The Star of the Magi
Here we return to an aerial view of Giza:
Above: notice that the middle pyramid is “offline” relative to the cross
It’s worth remembering that the stereographic projection is smooth and bijective. It is also conformal, meaning that it preserves the angles at which curves meet. However, it is neither isometric nor area-preserving—it corrupts the distances and areas of figures.
So if the “iron mountains” above reflect the “iron planets” of Mercury, Venus and Earth, it means that the stereographic projection refers to their more subtle attributes. What are these? Well, the inner planets have orbital periods that are in golden mean proportion to each other. While this is shown by the x-axis above, in tabular form it looks like this:
Recalling that the sides of the pyramids are 200, 411 and 440 Royal Cubits respectively, we can see that Mercury to Earth at aphelion is preserved at 0.45. The escape velocity of Venus relative to Earth is preserved at 0.93. Finally, the mass of Venus compared with Earth is preserved as 0.81 which is the ratio of the circle to the outer square.
So rather than measuring Mercury, Venus and Earth themselves, the stereographic projection really describes the RELATIONSHIP between these planets. While this is a more intangible way of viewing the solar system, it is also more powerful because it allows us to move between the macrocosmos and the microcosmos. This is the reason why the stereographic projection is so profound—it remains the universal road map that can express time, velocity and mass in terms of space.
This is where things get more subtle. While the graphic above is full of squares and golden mean rectangles, we have to remember that the inner planets are rotating around each other. This dance then, is really represented by the PENTAGRAM because this is the shape that rotating bodies make when they tango in golden mean CYCLES. In the reversed pentagram below, the ratios of a:b:d are reflected in the orbital ratios of Mercury:Venus:Earth.
So the pentagram is made up of golden mean spirals and golden triangles. (A golden triangle is an isosceles triangle in which the ratio of the duplicated side to the distinct side is φ.) This shape then, describes the dance of the planets around the Sun but more deeply the expression of life in the cosmos. The stereographic projection of iron can be used to represent the tango of the inner planets because they are made of iron, too.
This hexaferrum (ε-Fe) has a crystal structure made up of hexagrams and golden rectangles. Hexagonal crystals have a unique directionality that align with a planet’s spin axis within the core. If all the crystals point in the same direction, then their combined granularity hints not only at one big crystal, but at the role of iron as the arbiter of timespace.
Above: the middle pyramid was built “offline” to infer the pentagram of Isis
So the pyramid of “Khafre” is the geometric centre of the Giza plateau because its square base informs the central pentagon (the side lengths are the same). The duplicated sides of the isosceles triangles that make up the points of the pentagram are also the same length as the arms of the cross. So the pentagram and the cross fit together but ONLY if the middle pyramid is positioned “offline”.
The V-shaped pentagram is reversed because it refers to the “upside down” orientation of Venus. Indeed, Venus spins clockwise on her axis which is the opposite direction to most other planets. While modern day occultists may disagree, the inverted pentagram is mainly symbolic of Venus and the “retrograde motion” of this beautiful planet.
Above: Venus anchors the Ankh of the solar system
So from above, the Nile looks just like a tree in the desert. At the top is Giza, which is really a STAR. Like a gigantic “river tree” then, we start to see the hidden wisdom that eventually led to the “Christmas tree”. The roots of the Tree of Life then, go deeper than we might imagine because they celebrate a time of annual renewal.
Perhaps the most important of the nomes was the 23rd, the site of the Giza pyramids. This nome is where Upper and Lower Egypt became united into a single kingdom and this nome symbolises the visible form of the solar system as a whole. The 23rd nome is also the site of the cosmic egg at Heliopolis and where Horus defeated Set to become the ruler of Egypt.
At a deeper level the reversed pentagram is a sign of omnipotence that deals with the manifestation of spirit within the body. The downward pointing triangle then, has long represented feminine energy because it mimics the mons pubis. Writ large, Venus is essential because she bestows love upon the world through the uterus of the brain.
Above: the reversed pentagram yielding the pentagon
So the emotion we call “love” is reflected in our chemical and biological makeup. The brain therefore, is a gate which allows higher wisdom to flood the human body. Profound states of consciousness (both natural and artificial) are accessed when the brain gorges on chemicals that mimic the geometric architecture of the heavenly realms.
Pentagrams imply dodecahedrons. This is significant because the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons that use the φ ratio. The dodecahedron is a perfect tool to use in meditation because the energy held within it raises our vibration to connect with our higher selves. The dodecahedron also manifests in the chemical expressions of love and remains the inspiration for the pyramids:
Above: the pentagram is the shadow of the dodecahedron
The stereographic projection of the dodecahedron then, is the master blueprint for Giza—a bit like projecting the entire universe onto the desert. The element associated with the dodecahedron is gold, because this precious metal forms this structure naturally and is associated with spirit.
The Hermetic phrase, “as above, so below; as within, so without” describes relationships in favour of absolutes and invites us to travel seamlessly between the microcosmos and the macrocosmos. In mathematics, these patterns are described by fractals. When we ponder the Star of Bethlehem we are reminded of the reversed pentagram and the mathematicians, astronomers and philosophers who fashioned this symbol of ETERNAL LOVE.
Above: the Throne of Isis