A common ability that you see in science fiction and fantasy is the ability to manipulate time. Marvel characters like Doctor Strange and Magik can rewind or reverse time. This ability is also seen in the Prince of Persia games. Orhime from the anime series Bleach can reverse damage and heal people and things via reversing time. Creating temporal loops is a very useful magical skill to have. It is especially useful in spells designed to reverse damage and restore the integrity of things and objects. Temporal Loops Real magical spells to manipulate temporal histories are based on loops. A Read More

## Tag: Number Theory

## Geomancy and Thaumaturgy: Creating a Lo Shu Magic Square in Python

I am not a ceremonial magician; however, I practice Alchemy, Geomancy, and Thaumaturgy. There was a discussion on Thaumaturgy and how it relates to classical medieval figures such as Agrippa and John Dee. That conversation between zsd23 and I can be found here. I go in-depth on the mathematical basis for John Dee. I mention Agrippa, but I don’t explain too much the algorithms he was using. Agrippa was using a class of algorithms called magic square algorithms. In the book De occulta philosophia libri tres, Agrippa mentions 7 planetary magic squares. Those magic squares form the basis of a Read More

## John Dee and Thaumaturgy

zsd232 wrote: …John Dee is also a key author, but Enochian magic attributed to him was actually manufactured from a small portion of his surviving writings, recovered quite a long time after his death… I wrote: I’ve found I’m one of the few sorcerers who practice what John Dee meant tacitly by Thaumaturgy – what would be referred to as engineering abstractly. It seems like a lot of people practice Theurgy – Enochian magic, under the impression that’s what John Dee meant by Thaumaturgy. He was referencing the idea of the archetypal “black box” where a mechanism abstractly does something Read More

## Lecture 5: Number Theory II

## Lecture 4: Number Theory I

## What Does It Mean to Be a Number? (The Peano Axioms)

If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?

## A Computational Introduction to Number Theory and Algebra

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications.

## SageMath

SageMath is a computer algebra system with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.