Data and Patterns:
This is the core pattern that gives rise to the rest of the information in this system. It can all be derived from the first line:
1 + 2 + 1 = 4
1 + 2 + 4 + 2 + 1 = 10
1 + 2 + 4 + 8+ 4 + 2 + 1 = 22
This simple doubling and halving pattern produces the numbers 4, 10 and 22, which are obviously extremely important in kabbalah. What is really significant about this though, is that Crowley received the this formula through what is known as the Abuldiz working:
She then said that the 5 White Brethren were “turning red” and “Here is a book to be given to Fra. P. <<She did not know Fra. P. as such. This is not a “test”.>> The name of the book is Aba, and its number IV.’ It was the correspondence of the name and number (ABA = Aleph Beth Aleph = 4) that made Fra. P. think there might be something in the communication.
From looking at this pattern in geomancy, we can see that it fits the structure of the Major Arcana from the Tarot. The way in which a geomantic horoscope is cast, is done in a mathematical arrangement that uses a series of boxes with the pattern being: 1-2-4-8, which matches part of this pattern in the Major Arcana. I will come back to this in a moment though.
3 / 12 / 7 and the Hebrew Alphabet
Once the cards have been arranged in this manner, you can see new ways in which the cards can be grouped together.
1 + 2 = 3
4 + 8 = 12
4 + 2 + 1 = 7
What is extremely significant about this pattern is that the Hebrew alphabet also has the same numbers with in it as the 3 mother letters, the 12 single letters, and 7 double letters.
From how these can be grouped together, we can produce the following formula: ( 1 + 2 ) + ( 4 + 8 ) + ( 4 + 2 + 1 ) = 22
Once we have established this ordering, we can see that each grouping of the cards creates a number of layers or levels. For example, the smallest pattern, 1 + 2 + 1 creates 3 groups: a group of 1, a group of 2 and another group of 1.
The Major Arcana however create a total of seven groups: a group of 1, a group of 2, a group of 4, a group of 8, a group of 4, a group of 2 and a final group of 1. Once we’ve split up the cards in this way, we can say that we are splitting up 22 cards into 7 groups. Which, thought of in another way could be seen as 22 divided by 7, which is approximately Pi.
To visualize the pattern of how the I-Ching fits, we first start with about half of the 22 card pattern from the Majors. We will use just “1-2-4-8” to show one side of this sequence, then flip it over. First, we need to see the cards as individual points of energy, and the lines between them as paths between them. For example, you start with one point, then make two paths from there to the other cards. Below these two lines, you have another two points, which generate four lines below that. Then another four cards, and then eight lines below those, connecting to 8 more points.
By the time you are done connecting up these paths, you have 8 potential pathways you can go down, to go from the top card, to any one of the 8 cards below. Here’s an example, in this order we went Right, Left, Left:
Notice how this pattern mirrors that of the diagram of the Trigrams: http://www.internalartsinternational.com/wp-content/uploads/2012/11/wu-ji-tai-ji-10-000.gif
We can actually correlate this “Right, Left, Left” pathway to a trigram, which would be “Wind” according to this diagram.
Going back to the first 1-2-4-8-4-2-1 pattern, we can see this mirroring effect. Because of that, you can’t just take that same view from the top and then copy it to the bottom. What’s actually going on, is that the yin and yang model the spaces between the cards vertically. But, if you mirror the pattern, it will connect up all of the points in the system. For example:
Another to visualize it is to put them into a list like this; Western stuff (cards) are bold, and the eastern stuff is in italics:
The important thing to think is, “what” are the hexagrams? Yin and Yang are not “things”, but rather patterns of energy. When you lay the cards out in this way, it mirrors the binary structure of the I-Ching exactly. This pattern only emerges when you arrange the trigrams going in these opposite ways, from the bottom as 1 onto 8, and then middle points upwards, from 8 to 1.
3 – 5 – 7 : Magic Square
When looking at these cards as groups, rather than just individual cards, we can find another mathematical pattern with which to use. The number sequence 3 – 5 – 7 comes out from the groups that are created from the Court (3), the Minor Arcana (5) and the Major Arcana (7).
If you add these three numbers up, you get 15. This is actually extremely significant because it is these same number proportions that make up a 3×3 magic square, with the sequence of 3-5-7 being perhaps the most significant line in the series, since its comprised of only prime numbers.
Whats is also very significant about this is this formula is that in a certain mathematical sense, it’s perfectly balanced and immutably correct. Because of that, this sequence shows up in many major religions and spiritual systems. e.g: https://en.wikipedia.org/wiki/Magic_square#Lo_Shu_square_.283.C3.973_magic_square.29
357 – Winding Staircase – Trivium+Quadrivium
We can also connect this 3-5-7 grouping pattern to the 3-5-7 used in the Masonic diagram of the Winding Staircase, aka the 3-5-7 stairs: http://www.acacia11.com/winding_stair_case_op_640x960.jpg
When trying to understand this sequence though, lets first take a look at the top area with 7 steps. Laid out from the top step down:
This is the Trivium and the Quadrivium. As it is the case with many spiritual systems, this one has been changed slightly so that a couple of the pieces are out of order. If we take a look at each piece a closer, we can start to see what’s going on under the hood.
To give credit where credit is due, I learned a lot from this interview Jan Irvin here: https://www.youtube.com/watch?v=7altdvOvvZM
While I do think that the video is interesting and probably ultimately worth a watch, I disagree with Jan on many of his points. You won’t need to have watched this video to follow the logic presented here, but I will reference a couple in a few small ways. If you do watch it, don’t worry about the ordering of the system as he describes here. I will say that his video was critical in helping prime me to understanding these systems in a greater context, but I will show that with some correspondence work, there is a deeper and more intuitively natural way to understand how these systems fit together.
At 12:38 in the video, Jan talks about how the Trivium and Quadrivium are taught out of order: https://youtu.be/7altdvOvvZM?t=12m38s . He gives their ordering as:
Hes has established that bottom three are the Trivium, but he has changed the ordering here. On the diagram it was presented as: “Grammar – Rhetoric – Logic”, but Jan makes the case for “Grammar – Logic – Rhetoric”, wherein hes swapped Rhetoric and Logic.
I think he has a strong case here, and I agree with him on this ordering. However, how he describes it, I don’t really think captures really whats going on there. In order for me to explain though I’ll have to come back to it, lets go ahead and move on to the next section, the quadrivium.
At 39:05 he talks a little bit about how the connection between the trivium and the quadrivium connect together. The really important part though starts at 41:45, where he describes what the quadrivium is on a deeper level, namely being a relationship of numbers in a series of dimensions. He lists the four, and says that they must go in the following order:
- Math (Arithmetic) – Numbers
- Geometry – Numbers in space
- Music (Harmony) – Numbers in time
- Astronomy – Numbers in space and time
This is where I believe there is a discrepancy. If you really look closely and break down what each of those things roughly is, it makes more sense and then the proper ordering jumps out. If a group were to change the ordering of Trivium, wouldn’t they most likely also change the ordering of the Quadrivium as well? Jan is presenting the same ordering here, as is in the original diagram.
While it isn’t essential to understand the following, I had been watching a video about imagining higher dimensionality when I realized these things. I think it might have made it a little easier for me to understand it, when it came to proper ordering of the quadrivium. If the following doesn’t make sense, check out this video called “Imagining the 10th Dimension” here: https://www.youtube.com/watch?v=gg85IH3vghA
What is the proper ordering then? Numbers are at the bottom, this is the simplest so I believe that’s correct, and Astronomy at the end the other end is also correct, because that’s the highest abstraction of numbers. The switch then comes down to Geometry (Numbers in Space) and Music (Numbers in Time).
Consider that much of geometry requires 3 dimensions (an X, Y and Z plane), so it’s minimum number would be fair to say that this section could be thought of as Numbers in 3D. http://www.softwaresigloxxi.com/images/Tutorial29_XYZ_Surface.png
Music however only requires 2 dimensions: back and forth in time, and position in scale: http://www.8notes.com/school/riffs/images/beethoven_symphony5.gif
Considering though, if we again look at Astronomy, could we interpret it as numbers in 3D and 2D? Not exactly, it’s more accurately described as numbers in 4D.
After breaking these groups down into dimensions of numbers, we can view them as:
- Math – Numbers
- Geometry – Numbers in 3D
- Music – Numbers in 2D
- Astronomy Numbers in 4D
From this perspective, it becomes easy to see how that they are out of order. Geometry needs to be swapped with Music because the ordering should be 2, 3, 4, rather than 3, 2, 4. Therefor the system I use goes in the following order.
- Math – Numbers
- Music – Numbers in 2D
- Geometry – Numbers in 3D
- Astronomy – Numbers in 4D
These systems though, are just rough representations of the data that can be understood in that realm of dimensionality. The Trivium and Quadrivium are systems that are thousands of years old; they were actually the basis of the “7 liberal arts and sciences” that was the foundation of a liberal education.
When I’m referencing these things, I’m doing in terms of how they are presented within this system. If they could be labeled in whatever way, I would assign each one of them a much different name, since the way these words as they are used today, don’t quite fit in the way that they used to.
While “Music = Numbers in 2D” and “Geometry = Numbers in 3D” are rough just equivalents, it’s important to try to understand what the method of the system actually is. There is and reason behind it, I’m not saying these labels can describe these steps for are exactly what their academic equivalent is, but rather, what is the source structure from where this data is coming from?
After looking at how this system can be mapped to the Trivium and Quadrivium through the Winding Staircase, you can then further connect this to the Chakras. You can map them from top to bottom, from there we get the following correlations:
- Astronomy – Numbers in 4D – Crown [Sahasrara]
- Geometry – Numbers in 3D – Third Eye [Ajna]
- Music – Numbers in 2D – Throat [Vishuddha]
- Math – Numbers – Heart [Anahata]
- Rhetoric – Solar Plexus [Manipura]
- Logic – Sacral – [Svadhishthana]
- Grammar – Root – [Muladhara]
The connection between the Quadrivium at the top along with their correlated Chakras is pretty staggering once you’ve connected these pieces together. For example, the 3rd eye would then be connected to geometry, which is significant because eyes deal in 3D information. Whereas the throat would then be connected to music, which is also significant because the data which your throat produces (sound) is also 2 dimensional in nature.
If you then abstract that pattern even farther though, going above, if your brain is then connected to your crown Chakra, it would be responsible for 4th dimensional information (our brains think in 3D + Time). Going down to the Heart, there are more significant connections. While I haven’t talked about the dimensionality of “Math” if we take this system, and go from 4 to 3 to 2, the next obvious number in the pattern is then 1. The question then becomes “Does the heart work in one dimension?”. It expands, and contracts, this could be considered working in one dimension. Another interesting connection is to consider Ma’at, and how she is associated with the balance with the heart. It is interesting how this correspondence is correlated to “Math”; Considering algebra, you could say that it’s function is to balance an equation, which could be seen as a potential connection through the concept of balance.
How to understand the difference between the groups 3 / 5 / 7
After seeing this way to split up the cards, I’ve looked for other ways to interpret what it means. One way that I’ve seen as a very powerful way to understand this split is to think about the different between Subjectivity and Objectivity, and then how these two things interact.
For example, we can say that the Subjective view is the role of the Actor, and the Objective view is the role of the setting and physical objects that are needed. But these two things alone cannot do anything unless they are woven together in a Story, which shows how the Subjective interacts with the Objective. Consider how a Story is neither subjective nor objective, but rather is the data of those two things coming together.
In this sense, we can make a similar correlation from “Actor / Setting / Story” is equivalent to “Court / Minors / Majors”. The Court being the “Actors”, the Minors being the “Setting”, and the Major Arcana being the “Story”. We can then also show this as “Psychology / Physical world / Spirituality”
When we then map this system onto the Winding Staircase, the (3) of being an Actor/Court connects to masonic degrees that can be held. The (5) of the physical world/minor arcana then connects to the 5 sense. Finally the (7) of the story/major arcana then would connect to the Trivium and Quadrivium.
The Chaos Star?
Something interesting to note is how the Chaos Star was adopted as a symbol of “Chaos”, but if you read into different interpretations of what it means, one of them shows it as a “4th dimensional object” in the sense that its constructed from 4 lines that work as as dichotomies. The first line added would be just one dimension. The second line added creates a plane that works in 2 dimensions ( x / y axis). The third line added would create 3D space ( x / y /z ). And then the 4th line added would be a representation of 4th dimensionality. What’s interesting though, is that the height of the Quadrivium is 4th dimensional, and the highest value of order. Here’s an example from a book of chaos magick:
The “Chaos Star” then isn’t actually a symbol of “Chaos”, but rather it’s a symbol of 4th dimensional order. Pretty much the opposite of what it’s intended to be viewed as.
© 2015 Steven Glick All Rights Reserved