What kind of mathematical logic does this skill use?

The skill utilizes Lawvere's topos theory for internal logic, Girard's linear logic for resource management, and category theory for object morphisms.

What is the primary purpose of the Glass Bead Game skill?

It serves as an interdisciplinary synthesis engine that allows Claude to connect concepts from mathematics, music, and philosophy using rigorous structural mapping.

Does this skill support programmatic music analysis?

Yes, it includes moves to transpose mathematical structures like the circle method into musical domains such as spectral analysis and harmonic ratios.

How does the 'World Hopping' mechanic function?

World Hopping uses a Badiou-inspired triangle inequality to transition between different conceptual environments while ensuring that invariant structures, or 'Truths,' are preserved.

Glass Bead Game Synthesis

Name: Glass Bead Game Synthesis
Author: plurigrid

byplurigrid

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Game Development

Facilitates interdisciplinary synthesis between mathematics, music, and philosophy using category theory and topological logic.

About

The Glass Bead Game skill is a sophisticated synthesis engine inspired by Hermann Hesse, designed to find hidden connections between disparate domains like algebraic geometry, musical harmony, and ontological philosophy. It leverages Lawvere's topos theory and Badiou's ontology to map concepts as 'beads' and transitions as 'morphisms,' allowing users to 'hop' between conceptual worlds. This skill provides a structured framework for researchers and polymaths to explore structural invariants, perform domain transpositions, and maintain logical coherence across complex knowledge systems using a game-like scoring and move-based architecture.

Key Features

Topological World Hopping: Execute Badiou-style transitions between different ontological frameworks.
Metric Distance Calculation: Measure conceptual proximity using Hamming, temporal, and conjugacy distances.
Propagator Network Integration: Maintain game state and logical constraints through automated constraint satisfaction.
Interdisciplinary Morphism Mapping: Link concepts across math, music, and philosophy via structure-preserving morphisms.
Structure Transposition: Apply functors to move entire systems (e.g., Number Theory) into new domains (e.g., Music).
2 GitHub stars

Use Cases

Cross-domain research and discovering hidden structural links in complex knowledge sets.
Algorithmic music composition based on mathematical series and category theory dualities.
Philosophical modeling and ontological analysis using constructive intuitionistic logic.

About

Key Features

Topological World Hopping: Execute Badiou-style transitions between different ontological frameworks.
Metric Distance Calculation: Measure conceptual proximity using Hamming, temporal, and conjugacy distances.
Propagator Network Integration: Maintain game state and logical constraints through automated constraint satisfaction.
Interdisciplinary Morphism Mapping: Link concepts across math, music, and philosophy via structure-preserving morphisms.
Structure Transposition: Apply functors to move entire systems (e.g., Number Theory) into new domains (e.g., Music).
2 GitHub stars

Use Cases

Cross-domain research and discovering hidden structural links in complex knowledge sets.
Algorithmic music composition based on mathematical series and category theory dualities.
Philosophical modeling and ontological analysis using constructive intuitionistic logic.