Science and Certainty

Talmudology on the Parsha, Shmini: ~ How Many Letters are in a Sefer Torah?

ויקרא 10:16

אֵ֣ת ׀ שְׂעִ֣יר הַֽחַטָּ֗את דָּרֹ֥שׁ דָּרַ֛שׁ מֹשֶׁ֖ה וְהִנֵּ֣ה שֹׂרָ֑ף וַ֠יִּקְצֹ֠ף עַל־אֶלְעָזָ֤ר וְעַל־אִֽיתָמָר֙ בְּנֵ֣י אַהֲרֹ֔ן הַנּוֹתָרִ֖ם לֵאמֹֽר׃

Then Moses carefully inquired about the goat of sin offering, and it had already been burned! He was angry with Eleazar and Ithamar, Aaron’s remaining sons, and said,

In this week’s parsha, Moses gets angry with Eleazar and Ithamar, two of the sons of Aaron. What is of interest to us this week is not why Moses was angry. Instead we will focus on two short words in the verse above “דרש דרש” meaning “he carefully inquired.” Most of the classic commentaries interpret this to mean that Moses asked two questions, rather than just one. But the Talmud occupies itself not with the meaning of these words, but their location in a Sefer Torah. They are, according to talmudic tradition, the halfway point in the number of words in the 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...

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.

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.

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

According to the Talmud, 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?

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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.

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.

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 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?

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Shavuot Redux~ How Many Letters are in a Sefer Torah?

In honor of shavuot that celebrates the giving of the torah, a repost from the talmudology archives.

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...

This page of Talmud 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.

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 Lettlers
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?

May you be blessed with a meaningful Shavuot.

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Rabbinic Philosophies and the Scientific Method

Last time on Talmudology

Although permitted by Jewish law, in Victorian Britain it was illegal for a man to marry his dead wife’s sister – though many did.  There were attempts to change the law and permit this kind of marriage, but many in the Church of England remained opposed. Writing in 1887 in The British Medical Journal, an anonymous surgeon claimed that science could provide support for the permissive movement. But we now know that the science he offered (that all future children of a woman, regardless of the father, carry the traits of the man who first impregnated her) is wrong. This shows that science changes. But if science changes, what should we do when it seems to challenge Jewish tradition? 

What is stuff made of?

Several years ago, I had the pleasure of studying science with my then 13-year-old daughter Ayelet. She was preparing for a test, and the subject was “Atomic Structure.” Here is some of the content she shared with me: (Read it through - it's really not scary.)

(All slides courtesy of Berman Hebrew Academy, 8th Grade Science Class)

So to sum it up, Ayelet taught me that in addition to the model of Aristotle, we've had at least five explanations of what stuff is made of:

why don't kids reject science?

Now here is a fascinating thing. My daughter had no existential breakdown when she realized that the way scientists understand the world changes over time. She did not once say to me “Scientists are useless. They change their minds all the time. They must have no idea what they are talking about. I’m done with learning science…” Not even close (though, by the end, she was most certainly done with studying for her science test). Let's compare this attitude towards the changing nature of scientific knowledge with that of some Jewish thinkers, past and present.  

reuven landau & foucault's pendulum

Let’s start with someone who is not well known (unless you read the book).  Reuven Landau (d. 1883?) wrote strongly against the Copernican model of the solar system in which the sun is stationary and the earth revolves around it.  But in 1851 Foucault demonstrated with his pendulum that the earth really was revolving, (though it didn’t prove that it revolved around the sun). What to do with this evidence? Landau had no doubt. Science was fickle and changed all the time, so don’t worry about it.

Although the astronomers of our time pride themselves on finding a compelling demonstration that the earth moves by using the pendulum, you should dismiss this too. For it has happened many times that an earlier scientist proved a point beyond a doubt using an unequivocal demonstration, and yet a later one came and disproved that which was established earlier, including the [previously] convincing demonstrations, and showed a new explanation for the findings...

This skepticism about accepting the results of the famous pendulum experiment reflected Landau's attitude towards science in general, which can be best summed up like this. Since all scientific theories are in a state of constant flux, it's best not to pay too much attention to them. When Jewish beliefs are challenged by science, take the long view; in doing so, tradition will ultimately be vindicated. (His view was actually more nuanced than that, insofar as he was willing to quote from the science when it supported his anti-Copernican position, but criticized the same science as being fickle when it proved to be problematic.) 

Rav Kook 

Abraham Isaac Kook (1865–1935), the first chief rabbi of Palestine, is thought to have welcomed science as a tool to understudying God's universe. While this is generally correct, (he was famously sympathetic to Darwin's theory, though in none of his writings does he mention Darwin by name,) Rav Kook cautioned against accepting  all scientific theories "...even those about which there is general agreement, for they are like a fading flower (כי הן כציץ נובל). Soon enough new instruments will be developed, and people will mock these new theories . . . only the word of our God will last forever." Because scientific theories come and go so quickly, Rav Kook felt it was best not to get too attached to them.

The Ben Ish Hai

Joseph Hayyim (1834–1909) was born in Baghdad, where at the age of twenty-five, he succeeded his father as leader of the Jewish community. He authored a work that is widely read by Sephardic Jews to this day called Ben Ish Hai, but it was in another work that he advanced an example of extreme rabbinic skepticism towards science.

Even when [a scientific idea seems] persuasive, it is likely to be rejected and overturned, because later enlightened people will come to understand something that arises from the natural world that had not been understood by those earlier. [These earlier people] had invented their own system based on their understanding. When an objection to an earlier system arises, the entire system is destroyed, because when a foundation is destroyed the whole house crumbles...Over the last two thousand years a number of systems have been developed and overridden in the fields of natural sciences and astronomy. One builds and another destroys, like the building of [the Egyptian cities of] Pitom and Ramses. 

Note the language the Ben Ish Hai uses here.

When an objection to an earlier system arises, the entire system is destroyed, because when a foundation is destroyed the whole house crumbles.

But is this a fair description of the scientific method? Did Bohr's atomic model (work for which he won the Nobel prize in 1922) really destroy the entire edifice of physics, or did it nudge it closer to the truth? 

Pinhas hurwitz & Sefer Haberit

Sefer Haberit is probably the best selling Jewish book of science ever written. First published anonymously in 1797, it remains in print to this day.  Its author, Pinhas Hurwitz from Vilna, wrote the book in two parts; the first was a scientific encyclopedia dealing with what he called human wisdom, and the second part dealt with divine wisdom, (and was ostensibly focussed on explaining a sixteenth century kabbalistic work by Hayyim Vital).  

Hurwitz cautioned against ever accepting any particular scientific theory.  His notion of the way science changes is certainly not as extreme as that of the Ben Ish Hai, but it placed him in a rather odd situation. Hurwitz didn't much like the new Copernican model of the universe with the earth revolving around the sun, but neither could he go back to the old geocentric model. So in the spirit of compromise he suggested following the model proposed by Tycho Brahe some two centuries earlier, the details of which need not detain us.  But Hurwitz knew that this model had been utterly discredited in the scientific community. No problem, wrote Hurwitz, because science is always changing its mind.  Perhaps one day this old discredited model will come back into favor, and when it does, it will pose less of a problem for traditional Jewish belief than the current widely accepted Copernican model.

. . . who knows if at a later time or in one of the many future generations that will come after ours, [Tycho's discredited] theory may be accepted. Then it may become permanently accepted, for this is the way among the Gentiles that some opinions have their moment. At times they are rejected and at other times they are accepted. Even if a theory is rejected from its very inception . . . eventually there may arise a person who adopts the theory and succeeds in spreading it across the entire world...  

So according to Hurwitz, it made sense to accept a discredited theory that supported his notion of Jewish belief, because one day, perhaps, the scientists will go back to believing what they now reject as false.  It is as if today, we claimed that it's perfectly reasonable to believe the world is flat, because that was once an accepted belief, and who knows, perhaps one day scientists will return to the flat-earth theory and believe once again that it is a true description of the world.

The Maharal of Prague

Another Jewish skeptic of science is the great Rabbi Judah Loew (d.1609), known by his acronym Maharal. In a long essay he contrasted knowledge attained from observation of the universe and knowledge obtained from Jewish tradition.  The former is constantly changing, and inferior to the unchanging wisdom received through divine revelation.

 ... the [Gentile] nations want nothing more than to become wise through this knowledge, and indeed they became expert in this field of knowledge, as all know. Yet there always came other experts afterwards who overturned the knowledge that they had worked so hard to attain...However the Sages of Israel who received their information from Moses at Sinai—and who himself received this from God—are the only ones who alone possess the Truth...

Note that the Maharal made an expansive claim (and one that was very popular circa 1580): all true knowledge comes from religion  - or more precisely - from the rabbis. He did not say that the rabbis provided spiritual insights while "experts" (who we'd call "scientists" today) provided insights into the physical universe. Rather he claimed that truth can only come from the "Sages of Israel who received their information from Moses at Sinai".  As a consequence, scientists really have no seat at the table when we discuss knowledge.  

rabbi moshe meiselman

The last example we will look at is a contemporary figure, Rabbi Moshe Meiselman. His recent book states that he "was trained by some of the great names in mathematics, philosophy and the sciences at two of America's premier universities." Great! Rabbi Meiselman has studied outside of the walls of the Jewish ghetto - something the Maharal could not do, even if he had wanted.  So we should expect a fresh and sophisticated approach from a rabbi who gets science, right? Wrong.

Science has no sacred cows. Over the past hundred years, scientific theories have changed with unprecedented rapidity. Whoever weds his belief system to any particular scientific theory will soon find that system outdated and will be forced to look for a new one... (585)

Rabbi Meiselman here has the same old understanding of science as the Ben Ish Hai. When a new scientific theory replaces an older one, everything comes crashing down and we are left wandering in search of something new to grab on to. Elsewhere though, he sounds more like the Maharal, who objected to scientific hubris, and reminded us that science can make no truth claims, for these are reserved for the rabbis.

[A]t every juncture, just as soon as the dust of the latest revolution has settled, one inevitably finds scientists claiming that the ultimate secrets often universe have finally been unlocked and that there are few surprises left in store...Absolute truth has been attained! (584)

Now in fairness to Rabbi Meisleman, elsewhere in his long book he shows a better understanding of the  scientific method.

Science, when properly understood, lays no claim to the knowledge of truth. It embodies the search for theories that approach the truth. It inches in the direction of truth, but it never claims to be in possession of that precious commodity. (579)

Which is it then, Rabbi Meiselman? Do scientists claim to have attained the Truth (as he writes), or rather are they engaged in a process that brings us ever closer to this goal without their having arrived (as he also writes)? His is a a peculiar mix of positions. (You can read other critiques of Rabbi Meiselman's book here and here.)

Got a spare five minutes? Great, then we can go a little deeper, and see why these rabbinic philosophies don't really reflect what science is all about. To do that, let's consider the truth claims of the following pairs of scientific statements. 

1. The earth is flat vs The earth is round.

Both of these statements are incorrect. The earth is actually an oblate spheroid, that is, a globe which is slightly flattened at the poles.  But the statement "the earth is round" is much closer to the truth than the claim that "the earth is flat."  

 

 

2. All matter consists of just four elements vs  All matter is made up of just electrons and protons.

Again, both are false, but the second statement is a lot less false than the first. Matter is certainly not just made up of  the four elements of earth, air, fire and water. But it's also not just made up of electrons and protons; matter is now known to be made up of neutrinos and muons, and up quarks and down quarks and charm quarks and who what knows other kinds of elementary particles still waiting to be discovered. The second statement is truer that the first, but physicists would not claim that it's the last word on the subject.  

3. Vitamins prevent cancer vs vitamins don't prevent cancer

Here is starts to get complicated. While some studies are pretty conclusive (no-one really suggests that smoking doesn't cause lung cancer) other scientific claims seem to change over time. For example, the relationship between vitamins (especially vitamin D) and cancer is one that we have had different scientific answers to at different times. In 1999 the N-HANES study of over 5,000 women followed for twenty years reported that vitamin D was associated with a reduction in breast cancer. Then in 2007 the Journal of the National Cancer Institute looked at a group of 36,000 women in the Women's Health Initiative.  It reported that there was no effect of vitamin D on the risk of breast cancer. Today, the official position of our National Cancer Institute is this: it still isn't sure if there is any association.

And now a forth scientific claim, this time from the field of mathematics

4. In a right angleD triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

This theorem (like all mathematical theorems) is true in a special way. So long as we're talking about two dimensional geometry, then this theorem will be true in all possible places in the universe; it was always true in the past, and it will always be true in the future.  That's what makes a mathematical theorem true in a different way from a medical truth, or a truth about the physical universe.  The latter two may be partially true, or true of the basis of the best equipment we have available, but these are not true in the way that the Pythagorean theorem is true.  

KINDS OF SCIENCE

So there are different kinds of scientific claims, some of which are more true than others. And scientific progress advances in different ways depending on which area of knowledge we are addressing.  These differences were not noted by any of the rabbinic critics we've cited above, but once understood, they allow us to appreciate that science can make different claims over time and that some of these can change without the entire scientific enterprise being called into question.

One last thing- be careful of any appeal to relativism. It could be argued that each of the rabbis we cited (well, other than Rabbi Meiselman) lived at a time when these subtleties were not appreciated. As a result we should not be a harsh judge of their philosophies of science, which just reflect the way people thought at that time.  I am sympathetic to this claim, and I think it is a perfectly reasonable explanation of how they may have arrived at their opinions. But if these rabbis were just reflecting the way everyone thought when they lived, we are most certainly not bound to consider these opinions as anything other than of  historical  interest.  And since we now know differently, we can ignore these rabbinic opinions as we forge our own Jewish philosophies towards science.  If, on the other hand, the claim is made that these rabbis were reflecting a profound Jewish Truth that will remain so for ever, well, then we have a problem. Because you are then forced to reject the science, and end up arguing for all kinds of things we know are simply not true.

One other last thing. This is not a claim that science is the only path to knowledge, happiness and enlightenment.  I am not suggesting anything like that.  Steven Pinker argued for something  along these lines in the pages of The New Republic (ז'לֹ), and Leon Wieseltier wrote a persuasive  response, both of which are well worth reading.  (I find myself more sympathetic to the latter than the former.) But when it comes to scientific questions, well, that is where science does, perhaps know best.

Science confers no special authority, it confers no authority at all, for the attempt to answer a nonscientific question.
— Leon Wieseltier

where we've been

We noted that 130 years ago the laws of Yibbum were explained with a scientific fact that today we know is incorrect. This example raises the possibility that the scientific enterprise is only ever tentative and should be best ignored when it seems to raise questions about Jewish teachings. But that doesn’t really capture the way science progresses. We examined six rabbinic understandings of the philosophy of science, and noted that they do not capture the different meanings we have when we way that something is a fact of science. 

We need some new Jewish philosophies of science. They must take into account these different meanings, and need to be more sophisticated than the rabbinic understandings that we examined. There have been some really good efforts to address this area (like here and here and here), but more work needs to be done.  Who wants a shot?

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