Principles of Design


This section deals specifically with Priciples of Visual Design. I have several sets of webpages that are heavily laden with images that I have to keep subdividing as they get too big. As you read you will see that the articles cover the same material but from different angles. My purpose here is to try and explain some of the reasoning or visual logic behind what we see in visual designs. Consider the following facts.

In Genesis, as Jacob sets up his pillar he says 'of all you give to me, I will give the tenth to thee'. The implication is that the pillar displayed the 1:10 ratio. Egyptians manufactured their obelisks to the 1:10 ratio. The first ten numbers add to 55. The Washington Monument is 555.5 feet tall.

The Magic Square of the Sun is a 6x6 grid with 36 cells that contain the first thirty six numbers which add to 666. The constant of a magic sqaure is the total divided by the number, here that is 666/6, or 111. 111/2 is 55.5, the measure of the base of the monument.

A circle with a circumference of 1000 contains a square with a perimeter of 900. The ratio is 10:9. To learn the size of the square from the circle we multiply by .9. To find the size of a circle from the perimeter of the square we multiply by 1.11 (9x1.11 = 1).

The word triangle is not in the Bible, and the word circle appears only once. This means that some squares are indication circles. In Ezekiel we read of a 5000 square containing a square with sides of 4500 and a 'suburb' of 250 in the north, east, south and west. This is the 10:9 ratio from above. If we multiply by four, we get a square with a circumference of 2000, containing a square of 1800 and a border of 100 between them. If we make the square a circle the 1800 square inscribes in that.

If we make our square 500, and multiply by 1.11, we get a 555.5 circle. Two vesicas of 555.5 overlap 277.75; this is the short axis of a rhombus that has a long axis of 481, the height of the Great Pyramid.

William Stirling tells us that 'the old method' of determining the diameter of a circle with an area equal to a square was to divide the diagonal of the sqaure into ten parts, and use eight of those. You will recall that the diagonal of a square is 1.4142 times one of the sides, so that the radius would be .4x1.4142 x one of the sides. .4 x sqrt of 2 = .56568, which means that the diameter of the circle equal to the square is 113.136 percent of the side of the square. 5.657 squared is 319, and 100 divided by Pi is 318.3.

If we want to produce a square and circle with the same perimeter we use 127.1 percent of the side of the square. Taking the base of 755 feet and multiplying by 1.271, we get 962, dividing by 2 we get 481.

  • Geometric Design Principles

  • Christian Hermetic Principles   

  • Feeding of the 5000   

  • Circles and Squares   

  • Cutting of the Elm   

  • The DC Map Analogous to the Milan Cathedral plan.

  • The Master's Square

  • The Masonic Lodge Floor Explained

  • How to Derive the Sri Yantra


  • Symbolic Masonic Architecture A Lost Art?

    In The Canon, the evidence that he offers of the ancient design technique consists of images of the Milan Cathedral plan, one of the floor plan and one elevation plan. These images feature the 'regulating lines' for the design, just as Jonathan Hale speaks of in The Old Way of Seeing. Stirling states that the esoteric doctrine of the Cathedral builders was the Kaballah, and that Kaballistic number symbolism helped to structure medieval arts and literature. It is suggested that the book of Revelation and I Kings have 22 chapters since there are 22 Hebrew letters. Tarot Trumps follow this pattern.

    Next Stirling introduces us to the Tree of Life, and you hope that he is going to show you how it 'fits' some work of art, a Cathedral perhaps, but he never does. When he presents the cathedral elevation, he points to a rhombus and a cross as a sexual metaphor that supposedly underlies the design. The reason he never maps the tree to the Cathedral plan is that he used the Kircher version of the tree, which doesn't fit. I believe that if Striling had used a different version of the tree, he would have seen what I saw.

    In Stirling's defense, we will point to an image of Hugh Libergier, architect for the Reims Cathedral who died in 1263, where you see upright rhombus on the model that he is holding. This indicates a tradition of at least 300 years for that symbol in the early 1500's.

    In his Mysteries of the Cathedrals, Fulcanelli speaks of Offerus' belt that was marked with crisscross lines; he suggests that it is also a fish, and a net. He finally calls it a diamond pattern indicating the first matter of the Work, the very essence of things. Offerus is the origin of the name Christ-opher, and you can see him carrying the child over the water below.

    On page 70, he writes that the Chartres Cathedral appears to be based on alchemical science which investigates transformations of the original substance, elementary matter, and that the Virgin Mother (in all cultures), when stripped of her symbolic veil is none other than the personification of the primitive substance. Below we see the Priestess Tarot Card.

    On page 51 Fulcanelli depicts the Work as a Book sealed with seven bands marking seven sucessive operations. On page 70 he shows in the cathedral where alchemy is represented by a woman, seated on a throne with a ladder of nine rungs in front of her, indicating, he says, the nine sucessive operations of the hermtic labor. These both remind us of spheres on the Tree of Life.

    Below we see that Albert Pike's version of the Tree of Life features upright rhombus, and beside that we see that Aleister Crowley uses them too. Note that all Crowley's tens are trees of life. The upright rhombus appears to have been an abreviation for the Tree of Life.

         

  • Cornelius Agrippa published Three Books about Occult Philosophy in 1531, the Milan Cathedral plan image dates from 1521, and the first published image of the Tree of Life appeared in 1516. Compare that image (below left) to the full Libergier image (below right). Note the cap and cape. Compare the shape of the seat to the compasses in the Libergier image.

     

    Master Builders with Models

    [Please see this book excerpt about Hugh Libergier, which points out that he was a master craftsman-architect who was trained in carpentry and stone-cutting. While it is suggested that Hiram was such an architect (a builder who was in direct control of the entire project), we know that the plans for the Temple were given to David who passsed them on to Solomon. Hiram was not the architect there.

    It has been pointed out that during the Renaissance craftman-architects were replaced by gentlemen, humanist, artists. Still we see that Palladio was trained as stonemason.]

    Revisiting the cathedral image, we can now see that this form of the tree maps to that. Looking at the planning map, we see that the same template was used. As is shown above, New Hampshire Avenue forms a triangle with the same base angles as the GP, so the template was shortened to about 75% for the map, in order to match the pyramid cross-section. This produces 23 degree diagonals in the map instead of 30 degrees. The Kircher tree does not work there either. Note that 1) a pentagram overlapping a hexagram is essential to this image, and 2) 23 degrees is the angle of the tropics.

    The DC Map is analogous to the Milan Cathedral plan.

    Any triangle can be represented by compasses as they do not have a set angle, and the Masonic square is half an oblique (tilted) square and needs to be 90 degrees. A triangle and an oblique square can be understood as representative of the compasses and a square. If you look down the page you can see that the District of Columbia boundary is an oblique sqaure with 10 miles sides. That is the square that goes with the triangle above. (More on that later.)

     

    Sandusky, Ohio

    As the story goes, you can forget all that stuff about Masonic symbols in the DC map, because Sandusky, Ohio, "Is the only city in the world as far as is known to have been laid out according to a Masonic master plan". Remember that the cathedral plan dates from 1521, the map from 1792, and the Sandusky plan from 1818; and that is it. No pentagram or Tree of Life?

    By now you should be able to look and tell that the base angle of the triangle in the Sandusky map formed by the compasses there is about 52 degrees. (Go ahead and measure). You will recall that New Hampshire Avenue forms the same angle in the DC map, so maybe not 'the only city'. Master plan eh?

  • I recommend that this shows that Symbolic Masonic Architecture is not a lost art, that there is a direct line between the design principles of the map and the plans of cathedrals and the Great Pyramid, and that the esoteric doctrine of the Founding Fathers was the Kaballah, just like the Catheral Builders. Today the main Kaballistic branch of Masonry is the Scottish Rite, headquartered in Washington, D.C.

    Although the SR was not instituted in the US until 1801, the so-called 'higher degrees' were being offered in Lodges that were chartered by the Irish Grand Lodge that favored those rites before that time. The Royal Arch Degree is the thirteen Scottish Rite Degree, and is the crown jewel of the Rites. If you look, you will see that the first US lodge to offer that was the Fredericksburg Lodge where George Washington was a member.

    Just in case you missed it I am going to repeat that the version of the tree introduced by the Jesuit Kircher in 1652 does not fit either the map or the cathedral plan because it is composed of two hexagons, while the template for those uses a hexagon overlapping a pentagon, esoteric symbols of the macrocosm and the microcosm. You will also note that the Kircher version of the image doesn't look like a tree, but looks like a ladder that is described in Genesis 28.

    There we read where Jacob dreamed of a ladder set up on the earth that reached to heaven with the angels of God ascending and descending on it. Jacob sets up a stone as a pillar, and renames the place that was Luz at first (Light) to Bethel (house of God), saying that the pillar "shall be God's house and all that thou shalt give me I will surely give the tenth to thee".

  • Egyptian obelisks were built in a 1:10 ratio, with the base being 1/10th the height. The first ten numbers total 55. The Washington Monument is 55.5 feet wide and 555.5 feet tall. Two 555.5 foot diameter circles overlapping produce a vesica 481 feet tall, the height of the Great Pyramid. 55.5 x 2 = 111, the numerical constant for the magic sqaure of the sun.

    In the first chapter of Ezekiel we read where "the living creatures ran and returned as the appearance of a flash of lightning". If you limit the number of ornaments on the tree to nine and consider the base to indicate the earth at sphere ten, the Christmas Tree makes a good Tree of Life.

    The star at the top reminds us that the tree, just like Jacob's ladder or the Djed Pillar, connects the earth and the stars or heavens. The main difference being that the ladder sits upon the earth, while the tree is rooted in it. Both suggest a vertical journey of ten steps. Legend tell us that souls reside in the Milky Way (stars, the heavens, Heaven), and that they come from and return to there via seven planetary spheres (which includes the sun and moon). Adding the stars and earth gives us nine spheres, and adding the Throne of God at the top gives us ten.

    The ancient order of descent is given as Saturn, Jupiter, Mars, the sun, Venus, Mercury, and the moon. Since we know that Ptolemy's system is Copernicus system with the sun and earth swapped, we can substitute the earth for the sun and get the 'correct' order of Saturn, Jupiter, Mars, the earth, Venus and Mercury. Remember that the Catholic Church was still burning people in 1600 for saying out loud that the sun was the center of our system, and still burning old astronomy books.

    . . .

    The phrase 'occult blind' refers to a dis-information method where the non-initiated are kept further from the truth. In 1531 Cornelius Agrippa publishes Three Books about Occult Philosophy in which he ascribes each planet to a number and a specific magic square, in what he calls the divine order of celestial numbers. As Saturn is the farthest planets, and as there is no magic square of 2, Saturn is associated with the number 3. Jupiter is assigned 4, following the ancient order of descent.

    If you look at the correspondences for the tree ascribed by the Golden Dawn, we see that they follow the same numbering system, and put Saturn at 3. It makes sense. The soul descends on the tree in the order of numbers, and in the descending order of the planets, with the earth and sun switched. Now look at the Kircher tree and note where he puts the planets?

    He has removed the earth from sphere 10, and kept the sun at 6 and Jupiter at 4. He moves the moon from 9 to 10, Mercury from 8 to 9, and Venus from 7 to 8. He moves Mars from 5 to 7 and moves Saturn from 3 to 5.

  • I suggest that we can figure out the correct placement using the numbers and astrological signs for the planetary spheres. For instance, the sign for the moon looks like a 9, and the sign for Jupiter looks like a 4. The earth's sign is a circle with crossed lines inside of it, which is composed of the elements in the number 10. Also the Roman numeral for 10 is X. There is most of an 8 in Mercury's sign, and most of Mars' sign in the number 5. The sign for Saturn looks like the number 3 and the Hebrew letter yod.

    As you can see, Kircher uses Roman numerals so that the connection between the sign and the number is not noticeable. Note that the Kircher tree doesn't work on the dodecahedron below either, as that features pentagonal faces.

  • Simply stated, my primary thesis is that the Washington DC planners used more than one image as templates for the design of the city map - one of those images was the cross section view of the Great Pyramid as seen above , while two others were Metatron's Cube and the Kabbalistic Tree of Life. I suggest that they chose one version of the tree over others that were available for several reasons.

    When speaking of geometric solids, after the cube, tetrahedron, octahedron, and icosahedron Plato writes,"There still remained a fifth construction, which the god used for embroidering the constellations on the whole heaven". As 1) Plato's statement is vague, and 2) he gives no further explanation, and 3) the dodecahedron has 12 faces, and 4) our number symbolism associates 12 with the zodiac, later Greek philosophers assign the dodecahedron to the ether or heaven or the cosmos.

    Above we see an astrology chart drawn by Johannes Kepler. If you extend the lines across the center you will see that there would be 16 triangles. If we extend the sides of the central square we can produce a figure made of 16 squares. The squares and triangles have the same area, and the center square is four of either.

    If the outer square we the circle of the earth, the central square would be located between 30 degrees latitiude lines. As Mercury ranges to 31 degrees, and it is the most eccentric planet, we know that all the planets fit within this square conceptually. The band that surrounds this is the zodiac belt through which the planets travel. Outside that is the other fixed stars.

    I contend that this is the image that Plato alludes to, and that it also illustrates the Hebrew Camp in the desert, the New Jerusalem, and the city in Ezekiel 48. You will recall that the tribes were divided into groups of three that traveled under four different standards, and that the city had three gates to the north, three to the east, three south and west.

    Hamlet's Mill

    That 1969 book was subtitled 'An essay investigating the origins of human knowledge and its transmission through myth'. Unfortunately their interpretation of transmitting knowldge is not one that a Kabbalist or a Gnostic would use, as they propose that transmission need not entail understanding.

    They point out that myth was essentially cosmological and astronomical, and that the times and tenses are deliberately scambled, while the common language ignored local beliefs and cults, concentrating on numbers and measures to express their observations of natural lawfulness. They point to a huge framework of connections that is revealed at many levels, between myths. The purpose of myth was to express the behavior of the vast complex of variables once called the cosmos; of the general order of things as it could be conceived by the mind of Man.

    After noting the degree of difficulty that confronts the myth writer when addressing the wheels within wheels that comprise the system, they conclude that "there is no system that can be presented in modern analytical terms" that results from looking at a world of myths. They say that there is no key and no principles because the structure of myth comes from a time when "there was no such thing as a system in our sense"; it was they suggest a spontaneously generated Art of the Fugue.

    "We have insisted on the vanity of any attempt to give an image of the archaic cosmos. Even as a magic scheme it would have to be a design of insoluble complexity - and Plato's machinery promptly dissolves into contradictions, no real model at all."

    They appear not to remember how myth works when they say first of all that the 'floods' refer to an old astronomical image based on abstract geometry, theh right above that act suprized that 'there are many events described with appropriate terrestrial imagery, that did not happen on earth. Duh. Later, "features are scrambled for keeping up an impression of the wonderous".

    Even after speaking of scramblings and confusions, when confronted with the idea that the 'true earth' appears like a ball made of twelve pieces of leather of differing colors, the inclination is to say 'dodecahedron'. That the world is a dodecahedron. In the Timaeus there is a story that the Demiurge had the twelve faces of the figure decorated with figures which probably stood for the signs of the zodiac, but the image of a ball doesn't work for that as the zodiac belt is ony 14 degrees wide. Plutarch had suggested that the dodecahedron resembled the zodiac and the year.

    Others presume that it was the whole system that he was talking about. In Philolaos (by Plato) we read "In the sphere there are five elements, and what is the hull of the sphere, the fifth." Here he likens the dodecahedron to a hull, the containing frame of a ship, the cosmos. Once again, I suggest that the astrology chart above fits the bill as a 12 part frame for the zodiac and the year. You will recognize the notion of the four elements as signifying the earth.

    Here is how Aristotle depicted the four elements. Try doing a search for "Aristotle elements" in an image search, and you will see all the results will be squares. Once again, the four elements together refers to the earth, so what we see is a square representation of the earth that fits in the middle of the astrology chart above.

    The square that we are dealing with is the 4x4 square of Jupiter that has the same area as perimeter, 16. In the center there are four squares, and they are surrounded by 12 more. I recommend that the astrology chart with a square in the middlle, surrounded by 12 triangles (or squares) is the 2 dimensional analogy to the cube inside of Metatron's Cube seen above. In this case triangles were substituted for pentagons. This is the tree that brings forth twelve fruits.


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