How does the Triangle Inequality Constraint work?

It serves as a geometric sanity check during navigation, ensuring that the distance between two worlds via an intermediate point is logically consistent with direct path calculations, preventing invalid state 'hops.'

What is a 'Possible World' in this context?

A Possible World is a specific configuration of data, seeds, and invariants representing a unique state within a mathematical, musical, or conceptual system.

How do I find the shortest path between different states?

You can use the built-in shortest-path command, which utilizes a modified Dijkstra's algorithm pruned by triangle inequality and accessibility logic to find the optimal sequence of hops.

Can this be used for music theory?

Yes, it includes specific integrations for musical 'world hopping,' treating key changes, chord modulations, and mode shifts as ontological events within a tonal world-graph.

What is Badiou’s Event Ontology?

It is a philosophical framework where 'events' are ruptures in a situation that create new possibilities (new worlds) from the 'void,' which are then formalized through truth procedures.

World Hopping: Possible World Navigator

Name: World Hopping: Possible World Navigator
Author: plurigrid

byplurigrid

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データサイエンスとML

Navigates complex mathematical and philosophical state spaces using Badiou’s event ontology and modal logic constraints.

World Hopping is a specialized navigation engine designed for traversing 'possible worlds' within mathematical, musical, or philosophical domains. Built upon Badiou's ontology and Kripke semantics, the skill uses triangle inequality as a fundamental constraint to manage transitions between distinct states. It allows users to simulate ontological shifts, calculate distances between conceptual configurations, and model truth procedures as generative events. This tool is particularly useful for researchers and developers working on multi-state simulations, complex system modeling, or formalizing abstract transformations in creative coding environments.

主な機能

01Modal Logic Navigation: Implements reflexive, symmetric, and transitive accessibility relations between states.

02Dynamic Transition Moves: Perform Slides, Leaps, Reflections, and Compositions across complex world-graphs.

03Event Ontology Engine: Simulates structural ruptures and 'void-traces' based on Badiou’s philosophical framework.

04Cross-Domain Mapping: Seamlessly maps transformations between musical keys, mathematical domains, and distributed systems.

057 GitHub stars

06Triangle Inequality Constraints: Ensures valid state transitions using weighted Euclidean distances and Hamming metrics.

ユースケース

01Simulating conceptual shifts and accessibility relations in formal philosophical or mathematical research.

02Optimizing paths between high-dimensional data points using custom ontological constraints.

03Modeling complex state transitions in generative music or algorithmic composition.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi world-hopping

For use in Claude.ai and ChatGPT

Download Skill