גימטריאות Gematriot
The Midrash Tanaim (to the Baraita of the Thirty-two Methods of Rabbi Eliezer the son of Rabbi Yossi HaGelili), mentions a number of keys or ways of assigning each letter of the Hebrew alphabet to a number. The purpose is to capture the spiritual association between words that have the same gematria. The gematria equivalence relation can give deeper insight into the spiritual connection between the words whose gematria is the same. The use of gematria can expand our awareness of the relatedness of different ideas or concepts as they are spelled out in Hebrew. Gematria can help us understand meanings which are hidden. However, gematria equivalence between words suggesting an association which is not in accordance with Jewish tradition or which is not in accordance with Torah are not considered to be valid.
Gematriot is the plural of Gematria. Why is the subject called Gematriot? Because there are multiple techniques of gematria. We list here a few of the most common ones.
Two good references on gematriot are the books by Rabbi Glazerson, Rabbi Dovid Leitner. The book by Earl David makes a comprehensive use of some of the techniques of gematria in interpreting the different sections of the Torah.
- Matityahu Glazerson, Through the Lens of Gematria, Raz-Ot Lev Eliyahu, Jerusalem, 2007
- Dovid Leitner, Understanding the Alef-Beis, Feldheim, New York, 2007
- Earl Avraham David, Code of the Heart, Mazal and Bracha Inc., New York, 2004
גימטריא Gematria Values
The gematria value of a word is the sum of the gematria values of the letters of the word. There are two conventions for the final letters. In one convention, the one shown in the table below, the five Hebrew final letters are given gematria values of 500 through 900, respectively. By this convention the gematria value of ך is 500. In the other convention, a final letter takes the gematria value of its corresponding non-final letter. So by this convention, the gematria value for the letter ך is 20 since it is the final form of the letter כ.One of the important constants in mathematics is Π, pi. It relates the diameter of a circle to its circumference. As every grade school child knows, the relationship governing the circumference C of a circle with its diameter D is C=ΠD.
It is interesting, therefore, that the sum of the inverse gematria values of the 27 Hebrew letters totals 3.1401548 about .046 % smaller than 3.141592653589, which is Π, pi, accurate to 12 decimal places.
3.1401548=1/1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+
1/10+1/20+1/30+1/40+1/50+1/60+1/70+1/80+1/90+
1/100+1/200+1/300+1/400+1/500+1/600+1/700+1/800+1/900
To represent thousands, the letters used to represent the ones are used. So א, which is spelled as אלף, and is pronounced alef has the same spelling as elef, which means 1000. In a similar manner, ב represents 2000. If we sum the inverse gematria values of the 27 letters and then include then next two letters as thousands the resulting sum is more than 3.141592653589 by about .0019777 %.
3.1416548=1/1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+
1/10+1/20+1/30+1/40+1/50+1/60+1/70+1/80+1/90+
1/100+1/200+1/300+1/400+1/500+1/600+1/700+1/800+1/900+
1/1000+1/2000
| Hundreds | Tens | Ones |
|---|---|---|
| 100 = ק | 10 = י | 1 = א |
| 200 = ר | 20 = כ | 2 = ב |
| 300 = ש | 30 = ל | 3 = ג |
| 400 = ת | 40 = מ | 4 = ד |
| 500 = ך | 50 = נ | 5 = ה |
| 600 = ם | 60 = ס | 6 = ו |
| 700 = ן | 70 = ע | 7 = ז |
| 800 = ף | 80 = פ | 8 = ח |
| 900 = ץ | 90 = צ | 9 = ט |
The relationship between words or phrases that have the same gematria is one of the ways of expounding Torah. The source for this is found in the verse Deuteronomy 32:47.
It is not an empty thing from you, for this is your life. כי לא דבר רק הוא מכם כי הוא חייכם.
Rabbi Jacob Ben Asher commonly known as The Baal HaTurim and Rabbi Aharon Rokeach, commonly known as the Rokeach, both point out that the numerical value of the first part of the verse כי לא דבר רק הוא מכם is 679. The gematria of Gematriot, גימטריאות, the plural of gematria, is also 679.
For another example of how gematria works, consider the verse Genesis 49:10.
The scepter shall not depart from Judah nor a scholar from between his feet (among his descendants) until Shilo shall arrive and his will shall be an assemblage of nations.
.לא יסור שבט מיהידה ומחקק מבין רגליו עד כי יבא שילה ולו יקהת עמים
Both Rashi and Onkelos interpret the phrase until Shilo shall arrive as meaning until the Messiah comes to whom the kingodm belongs. The Sages have taught that this verse is a primary Torah source for the belief that the Messiah will come.
The gematria of the phrase יבא שילה, Shilo shall arrive, is 358. The Hebrew word for Messiah is משיח which also has gematria 358.
What does this gematria equivalence mean? The Sages tell us that there is no superfluous word in Torah. Every word and every letter has meaning. The first part of the verse כי לא דבר רק הוא מכם uses the word דבר which was translated as thing. But דבר also means word. Thus כי לא דבר רק הוא מכם literally means for there are no empty words from you. From your mouth should come no empty words of Torah. Every letter has meaning. Go study it. Words which have the same gematria will give you hints about the fullness of Torah.
Another example of gematrai equivalence is the gematria of the tetragrammaton, the great eternal name of God, יהוה, which has gematria 26. The gematria of each of the words love, אהבה, and one, אחד is 13. Together the gematria of the two words totals 26, the gematria of the tetragrammaton. This gematria equivalence reinforces that two of the principal attributes of God are that He is one and He is loving.
The verse of Genesis 28:10 tells us
And Jacob departed from Beersheva and went toward Haran. .ויצא יעקב מבאר שבע וילך חרנה
He had lived with his family for about 63 years and having to leave was hard for him. The gematria of ויצא יעקב, And Jacob Departed is 289 which is the same gematria as טרף meaning torn apart . Jacob was torn apart having to leave his family
The Hebrew word for world is עולם. In Psalm 105:4 King David says Seek His Presence. The word for presence, literally his face is פניו. Both עולם and פניו have gematria 146. There is a very deep truth that the world shows the face of God, in the sense of the Glory of God. But to have a sense of this we must look deeper than with our eyes. For the word for world עולם comes from the root עלם, which means hidden.
Milui מילוי
Each letter of the Hebrew alphabet has a name and the name has a spelling. Many of the letters have two spellings and a few have three different spellings. For example, one spelling of the letter א is אלף. The milui (full form) of a word is obtained by writing out the spellings of the letters in that word. For example, one form for the milui of the word משה is מם שין הא. The gematria value of this milui is 446 which equals the numerical value of האמת, the truth. By this correspondence, Moshe is the truth.
Some of the names of the letters can be spelled several different ways. The following table shows all the various possibilities.
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Small Gematria גימטריא קטנה
The small gematria is computed by adding together the digits of the regular gematria. If the result is greater than 9 then add together those digits and so on until the sum is 9 or less. For example the Hebrew word for Israel is ישראל is 10+300+200+1+30=541. Adding together the digits 5+4+1=10, which is greater than 9; So add together 1+0=1. The small gematria of ישראל is then 1.
The first word in Genesis is בראשית, meaning in the beginning or with a beginning. Its gematria is 913, which makes its small gematria 4. The word one, אחד has gematria 13, which makes its small gematria 4. From this we get the hint that every beginning has an inherent oneness within which in fact is the oneness of בראשית. If we are not cognizant of this oneness and all we are conscious of is diversity, manyfoldness, then we will not have a sense of the glory of God in our encounters which in fact are all beginnings.
There are an interesting set of words relating to the Sabbath, the seventh day of the week. These words have small gematria of 7. The Sabbath begins with the lighting of the candles. Candle is נר, whose gematria is 250. Its small gematria is 7. We greet our friends with Shabbat Shalom, שבת שלום, whose gematria is 1078. Its small gematria is 7. Then there is the Kiddush over wine, יין, which has gematria 70 and small gematria 7. Grape juice can be used as well as wine. The word meaning grape vine is גפן. It has gematria 133 and small gematria 7. Next there is the blessing over challah, חלה whose gematria is 43. Its small gematria is 7. After the challah we eat fish, דג, whose gematria and small gematria is 7. After fish we eat soup, מרק, whose gematria is 340. Its small gematria is 7. After the fish we eat meat, בשר, whose gematria is 502. Its small gematria is 7.
The gematria of Torah, תורה is 611. Its small gematria is 8. The gematria of the Tetragrammaton, יהוה is 26. Its small gematria is 8. The gematria of name of God indicating that He controls the world is שדי is 314. Its small gematria is 8. The gematria of the word good , טוב is 17. Its small gematria is 8.
The mathematically inclined will recognize that the small gematria is in fact a way of computing a number modulo 9. If N is an integer, and N is written as N=M*9+G, where 0 ≤ G ≤ 8, then N modulo 9 is G. If G > 0, then G is the small gematria of N. If G=0, the small gematria is 9.
Rabbi Jonathan Eybeshutz pointed out what he considered to be a remarkable relationship between the gematria of a hebrew letter, its small gematria and multiples of nine. Take the gematria of any Hebrew letter and subtract its small gematria from it. The result is always a multiple of 9. For example the gematria of the Hebrew letter א can be obtained from its spelling אלף. The gematria is 111. The small gematria is 3. Take away 3 from 111 and obtain 108=12*9. This relationship, however, is one that derives from the numbers in their decimal representation and will work with any integer number, not just the gematria of Hebrew letters.
The small gematria is also called Mispar Katan, מספר קתן and is related to the method of casting out nines, which of course is related to the number modulo 9.
Triangular Gematria מספר הקדמי
The triangular gematria of any letter is the sum of all the numbers up to and including the letter's numerical value. For example the letter ה has a gematria of 5. The triangular gematria is 1+2+3+4+5 = 15. In general, the triangular value of the number N is N*(N+1)/2.
The first verse in Genesis is
בראשית ברא אלהים את השמים ואת הארץ
Its gematria is 2701, which is the triangular gematria of the word חכמה, wisdom, whose gematria is 73: 73*74/2=2701. This hints to us that creation was done with wisdom.
Square Gematria מספר מרובע
The square gematria of a word is the sum of the squares of the gematria of its letters. For example the square gematria of the tetragrammaton יהוה is 10*10+5*5+6*6+5*5=186. The gematria of the word מקום, place, is also 186. מקום is the space and the place where the Shechinah rests. This is from the verse Exodus 33:21 where God is speaking to Moses.
Behold! there is a place (מקום) near Me. You may stand on the rock.
Also there is the verse of Deuteronomy 17:8
And you shall rise and ascend to the place that Hashem your God shall choose
This place was in fact the Temple. And the Temple is where the Shechinah rested.