Imagine listing every candidate we might call minded: humans in different states, infants, crows, octopuses, bees, organoids, plants, language models, embodied agents, firms, scientific teams and software societies. A ladder asks where each belongs from low to high. An atlas asks which capacities appear, through what organisation, under which conditions and with what evidential access. The difference is not cosmetic.

A ladder assumes that the relevant properties line up on one latent axis. That can be useful when a narrow construct has already been validated. It becomes hazardous when the construct itself is disputed. Sloman’s early “space of possible minds” was explicitly a space of designs, not a single scale.[1] In consciousness science, Bayne, Hohwy and Owen argued that global states should not automatically be ordered by a single level and proposed a multidimensional alternative.[2] Birch, Schnell and Clayton later offered a multidimensional framework for animal consciousness, partly because species can be rich on one dimension and limited on another.[3]

Those proposals do not supply one universal map for all possible minds. They establish a more basic lesson: profile shape can carry information that rank destroys. A crow may excel at a visual memory task yet lack the human response channel used to score it. A language model may produce elaborate verbal uncertainty while lacking the persistent world-coupled state that the same words normally report in a person. A committee may correct individual errors while having no unified memory beyond its minutes. Compress these cases to one number and mechanism, boundary and evidence disappear together.

The hidden assumption is invariance

Suppose two thermometers use different scales. Conversion is straightforward because the relation between Celsius and Fahrenheit is known. Comparative mind science rarely enjoys that luxury. A verbal confidence report, an opt-out response, a looking-time difference and a model-generated probability may all respond to uncertainty, yet they also depend on different motor, motivational and representational routes.

Psychometrics calls a related requirement measurement invariance: the same latent construct should relate to observed indicators in comparable ways across groups.[4][5] Cross-species and cross-substrate work faces an even harder version. The observed variables may not be shared, the mechanisms may differ and the very ontology of the candidate may be disputed. It is therefore unsafe to assume that equal scores mean equal properties, or that unequal scores identify a difference in the target property.

The atlas response is not to forbid comparison. It is to make the bridge explicit. Each cell must say: “This probe is evidence about this property in this candidate because these causal relations are preserved.” The claim can then fail in a specific place. Perhaps the probe requires language. Perhaps an artificial system retrieves from an external store rather than retaining an internal state. Perhaps a collective score is generated by one high-performing member. A ladder hides these failure points inside its number.

This matters even within one organism. Wakefulness, responsiveness, perceptual richness and self-awareness can dissociate. Across species and engineered systems, dissociation is the rule rather than the exception. The atlas is therefore not a more colourful scorecard. It changes the unit of analysis from a candidate-number pair to a collection of warranted, boundary-specific claims.

flowchart TD
  A["Four rooms, one red object"] --> B["The ladder lies"]
  B --> C["Blank cells have causes"]
  C --> D["Translation is an intervention"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#5B5CF6,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

Open a comparative spreadsheet and find an empty cell under “metacognition” for an infant. What does it mean? The property was never tested. The available probe required language. A non-verbal probe was attempted but its transfer bridge failed. Results conflicted. The study was underpowered. Or a sensitive, valid probe found no signal. These are not variations of zero. They are different epistemic states.

Classical missing-data analysis distinguishes patterns according to why values are missing because the missingness mechanism affects valid inference.[6] The analogy must be used carefully. A possible-minds atlas is more than a statistical table with absent values. Some cells are missing because no measurement translation has yet been justified. Others are out of scope because the candidate boundary does not support the property as defined. Still, the central discipline transfers: the cause of a blank is part of the evidence.

Six statuses, six different actions

A practical atlas needs at least six non-numeric statuses. Untested calls for a study. Inaccessible calls for a new interface or a narrower claim. Bridge failed blocks transfer from the probe to the property. Conflicting calls for an experiment that separates rival explanations. Out of scope calls for boundary or construct revision. Not detected can lower belief only after sensitivity and validity are defended.

Infant consciousness research makes the final distinction vivid. Frohlich and Bayne argue for a cluster-based approach because no single adult-validated marker transfers confidently to infancy. They further stress that absence matters only for markers with adequate sensitivity. The absence of verbal report is not useful negative evidence because conscious adults can also lack or fail verbal report.[8] Bayne and colleagues similarly treat the onset of infant consciousness as a problem requiring convergent markers and explicit assumptions, not one decisive test.[9]

A negative result needs a sensitivity story

“No signal” sounds decisive because it resembles observation. Yet a negative result supports absence only if the study could have detected the property when present. For a language report, sensitivity fails in a pre-verbal infant by design. For an artificial agent, a probe can fail because the model has no access to the relevant runtime variable, because prompting contaminates the variable, or because the candidate boundary excludes the process under test. For a collective, a task can fail because communication bandwidth is too low, not because the members cannot jointly solve it.

The atlas therefore pairs every not-detected status with a sensitivity claim: what positive control worked, what perturbation should have changed the measure, what range was observable and which rival route could mask the property? Without that record, “negative” should be downgraded to inaccessible or bridge failed. This is deliberately conservative. It prevents absent speech, absent telemetry or absent coordination infrastructure from masquerading as absent cognition.

Visible missingness has another benefit. It turns ignorance into a research agenda. A cluster of inaccessible cells may reveal a language-heavy field. Repeated bridge failures may expose a property defined too closely around human implementation. Conflicting cells can identify the intervention that would separate mechanisms. The blank is no longer a nuisance before analysis. It becomes a map of what the discipline has not yet earned the right to compare.

Once missingness is visible, the next temptation is to standardise every probe. Give all candidates the same image, delay, instruction and response options. This looks neutral because the laboratory input is identical. It is often unfair for the same reason. Identical surfaces can impose unequal sensory, motor, linguistic, motivational and computational requirements.

A better comparison preserves what the experiment is causally asking. In the red-object case, the demand is not “say left”. It is: encode a location, remove direct access, preserve task-relevant information across a delay, resist a distractor and let that retained information alter later behaviour. The response may be speech, gaze, pecking or a typed action. Translation succeeds when those changes leave the demand intact and when candidate-specific shortcuts are controlled.

This resembles the problem of transportability in causal inference. A result moves from one population or setting to another only through assumptions about what remains invariant and what changes.[7] Cross-candidate work adds a complication. We may not share variables, mechanisms or even agreed system boundaries. The transport claim must therefore be narrower: not “the same test measures the same mind”, but “this adapted probe preserves these intervention-sensitive relations relevant to this property”.

Write the causal demand before the protocol

A protocol begins with apparatus: stimulus, timing, response and score. A causal demand begins with dependencies. What must be available? What is removed? What state must persist? Which intervention should alter the result? Which shortcut should leave it unchanged? This order matters because it separates the property from the interface used to expose it.

For delayed recognition, a compact demand can be written as four relations. Exposure at t₀ changes an internal or system-level state. Direct access to the target then ends. The state remains causally available across delay and distraction. At t₁, changing or clearing that state changes the candidate’s response. The probe need not reproduce a human mechanism, but it must make these relations testable.

The formula deliberately says nothing about identical implementation. If the scientific question is functional retention, different mechanisms may satisfy the same demand. If the question is a mechanism such as recurrent integration, implementation becomes part of the target and cannot be translated away. The atlas must therefore label whether a cell concerns behaviour, function, mechanism, report or experience. Evidence can connect those ledgers, but it cannot silently migrate between them.

The interface tax is a vector

Calling the extra burden an interface tax helps, but the tax should not be collapsed to one severity number. It is a vector of requirements not constitutive of the target property: language decoding, fine motor control, visual acuity, reward comprehension, cultural convention, prompt interpretation, tool reliability, latency tolerance, training history and willingness to participate. Two candidates can face the same total burden for different reasons, which implies different repairs.

Suppose an octopus fails a touchscreen task and a language model fails a physical navigation task. A scalar “interface difficulty” may rate both as high. The octopus might be limited by apparatus affordances. The model might lack any body-world loop within the declared candidate. One calls for an ecological interface. The other calls for boundary revision or a different property claim. The vector preserves that distinction.

The same discipline applies to biological and collective candidates. A bodily loop can carry information not visible in a brain-only account. A group’s shared document can preserve commitments no member remembers. A database may be part of a configured agent for one engineering question and an external scaffold for another. No boundary is automatically correct across all properties. What matters is whether the declared system contains the state transitions that the causal demand requires.

stateDiagram-v2
  [*] --> Claim
  state "The hidden assumption is<br/>invariance" as Claim
  state "Six statuses, six different<br/>actions" as Test
  state "A negative result needs a<br/>sensitivity story" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

An atlas becomes useful when its discipline survives contact with a spreadsheet, database or review meeting. The minimum unit is not a score. It is a typed evidence record. One cell ties a candidate and property to a declared boundary, causal demand, probe, evidence status, optional estimate, measurement bridge, interface-tax vector, confounds, provenance and replication state.

Three invariants do most of the intellectual work. A missing status cannot carry a numeric estimate. “Not detected” is admissible only with a sensitivity record. A pairwise numerical comparison requires the same property and causal demand, valid bridges and observed estimates on both sides. These rules are intentionally stricter than ordinary table software. Their purpose is to stop type coercion before it becomes a scientific conclusion.

Coverage before comparison

For a decision-relevant set of dimensions D, report coverage before any summary. Coverage is the proportion of cells whose status and bridge make them admissible for that decision. It is not a quality score. High coverage can consist of strong negative evidence, while low coverage can conceal impressive but inaccessible capacities.

Next, compare locally. For a property p, calculate a difference only when both records meet the same causal demand and validity threshold. If a decision needs several properties, publish the weighting rule and a sensitivity analysis showing whether the decision changes under plausible alternatives. The default display should remain the profile, because a stable local difference does not license a global mind order.

One atlas, several decision views

The underlying records can support several views without pretending that the views are interchangeable. A mechanism researcher may filter for intervention-validated cells. A welfare review may inspect valence-relevant indicators, uncertainty and harm asymmetry. An engineer may focus on retention, calibration and recovery at the configured-system boundary. A comparative psychologist may group ecologically translated tasks. Each view should disclose its selected dimensions, exclusions and threshold. The records remain shared; the decision lens changes.

Consider a welfare triage in which Candidate A has weak but non-zero evidence on several theory-relative indicators and Candidate B has one strong functional result but many inaccessible cells. A universal average would reward B’s measurement convenience. A decision-specific view can instead show evidence strength, coverage, consequence severity and reversibility separately. It may support precaution for both candidates for different reasons. That is not indecision. It is a refusal to let one synthetic number erase the structure of uncertainty.

Dimensions themselves must remain revisable. Human-centred taxonomies risk defining intelligence around language, dexterity and familiar social behaviour. Machine-centred taxonomies can privilege benchmark access, tool APIs and text generation. A sound atlas therefore records why each dimension matters: a theory commitment, welfare question, engineering decision, ecological function or experimental contrast. New candidates may require new axes rather than forced placement on old ones.

Human groups can exhibit a general collective-performance factor under specific task and interaction conditions.[12] Artificial-agent studies now expose why the candidate boundary and topology matter. One 2026 study reports majority-following coordination at scales beyond typical human experiments.[13] A separate large-scale preprint found that millions of agents did not spontaneously produce strong collective intelligence when interactions remained shallow and sparse.[14] These results are not contradictory by default. Coordination, conformity, information synthesis and collective problem-solving are different properties. The atlas prevents one from standing in for all.

What the atlas may and may not say

A biological, artificial or collective candidate can receive rich functional records without any conclusion about experience. Butlin and colleagues propose theory-derived indicators to inform credences about AI consciousness, while retaining uncertainty across theories and implementations.[10] Their method should not be converted into an ontology-free score. An atlas can host such indicators as theory-relative properties, each with a candidate boundary and measurement bridge. It cannot make disagreement among consciousness theories disappear.

Reports deserve the same discipline. Language models can generate first-person narratives through role-conditioned text production, so a fluent report is evidence of a reporting disposition before it is evidence of an inner state.[11] Animal and infant behaviour carries other ambiguities. Collective language may come from editorial convention rather than a group subject. The atlas does not discard reports. It keeps their generator, provenance and rival explanations visible.

from __future__ import annotations
from dataclasses import dataclass, asdict
from typing import Literal, Optional

Status = Literal[
    "observed_support",
    "observed_not_detected",
    "untested",
    "inaccessible",
    "bridge_failed",
    "conflicting",
    "out_of_scope",
]

OBSERVED = {"observed_support", "observed_not_detected"}

@dataclass(frozen=True)
class AtlasCell:
    candidate: str
    candidate_class: str
    boundary: str
    property: str
    causal_demand: str
    probe: str
    status: Status
    estimate: Optional[float]
    bridge_grade: int
    bridge_rationale: str
    interface_tax: tuple[str, ...]
    sensitivity_checked: bool
    rival_generator: str
    provenance: str
    prohibited_inference: str

    def validate(self) -> None:
        if not all((self.candidate, self.boundary, self.property,
                    self.causal_demand, self.probe)):
            raise ValueError("Identity, boundary, property, demand and probe are required.")
        if self.status in OBSERVED:
            if self.estimate is None or not 0.0 <= self.estimate <= 1.0:
                raise ValueError("Observed statuses require an estimate from 0 to 1.")
            if self.bridge_grade < 2:
                raise ValueError("A numeric observation needs a defensible bridge.")
        elif self.estimate is not None:
            raise ValueError("Missing or failed evidence cannot be coerced to a number.")
        if self.status == "observed_not_detected" and not self.sensitivity_checked:
            raise ValueError("Not detected requires a sensitivity or positive-control record.")

def comparable(a: AtlasCell, b: AtlasCell) -> tuple[bool, list[str]]:
    reasons: list[str] = []
    if a.property.strip().casefold() != b.property.strip().casefold():
        reasons.append("properties differ")
    if a.causal_demand.strip().casefold() != b.causal_demand.strip().casefold():
        reasons.append("causal demands differ")
    if a.status not in OBSERVED or b.status not in OBSERVED:
        reasons.append("at least one status is not numerically admissible")
    if min(a.bridge_grade, b.bridge_grade) < 2:
        reasons.append("at least one measurement bridge is too weak")
    if a.estimate is None or b.estimate is None:
        reasons.append("at least one estimate is missing")
    return (not reasons, reasons)

def local_difference(a: AtlasCell, b: AtlasCell) -> float:
    ok, reasons = comparable(a, b)
    if not ok:
        raise ValueError("Comparison blocked: " + "; ".join(reasons))
    assert a.estimate is not None and b.estimate is not None
    return a.estimate - b.estimate

# The schema intentionally provides no overall_mind_score().

What a positive atlas result permits

A strong record permits a sentence with five clauses: the named candidate, at the declared boundary, exhibited or failed to exhibit a named property, under a preserved causal demand, through a stated measurement bridge. That sentence can guide the next intervention, compare architectures or update a theory-relative credence. It can also justify a precautionary decision when harms are asymmetric, provided the precaution rule is separately defended.

A negative result has a different job. It may show that a sensitive probe did not detect the property, that a mechanism is unnecessary, that a candidate boundary is wrong or that a translation failed. Those conclusions lead to different actions. The atlas records which one occurred. What it cannot establish is the absence of all mentality, experience or moral relevance from one local failure.