomena and was believed by heroes of the scientific revolution, along with everyone else, until Pasteur proved them all wrong.

[Partial repost from Chullin 127, and from this book.]

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From The Talmudology COVID-19 Dept: Social Distancing in the Rabbinic Tradition

The following essay appeared on The Lehrhaus on Monday. It is based on a previous post on Talmudology (Bava Kamma 60) available here. Click here to read the essay on The Lehrhaus.

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Shabbat 9b ~ Haircuts

Among the things we must not start on Friday afternoons, the eve of Shabbat, are haircuts. The Mishnah makes this clear:

שבת ט, ב

לֹא יֵשֵׁב אָדָם לִפְנֵי הַסַּפָּר סָמוּךְ לַמִּנְחָה עַד שֶׁיִּתְפַּלֵּל

A person may not sit before the barber adjacent to the time of mincha until he recites the afternoon prayer.

As Rashi points out, this ruling also applies to the other days of the week, when we may also not start complex acts that may cause us to forget our afternoon prayers. But this ruling is much more important with regard to Friday afternoons, because we might become so involved in the process that we could forget that Shabbat had begun.

The Talmud explains that this ruling applies even when the hairdresser begins early in the afternoon, if it involves a lengthy and complex hairstyling called “a haircut of Ben Elasah”:

 לְעוֹלָם סָמוּךְ לְמִנְחָה גְּדוֹלָה — וּבְתִסְפּוֹרֶת בֶּן אֶלְעָשָׂה

According to Rashi, Ben Elasah was the son-in-law of the editor of the Mishnah, Rabbi Yehudah HaNasi. Elsewhere, the Talmud notes that these kind of hairstyles meant a great deal to Ben Elasah:

נדרים נא, ב

מאי בן אלעשה דתניא לא לחנם פיזר בן אלעשה את מעותיו אלא להראות בהן תספורת של כ"ג 

דכתיב (יחזקאל מד, כ) כסום יכסמו את ראשיהם תנא כעין לולינית מאי לולינית א"ר יהודה תספרתא יחידתא היכי דמי אמר רבא ראשו של זה בצד עיקרו של זה והיינו תספורת של כהן גדול 

It is taught in a braita: Ben Elaah did not spend his money on his special haircut for nothing. Rather, he spent it to show others what the haircut of a High Priest looked like. 

As it is written with regard to the priests: “They shall poll their heads” (Ezekiel 44:20), and it is taught in a baraita: This haircut is like a luleyanit. The Gemara asks: What is a luleyanit? Rav Yehuda said: It is a unique haircut. The Gemara asks: What is this haircut like? Rava said: The edge of this shaft of hair is by the roots of that shaft of hair. The hair is cut so that it does not overlap. And this is the haircut of a High Priest, for which ben Elasah paid a large sum. 

The hairstyle called luleyanit has been translated as “Julian” or in the style of a roman official by the name of Julianus. As the independent scholar Eli Gurevich explains:

It is important to note that in the Hebrew/Aramaic text of the Talmud the word Julian is spelled Lulian (לולינית). It has been already pointed out by many scholars, including Marcus Jastrow in his dictionary, and by Alexander Kohut in Aruch Hashalem that Jews modified the Roman name Julianus and pronounced it Lulianus in a later time. This can be proven from the fact that the Jerusalem Talmud (Nedarim 3:2, Vilan Edition Daf 9a) in its vague description of the invasion of Persia and the Battle of Ctesiphon by the Roman Emperor Julian the Apostate, in 363 CE, calls him King Lulianus, and so from there we know that Lulianus is defintiely Julianus, as well as Lulian is definitely Julian.

All of which leaves the reader to wonder, just what did that haircut actually look like?

Alexander the Great, whose famous anastole, i.e., ascending locks from a central parting, became the model for the Hellenistic kings.
— Norbert Haas, Francoise Toppe, and Beate M. Henz. Hairstyles in the Arts of Greek and Roman Antiquity. J Investig Dermatol Symp Proc 2005.10:298–300.

Greek and Roman Hairstyles Revealed

To help figure this out let’s turn to a helpful 2005 paper published in the Journal of Investigative Dermatology titled Hairstyles in the Arts of Greek and Roman Antiquity. It turns out that thanks to lots of pottery shards and terracotta head that survived from this period, we can reconstruct the hairstyles of the day. For example, “Nero’s curls were corrugated with crimping tongs and carefully piled on each other in several rows.” The central greek god Zeus “typically has his hair aligned in an upward, followed by a downward sweep, which then radiates outward, forming a corona of individual strands. Asclepius, the healing god, is the only god to wear his hair similar to Zeus! He also appears as a mature bearded man, but with a milder expression…. Hera, Zeus’ wife and of royal stature, had shiny, perfumed locks covered by a veil. Athena, the city protectress, wore a helmet, with fine curls protruding from underneath.”

Eli Gurevich notes that from today’s page of Talmud and the source from Nedarim, we can deduce four points about the Ben Elasah hairstyle:

  1. It was called Julian Style.

  2. It was very expensive.

  3. It took a few hours (at least two) to cut.

  4. The hairstyle was shaped in such a way that the tip of one lock of hair touched the root of the next.

This may have been the very haircut of the Emperor Nero, whose hair we have already noted, appears to have been cut and layered vertically, with the tip of one curl touching the root of the curl below it.

A bust of Bust of Nero from the Musei Capitolini, in Rome. Notice how the bottom row of his hair on the forehead comes out directly from the tips of row above it. Just like the cut of Ben Elasha.

A bust of Bust of Nero from the Musei Capitolini, in Rome. Notice how the bottom row of his hair on the forehead comes out directly from the tips of row above it. Just like the cut of Ben Elasha.

Another example of this hairstyle is from a fresco of the Roman Emperor Domitian (c51-96 CE). His hair is clearly shown as being layered, again with the tips of the top layer touching the roots of the layer below it. Like this:

Domitian’s hairstyle on the Palazzo Della Cancelleria.

Domitian’s hairstyle on the Palazzo Della Cancelleria.

Gurevich concludes that

this hairstyle lasted for about a decade from about 64-73 CE, during the reigns of Nero and Vespasian, coinciding with the last years of the Second Temple in Jerusalem, where it was most probably was worn by the High Priest, who tried to copy the Roman Emperor, who in turn copied a street performer. How ironic life can be.

So the High Priest of the Temple in Jerusalem had his hair cut to mimic the trendy style of his day. It’s disappointing, given how much effort we put into protecting our children from the influence of the surrounding culture of the celebrity. Just make sure they don’t read this.

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Happy Pi Day 2020, and Happy Birthday Albert Einstein

In the midst of the never-ending news cycle about a certain virus, it is easy to forget the important things in life. Like Pi day, which is also the birthday of Albert Einstein, and which falls tomorrow, on Shabbat.

So let’s put aside the coronavirus for a few moments (can you do that?) and think about…

Pi Day

From here.

From here.

Tomorrow, 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

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.  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

[A repost, of course, from last year’s Pi day. Some things just don’t change…]

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