I am a big consumer of science fiction and fantasy, and like all big sci-fi/fantasy geeks, I am into Marvel and DC. Psionic characters were okay to me, but they didn’t interest me too much. Besides the Darkover series written by Marion Zimmer Bradley, psionic characters don’t really pull me in. I am a big fan of the sorcerers of DC like Zatanna and Constantine. When it comes to Marvel, I am a big fan of Doctor Strange. In fact, DC has an animated movie called Justice League Dark and Doctor Strange has his own movie and own presence in the Marvel Cinematic Universe. When you think of all the characters and movies I mentioned, one thing that they make use of are circles that are understood to be magical within the context of their fictional universe. In the case of Zatanna and Constantine, you see your familiar pentacle whereas Doctor Strange uses more complex, higher-dimensional magical circles. You can create those magical circles that function in a similar way by creating a moduli space:
In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes of the objects to be classified in some natural way. Moduli space can be thought of as the space of equivalence classes of complex structures on a fixed surface of genus g, where two complex structures are deemed “the same” if they are equivalent by conformal mapping.
This post is going to show you how to create a binding seal consisting of a formal magical ring by using the 86 times table. The purpose of this seal is to bind the magical power of whoever this is cast on. Technically, you’re creating a magical ring because all the interesting thing happens due to a mathematical structure called a ring. The circular shape is called your mod. In this article, I am going to be showing you how to make magical rings by arranging 200 elements in a circle – mod 200.
This binding seal is derived from two tables. The first table is an association of a concept to a number. That first table is a collection of 200 concepts to be arranged in a circle. The second table is a system of relationships governed by a rule from the 86 times table. You multiply 86 by wherever you are in the sequence of 0-199 and then you perform the operation mod 200 to formulate the rules of the seal.
Concept TableA table of the mapping of concepts to numbered nodes
Rules TableA table of the relationships of the concepts defined by a rule.
The first step is to take the nodes from the Concept Table and arrange them in a circle starting from 0 counting clockwise in a circle up to 199.
The next phase is to look at the Rules Table. The Rules Table is the table that defines the rules of how the concepts interact to form the magical rings within that circle you created in Phase 1. It uses the function f(x)=(86*x)mod200 where the input is the first column – x, and the output is the second column – y. What you are going to do is look at the Rules table and draw a line from the first column to the second column for each row. You have a pair of x and y that constitutes an edge. I’ve started you out by doing this for the first 10 edges. Looking at the Rules table, the first 10 pairs are: (0,0); (1,86); (2, 172); (3,58); (4,144); (5, 30); (6, 116); (7, 2); (8,88); (9, 174). Continue drawing lines between the x and y values for the rest of the table.
When you have done this for all the rows in the Rules Table, your seal should look like this:
Look at the Concept table and substitute the numbers with the concepts:
If you did this correctly, the shape of your magic binding seal should look like the image below.
How The Seal Works
What this does is that it takes the intention – in this case simple concepts, and defines a flow of psychic energy per the rules via the relations. Whenever this is intentionally applied to the target, magic power of the target is constrained by those rules. The paths of one concept to another concept represented by the pairs of x and y from the Rules Table can be interpreted as psychic energy. The reason that it can be interpreted as that is because there is a potential for displacement and change from one concept to another. The important word is interpreted. What you have are what are called eigenvalues and eigenvectors that I interpret to be psychic energy.
Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).
The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems, to name only a few. Each eigenvalue is paired with a corresponding so-called eigenvector (or, in general, a corresponding right eigenvector and a corresponding left eigenvector; there is no analogous distinction between left and right for eigenvalues).
Psychic constructs (an intentional arrangement of conceptual elements – like this seal) have a spectral graph. Spectral graphs have matrices and those matrices have spectrums. Those spectrums are the eigenvalues of that matrix. So, when I say psychic energy, what I am really referring to are spectrums of the concepts of the matrix via eigenvalues and how they are paired to eigenvectors. It’s not really a substance; rather, it is more like an aspect. In this case, it would be an aspect of your intention. So, psychic energy is an interpretation of the eigenvalues for the matrix of concepts/intentions. You can think of it as representing the frequency of how a system of concepts is oscillating/vibrating. Psychic energy would be the graph energy of a graph of the concepts.
If you look at how the concepts are arranged, they are arranged in a circle first. That is not arbitrary because that impacts the spectrum of the concepts and thus how they vibrate. If you were to move from 0 to 199 along that circular outer ring, you would be moving clockwise in a circle until you swung back to 0. What you are doing is rotating. Each number on the circle represents a degree of rotation. This implies you have angular vectors. This also means that you have sine and cosine functions. These sine and cosine functions create a series of waves that can be collectively referred to as harmonics. In other words, you have a rotating field of waves of psychic energy that has vectors predicated on intentionality that exerts a force on the target of the seal. There are 200 phase shifted waves and the rule that defines the relationship of each pair of concepts is defined in one of those phased shifted waves. Collectively, this creates a holistic coherence and resonance. The wave of the circle at position 0 is sin(x) where the derivative is cos(x). At position 1, you have the wave shifted over, so you now have sin(x+1) with a derivative of cos(x+1). This sequence holds true all the way up to 199.
This creates a resonance which amplifies the effect of the seal. That resonance makes it hard to “break” or “remove” the seal.
The five petal-like structures of the seal are called cardioids. If you have two circles side by side and you roll one circle around the other, you draw a cardioid. Cardioids show up in the Mandelbrot set. Like the Mandelbrot set, this seal exhibits a fractal geometry that is holistic. Think of it as instead of the whole is the sum of its parts, the whole reflects its parts. A part is not just a part. It’s also a whole. That holistic property makes it exceptionally hard to disrupt the effect of the seal.
The adjacency matrix of the binding seal can be found here:
Magic Binding Seal Matrix