## Psychic Energy, Waves, and Magical Networks

There is a relationship between magical potential, psychic energy, and influence. Energy is an abstract property that describes the rotation clockwise or counterclockwise to displace an object from its reference frame and transform it. The graph of a rotation is comprised of waves. A relationship exists between energy and the vectors of an ordered magical system by the angles formed. Energy is not very useful in its disordered states. By formalizing a set of axioms to build magical constructs, you are creating an order that corresponds with the energy of the construct. As such, the energy of your magical construct is less diffuse and is intrinsically more useful. You can see how the concepts of the magical system you created relate to ordered forms of energy by looking at the harmonics and the waves of your system.

The structure of a magical construct built in this manner will have a corresponding graph of a network and waves. The magical network has an adjacency matrix and a degree matrix. From these two matrices of a network, we can derive a Laplacian matrix. From a Laplacian matrix, we can derive a wave equation where the eigenvectors will describe the harmonics, and the eigenvalues would describe the frequencies at which these things resonate. Now, you do not have to know Linear Algebra to use the methods in this post. I am using concepts of Linear Algebra to explain that the energy of the system emerges from it being intentional. An arrangement of symbols defines the semantics that relate to the dimensions of phenomenological objects. The energy arises from the differentiation and resonance of phenomenological objects. Below is the adjacency matrix of the magical network in mod 10:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |

3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |

6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

8 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

You can discover an infinite number of spells and magical formulas through a basic set of axioms and a basic set of rules for an infinite number of entities.

**This post is an introduction into Thaumaturgy without having to default to occult ontologies.**

## Abelian Fields

The backbone for how we create this type of magical system is quotients. Unlike the set of all integers, the set of all rational numbers is a **mathematical field**; therefore, this field contains a collection of corresponding symbols and sigils. These groupings are **abelian groups**.