While I was bored, I made a decision to peruse the content on r/occult. In that subreddit, one of the moderators I dislike made a comment that appeared quite banal and dubious, engaging in a discussion regarding the mathematical “clues” within a grimoire.
Regrettably, my enthusiasm for engaging in scholarly exchanges with practitioners of the occult has waned. Within the occult community, the appetite for discussions rooted in philosophical or logical proofs, supported by the scientific method, appears to have diminished. Instead, grandiose and unconventional assertions, such as those presented by the aforementioned moderator, tend to assume central prominence, adorning their traditions with seemingly capricious and artificially contrived attributes that can be overlaid onto a multitude of other conceptual or cultural frameworks. This disposition forms the very rationale for my purposeful abstention from participation on Reddit.
The moderator wrote:
“Your conclusions are pretty much in line with my own. The Seal is a mnemonic wheel that marks the lunar mansion, the zodiacal ecliptic, seasons, months, and a range of other time allotments–and the tutelary spirits ruling them. Although there is a lot more to the Arbatel than focus on the Olympic Spirits, I came to believe that that geometric shapes in the seal correspond with the OS and the text contains mathematical clues about this. The shapes and numbers give information about the nature of each OS. It also seems that the seal is meant to be envisioned as a multidimensional cube–a multiverse with archons (the OS) and other tutelary spirits through which a person can best live in harmony with the cosmos. It is said to be highly influenced by Renaissance era alchemical philosophy, but I think it is also greatly influenced by neo-Pythagoric and neo-Platonic concepts.”
The concept of a relationship between the seals present in grimoires and the domain of mathematics might present itself as intuitive at first glance. However, to substantiate these connections, a rigorous approach is necessary, involving the use of Algebra or Analytical Geometry. Without empirical evidence or algebraic proofs, these connections could be relegated to mere aesthetic elements, potentially crafted to evoke an esoteric aura. Algebraic proofs, rooted in analytical methodology rather than intuitive leaps, provide a solid basis for assessing whether the structure of esoteric entities genuinely corresponds to specific geometries.
In the context of exploring symbols and terminologies, it remains paramount to view them as categories defined by distinct criteria. Consider the designation ‘moderator,’ which encompasses specific attributes. An individual assuming the role of a moderator becomes an extensional member of this category, symbolized by ‘moderator.’
This perspective implies that any utilization of a term exists within a semantic field and domain. A term functions as a symbol encapsulating adequate criteria for its inclusion in the given category. As we manipulate instances within this category, it effectively constructs a semantic field, thereby facilitating algebraic operations. This video presents an example of how the relationship between Algebra and Geometry can be illustrated.
Geometric series: sums of powers of 3 (visual proof)
[arve url=”https://www.youtube.com/watch?v=9IAm75UY2U8″]
This animation is based on a visual proof by David B. Sher from the Spring 1997 issue of Mathematics and Computer Education page 190.
Consider the intricate interplay of definitions within language—each term within the dictionary can be recursively defined by another, engendering a fractal and self-replicating geometric structure. This raises the query: Could there potentially exist an inherent mystical facet intrinsic to the English language itself?
Individuals knowledgeable about the mathematical aspects of Thaumaturgy possess a comprehension that language can be encapsulated within geometric forms such as triangles. However, we acknowledge that this notion might exude an esoteric sense of wonder and mystery, captivating those unfamiliar with its nuances as seen with this quote from The Lesser Key of Solomon:
“MAGIC is the Highest, most Absolute, and most Divine Knowledge of Natural Philosophy, advanced in its works and wonderful operations by a right understanding of the inward and occult virtue of things; so that true Agents being applied to proper Patients, strange and admirable effects will thereby be produced. Whence magicians are profound and diligent searchers into Nature; they, because of their skill, know how to anticipate an effort, the which to the vulgar shall seem to be a miracle.”
Notably, this attribute is a universal hallmark of language, transcending specialized fields. When this concept is illustrated through the medium of magical ciphers, it is carefully designed to enhance its mystique, generating an effect akin to an intricate parlor trick or an impressive cantrip. For instance, Sator squares, with their palindromic properties, essentially function as cantrips. This display serves as a clever method to captivate an audience, resembling a performance of stage magic. Despite the intriguing connections, a degree of skepticism remains regarding the assertion that it directly correlates with a periodic function denoted by astrological symbols, as suggested by the aforementioned moderator.
Furthermore, dimensions are denoted by independent variables—each symbol or term represents a discrete dimension. When terms stand independent from one another, they constitute separate dimensions; in other words, they form independent sets. Consequently, any proposition concerning the geometry of a grimoire should inherently involve the application of algebraic methodologies.
Shifting our focus to the nature of language, the recursive definition of any term within the English lexicon implies an intrinsic fractal pattern, highlighting the intricate layers of language. An intriguing application of this concept involves the utilization of specific fractal geometry manifestations, such as the Sierpinski Triangle, to the terminologies of the English language. This application vividly illustrates the theatrical and embellished components often embedded within grimoire traditions, contributing to the creation of a captivating spectacle.
I have wrote Python code to illustrate this concept, utilizing the subsequent roster of terms:
terms = [
“Nature”, “Universe”, “Galaxy”, “Solar System”,
“Planet”, “Landform”, “Mountain”, “Valley”,
“River”, “Tree”, “Leaf”, “Cell”,
“Molecule”, “Atom”, “Particle”, “Essence”,
“Concept”, “Idea”, “Thought”, “Understanding”,
“Wisdom”
]
Ontologically, languages serve to define and create virtual universes. The dimensions within the semantic domains of a language collectively encompass the entities within that constructed universe. Consequently, the special significance once attributed to a grimoire diminishes, as most languages similarly forge expansive virtual realms, each delineating a distinct universe rather than a multiverse.
This interconnectedness between language and universe-building becomes evident when we consider how we use language to construct fictional worlds. For instance, we can utilize the English language to create entire fictional universes like the Marvel universe or the Warhammer 40K universe. As we engage with these narratives, our minds decipher and decode the language, giving rise to intricate mental representations. This parallels the way magical languages correspond to abstractions, forming a virtual universe inhabited by various entities. Thus, the capability of language to craft virtual universes is not confined to esoteric contexts.
The question of realism raises a distinct topic that surpasses the scope of this post. In terms of logic, existential import hold no relevance; thus, from a purely logical standpoint, we can navigate through idealized versions of this concept without delving into the intricate matter of “Is it real?”
Existential import is a concept that extends into discussions of categorical propositions—a kind of statement that asserts aspects about a category of objects. It involves the notion that the proposition itself suggests the existence of at least one member from within that category. This concept frequently arises in conversations regarding the interpretation of categorical statements and their logical ramifications.
Nevertheless, within the domain of Boolean logic—concerned with the evaluation of truth values (true or false)—existential import doesn’t assume the same significant role as it does in classical categorical logic. Boolean logic primarily involves the analysis of propositions in terms of their truth values and logical relationships (AND, OR, NOT, etc.), with the concept of existential import not being explicitly taken into account.
Magical Ciphers
If you decode the code below, you’ll arrive at this passage. In occultism, sigils often function as ideograms within psychological frameworks, aiding in the organization and manipulation of experiences and concepts. The entities represented within these psychological gestalts of mental schemas exist subjectively and mentally. Sigils can also be used as talismans.
Many magical scripts are essentially ciphers that encode English or Latin. However, there are scripts like the Elder Futhark bind runes that constitute formal languages, not just ciphers. The cipher’s primary purpose is to obfuscate. For example, a commonly seen magical script on talismans is Theban. It operates as a substitution cipher, similar to the one employed in this section.
Here is another magical alphabet for magical scripts known as the Malachim alphabet. This system draws from Hebrew and Greek letters, which are then substituted with the Malachim alphabet. Rather than a substitition of Old Latin characters, the Malachim alphabet is a substitution cipher for Hebrew and Greek.
The code block below represents the numeric values of ASCII. Decoding it involves referencing ASCII values and inserting their corresponding characters. Considering Theban’s status as an old and well-known substitution cipher, anyone could decipher it, underscoring its predominantly aesthetic nature.
I’ve demonstrated the application of ciphers to English by encoding this section using a substitution cipher. This type of encryption is among the simplest to decode, which elucidates why Theban and other magical scripts lean more toward aesthetics than functionality.
This section using UTF-8 encoding
73 102 32 121 111 117 32 100 101 99 111 100 101 32 116 104 101 32 99 111 100 101
32 98 101 108 111 119 44 32 121 111 117 39 108 108 32 97 114 114 105 118 101 32
103 101 116 32 116 104 105 115 32 112 97 115 115 97 103 101 46 32 73 110 32 116
104 101 32 114 101 97 108 109 32 111 102 32 111 99 99 117 108 116 105 115 109 44 32 115 105 103 105 108 115 32 111 102 116 101 110 32 115 101 114 118 101 32 97
115 32 105 100 101 111 103 114 97 109 115 32 119 105 116 104 105 110 32 112 115
121 99 104 111 108 111 103 105 99 97 108 32 102 114 97 109 101 119 111 114 107 115 44 32 97 105 100 105 110 103 32 105 110 32 116 104 101 32 111 114 103 97 110
105 122 97 116 105 111 110 32 97 110 100 32 109 97 110 105 112 117 108 97 116 105 111 110 32 111 102 32 101 120 112 101 114 105 101 110 99 101 115 32 97 110 100 32 99 111 110 99 101 112 116 115 46 32 84 104 101 32 101 110 116 105 116 105 101 115 32 114 101 112 114 101 115 101 110 116 101 100 32 119 105 116 104 105 110
32 116 104 101 115 101 32 102 114 97 109 101 119 111 114 107 115 32 101 120 105
115 116 32 115 117 98 106 101 99 116 105 118 101 108 121 32 97 110 100 32 109 101 110 116 97 108 108 121 44 32 97 99 116 105 110 103 32 97 115 32 116 97 108 105 115 109 97 110 115 44 32 111 114 32 101 118 101 110 32 97 115 32 99 105 112 104 101 114 115 46 32 77 97 110 121 32 109 97 103 105 99 97 108 32 115 99 114 105 112 116 115 32 97 114 101 32 101 102 102 101 99 116 105 118 101 108 121 32 99 105 112 104 101 114 115 32 116 104 97 116 32 101 110 99 111 100 101 32 69 110 103 108 105 115 104 32 111 114 32 76 97 116 105 110 46 32 72 111 119 101 118 101 114
44 32 116 104 101 114 101 32 97 114 101 32 115 99 114 105 112 116 115 32 108 105 107 101 32 116 104 101 32 69 108 100 101 114 32 70 117 116 104 97 114 107 32 98 105 110 100 32 114 117 110 101 115 32 116 104 97 116 32 99 111 110 115 116 105
116 117 116 101 32 102 117 108 108 45 102 108 101 100 103 101 100 32 108 97 110
103 117 97 103 101 115 44 32 110 111 116 32 106 117 115 116 32 99 105 112 104 101 114 115 46 32 84 104 101 32 99 105 112 104 101 114 39 115 32 112 114 105 109 97 114 121 32 112 117 114 112 111 115 101 32 105 115 32 116 111 32 111 98 102 117 115 99 97 116 101 46 32 70 111 114 32 101 120 97 109 112 108 101 44 32 97 32 99 111 109 109 111 110 108 121 32 115 101 101 110 32 109 97 103 105 99 97 108 32 115 99 114 105 112 116 32 111 110 32 116 97 108 105 115 109 97 110 115 32 105 115 32 84 104 101 98 97 110 46 32 73 116 32 111 112 101 114 97 116 101 115 32 97 115 32 97 32 115 117 98 115 116 105 116 117 116 105 111 110 32 99 105 112 104 101
114 44 32 115 105 109 105 108 97 114 32 116 111 32 116 104 101 32 111 110 101 32 101 109 112 108 111 121 101 100 32 105 110 32 116 104 105 115 32 112 97 115 115 97 103 101 46 32 84 104 101 32 99 111 100 101 32 98 108 111 99 107 32 97 98 111 118 101 32 114 101 112 114 101 115 101 110 116 115 32 116 104 101 32 110 117 109 101 114 105 99 32 118 97 108 117 101 115 32 111 102 32 65 83 67 73 73 46 32 68 101 99 111 100 105 110 103 32 105 116 32 105 110 118 111 108 118 101 115 32 114 101 102 101 114 101 110 99 105 110 103 32 65 83 67 73 73 32 118 97 108 117 101
115 32 97 110 100 32 105 110 115 101 114 116 105 110 103 32 116 104 101 105 114
32 99 111 114 114 101 115 112 111 110 100 105 110 103 32 99 104 97 114 97 99 116 101 114 115 46 32 67 111 110 115 105 100 101 114 105 110 103 32 84 104 101 98 97 110 39 115 32 115 116 97 116 117 115 32 97 115 32 97 110 32 111 108 100 32 97
110 100 32 119 101 108 108 45 107 110 111 119 110 32 115 117 98 115 116 105 116
117 116 105 111 110 32 99 105 112 104 101 114 44 32 97 110 121 111 110 101 32 99 111 117 108 100 32 100 101 99 105 112 104 101 114 32 105 116 44 32 117 110 100
101 114 115 99 111 114 105 110 103 32 105 116 115 32 112 114 101 100 111 109 105 110 97 110 116 108 121 32 97 101 115 116 104 101 116 105 99 32 110 97 116 117 114 101 46 32 83 97 116 111 114 32 115 113 117 97 114 101 115 32 102 117 110 99 116 105 111 110 32 101 115 115 101 110 116 105 97 108 108 121 32 97 115 32 99 97
110 116 114 105 112 115 32 100 117 101 32 116 111 32 116 104 101 105 114 32 112
97 108 105 110 100 114 111 109 105 99 32 112 114 111 112 101 114 116 105 101 115 46 32 73 39 118 101 32 100 101 109 111 110 115 116 114 97 116 101 100 32 116 104 101 32 97 112 112 108 105 99 97 116 105 111 110 32 111 102 32 99 105 112 104 101 114 115 32 116 111 32 69 110 103 108 105 115 104 32 98 121 32 101 110 99 111
100 105 110 103 32 116 104 105 115 32 115 101 99 116 105 111 110 32 117 115 105
110 103 32 97 32 115 117 98 115 116 105 116 117 116 105 111 110 32 99 105 112 104 101 114 46 32 84 104 105 115 32 116 121 112 101 32 111 102 32 101 110 99 114 121 112 116 105 111 110 32 105 115 32 97 109 111 110 103 32 116 104 101 32 115 105 109 112 108 101 115 116 32 116 111 32 100 101 99 111 100 101 44 32 119 104 105 99 104 32 101 108 117 99 105 100 97 116 101 115 32 119 104 121 32 84 104 101 98 97 110 32 97 110 100 32 111 116 104 101 114 32 109 97 103 105 99 97 108 32 115
99 114 105 112 116 115 32 108 101 97 110 32 109 111 114 101 32 116 111 119 97 114 100 115 32 97 101 115 116 104 101 116 105 99 115 32 116 104 97 110 32 102 117
110 99 116 105 111 110 97 108 105 116 121 46 10
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