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
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:
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
# 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)