The Bead Game begins with a player presenting a starting point, that might be an image or symbol, a piece of music or text, on which he elaborates; then others are given a chance to contribute, after which there is a meditation on the subject of the Game, before more presentations. In the context of the book, this is a finite process, with a definite beginning, middle and end, but in real life, this is the same process as the development of science, religion and philosophy.

In the case of the map, the opening play consisted of 'staking out' the 40 mile boundary of the oblique (diagonal) square that constituted the District of Columbia by Andrew Ellicott, followed by establishing north-south and east-west lines (the basis of the orthogonal street grid) by Ellicott and Benjamin Banneker. L'Enfant adjusts the square street grid and overlays it with a system of diagonal streets that result in the templates that I have spoken of above.

A 40 Mile Oblique Square Boundary

Note that it was Thomas Jefferson who instructed that the district map be displayed with the corner up as we see in this 1792 Ellicott drawing entitled Territory of Columbia. The vertical blue line is 16th St. through the WH, and the horizontal blue line is E. Capitol St. through the CB, showing that it is not the case that "The east-west diagonal of the square also crosses over the Capitol building and the north-south diagonal also crosses over the White House as well as the Masonic headquarters" as suggested on this site. The Capitol was not the center of the map but was rather what is called a 'point of beginning' by surveyors, a control point.

The Introduction to Hesse's book "Journey to the East" describes the game as "the manipulation of a complex archive of symbols and formulas, based in their structure on music and mathematics, by means of which all knowledge, science, art and culture can be represented".

We are reminded of the story of Enoch who was told of the upcoming Flood (he was Noah's grandfather) and was commanded to build two pillars or columns on which to preserve all of human knowledge for future generations. To be effective, the pillars would have to somehow encode 'a complex archive of symbols by means of which all knowledge can be represented'.

Enoch represents Symbolic Art and Architecture, which, like the Kabbalah, seek to transmit and preserve knowledge through the use of symbols , like a building or landscape. This includes poetry, drama and literature as well - anything that promotes symbolic thinking and reasoning. The Enoch legend lies at the heart of both the Kabbalah and Masonry (especially the Scottish Rites).

Remember that Masonic and Kabbalistic Legends are not Histories. They rely on symbolism and allegory, like the parables in the Bible, and stories about Enoch don't depend on a person named Enoch in the way that stories about George Washington do. The description of Solomon's Temple that we read represents the canonical pattern for the guidance of architects in the design of temples and churches more than it does an historic account.

Design Principles

For his first Ceremonial Bead Game as Magister, Joseph Knecht's "idea was to base the structure and dimensions of the Game on the ancient ritual Confucian pattern for the building of the Chinese house: orientation by the points of the compass, the gates, the spirit wall, the relationships and functions of buildings and courtyards, their co-ordination with the constellations, the calendar and family life, and the symbolism and stylistic principles of the garden. Long ago ... he had thought that the mythic order and significance of these rules made an unusually appealing and charming symbol of the cosmos and of man's place in the universe". (page 24 ML)

What Knecht is saying is that the guiding principle for the design of the Confucian house was that it should symbolically represent man and/in the Universe, the micro and macro-cosms and how they relate conceptually to one another. Note that descriptions of Jacob's Pillar, the Tabernacle and Temple in the Bible are based on 'the ancient ritual Jewish pattern for the building of the place or house of worship (beth el)', which along with the Masonic Lodge are each a "symbol of the cosmos and of man's place in the universe".

Canon Law

The 'rules' to which Knecht refers can collectively be called canon law, or The Canon. Different cultures regulate different things for different reasons. Notions such as the ones that Knecht mentions were involved in the Canon of the Building Arts that regulated the Temple and Cathedral builders, at times when the priests and clergy were the Master Builders, when Building secrets were Church secrets...

Secrets like the symbolic significance of the patterns that are used to determine the structure and dimensions of these public buildings and spaces, which Schwaller de Lubicz calls 'libraries in stone'. To him, Temples were encyclopedic, archives of symbol sets, and I suggest that their design and construction constitutes a Bead Game for the initiated; that is, if you know where and how to look.

Please see this article about geometric design principles that suggests that "some of the great cathedrals were modelled on the 12th century (atomistic) conception of the form of matter". The idea being that they were imitating the shapes and patterns of Nature in their designs. Recall that Francis Bacon wrote in the Novum Organum, "We raise not a Capitol or Pyramid to the pride of man, but a Holy Temple in his mind on the model of the Universe, which model we imitate".

The Milan Cathedral Plan

In 1896 William Stirling published a book entitled "Canon: An Exposition of the Pagan Mystery Perpetuated in the Cabala as the Rule of All the Arts", which suggested that the esoteric doctrine of the cathedral building clergy was synonymous with the Ancient Mysteries and that the symbols of the Church were disguised symbols of that Mystery and the Kabbalah- the prime symbol of which is the Tree of Life.

The book presents a 1521 woodcut of the Milan Cathedral plan which is overlaid with geometric figures demonstrating the regulating points and lines of the design. Stirling calls the image "a most important illustration of the principles of architecture of all ancient peoples" and "one of the most direct evidences of the old mystical rule of building".

1521

According to the book, the geometrical figures forming the basis of the plan of the Milan cathedral are the rhombus or vesica and it's mystical compliment the cross, seen as emblems of the double soul of the Universe and what is called the Royal Wedding (hieros gamos). The cross is the masculine component and the vesica is the feminine one. It's a dualistic sexual metaphor at one level. As A.E. Wate puts it, 'the union of male and female is their adopted form of symbolism'.

The first thing that we notice about this image (see figure 4) is the three concentric circles and the equilateral triangles. Next we notice that the rhombus grid that results from projecting the sides of the triangles determines the distance between the columns (see figure 5). Units of the vertical grid are one small triangle wide, and ones of the horizontal grid are one small triangle tall; that is to say, the triangle and rhombus 'determine the structure and dimensions' of the elements of the cathedral plan.

This geometric method of design is called 'polygonal projection' in general and 'ad triangulum' (by the triangle) in particular. The projection method is the same as 'stellation' where the sides of regular polygons are extended until they intersect. Triangles and squares don't stellate, but if we stellate a hexagon we get a hexagram which is twin triangles, as you can see above. The equilateral triangle and the hexagram/gon are intimately tied to one another, as well as to the Vesica Pisces.

Looking at the central circle in the Milan cathedral plan (figure 6), we see a triangle, a hexagon and a square. All four corners of the square touch the circle and the cross. The triangles are formed by the diagonals of the hexagon. In the cathedral plan the triangulum form was used for the elevation and the quadratum was used for the floor plan. [Note the cross and thinly veiled phallus.]

Adding two more circles (figure 7) shows the ad triangulum to derive from the vesica. Where the circles intersect determines the corners of the triangles and hexagon/grams. The red triangle is six small triangles wide and six tall. The base of this triangle is floor level and it's height is the roof height.

Projecting the top sides of the hexagon in the central circle onto the sides of the triangle yields the image of the Tree of Life (figure 8) although Striling never points this out. Instead he uses the Kircher version of the tree, which does not fit the triangular form.

Modern Masonry

Stirling suggests that when the 'old conception' of religion was superceeded at the Protestant Reformation, the need for a body of architects and builders instructed in theological mysteries ceased to exist and "the secret methods of all previous temple builders left in the hands of Freemasons fell into disuse and were gradually forgotten". The implication is clearly that the modern Freemasons inherited the 'secret tradition' of the temple builders of old, but that they dropped the ball, so to speak.

Harwood writes (p 23 Freemasonry) "As the guild system began to break down, what is known as Operative Masonry started to evolve into what is termed Specualtive Masonry. Eventually the operative side was lost altogether". The implication is that builders became philosphers and stopped building, but the truth is that builders have always been philosphers, and the building has never stopped.

Looking at the central circle of the cathedral plan (below) we see that the top of the triangle and bottom of the square form the compass and square of Masonry. The compass represents the triangulum and the square represents the ad quadratum. The compass and square replaced the vesica and cross in the (dualistic sexual) building metaphor in modern times.

In the compass and square metaphor, the square and cube represent the earth and are characterized as feminine. The triangle and the circle and sphere that result from the compasses represent the heavens and are masculine. The Enoch legend tells of a white cube with a golden triangle, that is matter infused with the divine spark.

The metaphor is played out visually to a great extent in an image called the Rebis.

The Cathedral and the Map

While some have labeled this symbolic approach to architecture 'the old way of seeing' and have characterized it as a 'lost art', I contend that a close study of the DC map proves otherwise.

Below we see a comparison of the Milan Cathedral Plan (described as 'one of the most direct evidences of the old mystical rule of building') and the DC Map. The main visual difference between the two is that the cathedral plan does not emphasize the pentagram as the map does. Also, the equilateral triangle in the cathedral image has been reduced to 52 degrees in the map. Other than that,

The Washington DC template is analogous to the template used for the Milan Cathedral.

There are enough lines in the 1792 map to layout all of the Tree of Life (seen below) on a plan, even though the land where the Jefferson Monument sits did not exist until recently and was never explicitly mentioned in 1792, although it is suggested by Maryland Ave running from the CB to 16th St.

A Master Mason and His Model

The last of the monuments that make up the Tree of Life in the map weren't built until the 20th century; all three designed by non-Mason JR Pope. The House of the Temple (seen below) is sphere number one on the map tree, while the National Archives Building is sphere number seven and the Jefferson Memorial is number 10. Nicholas Mann rejects the idea of such long range planning on page 162 of his book, where speaking of the HOT he says, "I have found no evidence that this temple was intentionally related to the design of the city. What was more, it was built long after L'Enfant's work".

There are several ways that the temple is related to the design of the city. Note, first of all, how the HOT is a triangle on top of a rectangle like the tree in the map. The HOT features a truncated pyramid that is produced by any east west street in the map. The HOT represents the first sphere on the tree but is not located at the apex of the triangle, instead it is located within the small triangle above Logan and Du Pont Circles- that is it crowns the tree in the map.

In 1974 Henry Clausen wrote in his Commentaries on Morals and Dogma, "The Scottish Rites can be likened to a tree of sparking symbolic jewels, surmounted by a Blazing Star of Truth that displays the dazzling splendor of the Mystic Doctrine of the Universe, and the reflected glory of the Deity." Kabbalism has been described as a tree of symbolic jewels showing forth the doctrine of the universe as the vesture of Deity.

Ad Quadratum and Ad Triangulum

Striling pointed out in Canon that the Milan Cathedral plan (and presumably others) constituted an admixture of the quadratum and triangulum, or in his words, the cross and the rhombus. The quadratum derives from the images of the cross and oblique square in a circle, while the triangulum and the rhombus derive from the vesica piscis.

The House of the Temple ad quadratum

The ad quadratum is represented in the map by the shape of the district and the orthogonal grid of north-south, east-west streets and the House of the Temple. The triangulum is represented by the isometric grid of diagonal streets and the National Cathedral.

Speaking of games, you will note that baseball is also an admixture of quadratum and triangulum symbolisms. It is 90 feet between the bases, for a total of 360 feet- the same number as the degrees in a circle or a square. The field centers on an oblique square.

There are three strikes and four balls. Nine (3 squared) players on a side and nine innings. Three outs per inning yields 27 (3 cubed) outs per side.