64 bit binary-loop sequence base 10 numbers + king wen hexes

This article demonstrates and explains the relationship between the I Ching and binary code. 

Notes: There are several possible ways to read the binaries; 0 = Yin / 1 = Yang, read bottom-to-top in the hexagrams was the method Leibniz adopted but this is ultimately arbitrary. One could also read 0 = Yang / 1 = Yin, read top-to-bottom in the hexagrams as is occurring here. Either of these two methods has its own unique inverse read-option…[Continue on the forums]

This article is for members only. 

proximity principle: path assignments & positions…

A handy little chart for the Mutational Alchemy Tarot.

Atu 0 – Aleph, 1 – Air – (Fool) – path between sephiroth 1 & 2 – bright pale yellow [FFFF66]
Atu I – Beth, 2 – Mercury – (Magus) – path between sephiroth 1 & 3 – yellow [FFFF00]
Atu II – Gimmel, 3 – Luna – (Priestess) – path between sephiroth 1 & 6 – blue [0000FF]
Atu III – Daleth, 4 – Venus – (Empress) – path between sephiroth 2 & 3 – emerald green [00C957]
Atu IV – Hé, 5 –
Aries [was Aquarius] – (Star) – path between sephiroth 2 & 4 – violet [CB0FFF]
Atu V – Vau, 6 –
Taurus – (Hierophant) – path between sephiroth 2 & 6 – red/orange [FF4000]
Atu VI – Zayn, 7 –
Gemini – (Lovers) – path between sephiroth 3 & 5 – orange [FF8000]
[Continue on the forums…]

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the rational ordering of the elements in mutational alchemy

There are different orderings of the four (or five) elements, and in the 12 banners system, for example, every possible ordering is examined. In the doctrine of the Four Elemental worlds, sometimes overlaid on the Tree of Life, there are two common orderings which will be covered below.

Traditionally, according to most doctrines you will encounter, Fire always comes first, followed by Air then either Water or Earth. (Spirit, whence from Fire arises, self-created, does not come into being, its essential nature is unborn and eternal and is usually assigned the place of Ain Soph Aur when the Four Elemental Worlds are aligned along the Qabbalistic Tree of Life.) It depends on whether we are descending by gender or by generation. In the generation descension, Fire and Water come out first, because they are the oldest. In gender descension, Fire and Air come out first, because they are male in nature. Heaven precedes Earth in that lineup of elements. In all Alchemical discussions, Being precedes Matter. Since you’ll run into at least 2 predominant arrangements for *four elemental worlds* with virtually no rational explanation for either of them, it can be difficult to trust which one is real or useful.

Getting clear on this topic is vitally important since this is where the magickal universe begins; this is our *starting assumption* from which all other 4-elemental rationales proceed. Indeed the Tree of Life itself is built upon these starting assumptions, yet there has been almost nothing published in the form of a coherent thesis explaining why the Four Elemental Worlds might align one way vs another. What I will now reveal is one for the history books, a powerfully lucid and relevant solution. (This article is for members only, to continue, click “Join us” on the left to learn about applying for membership, otherwise, if you are already a member of The Abrahadabra Institute, click here to go to the full article.)

The Abrahadabra Grid, The Hidden Diamond Sutra and the Doctrine of the TwinTrees: Introduction

On Saturday I was handed the answer to a question which has been puzzling me for some time. How many unique triangles, including triangles with triangles within them, are inside the Abrahadabra Grid? I needed some help from math whizzes as I wasn’t about to spend all weekend tracing copies of the Abrahadabra Grid. So I asked a subreddit full of just such math whizzes what the answer was. The formula, for those of you who are into this sort of thing, is below.

(4n^3 + 10n^2 + 4n – 1 + (-1)^(n)) /16 where n= {1,2,3,4,5,6,7,8,9,10}

ANSWER (and detailed commentary)

After I received the answer, I felt pretty great, now I had one more piece of the grand puzzle of Abrahadabra, but also a little lame since I couldn’t figure out the solution myself. (Not likely, since I majored in Art to Advanced Art III throughout highschool and took the bare minimum of Algebra I.) I gave the two key problem solvers Reddit Gold. Throughout my inquiry I was reticent to discuss anything in particular about the vanilla grid I had posted to them, shown below in its full glory. The image I posted to the group only shows the 100 triangles. 

After I gave out the gildings, I received an astonishing and eloquent letter from one of the two recipients of the gilding. (The full correspondence is here, and yes he does have a silver tongue…not very many people outside of TAI can convince me to write an article in response to their query – but I was convinced that this mathematically disposed fellow could easily surpass my understanding in Mutational Alchemy if I could expose him to m1thr0s’ work…)


Your generosity is delightful and honestly made my day, many sincere thanks for the gold! I took the opportunity to check out your account, and it looks like you’re interested in more than a few interesting things yourself!

One of your recent comments stood out to me in particular. In a thread on the nature of Daath and the alleged Qliphoth, you note that you see the two trees as one aspect of a single tree.

This is an idea I have been grappling with myself lately, and I wonder if you might share with me another sort of gold and enlighten me as to your understanding of the tree?

Specifically, it seems as though many tarot decks hint at this same fact, that the two trees, knowldege of good and evil along with the tree of life, are two aspects of a single tree. I have been working with a somewhat obscure deck recently, the Sacred Rose Tarot, which seems to be using this mystery as its central theme.

But appealing to more common currents, when I look at the High Priestess of the standard RWS, I see the two pillars, with the Priestess herself as the central column. Yet also behind her visage is the virginal veil bearing yet another image of the tree in the form of palms and pomegranates, with Her lunar crown in the position of Daath. So there is the tree of which she herself is the central pillar and then there is the tree upon the veil.

This theme of the double tree can also be seen across many cards in many decks, but seems most clear in the Tower. The King and Queen flank the central pillar, but then the lightning takes the form of the flaming sword, indicating another tree. This is even more clear in the BOTA version, where the lightning takes again the form of the Flaming Sword, and, obscured by the prana like clouds above the queen, ten yods take the form of the tree of life. This almost implies 3 trees- the tower + king + queen, the lightning, and the yods.

This is even more pronounced in the golden dawn tarots of both Wang-Regardie and the Ciceros. Both of these versions show two trees clearly (one being the qliphoth) and one being the tree of life, with a central tower and a king and queen on the left and right. Cicero’s deck has the symbol of Mars stricking the tower, which makes enough sense, but Regardie keeps to the theme of the flaming sword bringing about the “calamity”. So there is a subtle implication of up to 4 trees in the vision provided by Uncle Al’s old secretary.

As I am sure you have noticed, the lightning itself, and not the tower, takes the most central and conspicuous place in the Crowley-Harris rendition, but here again the towers is also present, again implying at least a duplicity of trees.

I could go on and on, though such is clearly unwarranted. But again, while you asked for my expertise, I humbly ask for your wisdom in kind. Can you help me to understand this concept of the two trees as one, and how this somewhat illusory concept of the qliphot fits in, even though you clearly don’t buy into the concept yourself.

I am immensely grateful for the gilding, and am happy to have helped you! Now I would humbly ask that you bestow upon me a gold greater than that found in all the earth, but wholly accept if, for whatever reason, you cannot.

All the best!


9³ Phanes_,

There has been a tremendous amount of research done on this subject here at The Abrahadabra Institute, under the leadership of our founder, Magister Ouroboros 729 as he preferred to be called, or m1thr0s 729. Since you are familiar with Crowley it may be helpful to point out that he was initiated by Grady McMurtry and left the O.T.O. shortly after Hymenaeus Alpha’s death, for reasons I will not go into in great detail here, and I will try to keep this backstory only as long as necessary for you to get a full view of the origins of this work and what we are all about. First a photo of him so we know who we are talking about visually.

He began studying the occult in his early teens, and at the time that I made the decision to join him in his work as his lover and eventual wife, I had known him for 10 years already, and had been studying his work alongside many others at abrahadabra.com for about 10 years with varying degrees of understanding. Although we had merely had a casual flirting relationship before this, after I became completely absorbed and fascinated with his work, we had fallen madly in love due to our shared love of intellectual pursuits, especially Hermeticism and the discipline he had pioneered called Mutational Alchemy – a hybridized branch of Hermetic Alchemy. As it turned out, since I had been born to a witch and sorceress familiar with Crowley and his ilk in her own right, he also viewed me as an asset in his intellectual pursuits. Because he had been studying the occult without halting for over 40 years, you can imagine among other things it was an incalculably interesting and rewarding relationship for me up until his death on December 26th 2016. 
      Now to the lengthy answer to your question. So much of what we do here at TAI is focused on building on the understanding of those who are already here, it seems all of the introductory texts to what makes Abrahadabra.com special get buried under more advanced, or tertiary, essays and videos, that treat offhand subjects of not direct interest to TAI’s core discipline of Mutational Alchemy. For true intellectuals, and lovers of numbers, in the Pythagorean tradition, this is where the real treats are to be found. The proofs I am about to go over with you are utterly astounding and I know you will appreciate them as much as I do and a few rare individuals with just the right mix of knowledge and understanding who come across this stuff, although they are just completely lost on the vast majority of those who come to us for our tarot deck or just for a sense of belonging to an ooey occult organization with a dangerous looking sigil at its helm. 
       The first major observation that m1thr0s 729 made, at some point in the 1970’s, shortly after his departure from the dysfunctional O.T.O., who had no interest in his work anyways, was that the Sephiroth/Tree of Life fits within a talisman of the highest order he created called the Abrahadabra Grid. (Note that in the image below, if you highlight all of the Sephiroth and the Ain Soph Aur Coordinate, it spells ABRAHADABRA!)

This came about through the dedicated research he was doing into the alchemical formula of Abrahadabra at the time. He observed the importance with which the praeter-human intelligence of Ra Hoor Khut treated it, announcing it in the first line of his chapter, and designating it as a *reward.* This alone was enough to key him into its importance. This is the grid you solved with the formula you gave me.  Here it is, below, in its full glory for you to observe. 

Note that the Tree of Life’s Sephira are affixed upon the intersecting lines of the grid as if it was made for it. According to Crowley, as you might recall, Abrahadabra emerges from the Tree, not the other way around, but this proof clearly demonstrates that he was wrong. The Star gives rise to the Tree, not the other way around! Additionally, the Four Elemental Worlds cascade from apex at Ain Soph Aur itself and fit perfectly within the entirety of Abrahadabra. The dark grey triangles mirror the structure of the Tetractys of the Decad – we refer to these per m1thr0s’ naming conventions as *The Secret Chiefs*. The only *Secret Chief* that touches a Sephira is centered at the groin area of the Adam Kadmon, the shadowy figure in the center of the Abrahadabra Grid, and appears to uphold Tiphareth. There are countless other secrets in this, one of the master formulas of Mutational Alchemy, but this is as far I will go into this particular map for the moment, as I have a lot more to cover.
      You asked about the “two trees” and say you have been wondering about three, or even four trees. Although we have not answered the question of the third or fourth tree with any certainty, I can fill in more than a few huge blanks that you might have been missing.  The first concept I want to introduce you to is one that is newer than the TwinTrees which I will cover below, but it is the logical first step towards understanding that master formula. If one connects all of the Sephiroth via paths that are “not there” we find that the image is rather stunningly beautiful. More than this, there are exactly 16 paths all together, corresponding not only to the 16 Court Cards, but to the 16 Geomantic figures of Medieval Europe and the 16 personality types of C.G. Jung. We discovered this independently during our research on the Mutational Alchemy Tarot, which is why it figures so prominently in that deck, since the way we use sigils and talismans is different from any other meditative discipline on Earth, and we discovered it had some very intriguing properties when used with a methodology we call scryation and the building of Mutational Fields. (Mutationism is the professional term for those who study the science of change within binary or ternary structures, i.e., the I Ching) There’s a whole series of articles and charts pertaining to this structure, and very few people have noticed this structure over the centuries. It was documented only twice in literature that we know of, and never given any proper attention for whatever reason. Those two people who mentioned it are now dead and didn’t name it, so we gave it a name: The Hidden Diamond Sutra, after its presentation as an exotic diamond and its value to us. It is named a Sutra to emphasize to neophytes a different way of thinking about Sutra as merely a doctrine framed within literature.
      The mere fact that we could use it to unify both the Court Cards and the Geomantic Figures along with the Jungian personality types was enough for us to justify utilizing it in the Tarot, but m1thr0s also discovered that it crossed Da’ath, functioning as a precise and powerful weapon with which a Mutational Alchemist can launch an assault on Da’ath from all directions, rather than wading through it from the Abyss, something which has haunted those who work with the Tree of Life for generations. (See the Da’ath Hack article on the forums, under The Book of Mirrors)


The last doctrine we will go over is possibly the one that will attend to your questions as far as I can go within this short article, and it constitutes the master formula of Mutational Alchemy itself. This is the doctrine of the Twin Trees, which is an advanced set of Sephiroth paired to the I Ching. There have been at least half a dozen variations of this formula over the years in both single and twin form, (for reference, in order of creation they are called the *P’an Ku or Heaven Descending*, the *Nu Kua or Earth Ascending*, *The Emerald Tablet*,  The TwinTrees Prototype A and Prototype B [obsolete, kept in the archives for historical purposes, these were created in the search for the Temporals or a possible third Tree] and finally the TwinTrees Primordial and TwinTrees Temporals) but the two that concern us the most to this date are the *TwinTrees: Primordial* and the *TwinTrees: Temporal*.  The Mutational Alchemy Tarot itself is built on the framework of the Primordials. As we may remember it was Eliphas Levi who first thought of affixing the Tarot to the Tree of Life. While Aleister Crowley made a haphazard attempt at affixing some of the trigrams to the Tree of Life, he did so in such a sloppy nonsensical half-assed way as to render the attempt almost useless, and it was not ordered with any mathematical precision. He seemed to be oblivious to the nature of binary ordering, even though this knowledge would have been made available to him via the work of the much earlier genius of G.W. Leibniz. 

 One unfamiliar with the work of Leibniz or binary ordering in general might ask, how does one affix the Hexagrams in a rational way to the Tree of Life at all? This is a good question and lies in the way we assign numerical value to the binary structures, and to a little rule m1thr0s discovered called The Proximity Principle. Both of these will be covered in great detail in his upcoming book and will be taught in the upcoming March coursework, and a booklet has already been published on this material as well as a discussion available for free within the Mutational Alchemy Tarot Book itself, so it is really a subject for another time, but suffice it to say it allows us to determine in what order we should place the ATU and Hexagrams alike based on their inherent numerical value, and this determines where they are placed on the tree using the Proximity Principle. 
       The prime difference between the Primordials and the Temporals is that in the Primordials, the Hexagrams emerge and are affixed without any acknowledgement to Sephirothic primacy, they ascend on the left side (Earth Ascending) and descend on the right side (Heaven Descending) and this pays homage to both the Chinese observation of the natural tendencies of Heaven and Earth, as well as the placement of male and female elements in the West. (For example the Left Pillar on the Tree of Life is female, the Right is male, the right hand of the body is masculine, the left feminine and so on…) In the Temporals, special attention is paid to the Sephiroth, so that the paired Hexagrams with the nature of being reciprocal inverses (naturally, in the chronologies, this is not artificially arranged) are affixed in a rational ordering to the Sephiroth themselves first, and then the remainder of the Hexagrammal pairs are laid out according to the previously discussed Proximity Principle and binary value. 
      These two great charts are shown below for anyone to see for themselves what an astonishing and marvelous impact these will have on both the I Ching and the world of Hermetic Qabbalah.
      For an even more astonishing expose on just how perfectly these hexagrams are aligned with Western Hermetic Alchemy and Qabbalah, it’s suggested one examine the full range of the Tarot correspondences, both traditional and the new Mutational Alchemy ordering, where the Emperor has been corrected to be placed properly (with his new letter of Tzaddi, connecting him with the Liber Tzaddi transmission) instead of the Star. This was executed according to the Proximity Principle and it’s laws governing the rational ordering of the Hebrew letter system which Crowley failed to attend to, simply because he didn’t have the tools the scholars of antiquity used to formulate the Tarot correspondences that come down to us through the Golden Dawn lineage. (See the section on The Emperor in the MAT book for a detailed explanation. http://abrahadabra.com/mutational-alchemy-tarot-book/atu-xvii-the-emperor/)

The Twin Trees Imperial Edition 2012


I hope this little ditty has answered some of the more pressing questions that I hope more than a few of you are having. None of the assertions that we make here are based on guesswork, but on careful scholarly work and much time and effort has been put forth to assist anyone in handling this work for themselves in order that they might experience the amazing effects that m1thr0s 729 encountered decades before and than so many have testified to in working with this strong and powerful monstrosity of a system. It has so many secrets laying beneath its surface that we will certainly not see the end of its mystery in my lifetime, or the next few dozen generations is my guess. There is also a ton of work I have not discussed right here, but this is the core doctrine we adhere to around here that both deviates sharply from most other schools out there, yet is exceedingly attractive to those who are coming from old and stale Western traditions with seemingly no clue in sight as to where to go to next. “It furthers one to have somewhere to go.” the I Ching.
       Those who understand and appreciate this stuff will do so because they have the faculty to understand it at a fundamental and mathematical level and can check all of the godamned proofs for themselves. The detractors will whine on and on about how it “isn’t what Crowley believed” or that it is merely another New Age attempt at degrading their traditions, but those who understand and appreciate progress will see that this sort of work is the breath of fresh air Hermetic Alchemy has needed desperately for over a century now. The problem with tradition and the I Ching is nonexistent since the Chinese government has been actively hostile towards the mere mention of the I Ching for over a hundred years now, so that even my modern friends in China have never even heard of the I Ching and they are mostly forbidden from discussing it in depth, even though we now know that the underlying mathematics forms the backbone of the DNA code itself (See my article under the I Ching section: DNA and the I Ching explained, or Yan’s book DNA and the I Ching) The same goes for detractors on the scientific spectrum. They will all play catch up with this eventually, just as they did in 1952 with the official discovery of the DNA strand by Watson and Crick. 

“Dedicated evolutionists don’t much give a shit about the misconceptions of lesser mortals…they are already engaged in an aggressive dialog with nature itself at the highest levels…and they usually know this.[…] Proponents of modern science are routinely guilty of imagining that it is uniquely qualified to evolve and has therefore earned some special privilege to redefine its own parent disciplines in as pejorative a light as possible, as if the clock had somehow stopped for them. This may impress a few, for a time, but necessity is still the mother of invention. At the end of the day, Metaphysics will perpetually rediscover and redefine itself with or without the approval of modern science as mandated by the needs of real people in real time, attempting to answer the same questions that have been with us from the beginning. “

  • m1thr0s, Magister Ouroboros 729

I’ll leave it here since this article is already getting too long, but rest assured the proverbial rabbit hole does get a whole lot deeper than this for those who are brave enough to go there and who have the patience to continue receiving directives and dialogue from both necessity and Nature himself. We have never made a secret of our source work, but neither have we pretended that this work did not desperately need bright minds working on it and the further secrets that Mystery itself holds in hands, the promise of the future evolutionary dharma of our species and our theoretical starhood, encapsulated in the axiom *Every Man and Every Woman is a Star*.

Izi Ningishzidda, Magister Ouroboros 777


article + podcast: mutational alchemy essentials 002

Mutational Alchemy Essentials 002 article + podcast up:


“Despite appearances, Mutational Alchemy is the most powerful transmutational toolbox in existence today so your patience and diligence will be paid off 1000 times over the next best options available to you. It takes time to dig out the truth and then more time to make it accessible to people so things are happening as fast as they can happen.”

  – m1thr0s