The Hebrew Language:
An Ideal Model for Information Processing and Management
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 1x10 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.
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 :
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:
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
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:
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 ).
The 22 letters are written in order and divided into two segments, each time with the split between two different letters. For the first line (1A) they are divided after the first letter (alef), one letter on the right and 21 letters on the left. For the second line (1B) after the second letter (bet), two letters on the right and 20 on the left, and so on. Then the letters in each segment are paired, the first with the last, second with second to last, and so on. This is called reflective pairing. If the segments have an odd number of letters, the remaining letters in (the middle) of each segment are paired with one another.
We will use the first line (1A) to demonstrate this process:
א | ב ג ד ה ו ז ח ט י כ ל מ נ ס ע פ צ ק ר ש ת
Since א is alone in its segment and has no pair, it "waits." Now the letters in the left segment are paired reflectively, generating the pairs: כמ, ינ, טס, חע, זפ, וצ, הק, דר, גש, בת . The ל is left over in the right segment, so it is paired with the א . Thus we have 10 pairings and a duplicate pair (אל , which also appears regularly in the location 6B1).
This system of pairing is called reflective pairing. This is just one of many transformation systems of the Hebrew letters that are used, not only in kabbalistic texts, but in the Talmud as well. Even in the Bible we find examples word transformation that use these systems. The most important system, found explicitly in Biblical usage is the atbash system, as in occasions when the prophet calls bavel, Babelonia, shishakh. The atbash system is the basic reflective system by which the first letter is transformed into the last letter, the second letter into the second last letter and so forth. Since there it contains an even number of letters, the Hebrew alefbet can be split into two equal halves, pairs can then be generated either reflectively or by parallel pairing.
the atbash system
א ב ג ד ה ו ז ח ט י כ
ת ש ר ק צ פ ע ס נ מ ל
the albam system
א ב ג ד ה ו ז ח ט י כ
ל מ נ ס ע פ צ ק ר ש ת
In Kabbalah, the albam transformation is called the straight transformation because it pairs the letters of each half in a parallel fashion, whereas the atbash transformation pairs the letters of each half reflectively. In the later kabbalistic texts, for instance the Arizal, the most important alef-bet transformation is albam, and this is the alef-bet that appears twice in the array of 22 alphabets shown above, woven into the array like a golden thread. The bottom line in this array is the atbash alef-bet which is the most basic reflective alef-bet.
Having constructed this array, we can deduce the kernel meaning of each two-letter unit by analyzing its position in the array. In theory, one could create a perfect lexicon of etymology of the Hebrew language by analyzing the position in the array of each two-letter unit. One could then go on to apply this to other languages, since according to Abulafia, one of the great medieval kabbalists, the seventy languages of the nations on earth all derive in some way from the Hebrew language. This would give us insight into the kernel ideas of all words in every language.
Beginning with a Clear Example
In order to illustrate this idea, we will now analyze in short the first word of the Torah, bereishit, which means "In the beginning."
ב ר א ש י ת
The word bereishit has three root letters (ראש ) and three additional letters: a one-letter prefix (ב ) and a two-letter suffix (ית ). The three root letters spell the word rosh, head or beginning. However, in kabbalah, every letter and every combination of letters is analyzed and understood in its own right. The first two letter unit that begins the whole Torah and the whole creative process is therefore בר . The second two letters are אש , which means fire and the two suffix letters (ית ) are also considered as a third unit on their own.
The sha'ar בר appears at 11A2 in the array, however, the first unit in that array is אש , the sha'ar that follows בר in the same word. We thus immediately see that this particular alef-bet has great significance regarding the beginning of creation. The split in the alef-bet here is between the shin and the tav. The only alef-bet to follow this is the "invisible split," i.e. placing the line of the split after the final letter of the alef-bet, the tav, which generatres the atbash alef-bet (11B), mentioned previously.
Our aim is to arrive at the kernel meaning of the sha'arim, the first of which appears in the Torah is בר . If we examine the position of this shaar, we see that it is the inner wisdom within kingdom (see legend), this can be stated otherwise as the experience of selflessness, the inner dimension of wisdom, within lowliness, the inner dimension of kingdom. In terms of archetypal soul-roots this is Moses, who stated in complete annulment of self, "and what are we," in King David, who wrote in Psalms, "I am always lowly in my eyes. Although these two attributes may seem similar, selflessness is annulment of self-consciousness, having no sense of ego, whereas lowliness is a feeling of humility and a complete lack of arrogance, of existing very far and removed from God so much so that any successes achieved are attributed to God Himself who gave me the power to succeed. Each of the attributes of the sefirot possesses the property of inter-inclusion, which is a hologram-type phenomenon in which each sefirah is present in all the others.
Thus God began the creation with בר , with wisdom within kingdom. This is upheld by the Aramaic translation of the word bereishit, which is "With wisdom God created..." Another illustration of this point is the fact that the only other context in which the word bereishit appears in the Bible is in reference to the beginning of the kingdom of one of the kings. The word reishit also appears in Psalms together with the word wisdom in the verse, "the beginning of wisdom is fear of God." We can thus see that these two first letters are wisdom together with kingdom, and the creation was achieved through God's wisdom, as the verse states, "You have made all with wisdom," which the Zohar translates as kulam bechochmah itberiru, "All was clarified through wisdom." The word itberiru is itself a conjugate of the sha'ar bar, therefore bringing us closer to the kernel meaning of this sha'ar, which is clarification. The function of wisdom is to clarify reality, however in its original manifestation in the essence of the mind it is not capable of becoming involved in clarifying reality – only when wisdom is expressed through the prism of kingdom can it become an active clarifying force in creation. In fact one could say that if one had perfect clarity one would be able to create things ex-nihilo. The fact that we cannot create is because reality is dim and dull; light and darkness are mixed up together in all of life's phenomena, preventing us from differentiating and distinguishing between various phenomena in the world. As such we are not able to truly manifest and fulfill the potential that we have. God created us in His image in order to emulate Him and to create. Every soul is a part of God and has the potential to carry out its true function, to have a creative effect upon reality. In particular this is the special function of the Jewish People – to emulate God and to create light. The ability to create is simply a function of true clarity and this is the kernel meaning of the two first letters of the Torah בר .
Having arrived at the kernel meaning of a two-lettered sub-root, we must now examine all of the roots and all of the basic full meanings of the roots that derive from this two-letter sub-root. One can then give them a kabbalistic model of relationship to one another. The kabbalistic model is based upon basic phenomenon of ten or eleven sefirot.
The first three-lettered root constructed from the two-lettered root בר , is found in the second word of the Torah, the word that follows בראשית , which is ברא , bara, created. In fact, the first half of the first word is identical to the second word of the Torah. The second three letters of the first word read שית , which in Aramaic means "six." בראשית can thus be understood to mean ברא – שית , "He created six," God created the world in six days. Abulafia, mentioned earlier, actually says that the six here refers to the six permutations of three-letter roots.
[Before continuing to discuss the various three letter-roots that stem from בר , we will note another phenomenon connected to our algorithm of 2(n + 1), which generates the number 4 from1; 10 from 4, and 22 from 10, as mentioned previously. Another meaning of the 4, other than the four letters of God's ineffable Name, relates directly to the 22 letters since four of the 22 can function as consonants or vowels. Ibn Ezra, one of the literal commentators on the Torah, says that there are actually 26 letters to the Hebrew alphabet, 26 being the numerical value of God's Four-lettered Name, claiming that 22 are consonants but if we include the 4 letters that function as vowels the total is 26. Yet 4 and 22 are two numbers in the series: 1, 4, 10, 22, while 22 is the total numerical value of those 4 additional letters . In this case we have skipped over the 10 and related 4 directly to 22.]
Ten Clear Words
When one of the vowel letters is added to a two-letter root, the root remains unchanged (any other letter added produces a new three-letter root) and the following figure illustrates ten words generated from the two-letter root בר and one or more of the four vowel letters. These ten words are positioned in the figure according to the ten sefirot.
We will now continue to explain each word very concisely. The two letter root itself is situated in the place of keter, crown. The next word that is positioned in the place of wisdom is the word בהר , bohar, which is one of the thirteen synonyms in the Torah for light. Light is one of the most basic Torah concepts, which is why it can be described in so many different terms. The specific term of bohar relates to clear, brilliant light.
ברה , barah, is in the position of understanding and it means clarification or differentiation. This root is also used in the context of clearing an area, such as cutting down a forest or clearing an area of rubble etc.
אבר , eivar, is in the position of lovingkindness and it means a limb of the body, or the wing of a bird. In kabbalah in particular it refers to the power of love by which our souls fly up to heaven. The limbs of the body are clarified in the mother's womb until they are fully developed from the ubar , the embryo, into the perfected limbs of the newborn infant.
ברא , bara, the most important word in our case, is in the position of might and it means to create, as we explained that creation is a function of clarity.
בריא , bari, is in the position of beauty and it means healthy. One of the hassidic readings of bereishit bara, is actually bereishit bari, meaning that "in the beginning" one should be healthy. Being healthy implies that the body is clear of all extraneous matters and that all systems are functioning in harmony.
בירה , birah, is in the position of victory and it means a capital city. The capital city of a country must be more distinguished than other cities, faithful to the national themes and clear of foreign influences.
בור , bor, is in the position of thanksgiving and it means a pit, a vacuum, an area that is defined by the absence of matter. The beginning of the creative process involves creating a vacuum, an area clear of God's light, as it were. This is called the tzimtzum, the secret of the initial contraction of God's light.
ברית , brit, is in the position of foundation and it means covenant. This most important meaning of בר relates to the covenant that the Creator makes between Himself and His creations whom He created in His image – mankind. The brit is the point of connection and in order to affect a rectified relationship it must be clear of all extraneous intent.
באר , be'er, is in the position of kingdom and it means a wellspring. Our forefather Isaac was occupied with digging wells which is also a clarification process – a sub-terrestrial clarification process. The living, clear, pure waters that come from a wellspring have a much more intense power of purification than rainwater that comes from the sky above.
From this very concise explanation of these words we can see that there is a very strong common denominator that connects them all, the concept of clarity or clarification. The idea that clarity creates can be illustrated by a common example, for instance a scientist who has great clarity of mind and makes new discoveries. A true moment of clarity will immediately produce a new eureka experience of discovery, a new invention, or a new idea. A eureka experience, which is a very important concept in kabbalah, is the sudden revelation of a new idea that has never been revealed on earth coming into one's mind – a new creation in the mind. From the mind it continues to become a new creation in the world. Until that moment of clarity, the matter had been confused and some sort of mental or psychological block had existed, but once the confusion vanishes something new is created.
One of the most contradictory topics in kabbalah concerns the nature of creation. One opinion is that God created the universe ex-nihilo – nothing existed and God created something from nothing. The other opinion states that our world and our universe was created after worlds that were also created by God and He destroyed them. He created and destroyed worlds in a process that is called shevirat hakeilim, the breakage of the vessels, until finally at a certain stage He created this domain. This creation is still ex-nihilo, but it was preceded by a create/destroy scenario. These two opinions can be reconciled by explaining that God created worlds and destroyed them because He disliked them, until He created our world and saw that it was good. From the fact that God states specifically in the Torah that this world is good we deduce that there were other Godly experiences of creation in the ancient primordial past which were not good, therefore God destroyed them. What God disliked about the previous worlds was the confusion, the lack of clarity and differentiation between good and evil, light and darkness etc.
The second pair of letters in the Torah is אש , which is the sha'ar situated in the crown of kingdom in this array. Although one might think that the crown of kingdom should precede the wisdom of kingdom, as it does in the array, in the Torah the order is reversed. The crown of kingdom symbolizes the willpower to rule. As explained previously, God disliked the first worlds that He created and He therefore destroyed them. Although we cannot understand God's motives, nonetheless, in Torah and kabbalah there are different rationales offered for the logic of creation, one of which is that a king cannot be a king without a people, as we are taught in Tanya. God assessed all of the initial worlds that He created and they were all too egocentric to accept His rule, until He created this world which had the best potential to accept His kingdom.
This Godly "trial and error" process is similar to the process that God prepared for Adam, the first man, in finding His soul-mate. When Adam was first created he was single and did not have a mate. God brought him all of the animals and Adam tried them all but did not find himself a suitable soul-mate until God created Eve from Adam's own rib and then he truly felt that this was indeed his true soul-mate. Splitting Eve from Adam and then bringing them together once more was a clarification process. In the same way God created the worlds and he did not desire to be king of any of them so He destroyed them all and created a world that is good, over which He desired to rule. That willpower to rule is the אש that means fire, however first must come the wisdom of clarity and then it becomes manifest in the will to rule this particular domain.
We have thus seen an example of how each two-letter unit of the Hebrew language, the Holy Tongue, has a specific kernel meaning that is related to its position in the array. By analyzing each of the 231 sha'arim in this way it would be possible to achieve a systematic understanding of the language that would facilitate many and various actions in computer sciences. In this way, Hebrew may well be a perfect language for information processing and management in today's computerized world.
Although in the secular educational system the decimal system is considered to be an arbitrary system, Judaism holds that this is not so. One of the most basic precepts of Kabbalah is that there are ten sefirot. These are the ten channels of divine, creative energy through which the Creator continuously re-creates the universe. Each of these ten channels is holistic in character, including within it each of the characteristics of the other nine, and as such, every facet of creation manifests and reflects this decimality, making base ten the natural and simplest choice to use.
Although two letter units of the identical letter do exist in Hebrew, we do not calculate the appearances of double letters, since the rule in Hebrew is that when a letter is repeated it is merely reinforcing its own separate meaning (as mentioned in previous footnote) and does not convey any new significance as a pair.
The alef, the first letter of the Hebrew alphabet, usually has a numerical value of 1, however, its very name, alef is almost identical to the Hebrew word elef, meaning one thousand and this is sometimes used as the numerical value of alef in place of 1.
Editor's note: to get some idea of what this means physically, try building tetrahedrons from disposable cups. (By amazing divine providence, this is exactly what my 12 year old son just "happened" to be doing the week before I started working on this article!)
Each of the seven lower sefirot has an archetypal soul root that corresponds to it, as follows: chessed – Abraham; gevurah – Isaac; tiferet – Jacob; netzach – Moses; hod – Aaron; yesod – Joseph; malchut – King David. The three upper sefirot are considered:??