Achad's Physics

Traditional Thelemic circles recognize the fact that Frater Achad found the ‘Key’ to Liber AL vel Legis, though much discussion does not exist that examines its import. Nor has much use been made of this key with the exception of the formula of LAShTAL in Liber Reguli. One additional work exists that uses this key and its an English Qabalah (Cf. Liber 805) that relies on this key in its authentication arguments. But this Qabalah holds no recognition nor any acceptance in traditional Thelemic circles. And for most, Crowley’s later rejection of Frater Achad as his ‘Magickal Son’ has led to an overall rejection of Frater Achad’s contributions to Thelemic science; if only because his writings have been generally ignored. In effect, the baby has been thrown out with the bathwater.

Fortunately, two forward thinking theorists have found value in Frater Achad’s work. They are the physicist, Richard Miller and the psychologist, Iona Miller. Their writings on Bio-holography found easily on the Internet, provide for us, a marvelous second look at the work of a man that though his later personal failure has become a tragic footnote in Thelemic history, proves an important step in the reunification of science and religion. Of particular significance is the essay by Iona Miller entitled: The Dodecahedral Universe and the Qabalistic Tree-of-Life. In this essay, Iona Miller notes that Frater Achad’s 3-D projection of the Tree-of-Life “…is a key provided initiates to unlock the more comprehensive geometry of creation.”

Let’s start with Geometry and Frater Achad’s work, The Anatomy of the Body of God. Sharing the process by which he came to build his 3-D projection, he first instructs us to draw a vertical line as if running through the center of the Tree-of-Life and to overlay four concentric circles on it so that the diameters intersect with the central points of the other circles, producing three Vesica Piscis as shown in Figure I below. The four circles would be consistent with the four worlds of the Qabalah and the three Vesica Piscis would be consistent with the three veils on the Tree-of-Life.

However, the consistency of the veils as pertaining to the placement of the three Vesica Pisces is not precise and not consistent with Frater Achad’s model. This is simply an alternate extraction that we can draw from this figure at this point. As shown in Figure II below, the center of the top circle corresponds with Kether; the diameter of the top and subsequent descending circle corresponds with Chokmah and Binah; the center of the third circle corresponds with Tiphareth; the intersecting diameters of the second and third circles gives us Chesed and Geburah; the intersecting diameters of the third and fourth circles gives us Netzach and Hod with the center of the bottom circle corresponding with Yesod and the bottom point of its diameter corresponding with Malkuth.

In order to make this figure work, Frater Achad had to pull Malkuth, which normally hangs pendant to the other Sephiroth, up to a more equidistant relation to the rest of the Tree-of-Life as does Kether on the opposite end. This is consistent with the idea that matter does not represent a ‘fall from grace,’ which is not only a Christist viewpoint, but allows us to see now, the divine nature of matter. This would make more resonant the Qabalistic statement that ‘Kether is in Malkuth as Malkuth is in Kether, but in a different manner.’ And we also then can more clearly see the importance of the work of Mother and Sri Aurobindo (Cf. Liber Immortalitas vel Lucifuge and Liber Vox Viva Voce vel Video) as well as the work of Richard and Iona Miller along with Dr. Harold Aspden.

In examining the Vesica Pisces as formed in Sacred Geometry by two intersecting concentric circles, we find that we can fit two equilateral triangles perfectly in its midst, as shown in Figure III below. The equilateral triangle is of course, the strongest solid shape in architecture as wonderfully demonstrated by R. Buckminster Fuller’s geodesic dome; a real practical use of Sacred Geometry.

When laid out horizontally, the Vesica Piscis’ length and breath also forms a rectangle that may be cut into three equal parts by drawing straight lines parallel to its shorter sides as shown in Figure V below. The rectangles formed from these additional lines also contain each, a Vesica Piscis and two equilateral triangles, replicating the greater whole and clearly suggesting the Millers’ hologram theory, which holds that all parts of any organism are an exact replica of the whole organism; working of course, at the cellular level.

And of course, we can embed these rectangles, triangles and Vesica Piscis to both infinitely small and infinitely large dimensions as per Figure VII below.

Imagine my overwhelming joy when I discovered that the ancient Qabalistic Tree of Life, with all it wonderful possibilities as a means of mental classification of every idea in the Universe—Natural, Human and Divine—was in its entirety based upon the same fundamental principle of the Vesica Piscis, and was therefore not a fixed design but capable of indefinite progression towards the Infinitely Small or the Infinitely Great. For it can be so drawn that it appears with all its details and properties, repeating themselves indefinitely in every direction of Space to Infinity.

The Vesica Piscis is of course, an important shape in the Sacred Geometry of Thelema (Cf. Sacred Geometry in AL). It also comes to us by way of the East as the Vesica Piscis symbolized the womb, the importance of which can be found in the Sexual Alchemy of Thelema. This is hinted at in Frater Achad’s book in the several pages leading to Figures XVII and XVIII shown below. And it significantly, further validates his bringing Malkuth into a balanced geometrical relation to Kether, giving us a “true proportion” when drawing the Vesica Piscis.

Frater Achad then redraws the Tree-of-Life, removing the traditional interconnecting paths with exception of those lines that directly connect to Tiphareth and through Yesod, down to Malkuth as shown in Figure XX. Tiphareth of course, figures prominently in the Sexual Alchemy of Thelema as per the formula of ON (Cf. Liber Laiad and Liber LH). Liber LH is important in this regard as it hints at the idea of the ‘Golden Child’ for those interested in evolutionary Eugenics, which also seems a closely guarded secret in Thelemic circles.

He then swings this Sephiroth around, maintaining the line lengths, upon the axis of Tiphareth, giving us Figure XXI shown below.

This suggested to my mind, the idea of One Cell; first in process of Division, and then Divided except for a ray of Influence between the two. In other Words the Supreme Light one with Matter, dividing through Wisdom and Understanding, and becoming the Moon (Yesod) and Sun (Tiphereth). Or, The Sun and Moon uniting and producing the other symbolic ideas—who can say?

Frater Achad is clearly implying the process of mitosis, which is the division of cells involved in both the creation of a fetus and the maintenance of the body. The work of Mother and Sri Aurbindo was in getting all these separate cells to act in unison with full awareness that Immortality might be achieved. But if one thinks about this very carefully, there is also a further validation of Kenneth Grant’s connecting of Yesod with Da’ath and the subsequently evolving ‘Tunnels of Set’ (Cf. Howling of Liber CCXXXI).

As Frater Achad then considered the intersecting Vesica Piscis as shown in Figure XXI, formed by Yesod and Malkuth, and noticed that this could then create the Foundation for another Tree-of-Life as he surmised that this “…would exactly extend from the Centre of Yesod (as its Kether) to the lowest point of the Circumference of Malkuth (as its Malkuth)…” And from this, he further extends his hologram idea to drawing the Tree-of-Life in infinitely small and large repetitions as shown in Figure XXII below. This pre-figures what would eventually become known as Fractal Theory. And if we consider the subtle variations that we find inherent in any measurement, despite Frater Achad’s “true proportion,” that is the main idea in Chaos Theory, we have the foundation for understanding (pun intended) the lush variety of expression that is the known Universe.

As stated at above, Richard and Iona Miller show us that the bio-hologram that is the basic organizational component of human anatomy contains an identical appearance at the cellular level as it does at the anatomic[1] level and especially even atomic level. We can find other validation for this when we consider the free radicals that operate in the mitochondria at the cellular level and the beta decay on the atomic level, which are equivocated in Liber Immortalitas vel Lucifuge. Frater Achad anticipates the Millers’ theories by embedding smaller and larger Trees, built on combinations of Sephiroth in perfect harmonic relation. This also anticipates the Schumann’s Resonance theory that the Millers’ build their ideas upon (Cf. Liber Vox Viva Voce vel Video and Plate A below).

Frater Achad would then develop this out in all directions about Tiphareth—giving us what he calls the ‘Macrocosmic Snowflake’ shown in Plate B below. And he notes that the snowflake clearly shows us the infinite nature of all numbers. I'll leave this for the reader to ruminate.

Though
Chaos Theory may at first seem to throw a wrench in Frater Achad’s idea of
“true proportion” as discussed above, we can get around this easily enough
by recognizing that Frater Achad more than likely meant ‘true relation.’ 
In fact, Chaos Theory holds much in common with Achad’s ideas. 
We may also say that he also anticipated Chaos Theory along with its
cousin  Fractal Theory and the Koch Curve, a well-known fractal used to explain
Fractal Theory and integrates that all-important and powerful triangle into
organic matter!  The Koch Curve in
Chaos Theory uses a triangle, placed as a hexagram and repeated exponentially,
ultimately creates a snowflake as shown in Figure 4 below. 
And it may also be made into other organic figures, such as a twig or a
fern.

Gregory Rae’s website[2] provides a strong introduction for fractals and Chaos Theory as well as an interesting insight into the dynamic nature of this particular fractal as shown in the following quote:

One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve. (See figure 4) A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure. The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.

We can say with some confidence that Frater Achad has provided for us, the Qabalistic Key to Fractal and Chaos Theory as he also anticipates the ideas in Schumann’s Resonance and the Bio-holographic Theory of Richard and Iona Miller. But he doesn’t stop there. So far, we have only considered the 2-D expression of the Tree-of-Life. He would then go on to model it as the 3-D object as shown in Plate D below and recognized in its import by Israel Regardie in his magnum opus: The Complete Golden Dawn System of Magick. Only Regardie makes it seem as this was a part of Golden Dawn teachings, though he only includes a graphic as a plate at the beginning of the book. Research will show the investigating student that this 3-D expression originates with Frater Achad and not MacGregor Mathers and clan.

As mentioned above, Frater Achad’s idea about cellular mitosis corroborates Kenneth Grant’s ‘Tunnels of Set.’ The following quote by Achad on the nature of this 3-D Tree-of-Life provides for us yet, another validation. Indeed, the third pillar not normally depicted in 2-D renderings, would be the other end of those connections that formulate the tunnels and which is shown below in Plate C.

In reality we have been looking at the front surface of a Triangular Crystal Pism[3], and what we saw was not all in one plane. The “sides” of the Tree are but two angles of an equilateral solid; the third angle at the back, is invisible, being completely hidden by the Paths of the Central Pillar.

Frater Achad then gives us the compete 3-D solid, which extends in every direction, “completely filling all known space.” This is shown in Figure XXXI below.

He then builds this into twenty prismatic Trees as shown in Plate E below, and notes that twenty is the number of Yod, upon which the letters of the Hebrew alphabet are constructed. He then arranges the points of the twenty Kethers from the solid extended Tree to form twelve perfectly regular pentagrams and which then would clearly represent the twelve constellations of the Zodiac. This is explained a bit further by his note included with the graphic. And in my opinion, provides strong argument for not creating a thirteenth constellation in the zodiac as some contemporary Astrologers are attempting to do.

In conclusion, considering Frater Achad as a physicist or a physical theorist is more suppositional and relational than actual. But his work embodies a unique juncture point that harmonizes the world of Magick, Religion and Mysticism with the world of modern Science and especially Physics. And these two worlds are beginning to talk to each other and almost right from the start of this Aeon of Horus. It now seems so very important that one begin to learn the other’s language that they may each speak to each other with perfect clarity.

[1] One should note the Alchemical idea of the ‘Babe in the Egg’ as shown in so many Alchemical drawings and also Cf. Crowley’s on the homunculus as well as other hints in his IX^th Degree literature.

[2] http://www.imho.com/grae/chaos/chaos.html

[3] Frater Achad includes this footnote here: Chaos or Matter is potentially a prism which refracts the great Light-Source, splitting up the Supernal Light into stars, or the Supreme Consciousness into Ideas. As matter or substance becomes organized and develops mind, its power as a prism grows. As we clarify our minds they become as living, organic prisms which act with increasing precision and detail. The more definite and authentic our ideas, the more accurate and mathematical, the more will they focus Light from the Supreme, till ‘sleeping stars’ slip on their livery of light. The more exact the form, the closer the correspondence between the Son (or Form, Prism, Expression, Becoming) and the Father (or Light, Life, Love, Understanding).—J.S. Forrester-Brown, “The Two Creation Stories.”