songline-math

Mathematics of navigable knowledge graphs inspired by Australian Aboriginal songlines.

Songlines are Australian Aboriginal navigation systems — songs that encode geography. This package implements the mathematics of navigable knowledge graphs: paths through information that you can sing (traverse) to reach any destination.

Installation

npm install songline-math

Quick Start

import { SonglineGraph } from "songline-math";

// Build a knowledge graph
const sg = new SonglineGraph();
sg.addWaypoint("home", [0, 0]);
sg.addWaypoint("mountain", [10, 0]);
sg.addWaypoint("river", [10, 5]);
sg.addWaypoint("ocean", [5, 10]);

sg.addVerse("home", "mountain", 1.0);
sg.addVerse("mountain", "river", 1.5);
sg.addVerse("river", "ocean", 2.0);
sg.addVerse("home", "ocean", 10.0); // long way around

// Navigate: "sing your way" from home to ocean
const path = sg.sing("home", "ocean");
console.log(path.path);   // ["home", "mountain", "river", "ocean"]
console.log(path.cost);   // 4.5
console.log(path.dreamtime); // false

// Build and register songs (paths through the graph)
sg.buildSong(["home", "mountain", "river"], "mountain-song");
sg.buildSong(["home", "ocean"], "coastal-song");

// Find corroborees — where multiple songlines converge
const hubs = sg.corroborees();
console.log(hubs); // convergence at "home"

// Dreamtime topology — persistent homology of knowledge space
const topology = sg.topology(5.0);
console.log(topology); // { b0: 1, b1: 0 }

// Evolve a tradition of songs
const tradition = sg.evolve("my-tradition", 10);
console.log(tradition.generation); // 10

Modules

Song (song)

Core data structures for songlines:

• Waypoint: A node with coordinates in knowledge space
• Verse: An edge encoding traversal instructions
• Song: An ordered sequence of waypoints connected by verses

import { buildGraph, buildSongFromPath, reverseSong } from "songline-math";

const graph = buildGraph(waypoints, verses);
const song = buildSongFromPath(graph, ["A", "B", "C"], "my-song");
const reversed = reverseSong(song);

Navigation (navigation)

Pathfinding through knowledge graphs using songline algorithms:

• singPath: Find paths preferring well-known territory (high-connectivity nodes)
• dreamtimeTraversal: Always finds a path, even in disconnected graphs
• navigability: Fraction of node pairs with paths between them

import { singPath, dreamtimeTraversal, navigability } from "songline-math";

const path = singPath(graph, "start", "end");
// If no normal path exists, automatically uses dreamtime

Corroboree (corroboree)

Song convergence and graph clustering:

• findCorroborees: Find waypoints where multiple songs converge
• clusterBySongs: Cluster nodes by shared songline membership
• findHubs: Find high-degree knowledge hubs
• modularity: Evaluate clustering quality

import { findCorroborees, clusterBySongs } from "songline-math";

const hubs = findCorroborees(songs);
const clusters = clusterBySongs(songs, 2);

Dreamtime (dreamtime)

Persistent homology on knowledge graphs:

• bettiNumbers: β₀ (components) and β₁ (cycles) at a given scale
• persistentCycles: Topological features that persist across scales
• persistenceBarcode: Filtration evolution of topology

import { bettiNumbers, persistentCycles } from "songline-math";

const betti = bettiNumbers(graph, threshold);
const cycles = persistentCycles(graph, 20);

Tradition (tradition)

Living collections of evolving songlines:

• createTradition: Initialize a tradition from songs
• evolveGeneration: Mutate, recombine, decay, and select
• computeFitness: Score songs by navigability

import { createTradition, evolveGeneration } from "songline-math";

let tradition = createTradition("my-trad", songs);
tradition = evolveGeneration(tradition, graph);

API: SonglineGraph

The unified SonglineGraph class combines all modules:

| Method | Description | |--------|-------------| | addWaypoint(id, coords) | Add a waypoint | | addVerse(from, to, weight) | Add a directed edge | | sing(source, target) | Navigate from source to target | | buildSong(path) | Build and register a song | | corroborees() | Find convergence hubs | | topology(threshold) | Compute Betti numbers | | persistentCycles() | Find persistent topological features | | evolve(id, generations) | Evolve a tradition | | navigabilityScore | Overall graph navigability (0–1) |

Concepts

• Songline: A path through a knowledge graph, like a song that encodes geography
• Waypoint: A node with coordinates in abstract knowledge space
• Verse: An edge connecting waypoints with traversal cost
• Corroboree: A convergence point where multiple songlines meet
• Dreamtime: The metaphysical topology — persistent homology revealing true structure
• Tradition: A living collection of songlines that evolve over generations

License

MIT