Kiddushin 30a ~ How Many Letters are in a Sefer Torah?

קידושין ל, א

לפיכך נקראו ראשונים סופרים, שהיו סופרים כל האותיות שבתורה, שהיו אומרים: וא"ו דגחון חציין של אותיות של ספר תורה, דרש דרש  חציין  של תיבות, והתגלח של פסוקים

Therefore the early sages were called "counters" - soferim - because they counted all the letters of the Torah. They used to say: the letter vav of the word Gachon (Lev.11:42) is the half-way point of the letter of a Torah. The words "darosh darash" (Lev. 10:16) represent the half way point of the number of words in the Torah. The verse that begins with the word "Vehitgalach" (Lev.13:33) is the half way point of the number of verses in the Torah...

Today's page of Talmud in the Daf Yomi cycle covers some important material for those interested in the way in which Judaism and science interact.   The business of counting the letters in the Torah was apparently taken very seriously - so much so that one of the names by which the rabbis of the Talmud were known  - soferim - means "those who count."  To this day, the person who handwrites a Sefer Torah is called a counter (סופר), and not a writer (כותב). The Talmud emphasizes that this counting exercise was taken so seriously that the letters, words and verses were counted, and counted again. 

קידושין ל, א

בעי רב יוסף וא"ו דגחון מהאי גיסא או מהאי גיסא א"ל ניתי ס"ת ואימנינהו מי לא אמר רבה בר בר חנה לא זזו משם עד שהביאו ספר תורה ומנאום

Rav Yosef asked a question: This letter vav of the word Gachon, is it part of the first half or part of the second half of the letters of the Torah? They said to him, "let us bring a Torah scroll and count! For didn't Rabbah bar bar Channah say in a similar context: "They did not move from there until they brought a Torah scroll and counted all its letters"...

The View of Tradition, And OF the Journal Tradition

Writing in Tradition in 1964, the late scholar Louis Rabinowitz (d. 1984) asked how Orthodox Jews should regard the text of the Torah , "...upon which depends the whole enduring magnificent structure of the Oral Law and the Halakhah, in comparison with those texts which show variants from it?"  Here is his reply:

“The answer is surely simple and logical. “The early scholars were called Soferim,” declares the Talmud (Kid. 30a) “because they were wont to count (soferim) all the letters of the Torah.” The meticulous manner in which they carried out this task is sufficiently indicated in the same passage by the information which it elicited to the effect, for instance, that the vav of gachon (Lev. 9:42 - [sic]) marks the half-way mark of the letters of the Torah, the words darosh darash of Lev. 10:16 the dividing line between the words...


With what loving care and sacred devotion, then, did they jealously guard every letter of the text! What exhaustive and detailed regulations they laid down in order to ensure that the copying of the scrolls should be completely free from human error! There has been nothing like it in the history of literature or religion, and in this respect the Massoretic text stands indisputably in a class by itself.”

— Louis Rabinowitz. Torah Min Ha-Shamayim.Tradition: A Journal of Orthodox Jewish Thought, 1964-5: 7;1: 34-45

Leaving aside the ironic typographic error that mis-references the location of the vav of Gachon, was the late rabbi Rabinowitz correct in remarking on the "loving care and sacred devotion," with which "they jealously guard every letter of the text"?

So how many letters are there in a Torah?

There are varied counts given for the number of letters in the Torah, but a couple of results seem to be most popular.

• 304, 805 From here, and here and here, and from Even-Shoshan (see below).

• 304,801 From here.

One website shares the source code used to count the words and letters in Torah; its results are shown below, and are off by four when compared to others who claim to have counted.

Letters and Words in the Torah
	Words	Letters
בראשית	20,614	78,063
שמות	16,714	63,527
ויקרא	11,950	44,790
במדבר	16,408	63,529
דברים	14,295	54,892
TOTAL	79,981	304,801

And How Many Verses Are There?

The same website gives a count of 5,844 verses in the Torah.  Rabbi Yair Chaim ben Moses Bachrach (d. 1702), author of the Chavot Ya'ir, notes that there are 5,845 verses in the chumashim he used. But today's daf of Talmud records that there are 5,888 verses. And here is the count from Even-Shoshan's קונקורדנציה חדשה (New Concordance of the Bible):

From Even-Shoshan (ed.) A New Concordance of the Bible. Kiryat Sefer, Jerusalem 1987.

Side-Bar: From Where did Even-SHoshan Get his word count?

Even-Shoshan lists his reference as Rabbi Chaim Mordechai Brecher, who published a Yiddish translation of the entire Hebrew Bible. (Brecher was born in what is now the Ukraine in 1880 and died in New York in 1965.  His Yiddish translation was published in New York in 1941, and was republished six times, the last in 1957.)  At the end of the second volume of his translation (p. נא), R. Brecher addressed the thorny question of the letter and word counts in our Torahs, and had this to say:

The truth is, this [question of how many words there are in a Sefer Torah] is astonishing, and I couldn't rest because of it. So I decided to count them, and I, myself, counted all the words in the entire Torah. In order to make it clear to the reader that I didn't make a mistake in my count, I am here providing a list of all the verses in all the chapters as they are currently divided...My count is correct. As the ancient wise men say: Love Plato, love Aristotle, and love the truth most of all.

R. Brecher's total word count is 79,976 (although this count actually comes from here) - and so his half way point in the Torah is word #39,988. 

The Misplaced Middle of the Torah

Now back to today's page of Talmud. According to it, the middle letter of the Torah is the Vav of the word Gachon, (גחון) found in פרשת שמיני. However this claim is way off. Since there are about 304,805 letters in the Torah scrolls in use today, (I say about because of what we have just noted regarding the precise count,) the middle letter would be letter # 152,403, the first word of this verse (Lev 8.29):

ויקרא פרק ח פסוק כט 

ויקח משה את החזה ויניפהו תנופה לפני יקוק מאיל המלאים למשה היה למנה כאשר צוה יהו–ה את משה 

However the Vav of the word Gichon, is letter #157,236 - off by 4,833 letters. Oy.

It's no better regarding the words. If we go with the actual word count as being 79,980, then the middle words are # 39,990 and #39,991. These are the words יצק אל in verse below (Lev. 8:18):

ויקרא פרק ח פסוק טו 

וישחט ויקח משה את הדם ויתן על קרנות המזבח סביב באצבעו ויחטא את המזבח ואת הדם יצק אל יסוד המזבח ויקדשהו לכפר עליו

But the middle words of the Torah, according to Today's daf, are דרש דרש found over 900 words later (Lev.10:16):

ויקרא פרק י פסוק טז 

ואת שעיר החטאת דרש דרש משה והנה שרף ויקצף על אלעזר ועל איתמר בני אהרן הנותרם לאמר

That's a lot of letters to miscount, especially if your name is "the counter." Several suggestions have been made to address these discrepancies:

1.  The text of the Torah that the rabbis of the Talmud were using was significantly different to the one we use today.  This is possible, but then why does the Talmud never cite of any of these extra words and verses? The discrepant count is about 3% - that's a lot of missing text.

2.  The rabbis in the Talmud were not good at math. Again, possible, but the Talmud claims that they took the counting so seriously that they were called COUNTERS. It also claims that they undertook the counting exercise on several different occasions.  Were they really that bad at math?

3. The rabbis in the Talmud didn't mean this count to be taken literally. While many apologists like this answer, it is at total odds with the text. The Talmud states: they counted.

4.  The rabbis guesstimated the count. Perhaps the rabbis never really counted, but guessed at where the middle of the Torah lay: somewhere in the middle of the middle of the Five Books. After that, the letter vav of the word Gachon became the official midpoint, even though it was not accurate.  The problem with this suggestion is again, that the Talmud states that the soferim actually counted, and counted again. Not that they guessed, and guessed again.  

Science, Math and Judaism

Of all the scientific disciplines, it is mathematics that is first introduced to us. We teach toddlers to count, sometimes before they can even walk, and we all pursue some kind of mathematical training through high school.  Unlike medicine or physics or biology or astronomy, mathematics is something we all do, to some degree.  And we all understand what counting means.  This passage in the Talmud is the most readily understandable example of a conflict between science and Judaism. It is a conflict in which the basic text of rabbinic Judaism declares a fact that is, well, just not a fact.  Some find this conflict to be so intellectually troubling that their only path is to reject Jewish practice. Others, equally aware of the conflict, are comfortable with their intellectual position in which the scientific inaccuracies of the Talmud require no wholesale rejection of Jewish practice. Where do you fit on this spectrum, and, perhaps more importantly, what can you do to engage in a respectful dialogue with those whose opinions on these matters are not your own?

Kiddushin 29a ~ Swimming and Drowning

קידושין כט, א

האב חייב בבנו למולו ולפדותו וללמדו תורה ולהשיאו אשה וללמדו אומנות וי"א אף להשיטו במים רבי יהודה אומר כל שאינו מלמד את בנו אומנות מלמדו ליסטות ליסטות ס"ד אלא כאילו מלמדו ליסטות

With respect to his son, a father is obligated to circumcise him, to redeem him [if he is a firstborn], to teach him Torah, to marry him off, and to teach him a craft.  Some say, he is also obligated to teach him to swim...(Kiddushin 29a)

Every year, according to The World Health Organization, more than 5,000 children drown in Europe. And for every child who drowns (the majority of whom are under five years of age) at least two others suffer lifelong neurological disability.  

Average standardized mortality rates for drowning in children aged 0–19 years in the WHO European Region, 2003–2005 or most recent three years. From The European Report on Child Injury Prevention. World Health Organization 2008.

In the United States, there are an average of ten drowning deaths each day. Of the more than 3,500 people who drown each year in the US, about a fifth are children under the age of 14.  And here are some other facts that may surprise you about drowning in the US, courtesy of the Centers for Disease Control:

• Nearly 80% of people who die from drowning are male.

• Children ages 1-4 have the highest drowning rates. In 2009, among children 1-4 years old who died from an unintentional injury, more than 30% died from drowning.

• Among children ages 1-4, most drownings occur in home swimming pools.

• Drowning is responsible for more deaths among children 1-4 than any other cause except congenital anomalies (birth defects).

• Between 2005 and 2009, the fatal unintentional drowning rate for African Americans was significantly higher than that of whites across all ages.  The disparity is widest among children 5-14 years old. The fatal drowning rate of African American children ages 5-14 is almost three times that of white children in the same age range.

• The disparity is most pronounced in swimming pools; African American children drown in swimming pools at rates 5.5 times higher than those of whites.  

How We Drown

Unlike the movie depiction of a person loudly flailing as he tries to stay afloat, the process of drowning is actually very quiet; there is usually no noise and little to see.

Once the victim disappears under the surface, the oxygen content of the blood rapidly decreases and unconsciousness follows quickly. In most cases water enters the lungs and results in wet drowning: This causes constriction of the blood vessels in the lungs (and for the medically curious among you, hypertension with a ventilation/perfusion mismatch, aggravated by surfactant destruction and washout, decreased lung compliance and atelectasis. Acute respiratory failure is common.There. Now you know.)  But in 10–20% of deaths from drowning, a small amount of water entering the larynx causes persistent spasm, which results in chocking and an immediate outpouring of thick mucus, froth and foam, but without significant aspiration; this is called dry drowning.

What's more Dangerous - a swimming pool or a gun?

The dangers of children drowning is real. So real that it turns out that owning a pool is more dangerous that owning a gun. (Notice to readers outside the US: you can own a gun here...) Dunber and Levitt, in their wildly popular 2005 book Freakonomics (p135-6) explained why this is so:

Consider the parents of an eight-year-old girl named, say, Molly. Her two best friends, Amy and Imani, each live nearby. Molly's parents know that Amy's parents keep a gun in their house, so they have forbidden Molly to play there. Instead,Molly spends a lot of time at Imani's house,which has a swimming pool in the backyard. Molly's parents feel good about having made such a smart choice to protect their daughter.

But according to the data, their choice isn't smart at all. In a given year,there is one drowning of a child for every  11,000 residential pools in the United States. In a country with 6 million pools, this means that roughly 550 children under the age of ten drown each year.) Meanwhile, there is 1 child killed by a gun for every1 million-plus guns. In a country with an estimated 200 million guns, this means that roughly 175 children under ten die each year from guns.The likelihood of death by pool (1 in 11,000) versus death by gun (1 in 1 million - plus ) isn't even close: Molly is far more likely to die in a swimming accident at Imani's house than in gunplay at Amy's.

A Common Sense Halacha?

In his commentary on the Mishnah, Maimonides counts the command to teach a child to swim as one of the duties incumbent on a parent (or, more precisely on a father). 

פירוש המשנה לרמב"ם מסכת קידושין פרק א משנה ז 

 מצות הבן על האב שש מצות ואלו הן, למולו ולפדותו וללמדו תורה ולהשיאו אשה וללמדו אומנות ולהושיטו בנהר. ולמדו לכולם מן הכתובים בראיות שיארך ביאורם כאן ואין תועלת מרובה בכך, כל אלו חייב האב לעשותם לבן, ואין האם חייבת לעשותם לבנה והוא ענין אמרם האנשים חייבין והנשים פטורות

There are six duties incumbent on a father towards his son: 1) to circumcise him; 2) to redeem him [from a Cohen if he is a firstborn]; 3) to teach him Torah; 4) to marry him to a woman; 5) to teach him a trade and 6) to teach him to swim...A father is required to do each of these things, but a mother is not required to teach them to her daughter, for this is one of those things that fall into the category of "men are obligated and women are exempted"... 

However in his Mishnah Torah, Maimonides did not include the obligation to teach swimming, and this obligation is also omitted in the sixteenth century normative Shulchan Aruch. There is no obvious reason for this omission, though this question would make a great topic of conversion at your Shabbat table tonight. But not everything that makes sense needs to be part of the code of Jewish Law. It can just be...a sensible thing to do.  Perhaps there is no better example of this than a parent, (mother or father) teaching their child, (son or daughter,) to swim.  

“As a father who has lost a son, I know first-hand the unbearable pain that comes with a child’s death. Amidst my grief, I am able to take some small solace in the fact that everything possible was done to fight the disease that took my son’s life. If my son had died in a backyard pool due to my own negligence, I would not even have that to cling to. Parents who have lost children would do anything to get their babies back. Safeguard your pool so you don’t become one of us.”

— Steven Levitt, co-author of Freakonomics. "Pools more dangerous than guns". Chicago Sun-Times 7/28/2001

Kiddushin 25b ~ Can Elephants Jump?

In a discussion of how one acquires ownership of an animal, Rabbi Shimon rules that they must be lifted - literally, lifted.  And then the Talmud asks how exactly an animal is lifted.

קידושין כה, ב 

אלא מעתה פיל לרבי שמעון במה יקנה אמר ליה אביי בחליפין אי נמי בשוכר את מקומו רבי זירא אמר מביא ארבעה כלים ומניחן תחת רגליו

If so, how would one acquire an elephant according to Rabbi Shimon?  Abaye said to him - by means of chalifin [a token exchange of a utensil or piece of clothing to finalize the transaction]. Rebbi Zeira says, the buyer brings in four vessels and places them under the elephant's feet [demonstrating that the elephant has now entered the buyer's domain]. (Kiddushin 25b)

A.H Atwell, National Geographic.

Now leaving aside why the Talmud wondered about elephants when one could ask the same thing about say, cows or a horses, and leaving aside the question of just how Rebbi Zeira would go about getting his elephant to stand with each leg on a pot, the reader surely wants to know if there is um, an easier way to acquire an elephant. And yes, there is. The Talmud offers another helpful way to gain possession of your very own Dumbo. אי נמי בחבילי זמורות - "An alternative is to use bundles of vines." Rashi offers an explanation: the vines are three tefachim [about 30 cm.] heigh, and the elephant is led to stand on them, "and any lifting that is above three tefachim is called lifting [for the purposes of the transfer of ownership]."

Elephants at the circus in Washington DC. in 2016 They demonstrated - just in time - that Rebbi Zeira's suggestion was indeed workable. So long as you have a full time elephant trainer...

Tosafot's Solution - jumping elephants

Tosafot, a collection of medieval commentaries on the Talmud, is dissatisfied with Rashi for a number of reasons. First, if the Talmud had meant to suggest that a platform three tefachim in height be built, it would have said so, and not concocted some contraption using grape vines. Second, the grape vines, are legally considered to be part of the ground itself, so the elephant standing on them would not be separate from the ground, which is precisely what is needed to effect a legal transfer of ownership.    

In light of these objections, Rav Meshulam offers his own explanation of what the Talmud meant when it suggested using vines.

אי נמי בחבילי זמורות. פי' בקונטרס משכחת לה להגבהת פיל בחבילי זמורות הגבוהים מן הארץ שלשה ומעלהו עליהן דהגבהת ג' הגבהה היא דנפיק לה מתורת לבוד ולפירושו בכלים לא מצי למימר דליקני מדין הגבהה שיניח כלים תחת רגליו דסתמייהו אין בעוביין שלשה טפחים ולפי' ר"ת דמפרש דהגבהה בטפח קני צ"ל סתם כלים אין בעוביין טפח וקשה אמאי נקט חבילי זמורות לנקוט אבנים או עצים ומפרש הרב משולם דלהכי נקט חבילי זמורות לפי שהן מאכל פיל כדאמרינן פרק מפנין (שבת דף קכח.) מטלטלין חבילי זמורות בשבת מפני שהן מאכל לפילין ומגביהין לפיל חבילי זמורות למעלה והוא קופץ ומגביה את עצמו מן הארץ ואוכלן ואין לתמוה אי חשיבא הגבהה בהכי דכה"ג אשכחן בפרק שילוח הקן (חולין דף קמב.) כי היכי דליגבינהו ולקנינהו

...Rav Meshulam therefore explained that the Talmud offered the explanation of vines because elephants eat them...and we lift up the vines in front of the elephant , which will jump up to eat them, thereby lifting itself off of the ground...

Elephants stand on tip toe. From here.

There is one small problem with Rav Meshulam's explanation: elephants can't jump. Here is Tony Barthel, curator of Elephant Trails at the National Zoo in Washington DC.  "If you were to look at an elephant’s skeleton, you’ll see that they’re standing on their tippy toes...All the bones are pointed straight down.” This means that they cannot jump, even if they wanted to.  Elephants cannot jump, and they cannot technically even run, since that requires all four legs to be off the ground at once. Why then did Rav Meshulam suggest this explanation, one which is not biologically possible?  Here is Rabbi Dr. Natan Slifkin's answer, from his Torah Encyclopedia of the Animal Kingdom:

The answer is that he had no reason to believe otherwise. There were no zoos in medieval Europe, and very few elephants.The emperor Charlemagne, king of the Franks,received an elephant as a gift in 797.Frederick II used an elephant in his capture of Cremona in 1214. King Henry III of England received an elephant from Israel in 1254. Alfonso V of Portugal gave an elephant to Renew d'Anjou in 1477. The Vatican was given an elephant in 1514. But the average person in those times never saw an elephant. Illustrations from that era show that artists, basing themselves on stories,were very unsure about how to depict elephants.They were often portrayed as possessing a body like those of horses or deer, sometimes even with split hooves. Of particular relevance to us is that they are sometimes drawn with the hindlimb structure of lions or dogs, poised with elastic energy. Rav Meshullam ben Nathan, who was born in Provence in 1120 and passed away in Melun in 1180, never saw either a live elephant or an accurate drawing of one. He thus had every reason to believe that, like other animals elephants can jump.

So there you have it.  Don't suggest biological explanations if you've not studied biology. Even if you are Rashi's son-in-law.

From here, the thirteenth century Book of the Marvels of the World (Livre des Merveilles du Monde). Note the bent hind legs of the elephant, which suggest the ability to jump.

[An expanded version of Rabbi Dr. Slifkin's essay can be found here.]

Kiddushin 25a ~ Polydactyly

קידושין כה, א–ב

 א"ר חייא בר אשי אמר רב היתה לו יתרת וחתכה עבד יוצא בהן לחירות, אמר רב הונא והוא שנספרת על גב היד

Rav Hiyyah bar Ashi said in the name of Rav: if a slave had an extra finger and his master cut it off, the slave is freed on account of this act. Rav Huna said this only applies if the extra finger is in line with the others [lit. counted alongside the hand].  

Polydactyly (from the Greek daktylos, meaning finger), is a developmental abnormality in which there are more than the customary five fingers or toes at the end of the arms and legs. It has long been recorded in ancient civilizations - and is even mentioned in our own Hebrew Bible. Do you know who is described there as having a total of twenty four fingers and toes? (Click here to find out.)

Polydactyly is classified by the location of the extra digit: If it is found on the thumb or big toe, it is called preaxial polydactyly. If it is found on the the little (fifth) finger or toe it is called postaxial polydactyly.  Accessory digits in-between are classified according to their location and where they join the hand or finger. Syndactyly, on the other hand (!) occurs when there are fewer than five fingers or toes on each limb. (We will discuss syndactyly when we study tractate Bechorot, (daf 45a), on June 1st, 2019,  הבעל"ט.)

Rav Huna's Classification, and Swanson's classification

There are many different ways to classify polydactyly - although the most commonly used is the 1964 Swanson classification system, a modified version of which was adopted by the American Society for Surgery of the Hand and the International Federation of Societies for Surgery of the Hand in 1976. 

But Rav Huna, who died in Babylon around the year 296 CE, developed his own classification system long before Swanson, and it is based on simple observation: does the extra digit seem to begin in line with the other fingers, or does its origin seem to lie above them?  For Rav Huna, an extra digit that originated beyond the metacarpal-phalyngeal joint (the knuckle for our non-medical reader) in the hand, or beyond the metatarsal-phalageal joint in the foot did not have the legal status of a normal digit.  So an act of assault by the owner of a slave in which this kind of digit was amputated would not legally count as sufficient cause to allow the slave to gain his freedom.  With this information, look at the drawings below and decide in which case the loss of the extra digit would be sufficient cause for the slave to be freed.

Various forms of postaxial (ie. not on the big toe) Type A polydactyly of the foot, ranging from a partially duplicated fifth intermediate phalanx (top left) to a fully developed sixth digit, including the metatarsal (bottom right). From Case DT. Hill RJ. Merbs CF. Fong M. Polydactyly in the Prehistoric American Southwest.  Journal of Osteoarchaeology 2006: 6: 221–235.

If the slave had an extra fifth toe outlined in Figures 2-6, its loss would result in the slave going free. In all these cases, the extra digit arises in line with the base the the other toes (and in Figure 6, the extra toe is joined to an extra metatarsal). But in Figure 1, the extra fifth digit arises from the distal end of the fifth distal phalange (or, for our non-medical reader, the tip of the pinky); in this case its traumatic amputation by the slave's owner would not result in the slave gaining his freedom. 

This categorization appears to be another previously unrecognized medical first in the Talmud: Rav Huna's classification of polydactyly.   

“היתה לו אצבע יתירה וחתכה, אם עומדת בסדר האצבעות יוצא לחירות ”

— שולחן ערוך יורה דעה הלכות עבדים סימן רסז סעיף כט

Polydactylous feet from Newspaper Rock in Indian Creek State Park, Utah. These carvings in rock are called petroglyphs, and were made by native Americans as long as 1,500  years ago.