…In a generalized sense, energy is an abstraction of the orientation of a system in a vector space and the magnitude required to displace something from its reference frame. For example, rotation around a unit circle provides periodic functions. In the sense of displacement, energy is a differential. You are not using an energy model, because energy models are systems of differentials, periodic functions, and harmonics. You are using a sci-fi plot device. In the sense of Physics, physical energy is a property of sinusoidal waves. Specifically, energy is associated with wavelength. Valid models have consistent definitions and a theory, Read More

## Tag: Geometry

## Dimensions Chapter 3

Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension…

## Dimensions: Chapter 1

Hipparchus explains how two numbers can describe the position of a point on a sphere.

He then explains stereographic projection: how can one draw a picture of the Earth on a piece of paper?

## 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

## Mathematical Rose Patterns

Creating rose (rhodonea) curves using trigonometry function and polar coordinates.

## Conjuring Magical Crystals

Commonly, people conceptualize subtle energies as ephemeral, ethereal, and intangible quintessential entities. That assumption means that those entities have no solid substance that we can hold. Various ideas about magic propose that quintessential entities facilitate magical operations and applications such as enchantments. Manipulation of quintessential entities is an intuitive, easy, and common method of augmenting an object’s attributes. A common technique is to anchor, imprint, or link a quintessential, ethereal construct to the physical object so that the physical object emanates the enchantment’s properties. That method of enchantment is like painting or gilding an object. It does not change the Read More

## Higher dimensions get really weird…

This video covers a range of what shapes and properties you’d encounter in higher dimensions.

## Elegant Thaumaturgy

An arbitrary and random collection of symbols is not enough to create a consistent magical system. An issue with creating a magical system from random symbols is that there is no formal ontological framework. Consistent magical ontological frameworks can emerge from magical languages, and people can create magical languages through ordered and logical methods. A magical system is an abstraction comprised of a tuple of symbols and strings. Those strings encapsulate magical sigils, axioms, rules, and operations that relate sigils and entities. In classical, western, occult “magical systems”, there are formally articulated sets of axioms and rules. The dilemma of Read More

## Dissecting Hypercubes with Pascal’s Triangle

What does the inside of a tesseract look like? Pascal’s Triangle can tell us.

## Splitting Rent with Triangles

You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma.

## Modern Physics with Numerical Methods

This is an open-source, modern physics textbook typically for the third semester students majoring in engineering, physics or chemistry. An emphasis is placed on fundamental principles as well as numerical solutions to equations where no analytical solutions exist. The content begins with optics and uses that as a stepping stone to wave phenomena and quantum systems.

## Associahedra: The Shapes of Multiplication

What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren’t numbers.

## The Geometry of Causality

In this episode we dive deeper into the relationship between space and time and explore how we can geometrically map the causality of the universe and increase our understanding of how time and distance relate to one another.