In the abyss of limitless primordial potential any and all creation begins with the philosophic and principial **One**. This *one* action, *one* moment, or* one* qualitative thought vibrates in the most subtle fabric of pre-creation and is reflected and emanated to material existence. We can meditate upon this as how water ripples from a point; it ripples across the surface, but its effect extends to the depths at more subtle degrees of influence. In the primordial abyss, however, there are no physical forces to limit the radial expansion, and thus the ripple and its subtle influence extend indefinitely.

Geometrically speaking, **Pythagorean Unity** is the radius of our allegorical ripple, whether it be 1 or 1 billion, or 1 infinity; the unit itself is arbitrary. This first *circle* is a purely *conceptual* abstraction, it is only veiled in the symbol “circle” for us to understand it as the source for transmitting certain universal geometric Principles. The area of such a circle with a radius of **Pythagorean Unity** will always measure** Pi**; it is here where we are presented with our first transcendent principle of universal geometry, the relation of any ray to its origin and radial extent through **Pi**. This potential for primordial “circle” and the encoded principles of **Pi** and **Pythagorean Unity** corresponds to the Kabbalistic world of Atzilut, the realm of divine Principles.

The emanation process begins with the *reflecting* of the radius of **Pythagorean Unity** from the source point to the implied circumference of the conceptual circle. As a result of the reflection, the polar axis of the ray is shifted so that the source point is no longer the origin of the ray, it is instead a radial limit. It is the inversion of the compass so that the needle is now at the circumference instead of the center. From here a second circle is created replicating the first. This reflection of “circle principle” to create “circle symbol” is the first stage of creation occurring in the Kabbalistic world of *Beriah*, the realm of Creation. This process is repeated a total of **three** times resulting in **four** interlinked circles, or the** four** Kabbalistic worlds (*Atzilut*, *Beriah*, *Yetzirah*, and *Aziyah*). Each progressive circle is in principle less “pure” than the preceding one as it moves further and further away from the source.

The formation of the material universe takes place in *Yetzirah*, the third emanated world. Our geometric allegory represents this with** six** equal circles formed from their intersections along the circumference of the central* Yetzirah* circle. These **six** circles centered on the circumference of *Yetzirah* are to understood as the **six** dimensions of space in the universe.

From the center of *Yetzirah* a bounding Macro-Circle is formed, this is the circle and cycle of the formed universe. This Macro-Circle encompasses the three lower worlds reflected from *Atzilut*, and the circles along the circumference of *Yetzirah*. Taken together the **seven** circles encased within the Macro-Circle are understood as the **seven** days of creation, the **seven** planets, and the **seven** alchemical metals of the formed universe.

Since the inner circles measure a radius of **Pythagorean Unity** (1), the Macro-Circle doubles the inner circles and measures a radius of **Pythagorean Dyad** (2). This is symbolic of the universe where the **One** expresses itself through polarity and multiplicity. The diameter of the circle is 4 representing the totality of the **four** worlds as well as the bounding forces of the **four** classical elements within the formulated universe.

The process of creation is further symbolized by the macrocosmic Hexagram formed by the intersection of the inner circles to the Macro-Circle and repeated again at a microcosmic scale within the *Yetzirah* circle. The Hexagram is the first perfect polygon that can be inferred and created from purely circular geometry, it is a process akin to the “squaring of the circle” and is only fitting that it happens in the circle attributed to *Yetzirah* as the world of Formation.

Note that the first conceptual circle of *Atzilut* is not encased within this Macro-Circle; however, this outer circle connects the source to the circumference of the final circle of *Aziyah*. This exemplifies the Alef-Tau (or Alpha-Omega) principle whereby the source and final manifestation are, despite the perceivable polarities and multiplicities, **One**. In Kabbalistic terms, while the source Point is *Keter*, it’s very realization implies *Malkut* as the beginning cannot exist without the end, nor can a Crown exist without a Kingdom.

At this stage the central *axis mundi*, or Middle Pillar, is realized in the vertical diameter of the Macro-Circle connecting *Keter* to *Malku*t and extending through the four worlds. Within the Macro-Circle, the four “worlds” intersect at **six** locations. These **six** intersections are the **six **Sefirot of the left and right pillars (*Chokmah*, *Binah*, *Chesed*, *Gevurah*, *Netzach*, and *Hod*). This leaves the centers of the lower circles as the Sefirot of the Middle Pillar.

The center of the second circle (*Beriah*) heralds the point of separation of the lower worlds from *Atzilut*, it is the abyss that divides the realm of pure Principles from the manifestation of those principles in Symbol(*Beriah),* Form (*Yetzirah*), and Action (*Aziyah*). This center is therefore the non-sefirot *Da’at*. The center of the *Yetzirah* circle, and center of the Macro-Circle and consequently the formed universe, and also the only point that the three lower circles share, corresponds to *Tiferet* as the Solar Principle of the Kabbalistic Tree. This leaves the center of the *Aziyah* circle as *Yesod*, the foundation of the formed world and entry point into the *Yetzirah* circle.

The creation of the **four** worlds, results in **three** places of convergence between the worlds. These* Vesica Pisces* articulate yet another principle of Sacred Geometry. Given that the radius of each circle measures 1, the width of each of the *Vesica Pisces* measures the irrational sacred number √3. In traditional Kabbalah these **three** horizontal “paths” correspond to the **three** Mother Letters of the Hebrew alphabet (*Shim*, *Alef*, *Mem*) and consequently with the **three** elements of creation (Philosophic Fire, *Ruach*/Logos, and Philosophic Water). These **three** Mother paths are also the **three** planes over which the source point is reflected to create the **four** “circles” of the Kabbalistic worlds. In our geometric metaphor, as in Kabbalistic philosophy, these three Mothers/Elements are the very principles through which the **One** structures creation.

Moreover, the Mother letter paths and consequently the Sefirot connected by these paths relate to the Macro-Circle through yet another irrational and sacred number, **Phi**. For example, *Netzach* falls at the **Phi** ratio between *Hod* and the point where the plane of the *Mim* path intersects the outer Macro-Circle. Each Sefirah of the left and right pillars shares this transcendent relationship between its opposite Sefirah and the Macrocosmic circle.

This brings us to the end of this post. There is nothing to wrap up as this geometric meditation on the process of creation is not intended to be an explanation of anything. It is what it is; an exploration of transcendent geometric principles within a Kabbalistic framework. It is one of many ways to unveil the transcendent truths of our universe.

Nice blog. I was wondering if you have read the book The Secret Doctrine of the Kabbalah by Leanora Leet? She does a similar geometric mandala with seven interlaced circles and the Hexagram.

The last diagram displays the ratio root 2, you don’t addressand does not look to deal with any of the Sephirot directly. How does this number fit into the model?

888,

Yes! Leet’s geometric exegesis has definitely influenced my thought process in this post. I think that book has some really valuable information for those of us on the initiatic path. Aside from her geometrical analysis (which she gets really into in her last book “The Universal Kabbalah”), I find that her research into the pronunciation of the divine name YHVH as a signifier of the long vowels makes a lot of sense in terms of how Greco-Egyptian Magic and Vedic Mantras vibrate nomina barbara and mantras…hmm maybe a future post on this topic.

As for Root2, I think it is more of an implied ratio than one geometrically manifest by the model. If we think of how such a mandala mus be created using a compass, we find that the compass itself forms the Root2 ratio between the legs holding the pen and the needle. As such, the “reflection” of the center point is conceptualized as swapping the legs of the compass so that the point where the Root2 leg was previously becomes the pivot.

Also, Root2 is the ratio that defines the relationship of a central Middle Pillar Sefirah to the the location of the next Sefirah down the Middle Pillar through the point where the horizontal diameter intersects the circumference.

[…] Geometry of Life 2009 October 27 tags: Platonic Solids, Root 3, Sacred Geometry by Reflections From the Black Stone I recently came across these videos and found them to be a great overview of irrational numbers and the Platonic Solids. I recommend taking a look at the author’s site, Nature’s Word,as it is a very well put together resource for Sacred Geometry. These video along with the author’s site add a good amount of context to my ramblings in Creation: A Geometric Meditation. […]

Ask Stan Tenen about Leet’s work. I dare you.

[…] Here’s an amazingly written blog entry on the background of this subject. […]

[…] through drawing six duplicates of the circle that intersect the original point of origin (see Creation: A Geometric Meditation). This results in a greater bounding circle twice the diameter of the seven inner circles. When […]

[…] through drawing six duplicates of the circle that intersect the original point of origin (see Creation: A Geometric Meditation). This results in a greater bounding circle twice the diameter of the seven inner circles. When […]

[…] You can read an English version at : http://voces-magicae.com/2009/10/24/creation-a-geometric-meditation/ […]

The double square divided by a single diagonal line forms two right triangles each having a base of 1.

thus adding the Square Root of 5 as the third generative principle. The square root of 5 transverse two worlds….the worlds of spirit and body….The /5 is the proportion which opens the way for the family of relationships called the Golden Proportion. Sacred Geometry, Lawlor, Workbook 3.