“The city was laid out as a square, its length equal to its breadth. The angel measured the city with a rod and it was 12,000 stadia in length and breadth and height. He measured its wall, and this was 144 cubits high, according to the human measure he used.” — Revelation 21:16-17
Modern science confirms what our ancestors already new: the architecture of the universe (nature) is based on some key numeric proportions we can see on all levels of scale: from the atoms and DNA, through patterns and blueprints of life, all the way to solar system and galaxies…
NOTE: The New Jerusalem Diagram is also known as The Cosmological Circle
The New Jerusalem Diagram – Introduction
“The New Jerusalem Diagram” is the name given by the scholar of ancient lore, John Michell [The original explanations in John Michell's books, especially "The Dimensions of Paradise", Thames and Hudson, 1986] to a geometrical construction that allows the “squaring of the circle” and the division of the circle to 28 equal sectors (a zodiac wheel) and the ceremonial positioning of the twelve tribes (or constellations) in a pattern of four camps at the four sides of the square.
John Michell has reconstructed the geometric pattern of the ‘heavenly city’ which is the template of the New Jerusalem of Revelation 21.
He discovered that this diagram served as the design (blueprint) for many sacred sites, including the Stonehenge, The Great Pyramid, St. Mary’s Chapel at Glastonbury and the City of Magnesia in Plato’s The Laws.
The Great Pyramid, Earth and Moon fit the New Jerusalem Diagram
It turns out that also the Nazca glyph called “Mandala” aka “Sun-Star-Cross” perfectly matches the New Jerusalem Diagram.
Superimposed image of NJ Diagram and Mandala glyph near Nazca, Peru
It is no surprise that the NJ diagram matches blueprint for the The Dome of the Rock, a shrine located on the Temple Mount in the Old City of Jerusalem.
The wheel of 28 divisions is common to various esoteric systems and serves as representation for the schematic month: 4 weeks = 28 days. The solar calendar of the Dead Sea scrolls sect was of 364 days, which is a multiple of 28 ( 28×13 = 364). In many Sufi diagrams, including in the ceiling of the dome at the El-Aqsa Mosque* (not the Dome of the Rock) at the Temple Mount, there appears the motif of the wheel made of 28 divisions.
Al-Aqsa. The resplendent ceiling of the Al-Aqsa Mosque on the Temple Mount in Jerusalem. The mosque, one of Islam’s most holy sites, sits near the Dome of the Rock and above the Marwani Mosque, aka Solomon’s Stables.
The NJ diagram is also hinted and enfolded (according to Micheell), in the description of the holy city, The New Jerusalem, whose descent from heaven concludes the Christian Bible.
Below we present 3-D version of the New Jerusalem Diagram.
Is it possible the 3D NJ diagram was used as a blueprint for the Crown Jewels?… Perhaps this is a case of a “secret hidden in plain site”?
The collective term Crown Jewels denotes the regalia and vestments worn by the sovereign of the United Kingdom during the coronation ceremony and at other state functions. The term refers to the following objects: the crowns, sceptres (with either the cross or the dove), orbs, swords, rings, spurs, colobium sindonis, dalmatic, armill, and the royal robe or pall, as well as several other objects connected with the ceremony itself. The Crown Jewels have a religious and sacral connotation. Their hidden symbolism seems to be related to the sacred geometry of the New Jerusalem Diagram.
The Construction of the New Jerusalem Diagram
The construction of this diagram starts with the attempt to “square the circle” by drawing a circle and a square that have the same circumference.
- So in building this sacred diagram, one starts with a circle with a diameter of 22 units, and blocks it with a square of 22 x 22 units (like the number of the Hebrew letters, with which supposedly “heaven and earth were made”).
- Then one draws from the same centre an additional circle whose diameter is 28 units – “the perfect number” that is already the number of the letters in the first verse of genesis and marks the circle of the seasons. The circle with diameter 28 has circumference of Pi x 28, which is as noted 22/7 x 28 = 88 – just the circumference of the square with edges of 22 and circumference thus 2 x 22 = 88.
The circle and the square have the same circumference, and they intersect in 8 points, where the square juts out of the circle in 4 vertices.
- The building of the complete pattern continues with the drawing of 12 circles with diameter of 6 units – the number of letters in the first word of Genesis – Bereshit – as the first “perfect number”. The centers of these twelve circles are situated on the outer big circle, whose diameter is 28, and they touch (are tangent to) the inner circle, whose diameter is 22. Four of these circles are situated according to the points were the square is tangent to the inner circle, and the other 8 circles are placed according to the 8 points of intersection between the square and the outer circle.
There are two amazing consequences of this construction:
- This construction squares the circle
- It divides the circle into 28 equal segments
- It reflects ratio 22:7 which is good approximation of the “Pi”
- It reflects golden ratio 1.618
- It reflects the ratio of 22:6, which issues theoretical-geometrical considerations is also the exact real ratio between the diameter of the earth and the diameter of the moon!
There are many more features of the NJ diagram which will be presented in our upcoming articles (e.g. amazing connection with Teotihuacan).
The New Jerusalem Diagram and the Bible
The NJ diagram was known to the sages of ancient times, including the magi of ancient Egypt. It was also employed by the Hebrew, Abraham – along with certain magical letter operations.
The New Jerusalem diagram is already implied by the number of the letters pattern in the first verse of Genesis – 28, 22 and 6.This diagram indicates, first and foremost, the image of the camping of the Twelve Tribes around the Tabernacle. This diagram, which is relevant for the Tabernacle and the future Temple, is already enfolded in the first verse of Genesis: the same three numbers of the letters of the first verse of Genesis – 6, 22 and 28, and the number of its words, namely 7 – are the very components of “The New Jerusalem Diagram”.
In the first verse Genesis, made of seven Hebrew words and 28 letters, it says: “Bereshit bara Elohim et haShamayim vet haAre”. In these words is hinted the secret of geometry (namely of measuring the earth) of heaven and earth. In the ancient world, the sky was considered as circle or dome and the earth as a square or a cube. The desired harmony between heaven and earth was conceived as a geometric riddle of harmonizing the circle and the square, as well as between the cube and the dome.
The problem with “squaring the circle” is that the square represent “rational” relations between its components (that is, they divide into the ration between whole and finite numbers), whereas the circle represents “irrational” relations (the ratio between its elements, the circumference and the diameter, is infinite) and is expressed by the symbol “Pi” ( = 3.14159265…). It is therefore impossible to draw a square and a circle that have exactly the same circumference (or area). Yet there is a rational approximation that is good enough for a drawing or a physical construction - the approximation of 22/7 =>Pi. With this approximation, the circumference of a square whose length and its breadth are 22 units (22×4 = 88) equals the circumference of a circle whose diameter (D) is 28 units (DxPi = 28 X 22/7 = 88. What is striking is that these numbers – 28, 7 and 22 – are hinted and enfolded in the first verse of Genesis.
The First Story of Genesis – World of Creation Version of Bereshit
The Bible, Genesis 1, King James Version
1In the beginning God created the heaven and the earth. 2And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
- 3And God said, Let there be light: and there was light. 4And God saw the light, that it was good: and God divided the light from the darkness. 5And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
- 6And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters. 7And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. 8And God called the firmament Heaven. And the evening and the morning were the second day.
- 9And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so. 10And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good.
- 11And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. 12And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good. 13And the evening and the morning were the third day.
- 14And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: 15And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. 16And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. 17And God set them in the firmament of the heaven to give light upon the earth, 18And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good. 19And the evening and the morning were the fourth day.
- 20And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven. 21And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good. 22And God blessed them, saying, Be fruitful, and multiply, and fill the waters in the seas, and let fowl multiply in the earth. 23And the evening and the morning were the fifth day.
- 24And God said, Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so. 25And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good.
- 26And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. 27So God created man in his own image, in the image of God created he him; male and female created he them.
- 28And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
- 29And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat. 30And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so. 31And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.
About the Creation as Divine Utterance
It is plainly stated in the Book of Genesis that all the Creation of the six days was performed through divine utterances whose number is 10:
1. “Let there be light” – “And God saw… that it was good”.
2. “Let there be a firmament in the midst of the waters, and let it divide waters from water“.
3. “Let the waters under the heaven be gathered together to one place, and let the dry land appear” – “And God saw that it was good”.
4. “Let the earth bring forth grass, herb yielding seed, and fruit tree yielding fruit after its kind, whose seed is in itself, upon the earth”.
5. “Let there be lights in the firmament of the heaven to divide the day from the night, and let them be for signs, and for seasons, and for days, and years. And let them be for lights in the firmament of the heaven to give light upon the earth” – “And God saw that it was good”
6. “Let the waters swarm abundantly with moving creatures that have life, and let birds fly above the earth in the open firmament of heaven” – “And God saw that it was good”.
7. “Let the earth bring forth living creatures after their kind, cattle, and creeping things, and beasts of the earth after its kind” – “And God saw… that it was good”.
8. “Let us make Mankind in our image, after our likeness, and let them have dominion over the fish of the sea and over the birds of the air, and over the cattle, and over all the earth, and over every creeping thing that creeps on the earth”.
9. “Be fruitful, and multiply, replenish the earth, and subdue it”.
10. “Behold I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, on which there is the fruit yielding seed; to you it shall be for food. And to every beast of the earth, and to every bird of the air, and to everything that creeps on the earth, wherein there is life, I have given every green herb for food”.
The Six letters inside the first word – BeREShIT
The first word is made of six letters, the first one of which is accentuated. The word Bereshit is divided, as already noted in the Tiqqune Zohar, to two words: “Bara – Shith”, namely “created six” (shith is in Aramaic “six”). This is the beginning of the building of the cosmos in six days.
The ancient symbol for orderly building – for “Cosmos” – is the perfect cube, which has six faces. The cubic pattern expresses sanctity both in Judaism (the form of the Holy of Holies and of the phylacteries), in Christianity (the cube of “The New Jerusalem” at the ending of the Christian Bible) and in Islam (the Ka’ba).
The Pythagoreans saw in the number six “the first perfect number”, because the sum of the numbers it is divided by (1, 2 and 3) equals the number itself (1+2+3=6), and regarded these numbers as the secret of the perfect creation. It seems that the author of the Book of Genesis wanted to start the account of creation with such a perfect number. The scribes of the Torah conceived of the Creation as a building process with six-stages (a perfect number). Each Creation Day is likened to a face of a cube, each face in its turn connects with the former ones, so that the Third Day – the third face of the cube – already adds a dimension of volume, whereas the sixth day, the sixth face, closes the cube and forms inner space.
The accent point in the Beyt is the clue for the seventh element, to the conscious center that is nested within the six-sided cube. The whole sentence contains seven words (combinations of letters) and confirms the Principle of Seven – the Sabbath.
The seven words and 28 letters in the first verse of Genesis
The first sentence of the Torah is made of 7 words (in the language of the Sages Tevot – “boxes”) in which there are 28 letters. In the language of Sefer Ye?irah these are 7 “houses” (Batim) built from 28 “stones” (Avanim)
These two numbers are not random numbers, but are very intentional. The seven words correspond to the pattern of the seven days of creation, which are enumerated in the first creation story, which issues from this sentence.
But there is reason to note that the number 28 is the second “perfect number”. The number 28 is divided by 1, 2, 4, 7 and 14, whose sum is 28. Moreover, these two numbers, the 6 corresponding to the number of letters of the first word, and the 28 corresponding to the number of the letters in the first sentence of Genesis, comprise the sum of the Biblically most important primary numbers 3 and 7. Thus the first three numbers 1+2+3 = 6, whereas the first seven 1+2+3+4+5+6+7 = 28. Therefore it is appropriate to start the account of the creation by the perfect creator with these two perfect numbers.
Source article by Yitzhaq Hayut-Man
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 = Phi). 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.
Abraham’s Construction of the New Jerusalem Diagram
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.
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. 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 Jerusalem vertex.
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.
The Abraham Triangle contained within the New Jerusalem Diagram centered on Jerusalem
Secrets of Abraham’s Names
In the story of Noah we saw that a virtuous and whole man 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 could have been counted to save the wicked city.
Notes: 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.
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.
Beyond John Michell’s diagram
Michell’s New Jerusalem diagram, which is the reconstruction of the ‘heavenly city’
Beginning with the Pythagorean triangle of sides 3, 4, and 5, the large square (11 × 11) in this diagram is constructed such that the circumference of the circle cutting across its sides (the circle of Michell’s ‘heavenly city’) is, if Pi (?) = 22/7, a length (44 = 14 × 22/7) identically the length of the perimeter of the square (44). The diameter of the outermost circle (the circle enclosing the 12 ‘lunar circles’) is 17. The diameter of the circle inscribed in the square (the ‘earth circle’) is 11. The diameter of the circle inscribed in the four triangles is 5.5. The diameter of the circle nearest the center of the diagram (the ‘thirteenth moon’) is 3. The point at the center of the diagram is taken to be a ‘central dot’ (relative value = .0333 ) surrounded by a ‘circular space’ (relative value = .2), either of which is understood to represent the ‘pole of the universe, passing vertically through’ the center of the diagram, as here illustrated:
The whole figure is enclosed by a 12-sided polygon, corresponding to the sum of the sides of the Pythagorean triangle, 3 + 4 + 5 = 12. The product of 3 × 4 × 5 = 60. 12 + 60 = 72, while 12 × 60 = 720.The original dimensions of the diameters,. 0333 , .2, 3, 5.5, 11, 14, and 17, multiplied by 720 yield 24, 144, 2160, 3960, 7920, 10080, and 12240, where 7920 corresponds, on an adjusted scale, to the 12(000 furlongs) × 660 ft. side of the New Jerusalem square.
This New Jerusalem diagram fits neatly into the plan of the ‘heavenly whorls as revealed to Er’ in Plato’s Republic, ‘in the order given by Plato and proportioned in accordance with’ the values of the musical sequence, 6, 8, 9, 12, 18, 24, 27, and 36, as here illustrated
where the total diameter = 10368/36 = 288. The total diameter of the first three rings (34 × 2 = 68) times 180 = 12240, the total diameter of the New Jerusalem diagram, while that of first two rings (22 × 2 = 44) times 180 = 7920, the diameter of the circle inscribed in the large square of the New Jerusalem diagram.
Now the truly remarkable fact is that in the whole of Michell’s analysis of the geometrical pattern of the ‘heavenly city’, indeed, no doubt because of the fact that in the whole history of the appearance of the pattern from Stonehenge to Glastonbury there is no appearance of such an element, nowhere is it noticed that there is one fundamental element missing from the pattern these thousands of years, viz., the unmarked circle in which the 11 × 11 (or multiplied by 720, 7920 × 7920) square is implicitly inscribed, as here illustrated (where the green circle is the ‘missing circle’):
The diameter of this ‘missing circle’ is sqrt(2) × 11 = 15.55634919 (or multiplied by 720, 11200571428.)
If for the diameter 15.55634919 is substituted the L series value 15.5 (cf. Leahy, Foundation, Section IV.2, pp. 519ff.), then the sequence of the diameters of the major circles of the New Jerusalem diagram, including the ‘missing circle’, is 11, 14, 15.5, and 17, and the L series partial sums for these values are: S11 = .75(112 + 11) – 5.5 = 93.5, S14 = .75(142 + 14) = 157.5, S15.5 = .75(152 + 15) + 8 = 188, and S17 = .75(172 + 17) – 8.5 = 221. The sum of this sequence of L series partial sums is exactly 660, the multiple of 12(000) furlongs which produces the 7920(000) unit side of the New Jerusalem square, and exactly ten times the sum of all the whole number diameters of circles within the diagram (3 + 5.5 + 11 + 14 + 15.5 + 17 = 66). 8 (the cubic number) × 15.55634919 × 1832 (this last the transcendental constant, P1.5c [cf. Leahy, Foundation, Section III.5]) = 228096, exactly the total interior and exterior surface area of the triple ‘absolute dead center’ cube (cf., on this web, Logically Outfitted Cube[s]).
The sum of all of the first 1 billion natural numbers whose integral products are unit fractions of themselves the denominators of which are primary digits of the number system other than 1 or 3 (excluding 2985984 and 429981696, multiples of 82944 [cf. Leahy, Foundation, Section III.7]), is 47536, which is, with a difference ~ 3/1E4, the sum of all the whole number diameters of circles within the New Jerusalem diagram (see above) multiplied by 720 ([3 + 5.5 + 11 + 14 + 15.5 + 17 = 66] ×720 = 47520).
In terms of the original, i.e., unadjusted, scale of 12000 furlongs in Revelation 21, this diameter would be 15556.34919. Now, among the first 1 billion natural numbers there are only eight whose integral products are either the 1st or 3rd parts of themselves, that is, members of the classes to which belong, respectively, the uniquely related numbers, 82,944 and 27,648. The sum total of these eight numbers is 124451, so that the average value of the eight = 15556.375, with a difference ~ 1.7/1E6, the diameter of the ‘missing circle’ of the New Jerusalem diagram. 124,451 is at once, with a difference ~ 5/1E5, 10 times the circumference of the 1/(81/2 × 1E3) smaller circle (5.5 × 22/7 × 720 = 12445.714285) inscribed in the four triangles which, in turn, are inscribed in the circle twice its size whose circumference (11 × [Pi= 864/275] × 720 = 24,883.2) is exactly 0.3 times 82944, that is, 0.3 times the ‘absolute dead center’ number, and which is in turn inscribed in the New Jerusalem square, which latter is, again, in turn inscribed in the ‘missing circle’.
Dead Center Cube
Note: The shape of the New Jerusalem “coming down out of heaven from God” is a perfect cube (Revelation 21:16: “The plan of the city is perfectly square, its length and its breadth equal. He measured the city with his rod and it was twelve thousand furlongs, equal in length and in breadth, and equal in height”), 1000 the absolute dead center cube, and NJCf-d the face diagonal of the New Jerusalem cube (Revelation 21:16), NJCf-d = 829441/4 × 1000 furlongs.
The radius of the ‘missing circle’ (= 7.778174595, when the diameter is taken to be 15.55634919) is exactly (60501/2)/10, that is, 1/10th the ratio of the side of the New Jerusalem square (taken as 7920) to the side of the square (101.8233765) inscribed in the ‘circular space’ which is the central shaft through which passes the ‘pole of the earth and universe’, which latter square is the side of the ‘absolute dead center’ cube, as here illustrated (the side of the cube the square inscribed in the central shaft):
The ‘absolute dead center’ cube, first constructed in 1985 in the context of the elaboration of the logic of the essentially new thinking now actually occurring for the first time in history, fits perfectly, organically, and with absolute appropriateness into the place at the very center of the New Jerusalem diagram, the 1/36th part of its side (10368/36 = 288 = sqrt(82944) = 3168/11), its central square, corresponding precisely to the square (16.97056275 × 16.97056275) inscribed in the ‘central dot’ of the diagram [inset], the area of which ‘dot’ is the fundamental measure of the New Jerusalem diagram, 3168/7 or 452.571428, or 1 New Jerusalem unit.
The diameter of the ‘earth circle’ inscribed in the square inscribed in the ‘missing circle’ is 7920, which, divided by 720, is the original 11. This 11 is effectively the value of the diameter (= 11) of the decagon formed by the double helix structure of the DNA molecule, which decagon is visible in the top-down view of the molecule. The ratio of the circumference of the circle in which the DNA decagon is inscribed (? the circumference of the ‘earth circle’ divided by 720) to the circumference of the ‘missing circle’ of the New Jerusalem diagram is effectively 101.8233765, the edge of the ‘absolute dead center’ cube.
Source/Read more: http://dgleahy.com/p18.html
Mr. D.G. Leahy discovered what he calls the dead center cube which can be construed as ANY 3D cube in which the original face diagonal is divided into 144 ‘units’. Once so designated, this cube is neatly positioned to serve as a mensural standard whereby its hypercubic (4th dimensional) relations can be uniquely understood.
Without delving into the mathematics revealed by Leahy’s treatment of the dead center cube (‘unitary’ surface area = 82944 = 8 times the face area), suffice it to say that the existence of the dead center cube (which no one will deny) grounds the productive imagination and opens a neatly framed window into the 4th dimensional world of hypercubes.
Stated another way, hypercubes exist ‘in nature’ in the same manner as Time. Time is measured with simple geometric contrivances such as arrows or clockfaces or spirals. The dead center cube is a simple real life counterpart of a higher dimensional ‘imaginary’ structure. If Time exists, hypercubes exist. If Time can be measured and imaged with simple geometric structures, so too can hypercubes. If the understanding, standardization and incorporation of Time is important in everyday life, why not the analogous standardization of hypercubic space? Can you imagine such a thing?
Concept of the Dead Center Cube
Suppose we have a cube with edges of length x. We’ll refer to this as a “base cube,” or by the letter C. This cube has
volume(C) = and surface area(C) =
since an x-by-x-by-x cube has six x-by-x sides. The volume-to-surface-area ratio is then
Now we’re going to construct two four-dimensional hypercubes. The first one, hypercube A, will have sides of length x/6; the second, hypercube B, will have sides of length x. Hypercube A has
hypervolume(A) = , boundary volume(A) =
since the hypercube has 8 hyperfaces, each with volume .
Similarly, Hypercube B has hypervolume(B) = boundary volume(B) = .
Now suppose that we wish to choose our base cube in such a way that hypervolume(A) / volume(C) = boundary volume (B) / hypervolume(B)
Plugging in our formulae, we have
Cross-multiplying, we have
This has precisely one positive solution for x, namely
If we take our “base cube” C to have sides of this length, then we (and by “we” I mean D. G. Leahy and likely no one else) call this cube the “absolute dead center cube.”
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Unfolding 4D cube into 3 D space
Unfolding 3-D cube into 2-D plane results in a flat cross (3 squares across and 4 squares vertically – in total 6 squares since the middle square should be counted once). Unfolding 4-D hypercube into 3-D space results in 8 cubes:.
The average of the mean orbital distances of each successive planet in relation to the one before it approximates Phi
82944 & THE FOUR FUNDAMENTAL FORCES & THE GOD PARTICLE
the square of the quotient of factorial 9 divided by the sum of its constituents — the primary natural numbers — equals the product of the only three numbers in the natural number system which are — identically — their integral products.
( 10 ^ ( 143.9999879 / 37 )) / 37 / 18 = sqrt 137.035999701
…there have been many numbers associated to the divisor 37 and the collective unconscious forms:
Leahy’s dream number …..2808
Van Halen’s number……….5150
Hindu number ………………108
Hebrew number …………….288
John of Patmos number…..1260 and 666
Leahy triple logic number….82944
Denglers number as name…1069
John Michell number………..1080+666 = 1746
Mayan/Aztec number ……..2304
…the key has always been the divisor number 37 .
The following is from an article in the Jan. 10 , 2009 , magazine , New Scientist, called , ” Inside the Mind of a Autistic Savant “. The article goes on to talk about the savant Daniel Tammet , who is a human calculator of whose one of many feats , set a European record for the number of digits of Pi he recited from memory ( 22514 ). The article interviewer , Celeste Biever , interviewed D. Tammet and here is a portion of her interview concerning the number 37 and D. Tammet’s fascination with this particular number:
Question: When did you realize you had special talents?
Tammet: At the age of 8 or 9 , I was being taught maths at school and realised I could do the sums quickly , intuitively and in my own way–not using the techniques we were taught. I got so far ahead of the other children that I ran out of textbooks. I was aware already that I was different because of my autism, but at that point I realised that the relationship I had with numbers was different.
Question: To most people, the things you can do with your memory seems like magic. How do you do it ?
Tammet: The response that people often have to what I can do is one of ” gee whiz” but I want to push back against that. One of the purposes of the book I’ve written , ” Embracing the Wide Sky ” , is to demystify this, to show the hidden processes behind my number skills. I have a relationship with numbers that is similar to the relationship that most people have with language. When people think of words they don’t think of them as separate items , atomised in their head , they understand them intuitively and subconsciously as belonging to an interconnected web of other words.
Question : Can you give an example?
Tammet: You would’nt use a word like ” giraffe ” without understanding what the words ” neck ” or ” tall ” or ” animal ” mean. Words only make sense when they are in this web of interconnected meanings and I have the same thing with numbers . Numbers belong to a web. When somebody gives me a number , I immediately visualise it and how it relates to other numbers. I also see the patterns those relationships produce and manipulate them in my head to arrive at a solution, if its a sum , or to identify if there is a prime.
Question: But how do you visualise a number ? In the same way I visualise a giraffe ?
Tammet: Every number has a texture. If it is a ” lumpy ” number then immediately my mind will relate it to other numbers which are lumpy–the lumpiness will tell me there is a relationship , there is a common divisor , or a pattern between the digits.
Question: Can you give me an example of a ” lumpy ” number ?
Tammet: For me the ideal lumpy number is 37 . It’s like porridge. So 111 , a very pretty number which is 3 times 37 , is lumpy but it is also round. It takes on the properties of both 37 and 3 , which is round. It’s an intuitive and visual way of doing maths and thinking about numbers.
Question: Why do you think you treat numbers this way ?
Tammet: When I was growing up, because of my autism , I didn’t make friends. Numbers filled that gap. The numbers came alive. My mind was able to pick out patterns and to make sense of them. It was similar to how a child would aquire his first language….
Question: What can we learn from the way your mind works ?
Tammet: The differences between savant and non-savant ability have been exaggerated. Savants are not freaks, cut off from the rest of humanity. The thinking of savants is an extreme form of the kind everyone has. The aim of my book is to show that minds that function differently such as mine , are not so strange , and that anyone can learn from them. I also hope to clear up some misconceptions about savant abilities and what it means to be intelligent or gifted …( end of article quote )
Wolfgang Pauli knew through his mandelas and the collective unconscious parameters of Carl Jung that the fine-structure constant ( 1/137.035999701 ) , a primal number , has a connectiveness to the primal numbers of man.
This connectiveness number is the integer…37:
Leahy dream number ….2808:
( 10 ^ (( 2807.9999879 / 37 ) – 72 )) / 666 = sqrt 137.035999701
Van Halen’s number …5150:
( 10 ^ (( 5149.99999881 / 3.7 ) – 1388 )) / 666 = sqrt 137.035999701
( 10 ^ ( 107.999999879 / .37 ) – 288 ) / 666 = sqrt 137.035999701
Druid , John of Patmos number …144:
( 10 ^ ( 143.999987919 / 37 )) / 666 = sqrt 137.035999701
John of Patmos numbers …1260 and 666:
( 10 ^ (( 1259.99978254 / 666 ) + 2 ) / 666 = sqrt 137.035999701
Leahy’s triple logic number …82944:
( 10 ^ ( 82943.9930413 / 32 / 666 )) / 666 = sqrt 137.035999701
Plato’s number of the world soul…2592:
( 10 ^ ( 2591.99978254 / 666 )) / 666 = sqrt 137.035999701
Dengler’s name change number …1069:
( 10 ^ (( 1068.99998792 / 37 ) – 25 )) / 666 = sqrt 137.035999701
Mayan/Aztec number …2304:
( 10 ^ (( 2303.99978254 + 288 ) /666 ) / 666 = sqrt 137.035999701
Harlston’s Hunab number ( Aztec) …378
378 + 288 = 666
R.Tomes master harmionic number …3456:
( 10 ^ (( 3455.999789 / 666 ) – 46 ) / 666 = sqrt 137.035999701
The Works of Jerry Iuliano
Ancient Numbers Revealed in Scientific Formula
NJ Diagram and Ancient Metrology
Phi2 x 6/5 = Pi
Square 12 feet x 12 feet has area 144 sq. feet, 144 feet = 1728 inch (12″ per 1 foot).
Cube 12x12x12 has volume 1728 cubic feet, 1728 feet = 20736″
Volume of a cube (6/5 = 1.2) = 1.728
Coincidentally: Moon Radius = 1737 km
Sun and Moon (observed from Earth) appear to have size 30 arc minutes (0.5 degree);
Full circle has 21,600 minutes (360×60), so the moon fits the full circle 720 times
One day has 24 hours 60 min in each hour: 1440 minutes to one day and 86400 seconds to a day.
Sun (and Moon) moves by its diameter on the sky in 12o seconds (2 minutes)
Perfect cube numbers:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728
The 6th number is 216 or 6 x 6 x 6 and 6th sphere on the Tree of Life is Sun or Tiphareth on Hebrew.
37th triangular number is 666. 3 + 7 = 10 or tetraktys, Tree of Life.
Number 666 in binary is 1010011010, which contains 10 digits, or first ten Ideas in Universal Mind, the Tree of Life.
In magickal square (kamea) of the Sun, all numbers are added in any direction to produce the sum of 111, and since there is 6 columns and lines, 111 x 6 = 666.
In 1 Kings 10:14, Old Testament, there is a story of King Solomon receiving 666 coins of gold.
Sol-Om-On is the name of Sun in three languages: Word SOL means “Sun” in Latin, OM or AUM means “Sun” in Hindu Sanskrit and ON means “Sun” in Egyptian.
If we add up all numbers from 1-36 it will result in 666. 36 is sacred Pythagorean number of Sun.
King Solomon’s seal is 6-pointed star, the hexagram.
So, again the number of the Sun is 6 or 666.
Carbon (CO2) which is the chemical basis of all physical life on Earth has 6 protons, 6 neutrons and 6 electrons. The shape of carbon molecules points to hexagram, the symbol of unity.
The perfect cube (6 X 6 X 6) is perfect ashlar of Freemasonry and Philosophers Stone.
Number 216 or 6 x 6 x 6 is also produced of 3 x 3 x 3 + 4 x 4 x 4 + 5 x 5 x 5, the cubical number of perfect Pythagorean triangle c2 = a2 + b2. These ratios of 3:4:5 is ancient Egyptian symbol for Trinity of Osiris, Isis and Horus.
Serpent (TITh)= 419
Lion (ARIH)= 216
+ 31 (AL – the God associated to Chesed and the Key to Crowley’s Liber AL) = 666. Trinity of Serpent (female-energy), Lion (male-movement) and Son (neutral-individual life).
Interesting, multiples of 3 multiplied by 37 = repeating digits
(1×3) or 1+1+1=3 x 37 = 111
(2×3) or 2+2+2=6 x 37 = 222
(3×3) or 3+3+3=9 x 37 = 333
(4×3) or 4+4+4=12 x 37 = 444
(5×3) or 5+5+5=15 x 37 = 555
(6×3) or 6+6+6=18 x 37 = 666
(7×3) or 7+7+7=21 x 37 = 777
(8×3) or 8+8+8=24 x 37 = 888
(9×3) or 9+9+9=27 x 37 = 999
108 has 12 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
216 has 16 divisors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
360 has 24 divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
666 has 12 divisors: 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
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PS1 The Cosmological Circle – Symbol and Instrument for Universal Harmony
The New Jerusalem Diagram is also known as The Cosmological Circle.
The Cosmological Circle is a geometric diagram that has appeared in the arts, crafts, architecture, religion and literature of cultures around the world, and is associated with their golden ages. Because it’s the visual representation of the harmony naturally inherent in the structure of the numbers 1 through 12, it encodes the ideal patterns and proportions toward which nature’s forms strive.
It has been used as a symbol of universal harmony because it represents the complete order of the universe and thus is a microcosm appearing in the designs of cosmic temples and sacred spaces worldwide. It served as as an eternal standard of reference, a pattern and instrument of statecraft for civilizations which were “cosmologically ordered societies” seeking to attract to their citizens happiness, blessings, justice and prosperity. Its proportions were used as an intelligent model for integrating weights and measures with human dimensions, and for sanctifying the Earth with sacred architecture.
NJ Diagram (squared circle) as blueprint for Stonehenge and Native American Chetro Ketl Kiva
Its dimensions are described as the Heavenly City described in The Book of Revelation, seen in the plan of the Buddhist Brobodur temple, Stonehenge, Glastonbury, and described as Plato’s ideal city Magnesia. Its central “squared circle” plan is also found in the sizes and relationships among the Earth, Sun and Moon.
No one invented it – it’s just the way that numbers naturally harmonize, providing the ideal towards which nature strives and humans have designed art and society.
Worth a Look
Constructing the Cosmological Circle teaches how to construct the diagram by the traditional geometric method using a compass and straightedge. The book also provides the background necessary to appreciate its geometry, symbolism, and appearances in art, architecture and literature around the world.
Artists and architects will want to see how this model of harmony has been used in the past.
Readers interested in symbolism and philosophy will find a key to understanding traditional wisdom teachings.
This book is primarily based on the work of John Michell who has explored and written about the New Jerusalem Diagram and Cosmological Circle for over thirty years.
The book is organized in five sections. The first, From Chaos To Cosmos considers some ancient creation myths which describe mathematical aspects to the birth of the universe. Studying nature’s order, its “outbursts of truth” reveals first hand how the universe is organized and unfolds. Today, science, religion and mythology present differing views, although this wasn’t always the case. All societies organize and comport themselves in accord with the cosmology they perceive. In the past intentionally planned “cosmologically ordered societies” were formed. They’re sometimes recognized by their deep interest in particular numbers which recur in their religion, literature, statecraft and the proportions of their monuments and buildings. They did this to resemble as closely as possible the harmony they perceived in nature’s numbers at the heart of the universe and in themselves.
Thus the superior man Brings Order out of Chaos.”
– I Ching (kua 3, Chun)
The second section, called Geometer’s Heaven and Earth looks at two shapes central to the sacred art, architecture and philosophy of cultures where universal order was a main interest. These shapes are the circle and square, worldwide symbols of eternally existing heavenly perfection and its transitory, material approximations. Circle and square are predominant in the Cosmological Circle diagram so we benefit by understanding their geometry and symbolism.
Of all the ways that the circle and square interact, the most interesting is the “squared circle” where they have virtually the same perimeter or area. This next section, Squaring The Circle, looks at the geometry and history of this seeming impossibility. Symbolically, a squared circle signifies the meeting of Heaven and Earth, the ideal and the actual, which by definition are different. Cosmologically ordered societies often used squared circle geometry in their sacred architecture to indicate that “Heaven and Earth meet here”. By looking at various examples we’ll gain insight into the geometry, history and symbolism of the squared circle at the center of the Cosmological Circle construction.
The next section, Construct the Cosmological Circle is the heart of this book. It guides the reader along illustrated step-by-step directions for constructing the Cosmological Circle with a compass and straightedge. It’s steps are well worth pondering for the way they integrate different shapes and their proportions into one harmonious whole. Artists and architects may use the construction for creative projects. Some people will approach it as a meditative process and symbol.
The final section, called The Number Canon removes the geometric mask and looks into the numbers at the heart of the Cosmological Circle. The way the twelve numbers combine and organize into an all-encompassing whole was the model for most of the ancient world as a microcosmic representation of the harmonious universe. It was used as a standard for defining relationships among weights, measures, music and the proportions of sacred art and architecture. This section looks at some of the interesting numbers in the Cosmological Circle and their recurring appearances in various cultures and in nature.
A Bibliography lists some books and web pages useful for further exploration of the Cosmological Circle in mathematics, art and philosophy.
The book is thoroughly illustrated with many quotations. It is printed double-sided, 115 pages.
Table Of Contents
From Chaos To Cosmos 11
Cosmogeny and Cosmology 11
Chaos and Order 13
Divine Geometer 15
Cosmologically Ordered Societies 20
Geometer’s Heaven and Earth 28
Circle and Square 28
The Heavenly Circle 29
The Earthly Square 32
Heaven And Earth Together 33
Square Mediates Between Circles 36
Squaring The Circle 38
Pursuing the Impossible 38
Earth And Moon Square the Circle 42
The Great Pyramid 46
The Pantheon 48
Native American Kivas 49
Borobudur Temple 51
Cosmati Pavement of Westminster Abbey 52
Alchemical Fusion 53
Construct the Cosmological Circle 55
The Number Canon 81
Traditional Twelve 83
Highly Composite Numbers 85
Rhythms of Human and Celestial Bodies 87
The New Jerusalem Grid 88
Seven Hundred Twenty 91
Celestial Dimensions 98
Heavenly Cities 104
Five Thousand Forty 107
Perimeters and Areas 109
There are many other measurements which confirm that Teotihuacán was “laid out in a 3:1 pattern and more so, that this pattern is a reflection of the Citadel’s base perimeter measurements of 1,320’ x 1,320’ making the city comport to the duodecimal system of ancient metrology having its sides as 1 + 3 + 2 = 6 and 6 * 6 = 36 (per face) * 6 (six faces of a cube) = 216 (something Harleston would be pleased to see) * 12 such cubes = 2,592 and this 2592 is precisely the fractal of the Mazzaroth/Zodiac of 25,920 years – known, of course, as the Great Precessional. These 216s reflect the 12 constellations of the Mazzaroth (Hebrew for Zodiac). Likewise, and my World Mystery friends will appreciate this – the 216 is likewise the fractal of the Moon’s diameter of 2,160 miles and forms the “12 circles” of the New Jerusalem Diagram made popular by Dr. John Michell of the Dimensions of Paradise fame – philosopher to the hippies! And, of course, this is to say nothing of the fact that it reflects the circumference of the entire Nautical Earth at 21,600 nautical miles (6072’ = 1 nautical mile * 21,600 nautical miles (there being 60 miles per 1 degree * 360° = 21,600 nautical miles and 6072’ * 21,600 nautical miles = 131,155,200 Linear Feet/5,280’ (one mile) = 24,840 miles which approximates the circumference of the Earth in “statute miles.”
Read more here: TEOTIHUACAN – CITY of GOD or GODS?
- The Cosmological Circle
- DNA, APOCALYPSE, & THE END OF THE MYSTERY
- Unique Metric & the Apocalyptic New Jerusalem
- http://dgleahy.com/p04.html – Sorted Diagonals
- NJ in DNA structure? http://youtu.be/4fftPh0awuw
Please contribute your comments!