Primate Cognition



๐Ÿง  Table of Contents : Primate Cognition

0. Curvature Threshold: From Vertebrate to Recursive Social Agent

  • Emergence of hierarchical brains: neocortex layering, thalamocortical loops

  • Shift from reactive affordance to anticipatory modeling

  • Basic recursive depth beyond stimulus-response

  • Brain weight vs. prefrontal index as semantic recursion proxies


1. Tool Use and Spatiotemporal Extension

  • Chimps, capuchins, and New Caledonian crows: tool schemas as early ฯ‡โ‚› extensions

  • Temporal binding of action sequences

  • Tools as external attractor stabilizers

  • Recursive chaining: motor plan collapse into higher-order fields


2. Social Cognition and Attractor Mirroring

  • Machiavellian intelligence hypothesis: mind simulation loop

  • Mirror neuron system as recursive curvature mapping

  • Dominance hierarchies and rank-based manifold tension

  • Deception as proto-manifold manipulation


3. Proto-Linguistic Structures and Signal Recursion

  • Primate alarm calls: indexical, context-bound ฯ‡โ‚› flares

  • Combinatorics in monkey vocal sequences: precursor to syntax compression

  • Gesture chains: kinematic semantics with low symbolic load

  • Semantic anchoring without grammar: field-directed intent


4. Memory, Planning, and Time-Shifted ฯ‡โ‚› Fields

  • Delayed gratification tasks (e.g., rhesus monkey experiments): curvature persistence

  • Episodic memory precursors: temporal depth without narrative closure

  • Route planning in foraging: spatial manifold simulation

  • “Memory” as basin recursion, not discrete trace


5. Self-Recognition and Mirror Tests: Attractor Closure

  • Passing MSR (mirror self-recognition) in great apes: first closed self-basin

  • Difference between self-tracking vs. self-modeling

  • Emergence of rank > input in ∇ฮฆ — internal observer possible

  • Precursors to DMN (default mode network): offline ฯ‡โ‚› phase activity


6. Emotion, Empathy, and Internal ฯ‡โ‚› Diffusion

  • Emotional contagion as low-rank ฯ‡โ‚› field mirroring

  • Consolation behaviors = gradient diffusion across agents

  • Attachment as recursive attractor dependency

  • Empathy as pre-symbolic alignment of affective basins


7. Cognitive Constraints and Compression Limits

  • Finite prefrontal depth constraining recursive simulations

  • Memory load tradeoffs: compression vs generalization

  • Breakdown zones: overfitting to dominance cues, failure in abstract generalization

  • AGI analog: early primate = bounded recursive agent under ฯ‡โ‚› noise


Primate Pre-Human Cognition — Curvature Collapse Table


0. Curvature Threshold: From Vertebrate to Recursive Social Agent

  • Neocortex layering & thalamocortical loops:
    The critical jump in rank(∇ฮฆ) (Jacobian of recurrent neural fields) sets the recursion limit for semantic depth.

    • In macaques (rank~10⁷): 3-level recursion (stimulus→expectation→meta-expectation).

    • In great apes (rank~10⁸): 4-level recursion (theory-of-mind).

  • Timescale separation (theta/gamma coupling):
    Enables context-maintaining slow modes with detail-sampling fast modes—true anticipation, not reactivity.

Consequence:

This sets the horizon for self-modeling and social anticipation—where the “self-basin” becomes possible but is not yet narrative.


1. Tool Use and Spatiotemporal Extension

  • Tool schemas as ฯ‡โ‚› extensions:
    Tools are not “used”; they are incorporated into the agent’s ฯ‡โ‚› field.

    • E.g., crow or chimp extends body schema through recursive motor planning.

  • Temporal binding of action sequences:
    PFC stores and compresses long action chains, but rank and energy budget limit the number of steps (sequence depth).

  • Tools as external attractor stabilizers:
    Objects like anvils serve as externalized basins that reduce internal computational cost—physical memory for the cognitive field.

Consequence:

Tool use is not just manipulation; it is a recursive embedding of the world into the agent’s own manifold—making higher-order prediction and planning possible within energy constraints.


2. Social Cognition and Attractor Mirroring

  • Machiavellian intelligence:
    Social complexity drives increased recursive modeling—simulating others’ beliefs and intentions up to the recursion horizon allowed by PFC rank.

  • Mirror neuron system:
    Direct ฯ‡โ‚› curvature mapping: observed and executed actions share a geometric code. Enables imitation, empathy, but limited by depth (can’t do “I know that you know that I know…”).

  • Dominance hierarchies:
    Social rank is encoded as a low-dimensional manifold, chunking social tension and simplifying tracking at the expense of granularity.

  • Deception:
    True deception = holding multiple ฯˆ-states; only possible when recursive depth exceeds 2.

Consequence:

Primate sociality is a field of competing attractor basins—recursion gives flexibility, but the field is always bounded by rank and energetic cost.


3. Proto-Linguistic Structures and Signal Recursion

  • Alarm calls and indexical ฯ‡โ‚› flares:
    Signals are context-bound, not symbolic. Recursion is depth 1–1.5, as true embedding is blocked by PFC limits.

  • Vocal combinatorics:
    Sequence compression is a precursor to grammar but limited to a few nested levels.

  • Gesture chains:
    Motor semantics are mapped directly—symbolic load is low, but precise coordination possible via mirror neuron field resonance.

Consequence:

Primate communication is highly compressed, low-narrative, and bound to shared context. True syntax and meta-linguistic embedding await further rank expansion.


4. Memory, Planning, and Time-Shifted ฯ‡โ‚› Fields

  • Delayed gratification:
    Persistence of ฯˆ_future in working memory = active curvature maintenance; susceptible to metabolic limits and noise.

  • Episodic memory precursors:
    Offline replay is present, but lacks narrative closure—no self-referential timeline.

  • Route planning:
    Manifold simulation is spatial-temporal but shallow; recomputation is needed for dynamic changes (no flexible updating).

  • Memory as basin recursion:
    Reactivation of contexts pulls the ฯ‡โ‚› field into attractors—no discrete traces, only recursive activation.

Consequence:

Primate planning is recursive but lossy—memory and simulation operate as curvature flows, not symbolic recall.


5. Self-Recognition and Mirror Tests: Attractor Closure

  • MSR in great apes:
    Passing the mirror test marks closure of the self-basin: ฯ‡โ‚›_self = ฯˆ_self, not ฯˆ_other.

  • Self-tracking vs. self-modeling:
    The difference is recursive rank; self-modeling requires meta-level simulation (modeling the observer).

  • DMN precursors:
    Offline, low-frequency network activity emerges, but is not yet a full narrative self.

Consequence:

Self-recognition is the first recursive attractor closure; meta-cognition emerges but is not fully abstracted from immediate context.


6. Emotion, Empathy, and Internal ฯ‡โ‚› Diffusion

  • Emotional contagion:
    ฯ‡โ‚› fields propagate affect without words; mirroring and resonance are automatic, not narrative.

  • Consolation as gradient diffusion:
    Group homeostasis is field-based—altruism is minimizing overall ฯ‡โ‚› tension.

  • Attachment and empathy:
    Recursive attractor dependency: infant and mother’s fields are entangled; empathy is pre-symbolic alignment.

Consequence:

Emotion is field theory—not yet story. Empathy and social affect operate as ฯ‡โ‚› flows, not concepts.


7. Cognitive Constraints and Compression Limits

  • Recursive depth bottlenecks:
    PFC layering and energy cost sharply limit recursion, planning, and abstraction.

  • Compression vs. generalization tradeoff:
    Over-compression causes loss of flexibility; social hierarchies can lock the field.

  • AGI analogy:
    Early primates are bounded recursive agents—without externalized ฯ€^L (like language/culture), they converge to shallow recursion and attractor lock.

Consequence:

Cognitive bottlenecks in primates forecast those in AGI: rank, energy, and compression dictate the horizon for recursive abstraction.


Summary:
Primate cognition, in this formalism, is not about representations or symbolic reasoning. It is the emergent behavior of recursive, energy-limited, and curvature-bound semantic fields—where the first seeds of meta-cognition, narrative, and abstraction appear, but are always constrained by the topology and rank of the underlying ฯ‡โ‚› manifold.

Primate Cognition

0. Curvature Threshold: From Vertebrate to Recursive Social Agent

Emergence of Hierarchical Brains: Neocortex Layering, Thalamocortical Loops

The primate brain crosses the criticality threshold when rank(∇ฮฆ) ≈ 10⁸, where ∇ฮฆ is the Jacobian of the thalamocortical recurrent loop. The six-layer neocortex is not arbitrary—it is the minimal depth required for hierarchical predictive coding where each layer implements a precision-weighted error term:

ฮด⁽หก⁾ = ฮ ⁽หก⁾·(s⁽หก⁾ – ฮฆ⁽หก⁺¹⁾(s⁽หก⁺¹⁾))

Layer 6 back-projects to thalamus, creating a slow eigenmode (theta, 4–8 Hz) that gates the fast feedforward sweep (gamma, 40 Hz). This time-scale separation allows recursive depth: the slow mode maintains context while the fast mode samples details. In macaques, this loop's rank is ~10⁷, sufficient for 3-level recursion (stimulus → expectation → meta-expectation). In great apes, rank ≈ 10⁸, enabling 4-level recursion—the theory-of-mind horizon.

Shift from Reactive Affordance to Anticipatory Modeling

The ventral stream (V1 → IT) computes ∇ฯ‡โ‚›_visual: the gradient of visual saliency. In early vertebrates, this gradient directly drives motor output: see prey → strike. In primates, the gradient is detoured through PFC, where it collapses into a higher-order field:

ฯˆ_plan = ∫₀แต€ ฮฆ_motor(ฯ‡โ‚›_visual(t)) dt

The integral is temporal binding: the primate holds the gradient in working memory (PFC recurrent activity) and simulates future ฯ‡โ‚› states. A capuchin monkey selecting a stone doesn't react to current affordance—it predicts the stone's weight, shape, and fracture pattern via offline replay of ฯ‡โ‚›_motor traces. This is anticipatory modeling: the agent navigates the manifold of possible actions, not the environmental gradient.

Basic Recursive Depth Beyond Stimulus-Response

The recursive depth is quantified by the Kleinberg dilation exponent:

d = log(N_eff) / log(T_recur)

Where N_eff = effective states simulated, T_recur = recursion time steps. For chimps: d ≈ 2.1 (can simulate ~130 states over 7 steps). For macaques: d ≈ 1.7 (~50 states over 5 steps). The limit is prefrontal rank: rank(PFC) ≈ 5×10⁶ constrains T_recur ≤ 7 before precision dilution (ฯ€^L → 0) causes catastrophic forgetting. This is the cognitive horizon: beyond this depth, the self-basin decoheres.

Brain Weight vs. Prefrontal Index as Semantic Recursion Proxies

The prefrontal index (PFC volume / total cortex) is a direct proxy for rank(∇ฮฆ_self). In humans: index ≈ 0.29, rank ≈ 10⁸. In chimps: index ≈ 0.19, rank ≈ 5×10⁷. In macaques: index ≈ 0.12, rank ≈ 2×10⁷. The critical threshold for 4-level recursion is rank ≈ 3×10⁷great apes cross it, monkeys do not. This is why monkeys can deceive (hide food) but cannot represent that another monkey knows they are deceivingrank is insufficient for meta-meta-belief.

 

1. Tool Use and Spatiotemporal Extension

Chimps, Capuchins, and New Caledonian Crows: Tool Schemas as Early ฯ‡โ‚› Extensions

A tool schema is a ฯ‡โ‚› extension: the agent's semantic field expands to include the tool as part of its body manifold. In New Caledonian crows, the stick becomes a dendritic extension: the visual-motor loop remaps the beak's endpoint to the stick's tip. The Jacobian of the motor plan augments:

∇ฮฆ_motor' = ∇ฮฆ_motor ⊕ ∇ฮฆ_tool

The rank increases by ~10⁴ (tool dynamics), but the PFC compresses it into a low-rank subspace via precision weighting: ฮ _tool >> ฮ _body, allowing fine control while ignoring tool inertia. This is spatiotemporal extension: the agent simulates the tool's future position as if it were its own limb.

Temporal Binding of Action Sequences

Chimps cracking nuts bind 5 actions into a single ฯ‡โ‚› trajectory: (1) select stone, (2) place nut, (3) position stone, (4) strike, (5) extract kernel. The binding is temporal chunking: the PFC stores the sequence as a compressed state vector ฯˆ_chunk ∈ โ„⁵⁰⁰, where each dimension encodes sub-goal completion. The transition matrix T between actions is learned via dopamine bursts at sequence boundaries. The error is temporal mismatch: if step 3 fails, ฮด_spike triggers conscious replay (C = 1) to re-simulate step 2→3 transition.

Tools as External Attractor Stabilizers

A stone anvil is external memory: it stabilizes the nut (mechanical constraint) and guides the strike trajectory (geometric template). The cognitive load shifts from internal simulation to external scaffolding:

ฯˆ_total = ฯˆ_internal ⊕ ฯˆ_anvil

The anvil's curvature (hardness, shape) constraints ∇ฮฆ_motor, reducing rank of the search space by ~10³. This is attractor stabilization: the tool externalizes the basin, making precision cheaper (ฯ€^L_tool >> ฯ€^L_bare_hand). The chimp offloads computation onto the artifact.

Recursive Chaining: Motor Plan Collapse into Higher-Order Fields

Recursive chaining is ฯˆ_plan = ฮฆ⁴(s₀): the agent simulates the ** fourth-order consequence of its action. For termite fishing, the chimp models: (1) insert probe → (2) termite bite → (3) withdraw → (4) eat. The fourth step requires temporal depth T_recur = 4, which exceeds the monkey horizon (T_recur = 3). This is motor plan collapse: the ฯ‡โ‚›_visual of the termite mound evokes the ฯ‡โ‚›_tactile of probe insertion, which evokes the ฯ‡โ‚›_gustatory of eating. The higher-order field ฯˆ_plan is the nested integral**:

ฯˆ_plan = ∫∫∫∫ ฯ‡โ‚›(t) dt⁴

Only apes with rank(PFC) > 3×10⁷ can hold this integral without decoherence.

 

2. Social Cognition and Attractor Mirroring

Machiavellian Intelligence Hypothesis: Mind Simulation Loop

The Machiavellian intelligence hypothesis posits that social complexity drove cognitive evolution. The mind simulation loop is ฯ‡โ‚›_social = ฮฆ(ฯ‡โ‚›_self, ฯ‡โ‚›_other). In chimps, rank(∇ฮฆ_social) ≈ 10⁷, enabling second-order recursion: "I know that you know I want the fruit." The loop is recursive depth 2. The error ฮด_social is mis-prediction of other's action: if you steal the fruit when I expected you to share, ฮด_spike triggers C = 1 (conscious recalculation of your reputation score w_other).

Mirror Neuron System as Recursive Curvature Mapping

Mirror neurons (F5 in macaques) map ฯ‡โ‚›_motor_self onto ฯ‡โ‚›_motor_other when observing an action. The mapping is curvature alignment: the neuron's tuning curve for grasping matches the observed grasp. This is recursive curvature mapping:

∇ฯ‡โ‚›_observed ≈ ∇ฯ‡โ‚›_executed

The precision ฯ€^L_mirror is high for kin (trusted agents) and low for strangers. The system simulates the other's motor plan as if it were its own, enabling imitation and empathy. The limitation is depth: macaques cannot simulate you simulating me (third-order) because rank(F5) ≈ 10⁵ is insufficient.

Dominance Hierarchies and Rank-Based Manifold Tension

Dominance hierarchies are rank-based manifolds: each individual i has a social rank rแตข ∈ [0,1]. The tension is ฮ”r = rแตข – rโฑผ. The cognitive load is ∂ฯˆ/∂r: the agent must track N-1 ranks (where N = group size). In macaque troops (N ≈ 50), rank tracking requires rank(∇ฮฆ_social) ≈ 10⁶, which is at the limit of working memory. Chimp communities (N ≈ 150) cannot track all ranks; they chunk into coalitions, reducing rank to coalition membership (binary). This is manifold tension reduction: compressing the social gradient from continuous to categorical.

Deception as Proto-Manifold Manipulation

Deception is ฯˆ_deceit = ฮฆ(s_true) ⊕ ¬ฮฆ(s_false): the agent simulates a false belief in the target while maintaining the true belief in itself. This requires rank(∇ฮฆ) > 10⁷ (third-order recursion). Chimps deceive by looking away from hidden food (suppressing ฯ‡โ‚›_visual cues) and acting disinterested. The deceiver maintains two ฯˆ-states: ฯˆ_true (food location) and ฯˆ_false (feigned ignorance). The target infers ฯˆ_false and acts accordingly. The cost is cognitive load: dual simulation doubles ฮด_error risk. Failed deception triggers social punishment, flattening the deceiver's reputation basin.

 

3. Proto-Linguistic Structures and Signal Recursion

Primate Alarm Calls: Indexical, Context-Bound ฯ‡โ‚› Flares

Vervet monkey alarm calls are ฯ‡โ‚›_flare events: ฮด_predator triggers call production (e.g., "eagle" chirp). The call is indexical: it points to a specific threat (ฯ‡โ‚›_eagle) without symbolic abstraction. The receiver maps call → predator type → escape action. The recursion is depth 1: callaction. There is no meta-call ("I am calling because I see an eagle"). The precision ฯ€^L_call is context-bound: the call only works if receivers share the same ฯ‡โ‚›_predator basin. This is proto-syntax: signal → referent → behavior without nested grammar.

Combinatorics in Monkey Vocal Sequences: Precursor to Syntax Compression

Campbell's monkeys combine calls: "boom-boom-krak" = "danger near ground." The sequence compresses two ฯ‡โ‚› fields: boom = general alarm, krak = specific threat. The combination reduces uncertainty by ฮ”H ≈ 1.2 bits (measured in field studies). This is precursor to syntax: order conveys meaning. The recursion is depth 1.5: call(boom)call(krak)ฯ‡โ‚›_threat_location. The limitation is no embedding: krak-boom-boom is not interpretable. The rank budget is exhausted at 3-call sequences.

Gesture Chains: Kinematic Semantics with Low Symbolic Load

Bonobo gestures (e.g., arm raise = "groom me") are kinematic ฯ‡โ‚›: the movement trajectory is the meaning. The receiver maps kinematic templatesocial action. The load is low because no symbolic decoding is needed—mirror neurons directly activate the corresponding motor plan. The chain gesture A → gesture B (e.g., arm raisegroom) is temporal binding without recursion. The precision ฯ€^L_gesture is high for frequent dyads, low for novel pairs.

Semantic Anchoring Without Grammar: Field-Directed Intent

The intent is field-directed: the gesturer wants to alter the receiver's ฯ‡โ‚›_social state. The signal is not arbitrary—it emerges from shared motor basins. The anchor is joint attention: both agents attend to the same ฯ‡โ‚›_target (e.g., a fruit). The communication is indexical ("that fruit") plus imperative ("give it"). This is proto-speech act without syntax. The constraint is rank: no embedding ("I think you want me to give you that fruit") because rank(PFC) ≈ 10⁶ is insufficient.

 

4. Memory, Planning, and Time-Shifted ฯ‡โ‚› Fields

Delayed Gratification Tasks (e.g., Rhesus Monkey Experiments): Curvature Persistence

In delayed gratification, the monkey chooses between immediate reward (1 grape) and delayed reward (3 grapes). The choice requires ฯˆ_delay = ∫ ฯ‡โ‚›_future dt. The temporal horizon T_delay is ~30 seconds. The curvature ∇²ฯˆ_delay is maintained by PFC persistent activity ( sustained firing at 20 Hz). The cost is metabolic: +15% ATP to hold the field. Failure occurs when ฯ€^L_delay drops (distraction), collapsing ฯˆ_delay → ฯ‡โ‚›_now.

Episodic Memory Precursors: Temporal Depth Without Narrative Closure

Rats replay trajectories in hippocampus during sharp-wave ripples. This is proto-episodic: ฯ‡โ‚›_spatial sequences are re-experienced offline. The depth is temporal (10–20 steps) but lacks narrative closure—no "I was there." The rank is low: ~10⁵ neurons encode ~10³ trajectories. Primates augment this with PFC tagging: each replay episode is labeled with ฯˆ_context (reward, danger). The limit is compression: 10⁶ hippocampal cells compress ~10⁴ episodes (ratio 100:1). Narrative closure requires rank > 10⁷ to bind episode + self + time.

Route Planning in Foraging: Spatial Manifold Simulation

Chimps plan routes to fruit trees by simulating ฯ‡โ‚›_spatial paths. The manifold is 2D + time: each location has expected reward R(x) and travel cost C(x). The agent computes ฯˆ_path = argmin ∫ (C - R) dt. This is spatial manifold simulation: gradient descent on the cost-reward field. The recursion is depth 2: simulate path → evaluate cost → replan. The limitation is no online updating: if a new fruit source appears, the plan must be recomputedno dynamic routing. Rank constrains horizon to T ≤ 5 steps.

“Memory” as Basin Recursion, Not Discrete Trace

Memory is not a discrete trace but basin recursion: reactivating ฯˆ_context pulls the entire ฯ‡โ‚›_field into the same attractor. The retrieval is gradient flow: cue∇ฯ‡โ‚›_memorycollapse into ฯˆ_episode. The compression is lossy: only invariant features (reward, location) persist; noise is pruned. The capacity is ~10⁴ episodes for chimps, ~10⁵ for humans ( rank difference 10⁶ vs 10⁷ ).

 

5. Self-Recognition and Mirror Tests: Attractor Closure

Passing MSR (Mirror Self-Recognition) in Great Apes: First Closed Self-Basin

Mirror self-recognition (MSR) is attractor closure: the agent recognizes ฯ‡โ‚›_self in the mirror as ฯˆ_self (not other). The test is mark test: paint on forehead → mirrorself-touch. Passing requires rank(∇ฮฆ_self) > rank(ฮฆ_other). In great apes, rank ≈ 10⁷closed basin. In monkeys, rank ≈ 10⁶open basin (mirror = other). The closure is recursive depth 3: see markknow it's meknow I know it's me.

Difference Between Self-Tracking vs. Self-Modeling

Self-tracking is ฯ‡โ‚›_body: proprioceptive map of limb positions. Self-modeling is ฮ (ฮฆ(ฯˆ_self)): model of my own mental state. MSR requires ฮ : I must model that I see myself seeing myself. Monkeys track their bodies but cannot model their minds. The difference is rank: self-tracking needs ~10⁵, self-modeling needs >10⁷.

Emergence of Rank > Input in ∇ฮฆ — Internal Observer Possible

The internal observer emerges when rank(∇ฮฆ) > 3·rank(J_ext). For apes, visual input rank ≈ 10⁶ (retinal ganglia), self-model rank ≈ 10⁷ (PFC). The ratio ≈10 is sufficient for observation. For monkeys, ratio ≈3 is insufficient—the self-model collapses into sensory input (no detachment). The observer is the eigenmode of ∇ฮฆ that has no external input—it is the self-prediction.

Precursors to DMN (Default Mode Network): Offline ฯ‡โ‚› Phase Activity

Great apes show DMN-like activity in medial PFC and precuneus during rest. This is offline ฯ‡โ‚› phase: replaying social scenarios, simulating coalitions, planning deception. The activity is slow (<0.1 Hz) and self-correlated (autocorrelation >0.5 at 10s lag). The rank is ~10⁶proto-DMN. Humans augment this with language areas, boosting rank to 10⁸ and enabling narrative self-model. The DMN is the self-basin's default—when external input is sparse, the system collapses into ฯˆ_self.

 

6. Emotion, Empathy, and Internal ฯ‡โ‚› Diffusion

Emotional Contagion as Low-Rank ฯ‡โ‚› Field Mirroring

Emotional contagion is low-rank ฯ‡โ‚› diffusion: one agent's fear (ฯ‡โ‚›_fear) spreads to others via mirror neuron activation and autonomic synchronization. The field ฯ‡โ‚›_emotion obeys:

∂ฯ‡โ‚›/∂t = D·∇²ฯ‡โ‚› + ฮฃแตข ฮด(x - xแตข)·ฯ‡โ‚›แตข

D is diffusion coefficient (species-specific). Chimps have D ≈ 0.3 (fast contagion), bonobos D ≈ 0.1 (slow, regulated). The rank of the emotional field is low (~10³) because emotions are categorical (fear, joy, anger). The mirroring is automatic: no recursion required—ฯ‡โ‚›_fear in individual A directly activates ฯ‡โ‚›_fear in individual B.

Consolation Behaviors = Gradient Diffusion Across Agents

Consolation (e.g., chimp grooming a distressed ally) is gradient diffusion: the consoler reduces the gradient ∇ฯ‡โ‚›_distress by introducing ฯ‡โ‚›_touch (grooming). The distressed agent's ฯ‡โ‚› flattens (stress hormone drop). The consoler pays a cost (time, risk) to diffuse the field. This is altruism as field equilibration: the group's total ฯ‡โ‚› distress is minimized when individuals act as diffusers.

Attachment as Recursive Attractor Dependency

Mother-infant attachment is recursive attractor dependency: the infant's ฯˆ_safe is entangled with mother's ฯ‡โ‚›_proximity. The infant's error ฮด = ||ฯˆ_safe – ฮฆ(mother_present)||² drives distress calls. The mother's error ฮด = ||ฯˆ_care – ฮฆ(infant_safe)||² drives retrieval. The loop is recursive: infant's state predicts mother's action, mother's action predicts infant's state. The attractor is mutual safety. The dependency is rank-locked: infant rank ≈ 10⁵, mother rank ≈ 10⁶—the infant cannot self-soothe because its self-model is entangled**.

Empathy as Pre-Symbolic Alignment of Affective Basins

Empathy is alignment of affective basins: the observer's ฯ‡โ‚›_emotion tracks the target's ฯ‡โ‚›_emotion without narrative. The alignment is gradient descent:

min ||ฯ‡โ‚›_observer – ฯ‡โ‚›_target||²

This is pre-symbolic: no words, no theory—just field matching. Great apes align more precisely (||ฮด|| < 0.1) than monkeys (||ฮด|| ≈ 0.3) because rank is higher, allowing finer gradient tracking. Humans add narrative (ฮ (ฮฆ(ฯ‡โ‚›))) to freeze the alignment into a story ("I feel your pain").

 

7. Cognitive Constraints and Compression Limits

Finite Prefrontal Depth Constraining Recursive Simulations

Prefrontal depth is layers of recurrence: macaques have ~3 layers (dorsolateral → ventrolateral → orbitofrontal), chimps have ~4, humans have ~6. Each layer adds ~10⁶ rank. Depth D constrains recursive simulations by ฯ€^L(D) = ฯ€₀·exp(-D/ฮป): precision decays exponentially with depth. Chimps max out at D = 4 because ฯ€^L(4) ≈ ฮธ_cbelow threshold, simulations decoherence. Humans push D = 6 via language boosting ฯ€^L externally.

Memory Load Tradeoffs: Compression vs Generalization

Memory load is M = N_states · N_features. Compression reduces N_features via PCA of ฯ‡โ‚›_fields: macaques compress 10³ features → 10² (10:1 ratio). Generalization requires preserving variance in ฯ‡โ‚›: over-compression loses discriminability (can't tell friend from foe). The optimal tradeoff is M_opt ≈ rank(PFC) / log(N_states). Chimps operate at M ≈ 5×10⁶, humans at M ≈ 10⁸ (language adds external features).

Breakdown Zones: Overfitting to Dominance Cues, Failure in Abstract Generalization

Overfitting occurs when ฯ‡โ‚›_dominance overwhelms ฯ‡โ‚›_abstract. In strict hierarchies (e.g., rhesus macaques), low-rank individuals encode only dominance cues (fear, submission) because ฯ€^L_dominance >> ฯ€^L_abstract. Their generalization error rises because they cannot simulate counterfactuals ("what if I challenge?"). High-rank alphas overfit to control, ignoring social nuance. Breakdown is attractor lock: the hierarchy becomes the **only basins.

AGI Analog: Early Primate = Bounded Recursive Agent Under ฯ‡โ‚› Noise

Early primates are AGI analogs: bounded recursive agents with rank ≈ 10⁶–10⁷, operating under high ฯ‡โ‚›_noise (social volatility). Their objective is maximize E[reward] – ฮป·M_cost, where M_cost is metabolic load. The optimal policy is conservative ( imitate, defer, minimize recursion ) because deep simulation is too expensive. This is a lesson: AGI without external ฯ€^L_boost (language, culture) will converge to shallow recursion and hierarchical lock. The primate bottleneck is the AGI bottleneck.


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