Modulo Four brings algebras to life via information theory.
Welcome to Modulo Four
Modulo Four is a mathematical operations research and implementation group. We specialize in developing operational strategies based in abstract algebra and information theory. Our research focuses on understanding algebras as informational structures that can be ingrained into both theoretical and physical systems.
Our Vision
Constructing Information-Theoretical Algebras
Illuminating Existing Information-Theoretical Algebras
Illuminating Existing Information-Theoretical Algebras
Illuminating Existing Information-Theoretical Algebras
Illuminating Existing Information-Theoretical Algebras
Illuminating Existing Information-Theoretical Algebras
Articles
Algebras as Self-Regenerating Systems
Can symmetries, such as rotations and flips of a cube, be understood as circular processes in time, or as causal / probabilistic relations in self-sustaining systems? Can algebaric symmetries be quantified in terms of information theory?
What if Platonic Solids Could Be Built?
What if Platonic Solids Could Be Built?
What if Platonic Solids Could Be Built?
1️⃣ Select a Platonic Solid, such as a cube, dodecahedron, or tetrahedron.
2️⃣ Identify Its Symmetry Group: In mathematics, the symmetries of objects are captured by algebraic structures called groups. For instance, the rotational symmetries of a cube are represented by the Symmetric Group S4. Learn more here: https://lnkd.in/dE9hM3Aj
3️⃣ Map the Group Elements to Variables: Visualize the group’s elements (e.g., different positions of the cube) as variables that can exist in distinct states. For example, a variable X might be in a state of True or False.
4️⃣ Treat Group Generators as Probabilistic Relationships: Imagine the generators of the group (e.g., rotations of the cube) as probabilistic influences between the variables. For example, if X is True at time-step 1, this increases the probability of Y being True at time-step 2 by 5%.
💡 Voilà! You’ve built a Platonic Solid into a real-world system.
🤔 Why Does This Matter? Because this approach embeds the properties of the Platonic Solid and its symmetry group directly into the system. The result? A self-reinforcing, highly resilient structure.
So resilient, in fact, you might think it's a law of nature! 😉 An immutable form from the abstract realm, casting its shadows into the fabric of reality itself!
Contact Us
Modulo Four
Vancouver, British Columbia, Canada