Hebrew Numerology: Gematria the Mathematics of the Torah
Numerology - Gematria
The Mathematics of the Torah
introduction
In Hebrew, each letter possesses a numerical value.
home
Gematria is the calculation of the numerical equivalence of
Numerology
letters, words, or phrases, and, on that basis, gaining, insight
- Gematria:
into interrelation of different concepts and exploring the
The
interrelationship between words and ideas.
Mathematics
of the
Here is a basic introduction to Gematria that discusses
Torah
different systems for identifying the numerical equivalence
introduction
of individual letters, how these letters can be calculated
according to the implicit word-value of their names.
Four Ways to
Calculate
The assumption behind this technique is that numerical
numerical
equivalence is not coincidental. Since the world was created
value
through God's "speech," each letter represents a different
filling
creative force. Thus, the numerical equivalence of two
words reveals an internal connection between the creative
examples
potentials of each one. (see Tanya, Sha'ar HaYichud
charts
VeHaEmunah, chapters 1 and 12.)
There are four ways to calculate equivalence of individual
letters:
Absolute Value
Ordinal Value
Reduced Value
Integral Reduced value
The Tikunei Zohar explains that the concept of reduced
value is related to the spiritual world of Yetzirah. On that
basis, a relationship can be established between these four
forms of calculation, the four spiritual realms, and the four
http://www.inner.org/gematria/gematria.htm (1 of 2)31/05/2006 1:15:01
Hebrew Numerology: Gematria the Mathematics of the Torah
letters of God's name:
Letter Calculation Form World
yud Absolute value Atzilut
hei Ordinal value Beriah
vav Reduced value Yetzirah
hei Integral reduced value Asiyah
Next
The material contained on this site has been prepared by gal einai
institute, a United States non-profit organization dedicated to
disseminating and implementing the inner wisdom of the Torah--
Kabbalah and Chassidut--as taken from the teachings of rabbi
yitzchak ginsburgh
©5760-5765 (2000-2005) by Gal Einai Institute, All rights
reserved
http://www.inner.org/gematria/gematria.htm (2 of 2)31/05/2006 1:15:02
Untitled Document
Numerology -
Gematria
The Mathematics of the Torah
calculating the numerical value of a letter
Absolute Value
home
Numerology
Absolute value, (in Hebrew: mispar hechrachi)
- Gematria:
also known as Normative value. Each letter is
The
given the value of its accepted numerical
Mathematics
equivalent alef (the first letter) equals 1, beit (the
of the
second letter) equals 2, and so on. The tenth letter,
Torah
yud is numerically equivalent to 10, and
successive letters equal 20, 30, 40, and so on. The
letter kuf near the end of the alphabet, equals 100;
introduction
and the last letter, tav equals 400.
Four Ways to
Calculate
In this reckoning, the letters chaf sofiet (final
numerical
chaf), mem sofiet, nun sofiet, pei sofiet, and tzadik
value
sofiet which are the "final forms" of the letters
filling
chaf, mem, nun, pei,and tzadik, used when these
letters conclude a word, generally are given the
examples
same numerical equivalent of the standard form of
charts
the letter. However, sometimes the final chaf is
considered equivalent to 500, the final mem to
600, etc. (see chart below).
Following that alternate form of reckoning, the
Hebrew alphabet is a complete cycle. The final
tzadik equals 900 and thus, the alef equals both
one and one thousand. Indeed, in Hebrew the
same spelling is used for the name of the letter
alef, and elef, meaning "one thousand."
Noting this phenomenon, Rabbi Avraham
Abulafia interprets the verse (Deuteronomy
http://www.inner.org/gematria/fourways.htm (1 of 3)31/05/2006 1:15:32
Untitled Document
32:30): "How can one pursue one thousand!" to
mean: One, the first number, follows after one
thousand in a complete and perfect cycle.
ordinal value
Ordinal value (in Hebrew: mispar siduri) Each of
the 22 letters is given an equivalent from one to
twenty-two. For example, alef equals 1, kaf equals
11, taf = 22. The final kaf equals 23, and final
tzadik equal 27.
reduced value
Reduced value (in Hebrew: mispar katan)
(modulus 9 in mathematical terminology). Each
letter is reduced to a figure of one digit. For
example, in this reckoning, alef equals 1, yud
equals 10, kuf equals 100) would all have a
numerical value of 1; beit equals 2, kaf equals 20,
and reish equals 200 would all have a numerical
value of 2, and so on. Thus, the letters have only
nine equivalents, rather than twenty-two.
In both the Ordinal and Reduced reckonings, the
five letters whose form changes when they
conclude a word are generally equivalent to their
value when they appear within a word. However,
they are sometimes given an independent value.
For example, the ordinal value of the final nun is
at times considered 14, and is at times, 25.
Similarly, its reduced value is at times 5, and at
other times, 7.
integral reduced value
The fourth manner of reckoning, Integral Reduced
value (mispar katan mispari). Here, the total
numerical value of a word is reduced to one digit.
Should the sum of these numbers exceed 9, the
integer values of the total are repeatedly added to
each other to produce a single-digit figure. The
http://www.inner.org/gematria/fourways.htm (2 of 3)31/05/2006 1:15:32
Untitled Document
same value will be arrived at regardless of
whether it is the absolute values, the ordinal
values, or the reduced values that are being
counted.
Previous Next
The material contained on this site has been prepared by gal
einai institute, a United States non-profit organization
dedicated to disseminating and implementing the inner
wisdom of the Torah--Kabbalah and Chassidut--as taken from
the teachings of rabbi yitzchak ginsburgh
©5760-5765 (2000-2005) by Gal Einai Institute, All rights
reserved
http://www.inner.org/gematria/fourways.htm (3 of 3)31/05/2006 1:15:32
Hebrew Numerology: Letter Filling
Numerology - Gematria
The Mathematics of the Torah
letter filling
At times, the numerical value of a letter or word is given using another technique known as milui
home
("filling"; pl., miluim). Here, not only are the letters given numerical equivalents, they are
Numerology
considered complete words. In such cases, the letters used to spell out the main letter are
- Gematria:
considered to be "pregnant" within it.
The
Mathematics
For example, the word chen is made up of two letters: chet, nun. The letter chet itself is spelled:
of the
chet, yud, tav equals 418. Nun is spelled: nun, vav, nun equals 106. Thus, the value of chen with
Torah
its milui is 524.
introduction
In this context, we must add that certain letters have more than one possible milui. For example,
the letter hei can be spelled: hei, yud; hei hei; or hei, alef, arriving at equivalents of 6, 10, or 15
Four Ways to
respectively. Similarly, the letter vav can be spelled: vav, yud, vav; vav, alef, vav; or vav, vav, with
Calculate
equivalents of 12, 13, and 22 respectively.
numerical
value
It must be emphasized that these different calculations are not mere mathematical exercises.
filling
Rather each different numerical equivalent represents a different aspect of Divine influence.
examples
The most classic use of these alternate miluim is with regard to Divine Name Havayah (spelled:
charts
yud, hei, vav, hei). The gematria of the letters themselves is 26. However, with the milui, different
figures are reached dependent on how the vav and hei are spelled.
Following are the principal miluim of the Name Havayah discussed in Kabbalah:
Havayah of 72 Havayah of 63 Havayah of 45 Havayah of 52
yud yud, vav, dalet =20 yud, vav, dalet =20 yud, vav, dalet =20 yud, vav, dalet =20
hei hei, yud =15 hei, yud =15 hei, alef =6 hei, hei =10
vav vav, yud, vav =22 vav, alef, vav =13 vav, alef, vav =13 vav, vav =12
hei hei, yud =15 hei, yud =15 hei, alef =6 hei, hei =10
total milui =72 total milui =63 total milui =45 total milui =52
These four sums, 72, 63, 45, 52, correspond themselves to the four letters of God's name Havayah
(and the ten sefirot) as follows:
Letter of Havayah Havayah of: The Ten Sefirot
yud 72 Chochmah Insight, wisdom
hei 63 Binah Understanding
vav 45 chesed to Yesod The Emotional Attributes
hei 52 malchut Kingship
Each of the letters hei, vav, hei of the Name Havayah possesses three variant spellings. Thus,
there are 27 (3 to the 3rd) possible miluim of Holy Name. There are thirteen possible numerical
equivalents ranging from 44 to 72, with a midpoint of 58 (= chen). When added together, the total
of all the miluim is 1521, which equals 39 squared. Thirty-nine is the numerical equivalent of
Hashem Echad ("God is One").
http://www.inner.org/gematria/gemfull.htm (1 of 2)31/05/2006 1:15:44
Hebrew Numerology: Letter Filling
The four forms of the Name Havayah cited above are considered to be the most essential forms
and each correspond to a different letter of God's name, as above. When their sum, 232, is divided
by four, the number 58 (= chen) is again reached. Similarly, 232 is numerically equivalent to yehi
or ("Let there be light"), the first of the utterances of Creation.
Previous Next
The material contained on this site has been prepared by gal einai institute, a United
States non-profit organization dedicated to disseminating and implementing the inner
wisdom of the Torah--Kabbalah and Chassidut--as taken from the teachings of rabbi
yitzchak ginsburgh
©5760-5765 (2000-2005) by Gal Einai Institute, All rights reserved
http://www.inner.org/gematria/gemfull.htm (2 of 2)31/05/2006 1:15:44
Hebrew Numerology: Examples
Numerology -
Gematria
The Mathematics of the Torah
examples
home
Numerology
The Hebrew word, chesed ("lovingkindness")
- Gematria:
(spelled: chet, samech, dalet) has three letters.
The
The absolute or normative value of chet is 8,
Mathematics
that of samech is 60, and that of dalet is 4. The
of the
sum of these three figures is 72. Thus, the integral
Torah
reduced value is nine.
introduction
Similarly, the ordinal value of chet is 8, that of
samech is 15, and that of dalet is 4. The sum of
Four Ways to
these three figures is 27. Thus, the integral
Calculate
reduced value is again nine.
numerical
value
Finally, the reduced value of chet is 8, that
filling
of samech is 6 and that of dalet is 4. The sum of
these three figures is 18. Again, integral reduced
examples
value is nine.
charts
Another example: the word chen,
"grace," (spelled: chet, nun) is often used as an
appellation for the Kabbalah. Its absolute value is
58 (chet equals 8, nun equals 50), or 708
when nun is given an independent value of 700.
Its ordinal value is 22 (chet equals 8, nun equals
14), according to the normal reckoning, or 33
when the nun is assigned a value of 25.
Its reduced value is 13 (chet equals 8, nun equals
5), or 15 if the nun is assigned an independent
http://www.inner.org/gematria/gemexamp.htm (1 of 2)31/05/2006 1:15:52
Hebrew Numerology: Examples
value.
Its integral reduced value is 4 or 6.
Previous Next
The material contained on this site has been prepared by gal
einai institute, a United States non-profit organization
dedicated to disseminating and implementing the inner
wisdom of the Torah--Kabbalah and Chassidut--as taken from
the teachings of rabbi yitzchak ginsburgh
©5760-5765 (2000-2005) by Gal Einai Institute, All rights
reserved
http://www.inner.org/gematria/gemexamp.htm (2 of 2)31/05/2006 1:15:52