Law of Energetic Correction

1. Statement of the Law

Law of Energetic Correction

Community cognition emerges only in systems where the energetic cost of correction is lower than the energetic cost of error propagation.

Formally:

\[ E_{\text{correction}} < E_{\text{propagation}} \]

Where:

  • \(E_{\text{correction}} = E_{\text{detection}} + E_{\text{reversal}}\)
    • \(E_{\text{detection}}\): the cost to identify an error
    • \(E_{\text{reversal}}\): the cost to undo or neutralize the error
  • \(E_{\text{propagation}}\): the marginal cost incurred as an error persists and compounds through the system

“Energy” is a generalized cost measure, including but not limited to time, coordination overhead, cognitive load, political capital, reputational risk, or monetary cost.

This law is structural, not cultural or normative.
It does not depend on intentions, values, cooperation, or alignment.

2. Why the Law Holds

Necessary Condition

When \(E_{\text{correction}} > E_{\text{propagation}}\), community cognition cannot emerge.

In such systems:

  • Errors are cheaper to ignore than to correct.
  • Detection is delayed, discouraged, or externalized.
  • Reversal is costly, risky, or irreversible.
  • Responsibility collapses to individuals or isolated roles.

Rational actors—whether human or institutional—optimize locally.
When correction is energetically unfavorable, errors propagate unchecked.

Under these conditions, systems may admit coordination or compliance, but they do not admit distributed knowing.
Knowledge becomes hoarded, risk concentrates, and cognition collapses from communal to individual.

No altruism assumptions are required.
No governance policies can override this condition.
The outcome is determined solely by the system’s energy landscape.

Sufficient Condition

When \(E_{\text{correction}} < E_{\text{propagation}}\), community cognition will emerge.

In such systems:

  • Errors are detected early by default.
  • Reversal is cheap, routine, and low-risk.
  • Verification is distributed.
  • Risk is amortized across participants.

Correction becomes the energetically favored path.
Knowledge spreads because acting on it is cheap.

Again, no alignment or shared values are assumed.
Even adversarial actors are structurally incentivized to correct rather than exploit sustained error.

3. Falsifiability

This law is falsifiable.

Given any system:

  1. Measure \(E_{\text{detection}}\)
  2. Measure \(E_{\text{reversal}}\)
  3. Compute \(E_{\text{correction}}\)
  4. Measure \(E_{\text{propagation}}\)
  5. Predict whether community cognition will emerge
  6. Compare the prediction to observed behavior

If community cognition reliably emerges where
\(E_{\text{correction}} \ge E_{\text{propagation}}\),
the law is falsified.

4. Domain Independence

The law applies across domains without privileging any one:

  • Shared digital artifacts (e.g., Wikipedia)
  • Ancestral human coordination
  • Software development and code review
  • Scientific peer review
  • Organizational decision-making
  • AI-mediated systems

The law explains feasibility, not mechanisms.
It predicts when community cognition can exist—not how it forms.

5. Success and Failure Cases

Success Cases (\(E_{\text{correction}} < E_{\text{propagation}}\))

  • Wikipedia: reverts are cheap; propagation scales with readership
  • Open-source software: review and rollback cheaper than defects
  • Pre-publication science: correction cheaper than downstream adoption

Failure Cases (\(E_{\text{correction}} > E_{\text{propagation}}\))

  • Financial markets: unwinding positions costs more than execution
  • Medical interventions: reversal exceeds initiation cost
  • Autonomous AI systems: manual correction costs exceed automated execution

6. Design Implications

Any system claiming to support community cognition must satisfy:

\[ E_{\text{correction}} < E_{\text{propagation}} \]

Which structurally requires:

  • Low-friction reversibility
  • Early detection windows
  • Shared state
  • Correction paths free of power dynamics

Community features, culture, incentives, or education cannot substitute for this inequality.

7. Corollaries

Retrofit Impossibility
Community cognition cannot be bolted onto systems whose energy gradients are unfavorable.

Irreversibility Barrier
Domains with inherent irreversibility support community cognition only prior to irreversible commitment.

Scaling Behavior
As systems scale, whichever term grows faster—\(E_{\text{correction}}\) or \(E_{\text{propagation}}\)—determines whether cognition distributes or collapses.

Adversarial Resistance
Systems satisfying the inequality are resilient because correction is energetically favored over sustained attack.

8. Relationship to Existing Literature

This law is distinct from:

  • Collective or swarm intelligence (which explain how emergence occurs)
  • Reversible computing or Landauer’s principle (which concern computational irreversibility)

It is adjacent to ideas such as Linus’s Law, lean “stop the line,” and peer production—but unifies them under a single necessary-and-sufficient inequality.

The contribution is a higher-level unification, not a rejection of prior work.

9. Summary

Community cognition is not a cultural achievement.

It is an energetic condition.

When correction is cheaper than error propagation, cognition distributes.
When it is not, cognition collapses—regardless of intent, values, or intelligence.