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

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

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.

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:

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

Commands

# 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)