1) THE NUMBER OF LETTERS IN THE TORAH
QUESTION: The Gemara explains that the early Chachamim were called "Sofrim" ("scribes," or "those who count") because they were able to count all the letters of the Torah. They used to say, "The letter Vav of the word 'Gachon' (Vayikra 11:42) marks half of the total number of letters of the Sefer Torah." Rav Yosef asked whether the Vav of "Gachon" is the last letter of the first half of the Torah or the first letter of the second half. Abaye suggested that they simply bring a Sefer Torah and count the letters to answer Rav Yosef's inquiry, as was done by the Chachamim in the past. Rav Yosef replied that those Chachamim were experts in "Chaseros v'Yeseros" (the letters which may be omitted or included without affecting the meaning of the text; certain words may be spelled either with or without the letters Alef, Heh, Vav, and Yud, "supplementary letters" which are written to aid the recognition of vowels and are not always pronounced). Rav Yosef asserted that we are no longer experts in this matter, and thus our count will not reliably determine the central letter of the Sefer Torah.
The Gemara clearly maintains that the letter Vav of the word "Gachon" is the middle letter of the Torah. The Beraisa in Sofrim (9:2) states that to denote that Vav's unique position in the Sefer Torah, it is written larger than other letters.
However, one who counts the letters of the Torah will find that the Vav of "Gachon" is not the middle letter of the Sefer Torah. There are 304,801 letters in the Torah (according to the count of Rav Yakov Auerbach zt'l; according to the traditional listing at the end of Sefer Devarim in the standard Mikra'os Gedolos, there are 304,805 letters). The Vav of "Gachon" is not the midpoint letter (letter number 152,403). Rather, it appears nearly 5,000 letters later (letter number 157,336)! Although Rav Yosef himself said that we are not experts in the identity of the "Chaseros v'Yeseros," this lack of expertise does not seem to explain the great discrepancy of 5,000 letters. (Among all of the known traditions for the text of the Sefer Torah that have been handed down through the generations in the various Jewish communities around the world, there are only nine minor variations in how words are spelled.)
What does the Gemara mean when it says that the Vav of "Gachon" is the middle letter of the Sefer Torah?
ANSWERS:
(a) RAV ELIYAHU POSEK (Piskei Eliyahu 3:1) answers that perhaps the Sofrim who counted the letters of the Sefer Torah did not mean that the Vav of "Gachon" is the middle of all of the letters of the Sefer Torah. Rather, it is known that many words in the Torah should be written with a Vav or Yud and yet the Torah omits those letters for exegetical purposes, or it adds those letters when the words should have been written without them. In the list of all of the Vavs and Yuds which the Torah excludes (or includes) when grammatically it should include (or exclude) them, the Vav of "Gachon" is the middle of that list. (It is assumed that the word "Gachon" itself should have been written without a Vav.)
Accordingly, Rav Yosef asked whether the Vav of "Gachon" is the last letter of the first half of this list of letters or whether it is the first letter of the second half of this list. In order to ascertain the answer, Abaye recommended that they count all of the letters that the Torah excludes or includes contrary to grammatical convention. Rav Yosef responded that since they lacked the grammatical expertise necessary to determine in which words the Vav and Yud serve as extra letters and in which words they are part of the actual word, they are unable to determine which letters to count. (See article by Rav Yitzchak Zilber in "Shemaitsin," volume 43, for a similar explanation.)
(b) Another question arises with regard to the total number of letters in a Sefer Torah. The ZOHAR CHADASH (Shir ha'Shirim, p. 74) states that there are 600,000 letters in the Sefer Torah which correspond to the 600,000 souls of the twelve tribes of the Jewish people. Similarly, the MEGALEH AMUKOS (Va'eschanan #186) writes that the soul of every Jew stems from one of the 600,000 letters in the Torah. The name "Yisrael" itself can be viewed as an acronym for the words, "Yesh Shishim Ribo Osiyos La'Torah" ("there are sixty myriads (600,000) of letters in the Torah").
Why does the Zohar Chadash state that there are 600,000 letters in the Torah, when our count yields almost half that number?
The ZOHAR CHADASH itself suggests that when we count the letters of the Torah, we must not count each letter as a single letter. Rather, we must count each letter according to the number of letters it comprises when its name is spelled in full. For example, the letter Alef counts as three letters, Alef-Lamed-Feh. Beis is spelled Beis-Yud-Tav and counts as three letters, and so on. When all of the letters of the Torah are counted in this manner, the number of letters is 600,000.
The Zohar's method of counting may also explain how the Vav of "Gachon" is the midpoint of the Sefer Torah. The number of letters before that Vav may equal the number of letters which follow it when the letters are counted in the manner prescribed by the Zohar. When Rav Yosef pointed out his generation's lack of expertise in "Chaseros v'Yeseros," he may have intended to explain why he was unable to duplicate the Zohar's method of counting. Many letters of the Hebrew alphabet may be spelled with or without supplementary Vavs and Yuds to aid in their pronunciation. For example, Beis may be spelled Beis-Yud-Tav, or simply Beis-Tav. Vav may be spelled Vav-Yud-Vav, or simply Vav-Vav, and so on. As a result, our lack of knowledge about the spelling of many of the Torah's letters prevents us from accurately counting how many letters precede and succeed the Vav of "Gachon."
(c) RAV SHNEUR ZALMAN of Liady provides another answer (LIKUTEI TORAH, Behar, p. 43). He writes that in order to count 600,000 letters, one must identify every vowel that lacks its supplementary letter, and add that letter to the word. For example, it is possible to add an Alef or Heh after every Patach or Kamatz that is not followed by an Alef or Heh (see Rashi, beginning of Kesuvos 69b, and end of Makos 7b). A Vav may be added after every Cholem or Kubutz, and a Yud after every Chirik or Tzerei. If all of these additions are made, the count of letters in the Torah reaches 600,000.
This approach also explains Rav Yosef's statement here in Kidushin. The Vav in "Gachon" is the middle letter in the Torah after all of the vowels which lack supplementary letters are supplemented. Rav Yosef pointed out, however, that we lack expertise with regard to which vowels may support an extra letter without affecting the word's meaning. As a result, we do not know which of the unwritten supplementary letters are to be counted.
According to these answers, Rav Yosef's reservations involved only counting what is not written in the Sefer Torah itself. His doubts had no bearing on what is written in the Sefer Torah.
The above answers, however, are speculative, because if we follow the formula of the Zohar Chadash and count each letter as either two, three, or four letters, the count will result in far more than 600,000 letters. On the other hand, if we follow the formula of the Likutei Torah and count all of the supplementary letters of the unsupplemented vowels, there will be far less than 600,000 letters since many vowels of the Torah are already written in supplemented form and thus would not receive additional letters.
(See RAV REUVEN MARGOLIYOS in HA'MIKRA VEHA'MESORAH, chapters 4 and 12, for a compilation of various other answers. Rav Margoliyos raises difficulties with all of those answers and offers his own approach. See also TORAH SHELEIMAH, volume 27, pp. 286-9; THE HANDBOOK OF JEWISH THOUGHT by Rav Aryeh Kaplan, chapter 7, fn. 108; PRI TZADIK of Rav Tzadok ha'Kohen, beginning of Shemos.)
(d) Perhaps a different approach may be suggested to explain both the question of the Vav of "Gachon" and the question of the Zohar Chadash's 300,000 missing letters. It is an accepted tradition to leave a blank space of the width of nine letters at the beginning of every new Parshah in the Sefer Torah (RAMBAM, Hilchos Sefer Torah 8:1). The BEIS YOSEF (YD 275) points out that the letters of the Torah are of different widths, and thus the measure of a space equal to the width of nine letters depends on which letter is used as the standard. Since the tradition does not specify which letter's width to measure, the Beis Yosef rules that nine widths of the smallest letter in the Hebrew alphabet, the Yud, suffice.
According to the ruling of the Beis Yosef, it is possible to understand how the Vav of "Gachon" is the middle letter of the Torah and how there are 600,000 letters in the Torah. According to the Beis Yosef, an unspecified letter does not refer to an average-sized letter, but rather to the smallest letter. When the Sofrim, or the Zohar Chadash, counted the letters of the Torah, perhaps they did not count each character as a single letter. Rather, letters which must be written, according to the Halachah, with the width of two Yuds count as two "letters." A large letter, such as the Shin, counts as three letters, since its width is as wide as three Yuds (the Shin is comprised of three Yuds which extend from a single base). In fact, with the bit of space which separates each of the Yuds of the top of the Shin from each other, the Shin is two bits more than three Yuds wide.
A survey of the Hebrew alphabet reveals that there are only four letters which are one Yud-width wide: Vav, Zayin, Yud, and Nun Sofis (final Nun). Two letters are one and a half Yuds wide: Gimel and Nun (due to their bases). Fifteen letters are two Yud-widths wide, five letters are two plus-a-bit Yud-widths wide, and one letter is three-plus-two-bits Yud-widths wide. According to these numbers, the count of letters in the Sefer Torah nearly doubles! If each letter is counted by its Yud-widths, there indeed are 600,000 letters in the Torah. (The number of times that each letter appears in the Torah is recorded at the end of the Torah Temimah Chumash and in the new Concordance. The figures in the two sources vary slightly. See also Rav Aryeh Kaplan's footnote in "Menashe ben Yisrael: The Conciliator" (Hermon: New York, 1972), part 1, p. 250.)
This approach also explains Rav Yosef's statement that lack of expertise with regard to "Chaseros v'Yeseros" prevents us from verifying whether the Vav of "Gachon" is the midpoint of the Torah. Perhaps the term "Chaseros v'Yeseros" does not refer to words which lack or include supplementary letters. Rather, it refers to letters which lack width or are supplemented with extra width. Tradition requires that certain letters in the Sefer Torah be written in one place either smaller (i.e. lacking) or larger (i.e. supplemented) than in other places. For example, the Alef in the word "Vayikra" (Vayikra 1:1) is written smaller than usual, as is the Yud in the word "Teshi" (Devarim 32:18). The Beis of the first word in the Torah, "Bereishis," is written larger than usual, as is the Vav in "Gachon."
When the Sofrim stated that the Vav of "Gachon" is the midpoint of the Torah, perhaps they meant that when all of the letters of the Torah are counted by their Yud-widths, this Vav is at the center. When Rav Yosef commented that we cannot verify this assertion due to our lack of expertise in "Chaseros v'Yeseros," he may have meant that we do not know which letters to enlarge or reduce in size, or how much to enlarge or reduce them. This uncertainty, however, has no bearing on the validity of today's Sifrei Torah. The RAMBAM states explicitly (Hilchos Sefer Torah 6:9) that if a letter is written larger or smaller than its true Masoretic size, the Sefer Torah remains valid.
According to this way of counting the letters, the Sefer Torah indeed contains 600,000 letters, and the Vav of "Gachon" may be the middle letter of those 600,000 letters. (The basis for this approach is suggested by RAV YAKOV KAMINETZKY zt'l, end of EMES L'YAKOV.)

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