One of the main focuses in modern computer science is information processing and management. Gathering and retrieving relevant information is probably the most significant point of outset in almost any project that the modern professional or layman may undertake and it becomes imperative that the retrieval process quickly and efficiently find accurate sources that precisely serve his purposes. To this end there are many information management theories currently available.
The prophets have already promised that in the future there will come an era of peace on earth in which all nations will speak one language. In Hebrew the term the prophet uses is sapha berura, a clear language. Language is something far broader than mere words. As we can see from the term “body language,” the actions we perform and the way we move our hands is all a form of communication. In the future all the nations of the earth will speak, think and act out one clear, rectified language. Clearly, this language is the Hebrew language, which we are taught in the Torah and in Kabbalah is the language that God used to create the world. Unlike other languages, Hebrew, the ancient and holy language of the Bible, is the only completely logically structured language and it therefore presents us with an ideal model for organizing information and meaning.
Lights in Vessels
There are 22 letters to the Hebrew language. Although this is not the place to discuss all of the reasons why the number 22 is significant in itself, we will demonstrate here one connection between the number twenty-two in relationship to the universally accepted decimal system of counting.
One of the most basic relationships between the ten sefirot and the twenty-two letters can be observed very simply in the relationship between the area and the perimeter of a 1×10 rectangle, which are 10 and 22 respectively. We will later explore the general algorithm of this phenomenon [2(n+1)] in further detail. As a body is to a soul, so the twenty-two letters of the Hebrew alphabet are the relatively material vessels (the perimeter; the confining limit) that contain the spiritual lights of the ten sefirot (the area; the content of the rectangle).
Gates and Roots
None of the twenty-two letters of the Hebrew language bears any significant linguistic meaning when standing on its own. In order to generate meaningful units of language in Hebrew there must be a minimum of two letters together. One of the beauties of the Hebrew language is that all of the roots of all verbs and nouns are derived from two-letter units that are usually assembled as part of a three letter root.
In Kabbalah the two letter units are called sha’arim, gates, since if one would perceive each of the letters of the unit as a pillar on each side of a gateway, one can pass through the gateway from either direction, thus obtaining two different permutations of the two-letter units from one gate. These two-letter units are sub-roots, each sub-root being a gateway to meaning and understanding. We are taught in Kabbalah that there are 231 gates. This can be calculated mathematically: since there are 22 letters we take one of the 22 and match it with each of the 21 remaining letters which results in the number 462. This gives us all the possible permutations of two-letter units including both permutations of the same sha’ar, gate. In order to arrive at the exact number of sha’arim, we must divide the result by the number of permutations available for the same two letters (2!) by which we arrive at the number 231.
|The number of gatesin the Hebrew language:|
|22 x 212!||=||4622||=||231|
Developing from the two-letter sub-roots, we arrive at the three-letter roots, shorashim, in Hebrew. In a similar way to the sub-roots that have two permutations to each sha’ar, so each three-letter root has six (3!) permutations. We can thus calculate the number of possible three-letter roots in the Hebrew language:
|The number of rootsin the Hebrew language:|
|22 x 21 x 203!||=||3,0806||=||1,540|
Another quality unique to the Hebrew language is that each of the twenty-two letters bears a numerical value, by which the numerical value of any given word can be calculated. One of the seven disciplines of Torah study mentioned in the Zohar, is gematria, the study of the numerical value of words, and the sages often base their interpretations of meaning on the numerical value of words, letters or even complete phrases.
For illustrational purposes, interpreting the name Yisrael, Israel (the name of the Jewish people; our land of Israel; the Torah which is called the Torah of Israel; and even God Himself who is called the God of Israel), by means of its numerical value, especially highlights the beauty unique to our language, as we shall explain.
Kabbalah teaches us that one of the readings of the word Yisrael is yesh-rala, which simply means “there are 231 [gates].” However, a second way of interpreting the word Yisrael is by using the numerical value of 1,000 for the alef, the numerical value of the word Yisrael becomes 1,540 – exactly the number of three-letter roots derived from the 22 letters of the Hebrew alphabet. We can therefore see how the Hebrew language is an essential part of everything Jewish, including God Himself.
Triangles and Tetrahedrons
Besides their significance in the Hebrew language, mathematically speaking these two numbers (231 and 1,540) are also very significant numbers. The most basic geometric form is a triangle, even more basic than a square, since a square can be divided into two triangles. The fact that the triangle is the basic shape is apparent throughout nature, especially in crystallography and other natural sciences. The formula for a triangular number is △n=n(n+1)/2. When n=21 this formula renders an equation that is identical to the one we used to calculate the number of gates and it generates a sum of 231. The number of gates produced from the 22 letters is therefore equal to the sum of all numbers from 1-21.
Although the number 231 can be expected to be a triangular number, considering the way that it was generated in this case, more surprising is that 1,540 is also a triangular number – a triangular number being a relatively rare phenomenon – the triangle of 55 (△55). However, amazingly, this number is also the tetrahedron of 20 ( #.20), that is, the sum of all triangular numbers from △1 to △20. Physically, this is a three dimensional construction created by arranging each triangle one above the other from the largest to the smallest. It is an extremely rare phenomenon to find a tetrahedron that is also a triangular number, but 1,540 is one of these unique numbers, as displayed in the following series:
|The series of triangular numbersthat are also tetrahedrons|
|1, 10, 120, 1,540…|
There are three simple Hebrew words that denote this phenomenon of simultaneously being a 2 dimensional triangle and a 3 dimensional tetrahedron. For the number 10 the word is gad, the name of one of the twelve tribes. Gad is composed of the two letters gimel and dalet, with respective numerical values of 3 and 4. Regarding the number 10, this represents the fact that 10 is equal to △4 and #.3. Similarly, the word which alludes to the number 120 is chayah, which has a variety of meanings: Chayah is the name that the first woman, Eve, would have been given had she not sinned and also the name by which she will be called in the future when the primordial sin is rectified. Chayah also means, “a living being;” it is also one of the names of the angels, as seen in the vision of the chariot of Ezekiel; and the most important meaning of chayah in Kabbalah is the second highest of the five levels of the soul. Chayah is spelled with the letters chet, yud and hei, with respective numerical values of 8, 10 and 5, alluding to the number 120 which is △8 and #.15. The word relating to the number of roots in the Hebrew language is the word kohen, priest, spelled kaf, hei, nun, with respective numerical values of 20, 5 and 50, alluding to the fact that 1,540 = △20 = #.55. However, as we mentioned previously, 1,540 is one of the possible numerical values of the word yisrael, the non-priest, so we can see here a mathematical allusion to the close relationship between the two.
Within the context of the sha’arim and the three-lettered shorashim, we will note here another beautiful mathematical phenomenon that proves the harmony between the two. Since 1,540 is #.20, if one adds the next triangular number (△21) to the tetrahedron one has raised the tetrahedron by one level, producing #.21. Remember though, △21 is 231, the number of sha’arim in the Hebrew language, as mentioned!
A Simple, Double, Triple and Quadruple Song
As mentioned previously, there is a mathematical relationship between 10 and 22. The most important algorithm which appears in Kabbalah and the Torah is 2(n +1). Applying this algorithm when n=1 generates 2(1+1)=4. If we then continue to apply this algorithm to the result: n=4, 2(4+1)=10; n=10, 2(10+1)=22. We have thus generated the following series of numbers:
1, 4, 10, 22…
These first four numbers share the basic system of development of n2 = 2(n1 + 1). As we mentioned before, the relationship between 10 and 22 is the ten sefirot or lights and the 22 letters of the Hebrew language, which are the ten “soul” elements and the 22 relatively “body” elements of creation. However, if we consider the numbers that precede these two – 1 and 4 – we will realize that the number 4 is the triangular “root” of 10. This alludes to the “simple, double, triple and quadruple song,” which corresponds to the internal division of the 10 sefirot into four groups, as shown:
In the soul, or in the sefirot, the simple song refers to the superconscious crown. The double song refers to the two basic intellectual faculties, wisdom and understanding, referred to as the father and mother figures respectively. The triple song refers to the three emotive powers of the soul which are lovingkindness, awe and compassion. The quadruple song refers to the four emotions which manifest themselves in action.
Thus the number 4 is an even more basic model of creation than the number 10. Indeed, God’s ineffable Name, is composed of four letters. The Tetragrammaton, God’s unique and essential Name, which literally means “the four-lettered Name,” precedes the ten lights. Even in English this is not an arbitrary name because it is derived from the Talmudic idiom for God’s essential Name used by the sages themselves: shem ben dalet. This means that there is something special about the fact that it has four letters, otherwise it would not be referred to as the four-lettered Name.
Although the number 4 indeed precedes the number 10, however, God is One – 1 precedes everything, one is the beginning or God’s absolute and essential Unity. So the very fact that this algorithm generates 4 from1 and 10 from 4 and 22 from 10, producing three very significant numbers, proves that it is a very essential and important algorithm, and it provides us with the relationship between 10 and 22.
More About 2(n + 1)
Although there are generally only ten sefirot counted, an eleventh sefirah is often included – this is the sefirah of da’at, knowledge, which is the reflection in the consciousness of the superconscious crown and is often included with chochmah, wisdom and binah, understanding as a third intellectual faculty. The source of da’at comes from a point that transcends the division of the two levels of reality, the intellect and the emotions, bridging between the two extremes and connecting them. The algorithm
2(n + 1) can also be written: 2n + 2, however, writing it as 2(n + 1) is more relevant to our purposes, since n + 1 implies that one of the sefirot appears at two different levels; at the level of the surperconscious, the simple song, and in the conscious itself which in the soul is da’at, knowledge or unification. Da’at is not an intellectual power or faculty in its own right, it is the power to concentrate one’s mind in order to arouse emotion in one’s heart: a bridge between intellect and emotion.
We have now eleven sefirot, however each of the eleven possesses an inner and an outer dimension to it, which brings us directly to the completion of our algorithm:
2(n + 1). We have thus developed from n to n + 1 and then to 2(n + 1) since each of the
n + 1 sefirot has two dimensions to it. In our case, when n = 10, n + 1 = 11 and
2(n + 1) = 22.
An Ancient Logical Array
The original source for the concept of the 231 gates of the Hebrew language is sefer yetzira, Book of Formation. Since the gates initiate meaningful units of language, for the purposes of computer science logic it would be convenient if these 231 gates were organized in a logical system. This is exactly what sefer yetzira, an ancient text, attributed to our forefather Abraham, actually does, arranging the 231 gates in a square array, in which each column and each line corresponds to one of the eleven supernal sefirot. One of the axes incorporates both facets to it, the inner dimension and the outer dimension, as mentioned, generating a complete array of 22 x 11 (242 possible pairs), however eleven of these pairs appear twice in the array (these duplicates appear in a bold typeface), as we shall explain, reducing the number of differing pairs to 231. These duplicate pairs are also unique in that they make up the most basic alphabet transformation called albam (אלבם ).