Parsha Halacha

Parsha Halacha - Parshat Nasso

Torah Codes: How Gematriyah works

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The Torah portion of Nasso includes the sacrifices of the twelve leaders of the tribes.[1] Each of them brought the same sacrifices and donations, yet, according to our sages, they each had different intentions in mind when doing so. Many of these intentions had to do with the concept of gemtriyah (numerical values of the Hebrew letters). This article will discuss some of those gematriya’ot (plural of gematriyah) as well as explore the concept of gematriyah in general.

Here are some of the gematriya’ot which the sacrifices and gifts allude to.

·        קַעֲרַת כֶּסֶף = 930 - The Years of Adam

According to Rashi,[2] Netanel ben Tzu’ar, the leader of the tribe of Yissachar is the one who had the idea to bring these particular animals and gifts. His intention in bringing the silver spoon (filled with incense) is that the words קַעֲרַת כֶּסֶף (silver spoon) has the gematriyah of 930 which is the number of years in Adam Harishon’s (the first man’s) life.[3]

·        מִזְרָק אֶחָד כֶּסֶף = 520 - Noach’s age when he gave birth plus 20

The words מִזְרָק אֶחָד כֶּסֶף (one silver bowl) have the gematriyah of 520. This alludes to the age of Noa’ch when he had children (500) plus the 20 years before they were born, which is when the decree of the flood was made by G-d.[4]

·        קְטֹרֶת = 613 mitzvot 

The word קְטֹרֶת has the numerical value of 613 if the ק is switched for ד (under the principle of א"ת ב"ש ג"ר ד"ק [5]) which is the number of mitzvot in the Torah.

Basis for Gematriyah

The idea that every Hebrew letter has a numerical value and that this can be used to expound on the Torah is a tradition that Moshe received from Sinai. It is therefore included in the 32 methods of expounding on the Torah as enumerated by Rabbi Eliezer, son of Rabbi Yossi HaGlili.

Gematriyah in the Mishnah

The Mishnah in Pirkei Avot states[6] “Rabbi Eliezer (ben) Chisma states: ‘The laws of mixed bird offerings and the calculations of menstruation days, these are the body of the halakhah. The calculation of the equinoxes and gematria are פַּרְפְּרָאוֹת לַחָכְמָה – the desserts of wisdom.’”

According to the Meiri, this means that one should study the entire Torah up to and including the orders of Kodshim (sacrifices) and Taharot (laws of purity) which include the laws of mixed bird offerings (in Tractate Kinim) and calculation of menstruation days (in Tractate Niddah) respectively. Only after completing all of these may one study astronomy and mathematics (and similar sciences). (The Me’iri understands gematriyah to be referring to geometry[7] and mathematics in general.)

A Good Dessert

Many of the commentaries explain that gematriyah refers to the numerical value of the Hebrew numbers as the term is used today. 

There are differing opinions as to why this study is called פַּרְפְּרָאוֹת לַחָכְמָה – desserts of wisdom.

·        Rabbi Ovadiah of Bartenura explains that just as desserts are eaten for delight, so too when a person knows gematriyah it brings pleasure to those who hear it and honor to the one who shares it.

·        The Tosfot Yom Tov translates פַּרְפְּרָאוֹת as “appetizers.” He explains that knowing the gematriya’ot of the Divine names and other esoteric matters will whet a person’s appetite for more in-depth Torah study. 

·        Rabbi Ya’akov Emden explains (in his commentary Lechem Shamayim) that just as the dessert is only served after the main course, so too, one who is not expert in Torah cannot expound gematriya’ot on their own as this can lead to inappropriate teachings. Only a true Torah scholar can use the gematriyah method to bolster Torah concepts which are known to be true. As the Ramban says (beginning of Sefer HaGeulah) “One may not calculate gematriya’ot and derive from them whatever they think to be correct.” 

·        Similarly, Rabbi Shimon ben Tzemach Duran, known as the Rashbatz, explains (in his work Magen Avot) that, just as desserts aren’t a meal on their own but are eaten in conjunction with other food, so too gematriya’ot cannot be expounded in a vacuum. One must already know the point to be true and then one can support it with a gematriyah. He gives several examples of this:

o  The sages already knew, based on a tradition, that there are 39 forbidden types of labor on Shabbat. To support this, they used the gematriyah of אֵלֶּה הַדְּבָרִים [8] which totals 39.^[9] (אלה is 36, דברים is another two [since it is plural] while the letter ה adds one more.)

o  The sages had a tradition that the basic duration of a Nazirite vow is 30 days. So they used the word יִהְיֶה (from the verse קָדֹשׁ יִהְיֶה [10]), which has the gematriyah of 30, as a basis for this.[11]

o  The sages knew that the amount of olive oil needed for the anointing oil – the שֶמֶן הַמִשְׁחָה (a הִֽין - hin[12]) was 12 log. (Each log is the volume of 12 eggs.) So they used the word זֶה (in the verse [13]שֶׁמֶן מִשְׁחַת קֹדֶשׁ יִהְיֶה זֶה לִי לְדֹרֹתֵיכֶם), which has the gematriyah of 12, as a source for this.[14]

Meaning of the Word

·        Some say that the term gematriyah is borrowed from the Greek word geometry.[15]

·        Others say that the Greeks borrowed the word for geometry from the original Hebrew word of gematriyah.[16]

·        Rabbi Yosef Karro writes[17] that the term גימטריא (gematriyah) is made of two words – גיא and מטוריא which means “a valley from a mountain.” This refers to the fact that each letter (referred to as a mountain) has a corresponding number (referred to as a valley).

In the Chumash

There are many instances in Chumash where our sages interpreted verses in the Chumash using the concept of gemtariyah. Here are several examples:

1)     Eliezer, Servant of Avraham

When Avraham went to war against the four kings, the verse says that he took 318 men with him.[18] Our sages say[19] that he only took his faithful servant Eliezer with him, the gematriyah of whose name (אליעזר ) is 318.

2)     Im Lavan Garti

Ya’akov sent a message to Eisav that he had lived with Lavan (עִם לָבָן גַּרְתִּי).[20]According to our sages[21] he was alluding to the fact that he had observed the 613 mitzvot even while living with Lavan since גַּרְתִּי has the gematriyah of 613.

3)     210 Years in Egypt

When Yakov asked his sons to go to Egypt and buy food, he used the word רְדוּ (descend). Our sages point out that this word has the gematriyah of 210 and that Yakov was alluding to the 210 years that the Jews would remain in the Egyptian exile.[22]

4)     Tzitzit

The Torah says that by seeing the Tzitzit, we will be reminded of the mitzvot of G-d.[23] Our sages explain[24] that the Tzitzit remind us of the 613 mitzvot since the gematriyah of Tzitzit (צִיצִית) is 600 and by adding the five knots and eight stings that are on each corner, the total is 613 (which the total number of mitzvot given to the Jewish people).

In the Talmud

The Talmud uses gematriyah on various occasions to derive teachings. Here are a few examples:

1)     Yayin = Sod

The Talmud points out[25] that יַיִן (wine) has the same gematriyah as סוֹד (secret) since both equal 70. This is because when “wine enters (the body), the secrets come out.”

2)     Haman’s Money Brought about his Hanging

The word הַכֶּסֶף (the money),[26] referring to the money Haman offered Achashverosh to annihilate the Jewish people (G-d forbid), has the same gematriyah (165) as the word הָעֵץ (the tree)[27] which refers to the tree upon which Haman was hung.[28]

3)     Tzo’ar Was 51 Years Old

The Talmud[29] derives from the gematriyah of the word נָא (please) which was said by Lot concerning the angels sparing the city of Tzo’ar[30] that this city was 51 years old at that time.

4)     852 Years Is a Short Yime for the Almighty

The Talmud says[31] that the word וְנוֹשַׁנְתֶּם (and you shall have remained long)[32]indicates that the Jewish people were supposed to go into exile after 852 years of being in Israel. This is based on the gematriyah of וְנוֹשַׁנְתֶּם which is 852. Since the verse describes this exile as coming quickly, the Talmud derives from this verse that 852 years is a quick time for G-d.

Halachot We Learn from Gematriyah

There are various halachot (laws) that are derived from gematriyah. Here are some of them:

1)     Get Is 12 Lines

Tosfot says[33] that a get (bill of Jewish divorce) should have 12 lines. This is based on the gematriyah of the word גֵּט, which is 12.

2)     15 “Vav”s

If one is praying shacharit (morning prayers) without a minyan, he will be missing three words to complete the 248 words in the Shema which correspond to one’s 248 limbs. (When praying with a minyan, the chazzan repeats the last three words on behalf of the congregation.) One of the ways to make up for this is to concentrate on the 15 “vav’s” in the next paragraph (veyatziv). The gematriyah of these “vav”s is 90 which equals three time the name of Havayah. (That name equals 26 plus one for each of the four letters, equals 30.)[34]

3)     How Drunk on Purim?

According to the Talmud,[35] one is supposed to get drunk on Purim so that they can’t distinguish between   ברוך מרדכי (blessed is Mordechai) and ארור המן (cursed is Haman). The commentaries explain[36] that this means that one should drink to the point that one cannot calculate that the gematriyah of both of these phrases is the same – 502.    

4)     Salting Meat

The halacha states[37] that after salting meat to remove its salt, one should leave the salt on it for at least as long as it takes to walk one mil (approximately a kilometer or 18 minutes). The commentaries say[38] that the verse בַּמֶּלַח תִּמְלָח (You shall salt it in salt),[39] alludes to this as the gematriyah of בַּמֶּלַח (in salt) is the same as מיל mil (80).

Rabbi Yochanan ben Zakai 

The Talmud says[40] that Rabbi Yochanan ben Zakai was an expert in gematriyah (among many other things).

Includes At Bash and Notrikon

Rashi writes[41] that the term gematriyah includes the idea of switching the first and last letters of the alphabet (known as א"ת ב"ש - at bash) as mentioned above. The Rashbam writes[42] that it also includes the concept of nutrikon (that a word can be an acronym for many words). One example of this is that the first word of the Asseret HaDibrot, אנכי ("I"), stands for אנא נפשי כתבית יהבית (“I have given Myself over in my written word [the Torah]).[43]

Types of Gematriyah

In addition to the standard gemtriyah system in which each Hebrew letter has a numerical value, there are many other methods of gemtariyah that can be used.[44]Here are some of them:

1)     Mispar Kattan

The way this system works is that the zero is dropped from every number. So that the letter yud is 1 instead of 10, chof is 2 instead of 20 and so on.

2)     Im HaMiluy 

Another system involves counting the way a letter is spelled out when figuring out it’s gematriyah. For example, the letter א is spelled אלף. So, when counting those extra letters, the gematriyah is 111. In Hebrew this is called עם המילוי – (with the filling).

3)     Im HaKolel (plus one)

In addition to counting the numerical value of each letter, one can add one for the phrase and/or one for each word in the phrase.

4)     Gematriyah of Vowels 

Various sources say[45] that vowels also have a numerical value. Specifically, the vowels are made of either line, dots or both. (A patach is a line, a chirik is a dot while a komatz is a line and a dot.) In this system, each dot has the value of 10 (like the letter yud) while each line has the value of 6 (like the letter vav). So, a patach has the value of 6, a chirik has the value of 10 while a komatz has the value of 16.

5)     Breaking up the Letters

Many of the letters in the Hebrew language are a composite of other letters. For example, the latter alef (א) is made of a vav in the center, with a yud on the top right and a yud on the bottom left.[46] I once heard that, for the purpose of gematriyah one can add up the value of each part of the letter. As such, the gematriyah of an alef would be 26. (If any of my readers know a source for this, please let me know. – A.C.) 

May Hashem reveal the Secrets of the Torah to us!

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[1] Numbers chapter 7

[2] On Numbers 7:19

[3] See Genesis 5:5

[4] See Gen. 6:3 and Rashi

[5] Under this principle, the first and last letter of the Hebrew alphabet are interchangeable as are the second and the second to last, etc. This too is part of the gematriyah system, see below.

[6] 3:18

[7] It is appropriate that Rabbi Eliezer (ben) Chisma spoke about learning mathematics since Horayot 10a states that he was able to calculate how many drops of water there are in the sea.

[8] In Exodus 35:1

[9] Shabbat 70a

[10] Numbers 6:5

[11] Nazir 5a

[12] Exodus 30:24

[13] Ibid, verse 31

[14] Horayot 11b

[15] Tosfot Yom Tov

[16] Hon Ashir by Rabbi Immanuel Hai ben Avraham Ricchi (17th and 18th Century author of the Mishnat Chassidim)

[17] In Klalei HaGemara (a commentary on Halichot Olam by Rabbi Yeshua ben Yosef Halevi of Telemcon, Algeria), Sha’ar 4, chapter 3, ot 29

[18] Gen. 14:14

[19] Nedarim 32a

[20] Gen. 32:5

[21] Rashi

[22] Gen. 42:2 and Rashi

[23] Numbers 15:39

[24] Midrash Tanchuma, quoted in Rashi. See Rashi D.H Shekulah on Shavuot 29a

[25] Eiruvin 65a as explained in Rashi

[26] Esther 3:11

[27] Ibid 7:10

[28] Tosfot D.H. HaKessef on Megillah 13a

[29] Shabbat 10b

[30] Gen. 19:20

[31] Sanhedrin 38a

[32] Deut. 4:25

[33] D.H. Hamevi Get, Gittin 2a. See Even Ha’Ezer 125:20

[34] Shulchan Aruch HaRav 61:4

[35] Megillah 7b

[36] Be’er HaGolah on O.C. 695:2

[37] Yoreh De’ah 69:6

[38] Be’er Heitev of Maharam Tiktin on ibid

[39] Levit. 2:13

[40] Sukkah 28a and Bava Batra 134a

[41] On Sukkah ibid

[42] On Bava Batra ibid

[43] See Shabbat 105a

[44] See Kitvei HaKaballah LiBa’al HaTosfot Yom Tov, mamar 20 who explains the significance of these different sorts of gematriya’ot in a Kabbalistic manner.

[45] See Torah Moshe by the Chatam Sofer, Parshat Ki Tavo, D.H. Velakachta and in many places

[46] See Shulchan Aruch HaRav 36:2. See also Levush, Siman 36

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Wishing you a Shabbat Shalom UMevorach!