When silence conceals two different brains

A passive recording listens to whatever a system happens to do. That can be useful, but spontaneous activity mixes the system’s internal capacity with its current inputs, tasks, fluctuations and noise. A perturbation changes the question. Instead of asking, “What pattern is present?”, it asks, “What does this system do when a controlled cause enters here, now?”

This is why the 2005 sleep experiment by Massimini and colleagues was so revealing. During quiet wakefulness, a transcranial magnetic stimulation pulse over premotor cortex was followed by waves reaching connected areas. During non-rapid-eye-movement sleep, the initial response was stronger, yet it quickly extinguished near the stimulation site.[1] The crucial contrast was not more electrical activity versus less. It was a difference in effective connectivity: how one part of the cortex could causally engage others in that state.

The result motivates an instrument rather than a metaphysical conclusion. A perturbation can disclose latent response organisation that behaviour does not. It does not, by itself, tell us why that organisation is related to experience, whether the relation is constitutive or merely diagnostic, or whether a similar number in another system means the same thing.

Why not calculate complexity from the ongoing EEG and avoid the pulse? Sometimes that works as a classifier. Yet a spontaneous trace has no common causal question built into it. A quiet signal can mean reduced capacity, a temporarily stable state, a different sensory environment or a measurement failure. A variable signal can reflect rich intrinsic dynamics, muscle activity, electrode noise or an uncontrolled change in input. The perturbation supplies a reference event and lets the experimenter ask whether later structure depends on it.

This is a general lesson about measurement. A thermometer works because expansion has been tied to temperature under a specified material, scale and calibration. The height of the liquid alone is not temperature. Likewise, compressibility becomes perturbational evidence only after the pulse, the target, the response window, the sensor model and the control conditions are fixed. Intervention changes ambiguity into a conditional statement: given this cause, this bounded system produced this response.

Capacity, content and report

Three questions are often compressed into one. Does the system currently contain any experience? What kind of experience is present? Can the system turn that state into a report or action? A perturbational measure may correlate with the first question while being largely insensitive to the second and deliberately independent of the third.

The distinction matters in dreaming, ketamine anaesthesia, locked-in syndrome and disorders of consciousness. A person may be unresponsive while experience continues. Conversely, a brain may retain a general capacity that is not exercised during every measured moment. The safest interpretation of a high human perturbational response is therefore not “this exact content is present now”. It is closer to “this brain is in a causal regime that, in calibrated human conditions, has accompanied the capacity for consciousness”.

“Without report” must also be read carefully. The test can be administered to a person who gives no report at the time of measurement. Its interpretation was nevertheless learned from conditions in which reports, later dream recall, drug state and clinical diagnosis were available. Report has not vanished from the evidential history. It has moved into calibration. This is a strength because the bedside test does not require command-following, but it also creates a transport constraint: a domain with no comparable calibration cannot inherit the conclusion by copying the algorithm.

No-report paradigms face the same general issue. Removing overt report from the test can reduce decision and motor confounds, yet the remaining signal still needs an independent bridge to experience.[16] A measure can be report-free at application time while remaining report-dependent at validation time. Independence from report is a property of use, not an escape from evidential grounding.

flowchart LR
  A["When silence conceals two<br/>different brains"] --> B["A pulse makes causal capacity<br/>visible"]
  B --> C["The scalar cannot travel alone"]
  C --> D["Audit the echo before<br/>importing the inference"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#007D68,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

A pulse makes causal capacity visible

The perturbational complexity index, or PCI, was introduced to turn the qualitative sleep observation into an individual-level measure. The original method perturbs the cortex with TMS, records the evoked response with high-density EEG, estimates the significant source-level spatiotemporal pattern, then measures how difficult that binary pattern is to compress.[2] Each stage is load-bearing.

The pulse must be strong enough to engage cortex, yet comparable enough across sites and people to support inference. The EEG must preserve neural response while suppressing the enormous electromagnetic pulse artefact. Source modelling estimates where significant activity occurs. Statistical thresholding distinguishes reproducible evoked structure from baseline fluctuation. The binary spatiotemporal response is then compressed and normalised against the amount of activated information. In clinical work, several stimulation sites may be tested and the maximum reliable value used.

These operations jointly express the target mechanism. Distribution without differentiation would label one simultaneous flash as rich. Differentiation without distribution would reward isolated local noise. Compression without significance testing would reward any difficult string. A pulse without controls would mix cortical response with the click and muscle twitch. PCI is best understood as a constrained causal assay whose statistic is the last step, not the assay itself.

The smallest useful model

Consider four measured regions over eight time steps. A pulse arrives at region 1 at the first step. The binary matrices below mark whether each region shows a significant perturbation-locked response. They are not clinical EEG data. They isolate the logic that the full method operationalises.

The formal core can be stated without pretending that the equation explains consciousness. Let a bounded system be B, its starting state s₀, and a controlled intervention u. The experiment produces an observed trajectory:

F is the system’s response operator: what the bounded system does under that intervention. O is the observation map: electrodes, source reconstruction, time window and preprocessing. The pipeline then constructs a significant response matrix Ru and computes a complexity statistic C(Ru). The statistic is informative because repeated human experiments connect that complete construction to labelled states. The equation makes the hidden dependencies visible. It does not remove them.

The human calibration corridor

The original PCI study evaluated wakefulness, dreaming, non-rapid-eye-movement sleep, sedation with several agents, locked-in syndrome and disorders of consciousness.[2] Later work enlarged the clinical benchmark. In the 2016 validation, a maximum PCI value above an empirical cutoff of 0.31 separated the report-capable benchmark conditions from the unresponsive reference conditions used to derive and validate it, then stratified minimally conscious and unresponsive wakefulness syndrome patients.[3]

That result is powerful and easy to misuse. The value 0.31 is not a constant of nature. It belongs to the original PCI construction, the human population, the stimulation and recording protocol, and that validation design. PCI^ST, a faster state-transition variant, was separately evaluated on TMS/EEG from 108 healthy participants and 108 brain-injured patients and on intracranial stimulation recordings from nine patients.[5] A change of algorithm requires a new calibration, even when the scientific aim is shared.

Anaesthetics also reveal why “unresponsive” is not one causal state. Propofol produced predominantly local, low-complexity responses. Xenon could produce widespread but stereotyped responses. Ketamine preserved wake-like complexity and was associated with later reports of vivid experience.[4] The same low scalar can therefore arise from different mechanisms, while the same lack of behaviour can coexist with different perturbational regimes.

Independent studies make the clinical pattern more concrete. In a 24-patient replication sample, 11 of 12 minimally conscious patients had PCI values above the validated boundary, while four of 11 patients diagnosed with unresponsive wakefulness syndrome also had high values.[6] The latter group is not automatically a set of measurement errors. Behavioural diagnosis can miss covert capacity, but a high value can also reflect residual causal organisation that is insufficient for the current clinical category. The result creates a reason to investigate, not a licence to relabel.

A later study of 40 minimally conscious patients reported that all had PCI values above the externally validated cutoff despite substantial variation in their spontaneous EEG features.[7] This dissociation is exactly what an active assay should be able to find. A passive trace and an evoked response need not rank the same person similarly because they measure different relations. One describes ongoing activity; the other asks what the system can causally sustain after a common intervention.

The operational consequence is a three-step reading. First, verify that the recording and preprocessing satisfy the protocol. Second, interpret the value only against the correct method-specific calibration. Third, place that evidence beside repeated behavioural assessment, aetiology, imaging and other electrophysiology. A disagreement among measures is not something to average away. It can identify which assumption, such as reliable motor output or stable spontaneous state, has failed.

A rival mechanism: proximity to a critical regime

Integration and differentiation are not the only explanation for why conscious human states tend to produce complex echoes. A network near a transition between activity dying out and activity exploding can respond to a small pulse with long, varied cascades. Subcritical dynamics would extinguish the pulse. Supercritical dynamics could recruit the system in one redundant wave. Recent human anaesthesia work found that measures derived from spontaneous EEG could predict PCI and interpreted the result through critical dynamics.[13]

This account can coexist with the empirical value of PCI while competing with a stronger theoretical reading. Criticality might be the dynamical condition that makes integration and differentiation available, a correlate produced by another mechanism, or one of several routes to high perturbational complexity. The discriminating experiment would manipulate distance from criticality while holding relevant architecture as stable as possible, then test whether the response family and consciousness evidence move together. Until such interventions generalise, criticality is a serious rival explanation, not a settled bridge from complexity to experience.

The scalar cannot travel alone

Lempel–Ziv complexity was designed to characterise novelty and compressibility in finite symbol sequences.[10] It does not recognise neurons, meanings, subjects or experiences. PCI becomes relevant to consciousness because a particular causal experiment constructs the sequence and because human calibration constrains its interpretation.

This yields a sharp rule: the same computation can support different inferences when the process that generated its input differs. Lempel–Ziv over a perturbation-locked cortical response is one thing. Lempel–Ziv over spontaneous EEG, a cell culture, a model activation tensor or a pseudorandom bit stream is another. Similar output values do not erase the differences.

Cortical cultures make the point concrete. Researchers have adapted spontaneous and perturbational complexity measures to dissociated neuronal cultures and found that a cholinergic manipulation could increase some spontaneous measures while producing only moderate changes in perturbational complexity.[9] The experiment is useful for studying network dynamics. It is not a demonstration that a culture crosses a consciousness threshold. The preparation lacks the human calibration class, and the relationship between its architecture and the mechanisms sampled by TMS–EEG remains open.

Similarly, a high value in software may reveal that a perturbation reaches many components through a non-repetitive path. That could diagnose coupling, hidden state or cascade risk. The same observation could arise from a deterministic pseudorandom generator, a replay table or an external service. Before the score can carry a mental interpretation, those rivals must be challenged and a theory must explain why the preserved causal property bears on consciousness.

Move the system boundary

A machine example makes the boundary problem unavoidable. Suppose an agent appears to produce a complex internal cascade after a hidden-state bit is flipped. What is the candidate system? Model weights alone? Weights plus runtime state? The prompt, retrieval layer, controller, tool results and world-state store? Move the boundary and the same intervention may enter a different causal object.

Inside the model, a bit flip may be overwritten by normalisation at the next layer. At the runtime boundary, it may alter a cached plan. At the configured-system boundary, it may trigger a tool call whose response creates most of the later diversity. A single flattened activation tensor hides these distinctions. Calling all of them “memory” makes the problem worse because checkpoint parameters, transient activations, episodic records, external knowledge and authoritative world state have different causal and evidential roles.

Reliable noise is still noise

TMS–EEG adds another transfer hazard: the pulse reaches more than cortex. It can stimulate scalp muscles, create auditory clicks, induce somatosensory responses and interact with electrodes and amplifiers. Filtering a large pulse artefact can generate further structure. Reviews of TMS–EEG methods therefore distinguish reliability from validity. A reproducible late waveform may be an equally reproducible sensory consequence rather than the cortical mechanism of interest.[11][12]

The strongest recent caution comes from a repeated-awakening propofol study. Twenty participants underwent resting EEG and TMS–EEG during deep sedation. Across 52 attempted awakenings, 24 yielded experience reports, five yielded no-experience reports, and 23 could not support an interpretable classification. PCI^ST and spontaneous Lempel–Ziv complexity both fell from wakefulness to sedation, but neither distinguished the reported dreaming from non-dreaming episodes within sedation.[8]

The small no-experience sample and temporal mismatch limit the null result. It still weakens a simple claim that the metric directly reads current experiential presence. A more defensible view is that perturbational complexity tracks a broad human causal regime associated with conscious capacity, while finer content and moment-to-moment presence may require other measures. This is also why clinical guidelines recommend repeated, standardised and multimodal assessment rather than a single decisive biomarker.[14][15]

Temporal grain is part of the measurement contract. A ten-minute aggregate can characterise a relatively stable physiological regime while missing a brief dream that occurs near awakening. A millisecond evoked response can probe fast causal propagation while saying little about an experience unfolding over seconds. Neither timescale is intrinsically superior. The claim must match the window. When a metric is asked to predict a state at a finer grain than its construction supports, a null result may reveal temporal mismatch rather than absence of the underlying relation.

This gives another practical test. Before treating two measures as competitors, align the event they are supposed to track. A behavioural report may concern the immediate pre-awakening interval; PCI may summarise several perturbations across a longer period; resting complexity may average ongoing activity. Measurement disagreement can arise because the instruments answer questions about different times, not because one is simply wrong.

stateDiagram-v2
  [*] --> Claim
  state "Four dark rooms" as Claim
  state "Capacity, content and report" as Test
  state "The smallest useful model" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

Audit the echo before importing the inference

We can now derive a practical transfer rule. The scientific object is not the scalar C. It is the relation among a bounded system, a family of interventions, an observation process, an analysis pipeline and a calibration population. Call that relation an Echo Transport Contract.

The Echo Transport Contract

A proposed transfer from source system S to target system T should declare six fields. The contract does not prove consciousness. It tells us whether the target experiment preserves enough of the source measurement to inherit a bounded inference.

The contract changes the experimental unit from one response to a response operator. For source and target, choose mappings between comparable interventions and observations. Then test whether the response relation remains close across the declared family:

g translates interventions, M translates observations, d measures discrepancy, and ε is a preregistered tolerance. This is not a proof of formal equivalence. It is an empirical envelope. It becomes stronger when it covers several sites, amplitudes, timings, starting states and adversarial controls. It becomes weaker when the mappings are chosen after seeing the result.

A successful audit earns a deliberately narrow statement: within the tested boundary and intervention family, the target preserves specified response relations and rejects named rivals. It does not establish that every causal property is shared. It does not license the source cutoff unless the calibration class is also justified. It does not settle whether the preserved property is constitutive of consciousness.

from __future__ import annotations

from dataclasses import dataclass
from math import log2
from typing import Iterable

Matrix = list[list[int]]


def lz76_phrases(bits: Iterable[int]) -> int:
    """Simple exhaustive LZ76 phrase count for an illustrative binary string."""
    s = "".join(str(int(x)) for x in bits)
    if not s:
        return 0
    i, phrases = 0, 0
    seen: set[str] = set()
    while i < len(s):
        length = 1
        while i + length <= len(s) and s[i:i + length] in seen:
            length += 1
        seen.add(s[i:i + length])
        phrases += 1
        i += length
    return phrases


def flatten_row_major(matrix: Matrix) -> list[int]:
    return [value for row in matrix for value in row]


def normalized_lz(matrix: Matrix) -> float:
    bits = flatten_row_major(matrix)
    n = max(len(bits), 2)
    return lz76_phrases(bits) * log2(n) / n


def hamming(a: Matrix, b: Matrix) -> float:
    xa, xb = flatten_row_major(a), flatten_row_major(b)
    if len(xa) != len(xb):
        raise ValueError("Response matrices must have the same shape")
    return sum(x != y for x, y in zip(xa, xb)) / max(len(xa), 1)


@dataclass(frozen=True)
class Audit:
    reference_score_gap: float
    operator_family_distance: float


def audit(source: list[Matrix], target: list[Matrix]) -> Audit:
    """Compare one reference scalar and the full intervention family."""
    if len(source) != len(target) or not source:
        raise ValueError("Supply matched, non-empty intervention families")
    gap = abs(normalized_lz(source[0]) - normalized_lz(target[0]))
    family = sum(hamming(a, b) for a, b in zip(source, target)) / len(source)
    return Audit(gap, family)

# A small reference-score gap does not imply a small family distance.
# Replace the synthetic matrices with preregistered, matched interventions.

The notebook exposes the paper’s central mechanism. On the reference pulse, the recurrent system and replay rival can have identical matrices, Lempel–Ziv values, reach and diversity. Across pulse sites, they diverge. Increasing the observation boundary can also change the metric without changing the inner model. Positive evidence therefore permits only the conclusion named by the test. A family match supports transport of a response relation. A family mismatch forbids importing the source interpretation from one scalar.