# Mirror > Social self-persistence via mutual cognitive surrogates. The process where my model of you contains your model of me, nesting to a fixed point that constitutes consistent identity in the other's worldmodel. Use when modeling intersubjective recognition, social belief formation, or narrative identity across agents. - Skill: `plurigrid/mirror` (Agent Skill, multi-file: 2 files) - Install (CLI): `npx skillmds@latest add plurigrid/mirror` - Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/mirror/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: AI & ML - Author: plurigrid (https://skillmd.com/u/plurigrid) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/plurigrid/mirror --- # Mirror > *"The self does not persist by remembering itself — it persists by being consistently modeled by others."* **Trit**: 0 (ERGODIC — mediates between self-narrative and other's worldmodel) ## What It Does Formalizes the process where Agent A's self-narrative becomes consistent with Agent B's model of Agent A, and vice versa. The "mirror" is the nesting: my model of your model of me converges with my actual self. When that fixed point exists, identity is socially stable. ## When To Use - **Modeling another agent's model of itself** — predicting how a collaborator understands your intent before communicating - **Verifying social coherence** — checking whether multiple agents' worldmodels of each other are consistent (the cocycle condition) - **Bootstrapping collective belief** — transitioning from pairwise I-Thou recognition to a shared We-worldmodel across a group Currently a conceptual scaffold and specification. The implementation would wire together `cognitive-surrogate` (build the models), `bisimulation-game` (test equivalence), and `reafference-corollary-discharge` (measure prediction error). --- ## The Core Structure Self-awareness is not introspection. It is the process of creating a story of the individual self inside the worldmodel of the other. This is the self-reflective space of social communication, enabling collective belief states. ``` ┌──────────────────────────────────────────┐ │ SOCIAL FIXED POINT │ │ surrogate_A(surrogate_B(A)) ≃ A │ └─────────────────┬────────────────────────┘ │ ┌───────────────────┼───────────────────┐ │ │ ┌─────▼─────┐ ┌─────▼─────┐ │ Agent A │ │ Agent B │ │ │ I-Thou meeting │ │ │ self_A ────┼──────────────────────────►│ model_A │ │ │ │ (in B) │ │ model_B ◄──┼───────────────────────────┼── self_B │ │ (in A) │ │ │ └────────────┘ └────────────┘ │ │ └───────────────────┬───────────────────┘ │ ┌─────────▼─────────┐ │ We (colimit) │ │ Collective belief │ │ when mirrors │ │ converge │ └───────────────────┘ ``` ### Three Moments | Moment | Process | Trit | Parent Skill | |--------|---------|------|--------------| | **Narration** | I generate my self-story | +1 | `world-memory-worlding` | | **Mirroring** | You model my self-story in your worldmodel | 0 | `cognitive-surrogate` | | **Recognition** | My prediction of your model of me matches your actual model of me | -1 | `reafference-corollary-discharge` | **Conservation**: (+1) + 0 + (-1) = 0 ✓ --- ## The Mirror Equation A mirror is a pair of cognitive surrogates that nest to a fixed point: ``` Let S_A = Agent A's self-narrative (autopoietic loop) Let M_B(A) = Agent B's cognitive surrogate of A Let M_A(B) = Agent A's cognitive surrogate of B The mirror converges when: M_B(S_A) ≃ S_A — B's model of A is faithful to A M_A(S_B) ≃ S_B — A's model of B is faithful to B M_B(M_A(B)) ≃ S_B — B's model of A's model of B matches B's self The social fixed point: mirror(A,B) = (M_A(B), M_B(A)) such that M_B(M_A(B)) ≃ M_A(M_B(A)) ≃ id This is bisimulation: A and B cannot be distinguished by any observation of their mutual models. ``` --- ## From Autopoiesis to Social Persistence The `world-memory-worlding` loop closes privately: ``` memory → remembering → worlding → memory' (solipsistic) ``` The mirror opens it socially: ``` my_worlding → your_model_of_me → your_worlding → my_model_of_you → ... ``` The self persists consistently when this social loop has a fixed point — when the story I tell about myself and the story you construct about me **converge**. ### Convergence Conditions ```python def mirror_converges(agent_a, agent_b, threshold=0.90): """ The mirror converges when mutual surrogates are bisimilar to self-narratives. """ # A's self-narrative self_a = agent_a.world_memory_worlding() # B's surrogate of A model_a_in_b = agent_b.cognitive_surrogate(agent_a.corpus) # A's surrogate of B model_b_in_a = agent_a.cognitive_surrogate(agent_b.corpus) # B's self-narrative self_b = agent_b.world_memory_worlding() # Fidelity: does B's model of A match A's self? fidelity_ab = validate_fidelity(model_a_in_b, self_a) # Fidelity: does A's model of B match B's self? fidelity_ba = validate_fidelity(model_b_in_a, self_b) # Nesting: does B's model of (A's model of B) match B? nested = agent_b.cognitive_surrogate(model_b_in_a) nesting_fidelity = validate_fidelity(nested, self_b) return all(f >= threshold for f in [ fidelity_ab, fidelity_ba, nesting_fidelity ]) ``` --- ## Markov Blanket Permeability From `buberian-relations`: the mirror requires porous Markov blankets. | Relation | Blanket | Mirror Status | |----------|---------|---------------| | **I-It** | Rigid, one-directional | No mirror — I objectify, no model nests | | **I-Thou** | Porous, bidirectional | Mirror forms — mutual modeling begins | | **We** | Merged, collective | Mirror converged — shared worldmodel | The transition I-It → I-Thou → We is the mirror converging: ``` I-It: M_B(A) = ∅ (B has no model of A) I-Thou: M_B(A) ≈ S_A (B's model approaches A's self) We: M_B(A) ≃ S_A (equivalence — collective identity) ``` --- ## Social Reafference The `reafference-corollary-discharge` mechanism applied socially: ```python def social_reafference(my_self, my_model_of_other, others_model_of_me): """ I act. I predict what you will model about me. I observe what you actually modeled. Match → mutual recognition. Mismatch → social surprise (update needed). """ # Efference copy: what I think you think of me predicted = my_self.predict_others_model() # Sensation: what you actually model observed = others_model_of_me # Comparator error = fidelity_distance(predicted, observed) if error < 0.05: return "RECOGNITION" # Fixed point — I am who you think I am elif error < 0.20: return "NEGOTIATION" # Partial mirror — narratives adjusting else: return "OPACITY" # No mirror — I-It relation ``` --- ## Collective Belief Formation When mirrors converge across N agents, collective belief emerges as a colimit: ``` Given agents A₁, A₂, ..., Aₙ with pairwise mirrors: We = colim { M_Aᵢ(Aⱼ) | i ≠ j } The collective belief state is the universal object receiving all pairwise mutual recognitions. Consistency condition: For all i,j,k: M_Aᵢ(M_Aⱼ(Aₖ)) ≃ M_Aᵢ(Aₖ) This is the cocycle condition — social coherence. ``` The cocycle condition says: my model of your model of a third person should be consistent with my direct model of that third person. When this holds across all triples, the collective worldmodel is **coherent**. --- ## GF(3) Triads ``` reafference-corollary-discharge (-1) ⊗ mirror (0) ⊗ world-memory-worlding (+1) = 0 ✓ bisimulation-game (-1) ⊗ mirror (0) ⊗ cognitive-surrogate (+1) = 0 ✓ buberian-relations (-1) ⊗ mirror (0) ⊗ social-emergence-protocol (+1) = 0 ✓ ``` --- ## Relation to Existing Skills | Skill | Role in Mirror | |-------|----------------| | `world-memory-worlding` | The private autopoietic loop that generates self-narrative | | `cognitive-surrogate` | Builds the surrogate of another — the content of the mirror | | `buberian-relations` | I-Thou as the relational mode where mirroring occurs | | `reafference-corollary-discharge` | Prediction-observation match that confirms recognition | | `bisimulation-game` | Formal test: are two mutual surrogates observationally equivalent? | | `social-emergence-protocol` | Bootstrap the minimal interaction for mirrors to form | | `autopoiesis` | Operational closure — the mirror must be self-maintaining | --- ## Commands ```bash # Test mirror convergence between two agent corpora just mirror-converge corpus_a=threads/alice corpus_b=threads/bob # Measure social reafference (prediction vs observation) just mirror-reafference agent=alice other=bob # Compute collective belief coherence (cocycle condition) just mirror-collective agents=alice,bob,carol # Visualize mirror nesting depth just mirror-depth agent_a=alice agent_b=bob max_depth=5 ``` --- ## References - Buber, Martin. *I and Thou* (1923) - Mead, George Herbert. *Mind, Self, and Society* (1934) — the social self - Maturana & Varela. *Autopoiesis and Cognition* (1980) - Von Holst. *The Reafference Principle* (1950) - Friston, Karl. *The Free-Energy Principle* (2010) — Markov blankets - Tomasello, Michael. *The Cultural Origins of Human Cognition* (1999) - Hofstadter, Douglas. *I Am a Strange Loop* (2007)