This is a topic a lot of people have been asking me about (I’ve been getting emails like crazy). When I have time, I’ll write a more formal posting, but this is a conversation I had on reddit on this. The conversation has been redacted and cleaned up for clarity and relevancy.
…I don’t have, nor really believe in, a Great Work. I’m working on an article on this, but, from my perspective, magic is a type of game. Trying to come up with a theory of magic is like trying to come up with a theory of art. You run into all sorts of issues with the definition. You end up with what is similar when trying to define a “game” based on the arbitrary rules of that “game”. It’s sort of like trying to say Skyrim’s a game and Dragon Age is not because Dragon Age’s game mechanics are different than Skyrim’s ergo Dragon Age is not a game.
You have things and those things have rules denoted in their relationship to other things as strings. The forces and the energy of that game emerge from the eigenvalues, eigenvectors, and the derivatives of the rules of that “game”. The “game” is the ontology of the magical system. This isn’t to say that things referenced in the game are real; rather, the arrangement of the concepts leads to differentiation and facilitates power. In actuality, that’s sort of the idea behind magic circles, triangles of arts, seals, and talismans. The ontological properties of the entities involved have relationships that follow from rules denoted in the geometry. I am really big into objectivity and I hate pragmatism, so I am not saying these things are necessarily “real” and everything is subjective – I really hate that idea; rather, the point is that when it relates to power from intentionality, the “game” you pick is an arbitrary choice where how power emerges and is shaped is a consequence of the rules of your “game”. Your magical system, or your game, is not a sector of reality; rather, it is just merely a story of the causality and the consequences of your game that causes things from the system. It’s sort of like writing one page of a story and the story writes itself. The link between that and reality is the ability for that game to influence or exert a force on reality but that doesn’t come from the rules of the system themselves; rather, it comes from the capability to create those rules – the ability of consciousness to think of these things has power in itself.
…Are you into philosophy of language? If you have read Wittgenstein work, I think you’d really enjoy it (he goes over defining things like “games” like you do)…
…No I am not into Philosophy of Language, and what I explained about “games” is just an extension of Formalist ideas of Mathematics. My expertise and interests in it goes as far as my formal education and profession does, which is Applied Mathematics and your Applied Sciences. Godel and Hilbert are more relevant to this philosophical topic than Wittgenstein. The idea of “games” just references an abstraction for consistent axioms and the consequences of those axioms. Intuitively, it is sort of like the outline of rules that govern how chess pieces can move. Wittgenstein’s work is more concerned with how problems can be articulated in a language. Computationally think of Wittgenstein’s work more along the lines of how you would create the language for the algorithms in terms of a programming language. Do you pick Python or do you pick Java? A problem is just a string. Broadly, Wittgenstein is relevant, but Godel and Hilbert are more directly relevant to conversations about Formalism in Mathematics. A lot of the ontological assumptions Western occultism makes tend to be Neoplatonic which doesn’t play very well with this. By saying magic can be interpreted via a Formalist lens, I am pretty much stating we made all the rules for magic and you can play by the games others made or you can make your own. Personally, I like making my own or extending the work of more interesting systems I see in fantasy…
Every time I come across a magic square I start thinking about calculating Eigenvalues, massive matrices and various numerical methods associated with large matrices. Has the relationship between linear algebra, Markov Chains and magic been explored formally? Or are things implied and one has to connect the dots?…
There’s a direct connection between all the metaphysics of magic and Linear Algebra because there is a direct connection between Linear Algebra, Graph Theory, and Ontology. To make a graph of the ontology of something, you just regard the instances, extensions, and properties of the class as a tree and the matrices of your tree will give you what you need. The ontological tree would come from the metaphysics of the system. Calculating the spectral graph of the ontology will give you something similar to the structure of a molecule. It will give you an idea of how rules create relations and how relations create and build structures. Spectral Graph Theory is also used in Quantum Chemistry so the forms you will get will be similar in form to how you can build stuff.
If you want to experiment for yourself with this, Gephi is a great tool to use to build your graphs once you have your trees. It will also allow you to export the adjacency list and matrices of you graph. If you want to do some of the higher Linear Algebra Calculations, I would recommend SageMath.
Has the relationship between linear algebra, Markov Chains and magic been explored formally?
…you can actually see this with old school Dungeons and Dragons. The act of basing an action on the roll of a die is actually using a Markov Chain in a magical system. You also see this idea of a dice roll being used in the stats of computer game implementations that use D&D’s system such as Never Winter Nights.
You probably won’t see higher forms of Math explored much in Western esoterism simply because a lot of the systems are older than the Mathematics albeit they were able to use some of the ideas. For example, you can take John Dee’s work to the next level by using Modular Arithmetic and Abstract Algebra; however, it wasn’t formalized until hundreds of years after his death, so you would be extending his frameworks.
Personally, I study the more exotic branches like spells to increase my speed, spells to increase how hard I can hit, spells that allow me to conjure up blasts of heat and cold, and other things like that. Traditional magical text sort of don’t cut it, so I am having to utilize modern applied ideas…
…Your framework agnostic piecemeal approach is interesting…
…I wouldn’t call it agnostic. It’s technically abstract and not agnostic. I do this on purpose. A lot of magical systems teach their system from a particular perspective and not a generalized one as a means to regulate who has access to it and who can use it in accordance with their culture and cultural values. Unfortunately, a common attitude is that of viewing teaching magic as immoral or unethical if a person is going to use it in ways that don’t conform to the teacher’s normative attitudes. In perspective, that is like not teaching someone Physics or Chemistry because you don’t agree with their political views. Silly, right? I don’t agree with that, so I teach magic from an abstract perspective so you can apply it however you want to.
Honestly, I don’t think spiritual development should come from magic because that’s not how humans are wired. Spirituality is associated with pro-social behavior. It’s an idea of feeling interconnected, being of service, and thinking of something bigger than yourself. You can get this by being active in some pro-social initiative along with thinking about how you can be of service to people. The esoteric nature of occultism tends to cause people to become withdrawn where they lose the focus of spiritual development, ironically, because “progress” is viewed within the perspective of themselves. My enlightenment. My great work. My karma. My relationship with so and so deity. Spirituality is rooted in being pro-social and altruistic which means being plugged into the rest of humanity. A lot of occultists have become less altruistic, more selfish, and, ironically, less spiritually developed. Magic cannot make you more spiritually developed. Magic is just a force. You can become more spiritually developed not by magical means but just by thinking of how you can be more patient, more compassionate, how you can be of service to humanity that day, and other “mundane” ways. Magic is a lot like money, so saying you can become more spiritually developed as a person via magic is like saying you can become more moral by attaining wealth.
Who am I now is not who I used to be; however, the psychic and magical power I have is constant and I was born with it. Trust me, I used to be one of those people who literally would rain magic down on you to destroy your life if you looked at me funny because I could. Meaning that it is quite possible for not so nice people to have power. This idea that psychic and magical power is tied to morals, ethics, culture, and spiritual development is a myth in part perpetuated because to think otherwise is a terrifying thought. Statistically, there is no reason why serial killers can’t have psychic or magical abilities and, in fact, some likely do.
Bringing this conversation full circle to the idea of “games”, Game Theory can be used to mathematically justify the idea of morality where the empirical basis for this mathematical theory is in the fitness of the human species in the context of cooperation along with there being a positive correlation between pro-social behavior and how advanced humans as a species have become. To “win” the game of survival, evolution has designed a strategy of humans that focuses on spiritual development; therefore, spiritual development is essential to human evolution. That’s the game on Earth; rules can be totally different for life on another planet.
…The scope of my interest is limited to ‘healing’. Mostly armchair. Love to pontificate while I have my coffee or tea. Mental blocks on getting a good theoretical background prevents me from taking practical steps…
…I’m not an armchair person at all. For example, via manipulating ensembles of probable kinetic energy, I can increase my velocity meaning that in a fight, I can accelerate how fast I am moving and how hard it will hurt when I hit and, inversely, I can slow down a person’s movements and how hard it will hurt when they hit me. It’s not as simple as it sounds and it takes a lot of practice to be able to do this. I also spend like 3 hours a day on exercise and martial arts and I do the whole eating clean thing. How I am able to move faster and how that is correlated with the spell I understand from an aspect of theory as well as application. For example, physical vectors such as momentum are the result of the propagation of a phase state of sinusoidal waves of temporal histories; therefore, manipulating the future outcome of something is really all about manipulating harmonics by compressing the wave of probability thereby making that future state the one that happens. This means that talismans built using modules will resemble the form of sinusoidal waves which is basically what physical reality is comprised of. Conjuring up a future reality that you would like to happen, such as the configuration of kinetic states that will push your movements faster without you having to expend any physiological energy, is really an issue of harmonics which can be addressed via magical rings. Any time-dependent object – any physical object, can be deconstructed into its harmonics via Fourier Transforms.
I have models of myself covered in magical rings and modules that reference my actual body in such a way that those properties propagate to my body. I am metaphysically covered in magical spells designed for combat…
…Are you referring to spherical harmonics?…
I’m not sure what you mean by spherical harmonics. I am referring to Trigonometry where a lot of your trigonometric functions are derived from angles of a unit circle. I am referring to a class of periodic functions that occur simultaneously instead of a pure tone – say one sinusodial wave. You get an abstraction for pitches that can be applied to a variety of things but you typically see this applied to light, energy, and sound. I am specifically referring to Fourier Transforms. So, if you mean harmonics arising from a unit circle as far “spherical harmonics”, yes. If not, I have no clue what you mean. When you use Modular Arithmetic, you enumerate in layers of circles of some number. For example, a typical clock is mod 12, so you have an arrangement of numbers up to 11 where the second layer would be to 12-23 and then 24-47 and so on.
Here is a great resource on that: Modern Physics with Numerical Methods.
This part in particular will be of interests:
Waves are, essentially, abstract. When you deal with things and the rules governing those things, you are essentially dealing with a Graph. You can represent the spectrum of that graph in such a way that you have eigenvalues that act as energy and when you represent in a moduli space, you can get equations for waves.
Ohhhh, that’s what you meant! Sorry, brain fart! Spectral Graphs are orthogonal diagonalizable, so by working with spectrums of the graph of the magical ontology, you are working with something orthogonal diagonalizable which does relate to spherical harmonics. You are working with a Laplacian matrix. That’s what I meant earlier about talismans resembling the form of physical waves. By working with the matrices of the graph, you are technically working with the spherical harmonics. The eigenvalues and the eigenvectors would be your “energy”. You end up with things that look like the wave form of things like hydrogen. The end result is you end up working with harmonics I.e. waves of energy. This isn’t to say there is any relationship between that and Quantum Physics other than, abstractly, this type of Mathematics is very useful for working with waves and energy.