From asi
Synthesizes concepts from mathematics, music, and philosophy via category theory morphisms, Badiou triangle, and world-hopping mechanics. Useful for interdisciplinary exploration.
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The Glass Bead Game (Glasperlenspiel) is an interdisciplinary synthesis engine that connects:
Navigates conceptual possibility spaces by synthesizing glass bead games, world hopping, and ordered locales via observational bridges with Narya-verified transitions.
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The Glass Bead Game (Glasperlenspiel) is an interdisciplinary synthesis engine that connects:
Each bead represents a concept in a specific domain. Beads connect via morphisms that preserve essential structure. The game consists of finding paths between distant beads that illuminate hidden connections.
For any three worlds W₁, W₂, W₃:
d(W₁, W₃) ≤ d(W₁, W₂) + d(W₂, W₃)
This is the triangle inequality that governs world hopping:
Distance between worlds is measured by:
def world_distance(w1, w2)
being_diff = (w1.seed ^ w2.seed).to_s(2).count('1') # Hamming distance
event_diff = (w1.epoch - w2.epoch).abs # Temporal distance
truth_diff = conjugacy_distance(w1.invariant, w2.invariant)
Math.sqrt(being_diff**2 + event_diff**2 + truth_diff**2)
end
Find a morphism that connects bead A to bead B while preserving structure.
move = GlassBeadGame::Connect.new(
from: Bead.new(:prime, 17),
to: Bead.new(:pitch_class, 5), # 17 mod 12 = 5
via: :modular_arithmetic
)
Apply a functor to move an entire structure to a new domain.
move = GlassBeadGame::Transpose.new(
structure: :circle_of_fifths,
from_domain: :music,
to_domain: :number_theory,
functor: :chromatic_to_modular
)
Discover the contravariant counterpart of a structure.
move = GlassBeadGame::Reflect.new(
structure: :major_scale,
reflection: :phrygian_mode, # Dual via interval inversion
symmetry: :diatonic_mirror
)
Execute a Badiou-style event that transitions between possible worlds.
move = GlassBeadGame::Hop.new(
from_world: current_world,
event: :modulation,
to_world: target_world,
truth_preserved: :tonal_center
)
Points are awarded for:
| Move Type | Base Points | Multipliers |
|---|---|---|
| CONNECT | 10 | ×2 if cross-domain |
| TRANSPOSE | 25 | ×3 if structure-preserving |
| REFLECT | 15 | ×2 if self-dual found |
| HOP | 50 | ×(1/distance) for elegant hops |
Shorter paths between distant concepts receive elegance bonuses:
elegance = conceptual_distance / path_length
bonus = (elegance > 3) ? elegance * 10 : 0
Turn 1: CONNECT(Ramanujan's 1729, "taxicab number")
→ Linked to: Hardy-Littlewood circle method
Points: 10
Turn 2: TRANSPOSE(circle method, analysis → music)
→ Produces: Spectral analysis of timbre
Points: 25 × 3 = 75
Turn 3: REFLECT(timbre spectrum)
→ Dual: Temporal envelope (Fourier duality)
Points: 15 × 2 = 30
Turn 4: HOP(acoustic → electronic)
→ Event: Synthesis (analog → digital)
→ Truth preserved: Harmonic ratios
Points: 50 × 0.8 = 40
Total: 155 points
# Create game from mathematician broadcast
system = WorldBroadcast::TripartiteSystem.new([:ramanujan, :grothendieck, :euler])
game = GlassBeadGame.from_broadcast(system)
# Each mathematician contributes beads
game.add_bead_from_agent(system.agents[0]) # Ramanujan's partitions
game.add_bead_from_agent(system.agents[1]) # Grothendieck's schemes
game.add_bead_from_agent(system.agents[2]) # Euler's series
# Publish moves to NATS
SynadiaBroadcast.publish("game.move.connect", move.to_json)
# Subscribe to opponent moves
SynadiaBroadcast.subscribe("game.move.*") do |msg|
game.apply_move(GlassBeadGame::Move.from_json(msg.data))
end
# Create propagator network for game state
network = PropagatorNetwork.new
# Cells for each bead
beads.each { |b| network.add_cell(b.id, b.state) }
# Propagators for constraints
network.add_propagator(:triangle_inequality) do |w1, w2, w3|
world_distance(w1, w3) <= world_distance(w1, w2) + world_distance(w2, w3)
end
The game forms a topos where:
Resources are linear (used exactly once):
just glass-bead # Start interactive game
just glass-bead-solo # Single-player mode
just glass-bead-tournament # Multi-round competition
just world-hop from to # Execute world hop
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
game-theory: 21 citations in bib.duckdbThis skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.