Appendix 3-B: Abrahamic Mysteries:
Letters, Gematria, Earth Magic & the
Foundation of the Heavenly Jerusalem
Note - I Just noticed that the illustrations got lost. As some of this article (and the first about NJD in Genesis) was earlier imported into a booklet-size webpage, look for the illustrations at http://blog.world-mysteries.com/science/the-new-jerusalem-diagram/
1. Secrets of Abraham’s Names
2. Abraham as magician, according to Sefer Yeẓirah
3. Abraham as Geomancer, according to the Zohar
4. Abraham's Construction of the “New Jerusalem Diagram”
5. Charting "The Abraham Triangle"
1. Secrets of Abraham’s Names
As noted in the chapter, the original first name – Abram (אברם pronounced “Avram”, literally "High Father") has Gematria value of 243, which equals the fifth power of the number three (3x3x3x3x3 = 243). As noted in appendix 1-A, the raising of a number to the fifth power signifies its association with five dimensions (5D) and 5D constructs. Thus one to the fifth power still remains one, showing the unity of the One in all dimensions. Two to the fifth power equals 32 (2x2x2x2x2 = 32), the number of the “wondrous Paths of Wisdom” in God’s created world according to the opening of Sefer Yeẓirah, whereas the 5D World of Bri'ah (Creation), which is associated with the Sefirah of Wisdom (Ḥokhmah). We just noted three to the fifth power, and Four (Arbạ associated with plurality) to the fifth power amounts to 1,024 (4x4x4x4x4 = 1,024), which nowadays is considered as “k” (from “Kilo”, meaning “thousand”) that amounts to one thousand for most practical purposes.
The higher dimensions may best be grasped by considering the 4D (4-Dimensional…) and 5D hypercubes as products of integrations, similar to the integration of four 1D line sections to make a 2D square and the integration of six 2D squares to form a 3D cube. Likewise we can imagine the integration of eight 3D cubes to form a 4D hypercube and the integration of ten 4D hypercubes to create a 5D hypercube.
In the story of Noah we saw that a virtuous and whole man – Ẓadiq Tamim – could be “packed” in a box (Tevah, Ark) with his entourage - family and the biosphere sample – thus forming an assembly that may be represented by a 4D hypercube. This way, they escaped the destruction of the 3D scene - but could not save the rest of humankind. In the story of Abraham’s negotiating the fate of the people of Sodom, we shall see that, with Abraham’s (5D) influence, ten Ẓadiqim could have been counted to save the wicked city.
Note also that "Avram" may be read as "Avarim" (אברים) – the 248 body members, from which is structured the human pattern – body and soul. So both the two names, Avram and Avraham, hint at the number of body members and/or parts of the soul that can be rectified. According to the Mishnah (Ohalot A, 8) the whole human body has 248 members - Avarim (which are connected via 365 tendons, Gidim). The significance of this system is that it also is seen to describe the non-material human soul that is made in the pattern of the Torah instruction, which contains 248 positive commandments and 365 inhibitions. Fulfillment of the 248 positive commandments - Miẓvot Ạse - of the Torah can make a person into a Ẓadiq – a righteous person.
The changing of the name from "Abram" (Gematria 243) to "Abraham" (Gematria 248) reveals new characteristics. The number 248 is product of two very significant numbers: 248 = 8 x 31. As noted, the 4D hypercube is the product of integrating eight 3D cubes and (see the Maharal’s discussion of the 8 days of the Ḥanukah) the number eight (8) is symbolic of the wondrous higher world.
248 divided by 8 produces 31, and 31 is the Gematria value of El (אל), which means "god", "Power/Potency" and "Direction Towards". Abraham's journey of Lekh Lekha, as we noted, means "Go to (or into) thyself, in order to rectify thyself”. It has to do with Lekh El – "go to" – which has a Gematria value of 81, and 81 = 3x3x3x3, three raised to the fourth power or to the fourth dimensions. Thus all these numbers are associated with the 4-dimensional hypercube and with the hyperspace of the soul's journey.
We have already seen that Noaḥ built the cubical Ark with its special proportions, but Abraham is associated with the construction of a more characteristic and complete cube, which endures till today. The Qur’an (Sura 22:16 & 2:127) and the Islamic tradition regard Abraham, along with his son Ishmael, as the (re)builders of the ancient shrine of Mecca, the Ka’aba, namely "the Cube". But as we shall show below and complete in chapter four (Parashat vaYera), the place of the hypercube and the peak of Abraham's journey is at Mount Moriah.
248 is also the Gematria of the Hebrew root RḤM, which involves Compassion – Raḥamim and from which comes he word Reḥem – meaning Womb/matrix. El is, as noted, "Towards". It involves marking a direction from a person to other persons and has the value of 31. Now let's note that the 5D hypercube has 32 vertices and the 4D hypercube has 32 edges. 32 in Hebrew letters is L"B (ל"ב), and Leb (לב, pronounced "Lev") means "Heart", and is phonetically redolent of the English word "Love". The expression “One Heart” (Leb Eḥad) has the Gematria value of 32 + 13 = 45, which is the same as that of Adam – the generic human entity that can be a person, all humankind, or a connected group. Imagine an array of 32 people seeking reconciliation ceremony intended to attain "one Heart", each person has 31 directions to communicate with others and thus has 31 directions for reconciliation/completion (Hashlamah). So the number 248 represents a potential opportunity space.
Still another Hebrew word to have the value of 248 is baMidbar (במדבר), which is the name of the fourth book of the Pentateuch (in English "Numbers"). The word "Midbar" is commonly translated as "Desert", but it actually means "place of leading the sheep". This word derives from the root D.B.R. which means both "guiding" or "subduing" as well as "speech" (since speech is the mean humans use to guide and navigate any issue). Midbar thus means "that which can be spoken" and is equal to the Greek word Logos, which appears in the New Testament at the beginning of the Gospel of John – "In the beginning was the Logos (or "The Word") and the Logos was with God". This makes some sense, since the Creation – Bereshit – was through divine speech, and the capacity to speak must have preceded the actual speech. So the name of Abraham is associated with the expression "with the Logos/Word/Midbar", and as we shall presently see, the acts of Abraham were to bring the possibility of divine speech, and speech to God, namely prayer, to the place destined for the "House of Prayer for all Nations" (Isaiah 56:7).
Finally (for now), 248 is one half of 496, which is the third "Perfect Number. So with the shared change of names, of Abram to Abraham and of Saray to Sarah, there forms a fruitful and perfected whole couple and Abraham is the half of this perfection. Interestingly, the joint Gematria value of Ishmael (451) and of Israel (541) - the two of Abraham's seed who had twelve sons - equals 992, which is twice this perfect number and four time the number of Abraham.
It may be pertinent to note that the two protagonists of Abraham, Nimrod (נמרד, Gen. 10:8-9) associated with Abraham in the Midrash, and Melchizedek-Malkiẓedeq (מלכיצדק, Gen. 14:18) have the Gematria value of 296, which equals 7x7x6 – almost a cube of the holy number 7, but not quite so.
2. Abraham as magician, according to Sefer Yeẓirah
It is written that Abraham and Saray his wife took with them "the souls that they had acquired (literally "made") in Ḥaran" (Gen. 12:5). In the Qabbalah this came to mean that Abraham was a magus who made living persons (also Ḥaran itself was well known at the time as a place of magicians). Sefer Yeẓirah, which is the root from which almost all Qabbalah teachings derive, is even attributed to Abraham because its very ending says:
"After that our father Abraham had seen, and pondered over, investigated, and understood these things, he designed, engraved, and composed them, and received them into his power (hands). Then the Lord of all appeared unto him, made a covenant with him, and kissed his head, and naming him after his own name, called him his friend; and as it is written, completed a covenant with him and with his seed forever, who then believed on God, the Tetragrammaton, and it was imputed to him for righteousness.
God ordained a covenant between the toes of his feet, that of circumcision; and a covenant between the fingers of his hands, that of the Tongue. He bound the essences of the twenty-two letters on his tongue, and God disclosed to him the secrets of them. God has carried these through waters, He has borne them aloft through fire, and He has stamped them in the storms of the air; He has distributed them among the seven stars, and has assigned them to twelve celestial constellations. Amen.”
(Sefer Yeẓirah VI, 4, W.W. Wescott, tr., 1887)
Whether the book really attributes itself to Abraham or not, it certainly portrays Abraham as an expert in all the magical letter operations listed in Sefer Yeẓirah. All later attempts to emulate God's formation of Adam and create an artificial homunculus – the Golem – took the operations in Sefer Yeẓirah as their starting point. For later European alchemists, an early alchemist was called "Abraham the Hebrew" and alchemy was seen as a Jewish art, requiring knowledge of the Hebrew letters. For the Mequbalim, alchemy was called Ḥokhmat (wisdom of) haẒeruf, a word that means both “transmutation" and "(letter) Permutation". We shall bring these letter operations to bear upon Abraham's magical acts while journeying towards the destination of his destiny.
3. Abraham as Geomancer, according to the Zohar
The canonical mystical text in Judaism, the book of the Zohar, is a Midrash on the Torah. In its chapter on Lekh Lekha, the Zohar portrays Abraham as "Geomancer" – diviner of earth mysteries. Here is what it says about Abraham's journeys:
“'And the Lord said to Abram Lekh-Lekha'. Said Rabbi Eli’ezer: Lekh-Lekha, go to yourself, namely go to rectify yourself, to mend your level. Lekh-Lekha, because you should not locate yourself among these sinners. And the secret of this is in the phrase Lekh-Lekha, because the Holy One Blessed be He gave Abraham a spirit of wisdom, and he knew to compare the directions (“winds” or “spirits”) of the settlements of the world, and he would observe them and weigh them upon scales, and he knew and obtained the powers (of those) that govern the (four) directions (or sides) of the settled earth. When he reached the central point of the settlement, he weighed in the scales and did not accomplish it, he then observed to identify the power that controls it, and he could not cleave to its intention. He weighed it several times, and saw that it was from there that the whole world was planted and established. He looked and combined (permutated) and weighed to know the subject, and saw that the high power that controls it, is infinite, and is profound and covered, and is unlike the sides of the levels of the settlement. He looked and weighed it and knew that from this central point of the settled world, the whole world is planted from there to all the sides. He also knew that same as from the central point of the settled world, from there the world was planted for all the sides – he also knew that the power that is now controlling this point, from it issued all the other powers that control the sides of the world, they are all connected with it. And so he left from Ur Kasdim to go to the Land of Canaan. He further noticed and weighed and permutated, to clarify (literally “to stand upon”) the exact nature of that locus, and he could not comprehend and could not stand upon (clarify) that spot in order to cling to it. As he saw the rigor of the judgments (Dinim) of that site, and he could not stand upon it and cling to it, immediately “and they came to Ḥaran and dwelt there”. What was the reason that Abraham tarried in Ḥaran and did not immediately go to the Land of Canaan? But as he was cognizant of, and permutating/adding with, all those rulers of the world from all the sides of the settled world, and he was weighing and combining those who control the sides of the settled world who are the rulers of the planets and the constellations, how strong they are set against each other, and he was weighing all the settlements of the world and was succeeding in it. (But) When he came to that site, he saw the power of the abyss, and was not able to locate himself there. When the Holy One Blessed Be He saw his arousal and his passion, immediately (God) revealed Himself to Abraham and told him – Lekh-Lekha, to know thyself and to rectify yourself."
In the ancient world, the ceremonial arrangement of a land into twelve regions, and the marking of twelve directions from its sacred center were aimed to create upon earth the heavenly order expressed by the zodiac. With the creation of the luminaries, the sun and the moon, it was written “and let them be for signs, and for seasons, and for days, and years” (Gen. 1:14). The twelve months (namely moons) in the solar year enabled man to observe twelve sectors in the sky, with the groups of stars, the constellations, found in these sectors.
Let us examine how did Abraham find the center point of the whole earth from which the twelve sectors point to significant locations on earth and what ritual might he be performing there.
4. Abraham's Construction of the “New Jerusalem Diagram”.
“The New Jerusalem Diagram” is the name given by the scholar of ancient lore, John Michell, to a geometrical construction that allows the “squaring of the circle” and the division of the circle to 28 equal sectors and the ceremonial positioning of the twelve tribes (or constellations) in a pattern of four camps at the four sides of the square. In the first chapter and its appendix 1-C, we saw that the New Jerusalem diagram is already implied by the number of the letters pattern in the first verse of Genesis – 28, 22 and 6. Michell asserts that this diagram was employed at many ancient sacred sites, including the Great Pyramid. In the following we shall assume that if this diagram was known to the sages of ancient times, including the magi of ancient Egypt, then it was also employed by the Hebrew, Abraham – along with certain magical letter operations.
The “squaring of the circle” through this construction is based on the approximation of 22/7 for the (irrational) ratio - Pi - between the circumference and the diameter of the circle. In enacting this construction, first is drawn an inner circle with a diameter of 22 units. This circle is enclosed by a square, the four sides of which are 22 units long, and its perimeter is thus 88 units long.
Now is drawn an additional circle – with a center coinciding with the center of the inner circle and a circumference equaling the perimeter of the enclosing square. The diameter of this circle is 28 units. The circumference of that circle is 28 x 22/7 = 88, and thus equal to the perimeter of the square that encloses the inner circle. The symbolic meaning of this ritual of “squaring the circle” is to equalize and mediate between the masculine – the measured and rational – and the feminine – the natural that circles and recurs.
In this generic pattern of squaring the circle, the square and outer circle cut at eight points that mark four wide sectors in which the circle protrudes beyond the square and four narrow sectors where the corners of the square protrude beyond the circle. The four centers of the wide sectors and the eight crossing points mark reference points for placing twelve small circles of diameter 6 units each, so that their centers lie on the outer circle (diameter 28), and they touch the inner circle (diameter 22 units). There form thereby four groups of three circles along the four sides of the square. In this manner, the outer circle, whose diameter is 28 units, is divided to 28 practically equal sections. Each such section will have 360/28 = 12.86 degrees, or nearly 13 degrees, and each of the surrounding circles will have a sector of nearly 26 degrees.
Elaboration of the Diagram with the 28 sections (4 seven-pointed stars)
In the application of this diagram in the Great Pyramid, when the square coincides with the base of the pyramid, the width of the pyramid corresponds to the diameter of the inner circle and the height of its summit is exactly at the outer circle.
Width and height of the Pyramid determined by the NJD
While this is a purely abstract symbolic-geometrical construction, we know that the ratio between the diameter of the inner circle and the diameter of the small surrounding circles built upon it happens to be exactly the ratio between the mean diameter of the earth and the diameter of the moon. The diagram thus gives us an image of the twelve moons-months of the year arrayed in four groups like the eventual order of the Twelve Tribes around the Tabernacle.
Abraham was carrying with him the principles of the heavenly order, and he was searching for the appropriate site where to place the pattern of this order. He was searching for the site for the universal temple for sanctifying the earth and for renewing-healing humankind. Recall that Abraham, “the Hebrew”, is described in the Sefer Yeẓirah as the one who dealt with the magical combinations of the 22 Hebrew letters. We may therefore surmise that at every site that he reached on his journeys, Abraham would conduct a magical ritual and draw upon the ground a magic circle with a diameter of 22 units – the number of letters in the Hebrew alphabet (by which heaven and earth were presumably created) – and encloses it by a square of 22x22 units.
It is appropriate for Abraham that his square would contain the letter combinations. So this square forms a kind of game board (or play field) of 22 rows, marked by the letters from Aleph to Tav, and of 22 columns of square cells marked with these 22 letters. Each of the resulting 484 square cells holds a two-letter root for a Hebrew word (such as “AB” and “RaM”, for example). This fulfils the practice of the two-letter "gates", or roots of the Hebrew words of Sefer Yeẓirah.
In as much as this square could represent the base of the Pyramid; it marks the base of a virtual cube (which the Moslems allude to as “The Heavenly Ka’aba"). This now begs the contemplation of a 3D cube of letter combinations 22 letters high, marking a myriad (22x22x22=10648) of cubical cells that contains all the Hebrew three-letter word roots. This would be a representation of the Midbar – all that could be said, in fact a representation of the "Mouth of God/haShem" or “The Kingdom of the Name”. Thus at every place that he drew his “magic square”, Abraham places a possible base for the “Temple of haShem” upon earth.
When Abraham draws the New Jerusalem pattern, he must draw an additional magic circle – a circle with a circumference equaling the perimeter of the enclosing square. The diameter of the requisite circle is 28 units – “the perfect number” which is already given in the number of letters in the first verse of Genesis and refers to the passage of time.
As already noted, the ritual of “circling the square” is meant to encircle the masculine – that which is measured and marked by words (words are used to recall – lehazkir, and masculine is Zakhar) - and to find in it the natural and recurring quality, which is the feminine.
5. Charting the Abraham Triangle
Soon after reaching the Land of Canaan, Abraham went southwest to sojourn in Egypt, a land marked by the Great Pyramid. He then returned to cana'an where he had his two sons, Ishmael and Isaac. Some 20-40 years after casting out Ismael, according to the Qur’an and the Midrashim, Abraham left Canaan to visit Ishmael at Mecca or nearby.
We may expect that much as there symbolic meaning to the places that Abraham consecrated in the Land of Cana’an/Israel, there aught to be some symbolic-geomantic meaning to the places that he visited outside of Cana’an, and that the points fixed thereby have a larger regional significance.
When starting land surveying and mapping, it is necessary to fix a base point and a measured triangle. Egypt was certainly a centre of the ancient world, and the site of the Great Pyramid must have been considered then as the centre of the world.
An independent Egyptian investigator who lives in Holland, Muhhamad Sabet, has examined the relations between the vertices of the triangle made by the Great Pyramid at Gize, the Ka’aba at Mecca and Jerusalem. Sabet called it “The Abraham Triangle” and found several special characteristics, of which we shall mention here but two:
1. this is a right angle (90°) triangle, and this right angle is at the
2. the direction of the axis from the Gead Pyramid (the sides of which are precisely orientated to the four cardinal directions) is at about 26° north (left) of the west-east axis. (It continues to the deep center of Asia at the Altai region between Russia, China and Mongolia)
Interestingly, we find this direction of about 26° built within the Great Pyramid in the rise of the great gallery built inside the pyramid and leading to the “King’s Chamber”. Moreover, as we saw above, it is that angle of about 26° that characterizes the New Jerusalem Diagram that Abraham might have been utilizing. If he laid the pattern (or had it shown to him by the Egyptian priests) in Egypt, he would have noticed that the direction of 26 degrees north of the eastern direction is orientated back towards somewhere in the Land of Canaan.
Somewhere in the
Now in the “New Jerusalem Diagram”, the twelve small circles that surround the inner circle (and the sectors of the outer circle) also have the very same measure of nearly 26 degrees (360º/28x2 = 25º43'). The twelve circles correspond to the 12 Tribes, whose pattern of sojourn will be presented in the discussion of the Tribes in the appropriate chapters. But here is where their outline is formed: in his descent to Egypt Abraham formed the axis of “The Flag of the Camp of Ephraim” (The House of Joseph), and in the sending off of his firstborn son Ishmael towards Mecca, Abraham formed the axis of “The Flag of the Camp of Re’uven", the firstborn of Israel. In his journeys to Egypt and to Mecca Abraham therefore drew the guidelines for forming the complete pattern of the New Jerusalem centered upon Mount Moriah.
The Abraham Triangle within the New Jerusalem Diagram centered on Jerusalem
 When we imagine cloning the 2D square and translating the clone in a direction perpendicular to its two dimensions (i.e. height) to a distance equal to the length of its edges, there would form a cube made out of the intial square, the new square and four sqare faces formed between the four edges of the initial square and the four edges of the moved clone (the other edges of these square cube faces are formed by the four vertices of the clooned square as they trace their trajectories in the 3rd dimension.
In a similar fashion, cloning a 3D cube and moving it to the length of the cube edges, but in an imagined 4th dimension perpendicular to the three space dimensions, will result in a 4D hypercube made out of the original cube and the translated cloned cube, along with connected six cubes created by the movement of the six square faces of the cube in the perpendicular 4th dimension.
And again, in a similar fashion, cloning and moving the 4D hypercube in a perpendicular 5th dimension will yield a 5D hypercube made of the initial and cloned 4D hypercubes along with eight new 4D hypercubes formed from the eight 3D cubes contained in the 4D hypercube as they move to connect with the eight 3D cubes contained in the cloned 4D hypercube.
 A "Perfect Number" is equal to the sum of all its divisors; here 1+2+4+8+16+31+62+124+248 = 496. Such numbers are very rare. Only four or five of them were known in the ancient world. Even with all present computer power, we know only about 30 of them.
 We saw a somewhat akin case where the Gematria value of the Tree of Life was one fourth of the value for the Tree of Knowledge, which has four levels.
 This fascinating aspect of Jewish mysticism – the formation of the Golem – is detailed in Moshe Idel: "Golem: Jewish Magical and Mystical Traditions on the Artificial Anthropoid" (S U N Y, 1990).
 See Raphael Patai: Jewish Alchemists, a History and Sourcebook, Princeton U. Press, 1994.
 See John Michell and Christine Rhone: “Twelve Tribe Nations and the Science of Enchanting the Landscape”, Thames & Hudson, 1991 for global survey; and Jean Richer: “Sacred Geography of the ancient Greeks – Astrological Symbolism in Art, Architecture and Landscape”, SUNY Press, 1994, for Greece.
 See John Michell’s books: “City of Revelation” and/or “Dimensions of Paradise", and especially his post-mortem testimony: "How the world is made, the story of creation according to Sacred Geometry". Thames & Hudson, 2009.
 Sefer Yeẓirah deals with two triangular set of 231 (רל"א - 21x11) "gates" of two Hebrew letters, back and forth, which add to a square with a main diagonal nul. But this is actually a mistake of sefer Yeẓirah, because there are many two-letter Hebrew word roots of the same letter. It is only with three-letter word roots that this repetition becomes ilegitimate.
 This Qur’an version (Sura 22:16 & 2:127) is supported, to an extent, by the Midrash that Abraham rode to Arabia to meet Ishmael there - Pirke deRabbi Eliezer 30; Midrash haGadol, vaYera).
 The Royal Astronomer to Scotland, Piazzi Smyth, showed in the 19th century that the Great Pyramid stands at the cross of the latitude and altitude lines that pass the longest stretches of continents, so that Gizzeh can be seen as the center of the world. Piazzi Smyth: Our Inheritance in the Great Pyramid. London 1864. However, the method we proposed for the centrality of Jerusalem is more appropriate, because it relates to surface areas of the continents and not their length.
 While Mecca might have been a very marginal place at the time, other Moslem investigators have shown an objective global significance to the Meccan position, or at least the lattitude of Mecca has significance in as much as the distance between the North Pole and the Meccan latitude (say A) and the distance of this latitude and the South Pole (B) have the “Golden Section” relation (B/A = Φ). According to Sabet’s calculations, Mecca is on the right latitude, but a bit to the west (and Medina a bit to the east) of the ideal line directing to Jerusalem.
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