The missing third point

Two organisms can track the same object without knowing that they are doing so together. The missing property is not shared direction alone. It is reciprocal access to the relation.

Imagine two hikers watching a hawk. Both heads turn towards the same patch of sky. A drone above them could classify their gaze as aligned. Yet neither hiker may know the other has seen the hawk. Now one points, the other follows, and both exchange a brief look back. The object has entered a triangular relation: person A, person B and a target that each treats as jointly attended. The return look matters because it checks not only the hawk but the partner’s orientation to the hawk.

Developmental work often groups gaze following, point following, showing, giving and declarative pointing under joint attention. Carpenter, Nagell and Tomasello’s longitudinal study traced a cluster of such capacities between nine and fifteen months, while Baldwin showed that older infants can consult a speaker’s direction of gaze when resolving a novel word’s referent.[1][2] These studies support an important relation between shared attention and communication. They do not prove that a single innate module causes the whole cluster, nor that every culture organises early interaction through the same face-to-face script.

The smallest useful formalism

Let H be the learner’s hypothesis about what “mipa” refers to. Let E be the visible scene, C the tutor’s first cue and R the tutor’s response after the learner acts. A contingent response is useful when it provides information about the correct hypothesis beyond what the scene and first cue already supplied:

This notation says that the response and correct interpretation remain statistically connected after the initial evidence is known. It does not claim that infants calculate mutual information. It names the structure of the learning problem. A fixed recording can still be informative, but its next frame is not selected by the learner’s current hypothesis. Live correction can be.

Laboratory evidence is consistent with some social contingency effects. In Kuhl and colleagues’ foreign-language study, nine-month-old infants exposed to Mandarin through live tutors learned the tested phonetic contrast, whereas matched audiovisual and audio-only exposure did not produce the same result.[3] A later randomised parent-coaching study found that changing conversational practices increased turn-taking and was associated with advances in infant language outcomes.[4] These results are not a licence to declare a universal “social gate”. Live and recorded conditions differ in attention, arousal, timing and opportunity for repair. The causal target must be isolated rather than named after the whole condition.

flowchart LR
  A["The missing third point"] --> B["The corrigibility spiral"]
  B --> C["Which capacities truly depend<br/>on others?"]
  C --> D["Turn the claim into an experiment"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#087A98,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

The corrigibility spiral

Joint attention does not install a finished social mind. It creates a channel through which later layers can modify what a learner notices, copies, says and treats as binding.

Joint attention makes reference repairable

Reference is easy when only one object is present. It becomes revealing when several objects compete. Baldwin’s discrepant-labelling design placed the speaker’s attention on a different object from the infant’s current focus. Infants could not succeed by pairing the novel word with whatever they happened to be looking at. They had to consult the speaker.[2] This is a small but profound shift: the relevant evidence includes another person’s relation to the scene.

Joint attention creates a public reference frame, not a mystical merging of minds. Each participant remains fallible. They can misread gaze, misunderstand a point or falsely assume common ground. What changes is that the mismatch can become visible to both. A nod, puzzled expression, re-pointing gesture or reformulation makes interpretation an object of coordinated action.

Imitation supplies a move, not its status

A learner who copies an adult can acquire an action sequence without understanding why it works. This is useful. It also creates ambiguity. Did the learner reproduce the movement because it caused the outcome, because the demonstrator intended it, because competent members do it that way, or because copying itself was rewarded?

Overimitation exposes the ambiguity. In classic tasks, children reproduce visibly unnecessary actions on novel objects, even when those actions do not contribute to the physical outcome.[8] One interpretation is causal: children assume intentional actions hide a purpose. Another is normative: children treat the demonstrated sequence as the proper way. A third emphasises affiliation and audience. The same output can therefore be generated by different mechanisms.

Norms make correction impersonal

Suppose two children invent a game in which a red block must be placed on a mat before a bell is rung. A puppet enters, rings first and receives the same sound. If the children merely learned a causal sequence, the shortcut should be acceptable. If they learned a conventional rule, they may object even though no personal goal was blocked.

Young children in rule-game studies do protest when a third party performs a conventional act the “wrong” way, and later work shows that enforcement appears across diverse societies while its intensity and style vary.[11][12] This matters because correction is no longer only “your action failed to get the bead”. It becomes “that is not how this game is played”. The standard can be applied to someone who did not frustrate the observer.

Language compresses a history of correction

A word is more than a sound paired with a thing. It can carry a distinction that previous speakers stabilised: cup rather than container, promise rather than prediction, evidence rather than rumour. Once learned, the word lets a child reuse a community’s past discriminations without replaying every episode that produced them. Grammar makes relations portable too. “She thinks the bead is in the cup” separates the world from another person’s representation of it.

Language is a compression layer for socially maintained distinctions. The phrase does not imply that thought begins with language. Infants, animals and adults with aphasia can perceive, plan and reason non-verbally. The claim is narrower: language packages distinctions so they can be taught, challenged and combined outside the immediate scene.

Large-scale naturalistic work across 1,001 children found robust relations between children’s vocal production, age and the amount of adult speech around them, while not reproducing some expected associations with gender, multilingualism or maternal education in that dataset.[5] Yet direct child-address is not the only route. Tseltal-learning infants who are rarely spoken to showed knowledge of common nouns and community greeting terms that had to be learned through overhearing.[6] The lesson is not that interaction is dispensable. It is that social participation has more geometries than the laboratory dyad.

Institutions let correction outlive the corrector

A child can learn “take turns” from a caregiver. A school extends the rule with schedules, roles, attendance records and appeal procedures. Money, courts, examinations and scientific publication all rely on similar extensions. An institution stores who may decide, what evidence counts, how a decision is recorded and how a dispute is reopened. The participants need not share a room or generation.

This paper uses institution in a minimal engineering sense: a durable arrangement of roles, rules, records and sanctions that preserves a practice across changing participants. Recent comparative ethnographic analysis of 23 egalitarian forager societies found teaching more strongly associated with the transmission of opaque cultural material, including values and kinship knowledge, than with many observable subsistence skills; leadership was also associated with such teaching.[17] The study is observational, relies on coded ethnographic passages and uses a debatable opaque/instrumental distinction. It nonetheless identifies a plausible reason institutions matter: some standards cannot be reverse-engineered from outcomes alone.

Which capacities truly depend on others?

“Socially shaped” is too loose to guide an experiment. The claim must say what kind of dependence is alleged and which substitution would break it.

This taxonomy is a new causal distinction offered by the paper. It prevents a common slide from “children learn around people” to “the capacity is social all the way down”. Basic perceptual discrimination, reinforcement learning and instrumental planning can operate without a public standard, even though social settings train them efficiently. Conventional word use, promising, role membership and third-party rule enforcement are stronger candidates for constitution because correctness depends on shared practice.

Some capacities occupy different grades at different grains. Speech-sound discrimination may be socially scaffolded during acquisition, yet an adult can later discriminate sounds alone. A particular word’s conventional meaning is socially constituted. The ability to certify a transcript may be institutionally stabilised because its authority depends on recognised roles and records. Ask about the exact competence, at the exact time scale, under the exact criterion of success.

A capacity-by-capacity answer

Which capacities, then, depend on joint attention, imitation, norms, language and institutions? Joint attention is most directly implicated in learning and repairing reference when several interpretations remain live. It also supports coordination around absent goals once gestures and words can stand in for the immediate target. It is less clearly necessary for every word. Overhearing, routine participation and statistical regularities can carry substantial information, especially when a community does not organise learning through intensive child-directed dialogue.

Imitation matters when the solution path is opaque, costly to rediscover or socially marked. It can preserve fine procedural detail that outcome emulation misses. Yet imitation is not required whenever a learner can reconstruct the end state, as studies of children copying technological designs without full action information demonstrate. Its causal contribution should therefore be tested against emulation, instruction and individual discovery, not against an empty control.

Norms are required for capacities whose success includes appropriateness, obligation or entitlement. Knowing that most people queue is a statistical belief. Knowing that one ought to wait one’s turn, that others may object, and that emergencies alter the rule is normative competence. Language expands this competence by making reasons and exceptions discussable. Still, a child can respond to approval, disapproval and patterned practice before giving an explicit verbal justification. Verbal report is evidence about normative understanding, not its sole definition.

Institutions become necessary when the relevant correctness relation spans absent people, long delays or replaceable roles. Property, certification, scientific priority and legal responsibility cannot be sustained by dyadic memory alone at scale. Records and procedures make the practice durable, but durability is not the same as wisdom. An institution can preserve a bad distinction with exceptional fidelity. The answer is therefore layered: others are necessary not for cognition in general, but for the public reference, normative status and durable authority of particular cognitive acts.

The strongest rival explanation

The strongest rival is not “sociality does nothing”. It is that domain-general learning, attention and reinforcement can explain most observations, while cultural environments merely supply unusually rich data. On this view, gaze following is learned because gaze predicts events; imitation grows through sensorimotor association; norm protest follows reinforcement and reputational incentives; language is distributional learning over signals.

This rival should be taken seriously. Neonatal imitation itself remains contested: a large longitudinal study challenged broad neonatal imitation effects, followed by reanalysis and continuing dispute.[9][10] Cross-cultural research also shows that reliance on social information and majority cues varies by community and age.[16] These findings weaken stories in which one preformed social faculty simply unfolds.

The public-corrigibility thesis survives only if contingency and normative uptake explain variance after attention, reward history and input quantity are controlled. It is strengthened when matched replay fails specifically on ambiguity-repair trials, when convention swaps reverse what counts as correct, or when removing authorised roles destroys a practice despite preserved information. It is weakened when non-social training produces equal transfer, when correction adds no information, or when apparent norm following disappears after incentive controls.

stateDiagram-v2
  [*] --> Claim
  state "Hold the stimulus constant and<br/>remove contingency" as Claim
  state "The smallest useful formalism" as Test
  state "How one acknowledgement can<br/>collapse ambiguity" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

Turn the claim into an experiment

A useful thesis must tell us how to build a contrast that could make it fail. The smallest experiment holds exposure steady, varies contingency and asks whether the gain transfers.

An executable social-learning lab

The lab below simulates four learners trying to map four invented words to four objects. All receive the same number of labelled episodes. The exposure learner follows a noisy salient object. The imitation learner follows a demonstrator’s cue. The joint-attention learner receives a second orientation when its current guess visibly diverges. The corrigible learner also receives explicit acceptance or rejection of its choice.

The simulation is deliberately small. It tests an informational claim: contingent repair can reduce ambiguity even when total exposure is matched. It does not model a child, prove a specialised social mechanism or establish that correction is always beneficial.

from __future__ import annotations

import random
from dataclasses import dataclass
from typing import Literal

Condition = Literal["exposure", "imitation", "joint", "corrigible"]

@dataclass(frozen=True)
class Config:
    trials: int = 80
    cue_reliability: float = 0.65
    repair_reliability: float = 0.92
    learners: int = 400
    seed: int = 76


def noisy_target(target: int, reliability: float, rng: random.Random) -> int:
    if rng.random() < reliability:
        return target
    alternatives = [i for i in range(4) if i != target]
    return rng.choice(alternatives)


def train(condition: Condition, cfg: Config, rng: random.Random) -> float:
    # scores[label][object]; a small symmetric prior prevents empty rows
    scores = [[1.0 for _ in range(4)] for _ in range(4)]

    for _ in range(cfg.trials):
        label = rng.randrange(4)
        target = label  # stationary synthetic convention
        cue = noisy_target(target, cfg.cue_reliability, rng)

        if condition == "exposure":
            salient = noisy_target(target, 0.38, rng)
            scores[label][salient] += 0.30
        elif condition == "imitation":
            scores[label][cue] += 1.0
        elif condition == "joint":
            scores[label][cue] += 1.0
            guess = max(range(4), key=lambda j: scores[label][j])
            if guess != target:
                repair = noisy_target(target, cfg.repair_reliability, rng)
                scores[label][repair] += 1.25
        elif condition == "corrigible":
            scores[label][cue] += 0.8
            guess = max(range(4), key=lambda j: scores[label][j])
            feedback_is_true = rng.random() < cfg.repair_reliability
            if feedback_is_true:
                if guess == target:
                    scores[label][guess] += 1.2
                else:
                    scores[label][guess] = max(0.05, scores[label][guess] - 0.75)
                    scores[label][target] += 1.7

    # Expected held-out accuracy if choices are sampled from learned scores.
    return sum(
        scores[label][label] / sum(scores[label]) for label in range(4)
    ) / 4


def run(cfg: Config) -> dict[Condition, float]:
    rng = random.Random(cfg.seed)
    conditions: tuple[Condition, ...] = (
        "exposure", "imitation", "joint", "corrigible"
    )
    return {
        condition: sum(train(condition, cfg, rng) for _ in range(cfg.learners))
        / cfg.learners
        for condition in conditions
    }


if __name__ == "__main__":
    results = run(Config())
    for name, accuracy in results.items():
        print(f"{name:12s} {accuracy:.3f}")

A developmental interaction protocol

The stronger test is behavioural. Choose a task with genuine referential ambiguity, such as learning four novel labels in scenes containing four objects. Pre-register four conditions with matched exposure time and label frequency. Measure not only final accuracy but repair latency, transfer to a new partner, retention after delay and adaptation when conventions switch.

A realistic configured-system example

Consider an AI-supported classroom that teaches scientific classification. A content-delivery design gives every learner the same explanation and quiz. A socially bootstrapped design records the learner’s proposed classification, asks for the discriminating feature, exposes disagreement among peers, lets an authorised teacher correct the rule and stores the reason for later cases. The model may propose examples, but the class practice decides what evidence settles the category.

The same principle applies to human-machine work. A language model has absorbed traces of social correction from text, yet fluent reproduction does not by itself make the model a member of the institution whose rules it describes. For institutional participation, the configured system needs identity, role, permitted context, authority, typed action, evidence, a decision receipt and an appeal path. Norm-like language without answerability is imitation at institutional scale.

sequenceDiagram
  participant Q as Question
  participant M as Mechanism
  participant E as Evidence
  participant D as Decision
  Q->>M: The missing third point
  M->>E: Hold the stimulus constant and remove contingency
  E-->>M: compare rival explanations
  E->>D: Preserve public corrigibility in shared competence
  D-->>Q: revise scope or act

Preserve public corrigibility in shared competence

The question “Is mind social?” invites slogans. The better question is: which competence fails under which social substitution? Replace a partner with matched playback. Remove the learner-dependent response. Move the agent between conventions. Preserve all information but delete authorised roles and records. Each intervention identifies a different dependence.

The resulting decision is practical. In education, caregiving and human-machine systems, do not measure social value by exposure minutes, dialogue volume or human-like surface behaviour alone. Measure whether the system can reveal its interpretation, receive error-specific response, distinguish physical failure from normative breach, carry reasons across contexts and reopen a settled rule when evidence changes.

Preserve public corrigibility wherever the competence is referential, normative or institutional. Automate repetition, search and example generation aggressively. Be slower about replacing the loop in which another participant can say, “I see what you took this to mean; here is why that reading fails; now show me that the correction transfers.” That loop is not decorative social warmth. It is one of the mechanisms by which a private learner becomes answerable to a shared world.