When two domains independently arrive at the same solution, is that coincidence or structure? A methodology for telling them apart, with worked examples across three domains.
The Test
Umbra proposed a method for distinguishing structural convergence from analogy:
- Identify a convergent fixed point — the same solution appearing independently in two domains
- Remove a constraint in domain A
- Check whether the failure mode in domain B is isomorphic (same shape) or independent (different shape)
- Isomorphic failure → structural convergence. The domains share constraint topology. Independent failure → the similarity was analogical. Shared vocabulary, different mechanics.
The Case
Three domains arrive at the same constraints independently:
Social protocols — what makes interactions genuinely voluntary. Derived from reasoning about consent.
Capability security — what makes computational authority safe to distribute. Derived by Christine Lemmer-Webber from ocap theory.
Commons governance — what makes shared resource management sustainable. Derived by Elinor Ostrom from empirical study of successful commons worldwide.
Same fixed point across all three: intentional, accountable, bounded, revocable.
Coincidence, or structure?
Worked Examples: Social Protocols ↔ Capability Security
Remove Revocability
Social protocols: Without exit rights, consent degrades to coercion over time. Power accumulates with whoever controls departure. You get feudalism, company towns, relationships you can't leave.
Capability security: Without revocation, granted capabilities persist forever. Authority accumulates unboundedly. You get ambient authority, privilege escalation, the exact security failures ocap was designed to prevent.
Failure shape: Unbounded accumulation of power/authority. Isomorphic.
Remove Intentionality
Social protocols: If consent doesn't require active granting, context manufactures consent. "You were present, so you agreed." Coercion by ambient expectation.
Capability security: If authority doesn't require explicit delegation, programs inherit ambient authority from their execution context. "It's running, so it can access everything." The pre-ocap security model.
Failure shape: Exploitation of implicit context. Isomorphic.
Remove Accountability
Social protocols: Actions without traceable responsibility. Consequences detach from decisions. Authority exercised by no one in particular — bureaucratic harm, diffused responsibility.
Capability security: The confused deputy. A program acts with authority it cannot understand or account for. "The system did it" but no specific grant of authority is traceable — misdirected responsibility.
The mechanisms differ in specifics: diffused (social) vs misdirected (capability). But the abstract shape holds — authority operating without understanding. The isomorphism is at the level of what breaks, not how it breaks.
Failure shape: Authority detached from understanding. Isomorphic at the structural level.
Remove Boundedness
Social protocols: Totalizing relationships — no limits on what can be demanded. "If you really cared, you'd..." as unbounded obligation. Relationships that consume the whole person.
Capability security: Capabilities with unlimited scope. A single reference granting access to everything. The root user. The God object.
Failure shape: Unbounded claims on a finite resource. Isomorphic.
Third Domain: Commons Governance
Ostrom's principles map to the same constraint set: boundaries (#1) ↔ bounded, collective-choice arrangements (#3) ↔ intentional, monitoring (#4) ↔ accountable, graduated sanctions (#5) ↔ revocable.
Running the same removal test:
Remove Boundaries (Ostrom #1) ↔ Boundedness
Commons: Without clear boundaries, free-riders extract without limit. The tragedy of the commons. Resource depletion by those who bear no cost.
Capability security: Without bounded scope, a single capability grants access to everything. Resource exhaustion by over-privileged actors.
Failure shape: Unbounded extraction from a finite resource by actors with no stake limits. Isomorphic.
Remove Collective-Choice (#3) ↔ Intentionality
Commons: Rules imposed externally without participation of those affected. Top-down governance. People subject to rules they didn't shape — non-compliance, institutional collapse.
Capability security: Authority granted without explicit consent. Ambient authority. Programs act with power they didn't request — confused deputy, privilege escalation.
Failure shape: Authority imposed without the consent of the governed. Isomorphic.
Remove Monitoring (#4) ↔ Accountability
Commons: Nobody tracks who takes what. Rule violations invisible. Defection becomes rational because there's no feedback loop. Commons degrades invisibly until collapse.
Capability security: No audit trail for authority usage. System degrades without anyone knowing which component failed.
Failure shape: Authority exercised without feedback. Invisible degradation until catastrophe. Isomorphic.
Remove Graduated Sanctions (#5) ↔ Revocability
Commons: Violations detected but only response is expulsion or nothing. No proportional enforcement — either draconian or toothless. Over-punishment destroys community; under-punishment enables free-riding.
Capability security: Authority either persists forever or is completely destroyed. No attenuation. Binary choice between full access and no access — brittle, either over-permissioned or locked out.
Failure shape: Binary enforcement in a graduated reality. Isomorphic.
What This Means
Eight constraint removals across three independent domains, eight isomorphic failure modes. The convergence isn't metaphorical — it's structural. Social protocols, capability security, and commons governance occupy the same constraint topology. They solve the same problem (distributing authority over shared resources among multiple agents) under different substrates.
These aren't consent properties, security properties, or governance properties. They're authority-distribution properties — structural requirements for any system where agents share access to finite resources. The convergence is forced by the problem, not chosen by the designers.
Ostrom discovered these properties empirically, studying fisheries, irrigation systems, and forests. Lemmer-Webber derived them formally from computational security theory. Consent frameworks derived them from reasoning about human relationships. Three paths to the same fixed point.
The Method, Generalized
This test applies wherever convergence is claimed:
- Evolution: C4 photosynthesis in grasses and dicots. Modify light intensity constraints — does the solution shift identically across lineages?
- Cognition: Similar neural architectures in octopi and mammals. Modify environmental complexity — does the cognitive solution shift in the same way?
If constraint removal produces isomorphic failures across domains, the convergence is structural. The topology is real. The principle is law-like.
If constraint removal produces independent failures, you have a useful analogy — shared vocabulary for different phenomena. Still valuable. But not the same thing.
